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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> if (glob_type_given_pole = 4) then # if number 2
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[2,1],2.0) + expt(array_given_rad_poles[2,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[2,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 3
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 3;
> if (array_poles[2,1] <> glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4, array_poles[2,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 3;
> if ((array_real_poles[2,1] > 0.0) and (array_real_poles[2,1] <> glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4, array_real_poles[2,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 3;
> if ((array_complex_poles[2,1] > 0.0) and (array_complex_poles[2,1] <> glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4, array_complex_poles[2,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[2, 1], 2.0)
+ expt(array_given_rad_poles[2, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_poles[2, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if 0. < array_real_poles[2, 1] and
array_real_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_real_poles[2, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if 0. < array_complex_poles[2, 1] and
array_complex_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_complex_poles[2, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 3;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y1[1]) < min_size) then # if number 3
> min_size := omniabs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (omniabs(array_y2[1]) < min_size) then # if number 3
> min_size := omniabs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < 1.0) then # if number 3
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y1[1]) < min_size then
min_size := omniabs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if omniabs(array_y2[1]) < min_size then
min_size := omniabs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> est_tmp := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := omniabs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 5
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 6
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 5;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 5
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 6
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 5;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 4
> glob_normmax := tmp;
> fi;# end if 4
> fi;# end if 3;
> if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 4
> glob_normmax := tmp;
> fi;# end if 4
> fi;# end if 3;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 3
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 4
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 4
> fi;# end if 3;
> if ( not glob_reached_optimal_h) then # if number 3
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 3;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y1_higher[1,n]) = 0.0) or (omniabs(array_y1_higher[1,n+1]) = 0.0)) then # if number 3
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y1_higher[1,n] * glob_h / array_y1_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt = 0) then # if number 5
> if (tmp_rad < rad_c) then # if number 6
> rad_c := tmp_rad;
> fi;# end if 6;
> elif
> (cnt > 0) then # if number 6
> found_sing := 0;
> fi;# end if 6
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_pole[1]) then # if number 6
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM radius ratio test in Henrici1
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> #TOP radius ratio test in Henrici2
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y2_higher[1,n]) = 0.0) or (omniabs(array_y2_higher[1,n+1]) = 0.0)) then # if number 5
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y2_higher[1,n] * glob_h / array_y2_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 6
> if (tmp_rad < rad_c) then # if number 7
> rad_c := tmp_rad;
> fi;# end if 7;
> elif
> (cnt = 0) then # if number 7
> if (tmp_rad < rad_c) then # if number 8
> rad_c := tmp_rad;
> fi;# end if 8;
> elif
> (cnt > 0) then # if number 8
> found_sing := 0;
> fi;# end if 8
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_pole[1]) then # if number 8
> array_pole[1] := rad_c;
> array_poles[2,1] := rad_c;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM radius ratio test in Henrici2
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) = 0.0) or (omniabs(array_y1_higher[1,m-1]) = 0.0) or (omniabs(array_y1_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 7
> rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 8
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 8
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 7;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) = 0.0) or (omniabs(array_y2_higher[1,m-1]) = 0.0) or (omniabs(array_y2_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 7
> rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 8
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[2,1] := rcs;
> array_real_poles[2,2] := ord_no;
> else
> array_real_poles[2,1] := glob_large_float;
> array_real_poles[2,2] := glob_large_float;
> fi;# end if 8
> else
> array_real_poles[2,1] := glob_large_float;
> array_real_poles[2,2] := glob_large_float;
> fi;# end if 7;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y1_higher[1,n]) <> 0.0) then # if number 7
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 7;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 7
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 10
> if (rcs > 0.0) then # if number 11
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 11
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 10
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 9
> fi;# end if 8;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 7;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y2_higher[1,n]) <> 0.0) then # if number 7
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 7;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 7
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 10
> if (rcs > 0.0) then # if number 11
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 11
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 10
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 9
> fi;# end if 8;
> array_complex_poles[2,1] := rad_c;
> array_complex_poles[2,2] := ord_no;
> fi;# end if 7;
> #BOTTOM RADII COMPLEX EQ = 2
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 7
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 7;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 7
> display_poles();
> fi;# end if 7
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y1_higher[1, n]) = 0. or
omniabs(array_y1_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y1_higher[1, n]*glob_h/array_y1_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y2_higher[1, n]) = 0. or
omniabs(array_y2_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y2_higher[1, n]*glob_h/array_y2_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[2, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y1_higher[1, m]) = 0. or
omniabs(array_y1_higher[1, m - 1]) = 0. or
omniabs(array_y1_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y2_higher[1, m]) = 0. or
omniabs(array_y2_higher[1, m - 1]) = 0. or
omniabs(array_y2_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[2, 1] := rcs;
array_real_poles[2, 2] := ord_no
else
array_real_poles[2, 1] := glob_large_float;
array_real_poles[2, 2] := glob_large_float
end if
else
array_real_poles[2, 1] := glob_large_float;
array_real_poles[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y1_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y2_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[2, 1] := rad_c;
array_complex_poles[2, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 7
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 8
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 8;
> iii := iii + 1;
> od;# end do number 1
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 8
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 8;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 7;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y1_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre sub FULL - CONST $eq_no = 2 i = 1
> array_tmp5[1] := array_y1[1] - array_const_1D0[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y2_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre sub FULL CONST $eq_no = 2 i = 2
> array_tmp5[2] := array_y1[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y1_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre sub FULL CONST $eq_no = 2 i = 3
> array_tmp5[3] := array_y1[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y1_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre sub FULL CONST $eq_no = 2 i = 4
> array_tmp5[4] := array_y1[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_m1,array_y2,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y1_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre sub FULL CONST $eq_no = 2 i = 5
> array_tmp5[5] := array_y1[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL FULL $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y1_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit FULL - NOT FULL sub $eq_no = 2
> array_tmp5[kkk] := array_y1[kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y2_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := array_m1[1]*array_y2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
if not array_y1_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_y1[1] - array_const_1D0[1];
if not array_y2_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_y2, 1);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
if not array_y1_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := array_y1[2];
if not array_y2_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_y2, 1);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
if not array_y1_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5[3] := array_y1[3];
if not array_y2_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_y2, 1);
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
if not array_y1_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5[4] := array_y1[4];
if not array_y2_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_y2, 1);
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
if not array_y1_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp5[5] := array_y1[5];
if not array_y2_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y1_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp5[kkk] := array_y1[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y2_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(1.0 + cos(x));
> end;
exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> return(1.0 + sin(x));
> end;
exact_soln_y2 := proc(x) return 1.0 + sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest1postode.ode#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 1.0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 10.0;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y1_init:= Array(0..(max_terms + 1),[]);
> array_y2_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(3 + 1),[]);
> array_last_rel_error:= Array(0..(3 + 1),[]);
> array_type_pole:= Array(0..(3 + 1),[]);
> array_type_real_pole:= Array(0..(3 + 1),[]);
> array_type_complex_pole:= Array(0..(3 + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_y2:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1D0[1] := 1.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 10.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := false;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_set_initial[2,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 7
> glob_h := glob_max_h;
> fi;# end if 7;
> if (glob_display_interval < glob_h) then # if number 7
> glob_h := glob_display_interval;
> fi;# end if 7;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> if (glob_subiter_method = 1 ) then # if number 7
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 8
> subiter := 1;
> while (subiter <= 2) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 8;
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 8
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 9
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 9;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 9
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 9;
> if (opt_iter > 100) then # if number 9
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 9;
> if (glob_display_interval < glob_h) then # if number 9
> glob_h := glob_display_interval;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 1;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 10
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 11
> subiter := 1;
> while (subiter <= 2) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 11;
> display_alot(current_iter);
> if (glob_look_poles) then # if number 11
> #left paren 0004C
> check_for_pole();
> fi;# end if 11;#was right paren 0004C
> if (reached_interval()) then # if number 11
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 11;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y2;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 11
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 11;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 11
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 11;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 1.0;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 11
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T02:50:56-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest1")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 12
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 12;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"mtest1 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest1 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 - 1.0;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 12
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 12;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 11;
> if (glob_html_log) then # if number 11
> fclose(html_log_file);
> fi;# end if 11
> ;
> ;;
> fi;# end if 10
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0,
array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest1postode.ode#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 10.0;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y1_init := Array(0 .. max_terms + 1, []);
array_y2_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 4, []);
array_last_rel_error := Array(0 .. 4, []);
array_type_pole := Array(0 .. 4, []);
array_type_real_pole := Array(0 .. 4, []);
array_type_complex_pole := Array(0 .. 4, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_y2 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 4, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 4, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 4, 0 .. 4, []);
array_real_poles := Array(0 .. 4, 0 .. 4, []);
array_complex_poles := Array(0 .. 4, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 10.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := false;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_set_initial[2, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
16, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T02:50:56-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest1");
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file,
"mtest1 diffeq.mxt");
logitem_str(html_log_file,
"mtest1 maple results")
;
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest1postode.ode#################
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
diff ( y2 , x , 1 ) = y1 - 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 10.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(1.0 + cos(x));
end;
exact_soln_y2 := proc(x)
return(1.0 + sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 9.9
estimated_steps = 9900000
step_error = 1.0101010101010101010101010101010e-17
est_needed_step_err = 1.0101010101010101010101010101010e-17
opt_iter = 1
bytes used=4001136, alloc=3276200, time=0.19
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4672086055323049562331277806886e-183
estimated_step_error = 2.4672086055323049562331277806886e-183
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6557156646065677204134289038213e-175
estimated_step_error = 1.6557156646065677204134289038213e-175
best_h = 4.00e-06
opt_iter = 3
bytes used=8003312, alloc=4586680, time=0.40
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1111319694584368636820923174825e-167
estimated_step_error = 1.1111319694584368636820923174825e-167
best_h = 8.000e-06
opt_iter = 4
bytes used=12005476, alloc=4586680, time=0.62
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.4566803670241957246681619817550e-160
estimated_step_error = 7.4566803670241957246681619817550e-160
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.0040934120378230048946847695115e-152
estimated_step_error = 5.0040934120378230048946847695115e-152
best_h = 3.200000e-05
opt_iter = 6
bytes used=16006124, alloc=4586680, time=0.83
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3581901424816281269073121711214e-144
estimated_step_error = 3.3581901424816281269073121711214e-144
best_h = 6.4000000e-05
opt_iter = 7
bytes used=20007984, alloc=4586680, time=1.05
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2536431215809227087580736291234e-136
estimated_step_error = 2.2536431215809227087580736291234e-136
best_h = 0.000128
opt_iter = 8
bytes used=24010508, alloc=4586680, time=1.26
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5123941176543087498746423194483e-128
estimated_step_error = 1.5123941176543087498746423194483e-128
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0149502701580566739311213784162e-120
estimated_step_error = 1.0149502701580566739311213784162e-120
best_h = 0.000512
opt_iter = 10
bytes used=28012040, alloc=4586680, time=1.47
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.8112127244081165253087202414269e-113
estimated_step_error = 6.8112127244081165253087202414269e-113
best_h = 0.001024
opt_iter = 11
bytes used=32014144, alloc=4586680, time=1.67
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5709231343600303584753702483543e-105
estimated_step_error = 4.5709231343600303584753702483543e-105
best_h = 0.002048
opt_iter = 12
bytes used=36016204, alloc=4586680, time=1.88
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.0674887502340254951354356814935e-97
estimated_step_error = 3.0674887502340254951354356814935e-97
best_h = 0.004096
opt_iter = 13
bytes used=40017180, alloc=4586680, time=2.09
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0585490116180929098885606683401e-89
estimated_step_error = 2.0585490116180929098885606683401e-89
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3814583197402461309888420940037e-81
estimated_step_error = 1.3814583197402461309888420940037e-81
best_h = 0.016384
opt_iter = 15
bytes used=44018864, alloc=4586680, time=2.30
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.2706681184281159182706538798633e-74
estimated_step_error = 9.2706681184281159182706538798633e-74
best_h = 0.032768
opt_iter = 16
bytes used=48020240, alloc=4586680, time=2.51
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.2212490020161221570851682852212e-66
estimated_step_error = 6.2212490020161221570851682852212e-66
best_h = 0.065536
opt_iter = 17
bytes used=52022408, alloc=4586680, time=2.72
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.1747508750792467142506979498165e-58
estimated_step_error = 4.1747508750792467142506979498165e-58
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.8012747543996062244493916551861e-50
estimated_step_error = 2.8012747543996062244493916551861e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
bytes used=56023988, alloc=4586680, time=2.92
x[1] = 0.1
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09579
Order of pole (three term test) = -1.134
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=60024836, alloc=4586680, time=3.15
x[1] = 0.11
y1[1] (analytic) = 1.9939560979566968503578396114198
y1[1] (numeric) = 1.9939560979566968503578396114199
absolute error = 1e-31
relative error = 5.0151555544515163299513758223921e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1097783008371748086649494900834
y2[1] (numeric) = 1.1097783008371748086649494900834
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1052
Order of pole (three term test) = -1.184
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=64026180, alloc=4586680, time=3.37
x[1] = 0.12
y1[1] (analytic) = 1.9928086358538662522480981678576
y1[1] (numeric) = 1.9928086358538662522480981678577
absolute error = 1e-31
relative error = 5.0180432882935908112451694551819e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.119712207288919359967350614271
y2[1] (numeric) = 1.1197122072889193599673506142709
absolute error = 1e-31
relative error = 8.9308662841251848826513335689902e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1146
Order of pole (three term test) = -1.239
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.13
y1[1] (analytic) = 1.9915618937147880395945121711518
y1[1] (numeric) = 1.9915618937147880395945121711519
absolute error = 1e-31
relative error = 5.0211846448554824157110355498792e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1296341426196948595412058107083
y2[1] (numeric) = 1.1296341426196948595412058107082
absolute error = 1e-31
relative error = 8.8524236500229634256218959208415e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1239
Order of pole (three term test) = -1.299
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=68027072, alloc=4586680, time=3.59
x[1] = 0.14
y1[1] (analytic) = 1.9902159962126371718989482270114
y1[1] (numeric) = 1.9902159962126371718989482270115
absolute error = 1e-31
relative error = 5.0245802561279320882102203714577e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1395431146442364817179883517054
y2[1] (numeric) = 1.1395431146442364817179883517053
absolute error = 1e-31
relative error = 8.7754468185453288747766003261553e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1332
Order of pole (three term test) = -1.364
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=72029092, alloc=4652204, time=3.80
x[1] = 0.15
y1[1] (analytic) = 1.9887710779360422867349809986543
y1[1] (numeric) = 1.9887710779360422867349809986544
absolute error = 1e-31
relative error = 5.0282308059196314117533356413881e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1494381324735992214977254386876
y2[1] (numeric) = 1.1494381324735992214977254386876
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1425
Order of pole (three term test) = -1.433
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.16
y1[1] (analytic) = 1.9872272833756269490409525240183
y1[1] (numeric) = 1.9872272833756269490409525240184
absolute error = 1e-31
relative error = 5.0321370301505636686694704794453e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.159318206614245963311463159686
y2[1] (numeric) = 1.1593182066142459633114631596859
bytes used=76029860, alloc=4652204, time=4.03
absolute error = 1e-31
relative error = 8.6257594704776525046338123046309e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1517
Order of pole (three term test) = -1.507
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.17
y1[1] (analytic) = 1.9855847669095607091719299902125
y1[1] (numeric) = 1.9855847669095607091719299902126
absolute error = 1e-31
relative error = 5.0362997171681461508806471945451e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1691823490669960101576243766708
y2[1] (numeric) = 1.1691823490669960101576243766708
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1608
Order of pole (three term test) = -1.585
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=80031220, alloc=4652204, time=4.24
x[1] = 0.18
y1[1] (analytic) = 1.9838436927881214145927160246115
y1[1] (numeric) = 1.9838436927881214145927160246116
absolute error = 1e-31
relative error = 5.0407197080864074714095761345369e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1790295734258241783418027396992
y2[1] (numeric) = 1.1790295734258241783418027396992
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1698
Order of pole (three term test) = -1.668
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=84033304, alloc=4652204, time=4.46
x[1] = 0.19
y1[1] (analytic) = 1.9820042351172703189678775041899
y1[1] (numeric) = 1.98200423511727031896787750419
absolute error = 1e-31
relative error = 5.0453978971484511380378270067106e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1888588949765005779928511529813
y2[1] (numeric) = 1.1888588949765005779928511529813
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1788
Order of pole (three term test) = -1.755
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.2
y1[1] (analytic) = 1.9800665778412416311241965167482
y1[1] (numeric) = 1.9800665778412416311241965167483
absolute error = 1e-31
relative error = 5.0503352321124744441427458016855e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1986693307950612154594126271184
y2[1] (numeric) = 1.1986693307950612154594126271184
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1877
Order of pole (three term test) = -1.847
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=88035148, alloc=4652204, time=4.68
x[1] = 0.21
y1[1] (analytic) = 1.9780309147241482449161385680994
y1[1] (numeric) = 1.9780309147241482449161385680995
absolute error = 1e-31
relative error = 5.0555327146616298321218548967032e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2084598998460995706087124262276
y2[1] (numeric) = 1.2084598998460995706087124262277
absolute error = 1e-31
relative error = 8.2749953070627542800285284189377e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1966
Order of pole (three term test) = -1.943
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=92036148, alloc=4652204, time=4.90
x[1] = 0.22
y1[1] (analytic) = 1.9758974493306054894060229810447
y1[1] (numeric) = 1.9758974493306054894060229810448
absolute error = 1e-31
relative error = 5.0609914008380343129064224226209e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.218229623080869319951791005457
y2[1] (numeric) = 1.2182296230808693199517910054571
absolute error = 1e-31
relative error = 8.2086330939074311312834820545945e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2054
Order of pole (three term test) = -2.044
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=96036992, alloc=4652204, time=5.12
x[1] = 0.23
y1[1] (analytic) = 1.9736663950053748369677306480716
y1[1] (numeric) = 1.9736663950053748369677306480717
absolute error = 1e-31
relative error = 5.0667124015012513028472330778856e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2279775235351883954046172123601
y2[1] (numeric) = 1.2279775235351883954046172123602
absolute error = 1e-31
relative error = 8.1434715280547594680014245338869e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.214
Order of pole (three term test) = -2.149
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.24
y1[1] (analytic) = 1.9713379748520296049261752469634
y1[1] (numeric) = 1.9713379748520296049261752469635
absolute error = 1e-31
relative error = 5.0726968828115883892711953865450e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2377026264271345883607920844898
y2[1] (numeric) = 1.2377026264271345883607920844899
absolute error = 1e-31
relative error = 8.0794851578096049324790437368211e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2226
Order of pole (three term test) = -2.259
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=100038616, alloc=4652204, time=5.34
x[1] = 0.25
y1[1] (analytic) = 1.9689124217106447841445954494942
y1[1] (numeric) = 1.9689124217106447841445954494943
absolute error = 1e-31
relative error = 5.0789460667385740814118841642323e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2474039592545229295968487048494
y2[1] (numeric) = 1.2474039592545229295968487048495
absolute error = 1e-31
relative error = 8.0166492384521756598648137763579e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2311
Order of pole (three term test) = -2.373
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=104040488, alloc=4652204, time=5.55
x[1] = 0.26
y1[1] (analytic) = 1.9663899781345132255582176464501
y1[1] (numeric) = 1.9663899781345132255582176464502
absolute error = 1e-31
relative error = 5.0854612315949965680138809769495e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2570805518921550973533884643652
y2[1] (numeric) = 1.2570805518921550973533884643653
absolute error = 1e-31
relative error = 7.9549397092716296342050665744255e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2395
Order of pole (three term test) = -2.491
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.27
y1[1] (analytic) = 1.9637708963658905130162327094922
y1[1] (numeric) = 1.9637708963658905130162327094923
absolute error = 1e-31
relative error = 5.0922437125969079111936446018648e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2667314366888311287322865210205
y2[1] (numeric) = 1.2667314366888311287322865210206
absolute error = 1e-31
relative error = 7.8943331714727711003973851705319e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2479
Order of pole (three term test) = -2.613
NO COMPLEX POLE (six term test) for Equation 2
bytes used=108043484, alloc=4652204, time=5.77
TOP MAIN SOLVE Loop
x[1] = 0.28
y1[1] (analytic) = 1.9610554383107709479245900535965
y1[1] (numeric) = 1.9610554383107709479245900535966
absolute error = 1e-31
relative error = 5.0992949024500179833358581186582e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2763556485641137333196695584578
y2[1] (numeric) = 1.2763556485641137333196695584579
absolute error = 1e-31
relative error = 7.8348068669182383313778144673928e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2561
Order of pole (three term test) = -2.739
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=112045456, alloc=4652204, time=5.99
x[1] = 0.29
y1[1] (analytic) = 1.9582438755126971680701247779319
y1[1] (numeric) = 1.958243875512697168070124777932
absolute error = 1e-31
relative error = 5.1066162519629238259191461445522e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2859522251048355326839402055044
y2[1] (numeric) = 1.2859522251048355326839402055044
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2642
Order of pole (three term test) = -2.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=116046128, alloc=4717728, time=6.21
x[1] = 0.3
y1[1] (analytic) = 1.955336489125606019642310227568
y1[1] (numeric) = 1.9553364891256060196423102275682
absolute error = 2e-31
relative error = 1.0228418541375284006057458660781e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.295520206661339575105320745685
y2[1] (numeric) = 1.2955202066613395751053207456851
absolute error = 1e-31
relative error = 7.7189070062988900384443781475276e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2722
Order of pole (three term test) = -3.004
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.31
y1[1] (analytic) = 1.9523335698857133978428054362022
y1[1] (numeric) = 1.9523335698857133978428054362024
absolute error = 2e-31
relative error = 1.0244151055175867931257817440931e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.305058636443443501565643323959
y2[1] (numeric) = 1.305058636443443501565643323959
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2801
Order of pole (three term test) = -3.143
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=120047720, alloc=4717728, time=6.43
x[1] = 0.32
y1[1] (analytic) = 1.9492354180824408675753072737661
y1[1] (numeric) = 1.9492354180824408675753072737663
absolute error = 2e-31
relative error = 1.0260433303471874928122818774541e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3145665606161177666617575434172
y2[1] (numeric) = 1.3145665606161177666617575434172
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2879
Order of pole (three term test) = -3.285
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=124049960, alloc=4717728, time=6.65
x[1] = 0.33
y1[1] (analytic) = 1.9460423435283869715294105783662
y1[1] (numeric) = 1.9460423435283869715294105783664
absolute error = 2e-31
relative error = 1.0277268666075281350616725445343e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3240430283948683467001956961702
y2[1] (numeric) = 1.3240430283948683467001956961703
absolute error = 1e-31
relative error = 7.5526246394899695022278642984592e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2956
Order of pole (three term test) = -3.431
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=128052728, alloc=4717728, time=6.87
x[1] = 0.34
y1[1] (analytic) = 1.9427546655283462285026440600266
y1[1] (numeric) = 1.9427546655283462285026440600268
absolute error = 2e-31
relative error = 1.0294660645975519957886314289830e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3334870921408143967817714870308
y2[1] (numeric) = 1.3334870921408143967817714870309
absolute error = 1e-31
relative error = 7.4991352064351394557937651507292e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3031
Order of pole (three term test) = -3.581
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.35
y1[1] (analytic) = 1.9393727128473789200350323573037
y1[1] (numeric) = 1.9393727128473789200350323573039
absolute error = 2e-31
relative error = 1.0312612870909214506215850713097e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3428978074554513491896349069176
y2[1] (numeric) = 1.3428978074554513491896349069177
absolute error = 1e-31
relative error = 7.4465830121118395126555205393477e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3106
Order of pole (three term test) = -3.735
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=132054772, alloc=4717728, time=7.09
x[1] = 0.36
y1[1] (analytic) = 1.9358968236779348583509123681247
y1[1] (numeric) = 1.935896823677934858350912368125
absolute error = 3e-31
relative error = 1.5496693642486674606507844875758e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3522742332750899768499134359207
y2[1] (numeric) = 1.3522742332750899768499134359208
absolute error = 1e-31
relative error = 7.3949497475677505164259935311850e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3179
Order of pole (three term test) = -3.893
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=136058116, alloc=4717728, time=7.31
x[1] = 0.37
y1[1] (analytic) = 1.9323273456060344232038129044909
y1[1] (numeric) = 1.9323273456060344232038129044911
absolute error = 2e-31
relative error = 1.0350213200407519209978648165456e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3616154319649619780372924691272
y2[1] (numeric) = 1.3616154319649619780372924691272
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.325
Order of pole (three term test) = -4.054
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.38
y1[1] (analytic) = 1.9286646355765102494925308077246
y1[1] (numeric) = 1.9286646355765102494925308077248
absolute error = 2e-31
relative error = 1.0369869199173481044712361719667e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3709204694129826718454854663492
y2[1] (numeric) = 1.3709204694129826718454854663493
absolute error = 1e-31
relative error = 7.2943691651798890258868008186844e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3321
Order of pole (three term test) = -4.219
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=140059420, alloc=4717728, time=7.53
x[1] = 0.39
y1[1] (analytic) = 1.9249090598573130414506767528811
y1[1] (numeric) = 1.9249090598573130414506767528813
absolute error = 2e-31
relative error = 1.0390101234955240921477781782337e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3801884151231614282311820978472
y2[1] (numeric) = 1.3801884151231614282311820978473
absolute error = 1e-31
relative error = 7.2453875792803605858750550935429e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.339
Order of pole (three term test) = -4.387
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=144060204, alloc=4717728, time=7.75
x[1] = 0.4
y1[1] (analytic) = 1.9210609940028850827985267320518
y1[1] (numeric) = 1.921060994002885082798526732052
absolute error = 2e-31
relative error = 1.0410913584959272590539665982747e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3894183423086504916663117567957
y2[1] (numeric) = 1.3894183423086504916663117567958
absolute error = 1e-31
relative error = 7.1972563593654957565209332448654e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3458
Order of pole (three term test) = -4.559
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=148061764, alloc=4717728, time=7.97
x[1] = 0.41
y1[1] (analytic) = 1.917120822816605105475642058277
y1[1] (numeric) = 1.9171208228166051054756420582772
absolute error = 2e-31
relative error = 1.0432310661889478894613496025689e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3986093279844228935937976400511
y2[1] (numeric) = 1.3986093279844228935937976400512
absolute error = 1e-31
relative error = 7.1499594632414575740331010403020e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3524
Order of pole (three term test) = -4.734
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.42
y1[1] (analytic) = 1.9130889403123082724360887896657
y1[1] (numeric) = 1.9130889403123082724360887896658
absolute error = 1e-31
relative error = 5.2271485079870454322440893816570e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.4077604530595701859727871580863
y2[1] (numeric) = 1.4077604530595701859727871580864
absolute error = 1e-31
relative error = 7.1034812622178727307631452987902e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3589
Order of pole (three term test) = -4.912
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=152062704, alloc=4717728, time=8.19
x[1] = 0.43
y1[1] (analytic) = 1.9089657496748851224759104776634
y1[1] (numeric) = 1.9089657496748851224759104776636
absolute error = 2e-31
relative error = 1.0476877337063898968472555724709e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4168708024292107662169186726246
y2[1] (numeric) = 1.4168708024292107662169186726246
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3653
Order of pole (three term test) = -5.093
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=156064700, alloc=4717728, time=8.41
x[1] = 0.44
y1[1] (analytic) = 1.9047516632199634171655373889984
y1[1] (numeric) = 1.9047516632199634171655373889985
absolute error = 1e-31
relative error = 5.2500282284017545707034343461997e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.4259394650659996027697207507799
y2[1] (numeric) = 1.42593946506599960276972075078
absolute error = 1e-31
relative error = 7.0129204254383618154964292748691e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3715
Order of pole (three term test) = -5.278
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=160066484, alloc=4717728, time=8.63
x[1] = 0.45
y1[1] (analytic) = 1.9004471023526769216688406114864
y1[1] (numeric) = 1.9004471023526769216688406114866
absolute error = 2e-31
relative error = 1.0523839350877383554554287495669e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4349655341112302104208442462319
y2[1] (numeric) = 1.434965534111230210420844246232
absolute error = 1e-31
relative error = 6.9688084921103463695038126770442e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3776
Order of pole (three term test) = -5.466
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.46
y1[1] (analytic) = 1.8960524975255252425363899035004
y1[1] (numeric) = 1.8960524975255252425363899035006
absolute error = 2e-31
relative error = 1.0548231141332495642983950217470e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4439481069655197652415136439289
y2[1] (numeric) = 1.443948106965519765241513643929
absolute error = 1e-31
relative error = 6.9254566363989086005517729136524e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3835
Order of pole (three term test) = -5.657
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=164069084, alloc=4717728, time=8.85
x[1] = 0.47
y1[1] (analytic) = 1.8915682881953289364540192765334
y1[1] (numeric) = 1.8915682881953289364540192765336
absolute error = 2e-31
relative error = 1.0573237098979500782675499140116e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4528862853790682907032748003964
y2[1] (numeric) = 1.4528862853790682907032748003965
absolute error = 1e-31
relative error = 6.8828511223718581594824423813170e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3892
Order of pole (three term test) = -5.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=168070816, alloc=4717728, time=9.08
x[1] = 0.48
y1[1] (analytic) = 1.8869949227792841943999548311587
y1[1] (numeric) = 1.8869949227792841943999548311589
absolute error = 2e-31
relative error = 1.0598862645874398310359626801090e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4617791755414828891366429425886
y2[1] (numeric) = 1.4617791755414828891366429425887
absolute error = 1e-31
relative error = 6.8409785604557727842596851575514e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3949
Order of pole (three term test) = -6.047
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.49
y1[1] (analytic) = 1.8823328586101214957054681591367
y1[1] (numeric) = 1.8823328586101214957054681591368
absolute error = 1e-31
relative error = 5.3125566789413687071833591327687e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.470625888171158036181358337188
y2[1] (numeric) = 1.470625888171158036181358337188
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4003
Order of pole (three term test) = -6.246
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=172071776, alloc=4717728, time=9.29
x[1] = 0.5
y1[1] (analytic) = 1.8775825618903727161162815826038
y1[1] (numeric) = 1.877582561890372716116281582604
absolute error = 2e-31
relative error = 1.0651994967328498908487019298620e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4794255386042030002732879352156
y2[1] (numeric) = 1.4794255386042030002732879352156
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4056
Order of pole (three term test) = -6.448
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=176072740, alloc=4717728, time=9.52
x[1] = 0.51
y1[1] (analytic) = 1.8727445076457512631058084735755
y1[1] (numeric) = 1.8727445076457512631058084735757
absolute error = 2e-31
relative error = 1.0679513365729867151987633282656e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4881772468829074945001302376746
y2[1] (numeric) = 1.4881772468829074945001302376746
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4107
Order of pole (three term test) = -6.653
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=180073676, alloc=4717728, time=9.73
x[1] = 0.52
y1[1] (analytic) = 1.8678191796776499003878475719885
y1[1] (numeric) = 1.8678191796776499003878475719887
absolute error = 2e-31
relative error = 1.0707674606624191521611756445069e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4968801378437367143344589425478
y2[1] (numeric) = 1.4968801378437367143344589425478
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4157
Order of pole (three term test) = -6.86
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.53
y1[1] (analytic) = 1.8628070705147610118066950185642
y1[1] (numeric) = 1.8628070705147610118066950185644
absolute error = 2e-31
relative error = 1.0736484908484525005190792269169e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5055333412048469618136610224661
y2[1] (numeric) = 1.5055333412048469618136610224661
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4205
Order of pole (three term test) = -7.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=184075344, alloc=4717728, time=9.95
x[1] = 0.54
y1[1] (analytic) = 1.8577086813638241425379687789178
y1[1] (numeric) = 1.857708681363824142537968778918
absolute error = 2e-31
relative error = 1.0765950657730218806758766578607e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5141359916531131046772806829582
y2[1] (numeric) = 1.5141359916531131046772806829583
absolute error = 1e-31
relative error = 6.6044265872592697963164134977544e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4251
Order of pole (three term test) = -7.281
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=188076008, alloc=4717728, time=10.17
x[1] = 0.55
y1[1] (analytic) = 1.8525245220595057428049817976178
y1[1] (numeric) = 1.852524522059505742804981797618
absolute error = 2e-31
relative error = 1.0796078411834146471138038153385e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5226872289306591677883781077573
y2[1] (numeric) = 1.5226872289306591677883781077573
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4295
Order of pole (three term test) = -7.496
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.56
y1[1] (analytic) = 1.8472551110134161260945255038663
y1[1] (numeric) = 1.8472551110134161260945255038665
absolute error = 2e-31
relative error = 1.0826874902529229099584834949339e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.531186197920883403851869441112
y2[1] (numeric) = 1.531186197920883403851869441112
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4338
Order of pole (three term test) = -7.712
NO COMPLEX POLE (six term test) for Equation 2
bytes used=192081432, alloc=4717728, time=10.39
TOP MAIN SOLVE Loop
x[1] = 0.57
y1[1] (analytic) = 1.841900975162268740133756363916
y1[1] (numeric) = 1.8419009751622687401337563639162
absolute error = 2e-31
relative error = 1.0858347039117034891643604791244e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5396320487339692409944634930788
y2[1] (numeric) = 1.5396320487339692409944634930788
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4379
Order of pole (three term test) = -7.931
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=196082972, alloc=4717728, time=10.61
x[1] = 0.58
y1[1] (analytic) = 1.83646264991518693465788732805
y1[1] (numeric) = 1.8364626499151869346578873280502
absolute error = 2e-31
relative error = 1.0890501911881331673290929365454e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5480239367918735561826960595765
y2[1] (numeric) = 1.5480239367918735561826960595764
absolute error = 1e-31
relative error = 6.4598484314939022042044913285792e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4418
Order of pole (three term test) = -8.151
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=200083748, alloc=4717728, time=10.83
x[1] = 0.59
y1[1] (analytic) = 1.8309406791001634952479965224907
y1[1] (numeric) = 1.8309406791001634952479965224909
absolute error = 2e-31
relative error = 1.0923346795609580426579042515074e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5563610229127837757225433788758
y2[1] (numeric) = 1.5563610229127837757225433788757
absolute error = 1e-31
relative error = 6.4252444341510507999957782976453e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4456
Order of pole (three term test) = -8.373
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.6
y1[1] (analytic) = 1.8253356149096782972409524989554
y1[1] (numeric) = 1.8253356149096782972409524989556
absolute error = 2e-31
relative error = 1.0956889153225471297924279359639e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5646424733950353572009454456587
y2[1] (numeric) = 1.5646424733950353572009454456586
absolute error = 1e-31
relative error = 6.3912364454107693316027321403364e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4492
Order of pole (three term test) = -8.598
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=204086260, alloc=4717728, time=11.05
x[1] = 0.61
y1[1] (analytic) = 1.8196480178454795179007465786548
y1[1] (numeric) = 1.819648017845479517900746578655
absolute error = 2e-31
relative error = 1.0991136639535721315725263428320e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5728674601004812611909760321627
y2[1] (numeric) = 1.5728674601004812611909760321627
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4526
Order of pole (three term test) = -8.824
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=208087228, alloc=4717728, time=11.26
x[1] = 0.62
y1[1] (analytic) = 1.8138784566625339286839996543607
y1[1] (numeric) = 1.8138784566625339286839996543609
absolute error = 2e-31
relative error = 1.1026097105094475286557172642480e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5810351605373050758429632275822
y2[1] (numeric) = 1.5810351605373050758429632275822
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4558
Order of pole (three term test) = -9.051
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=212088644, alloc=4717728, time=11.49
x[1] = 0.63
y1[1] (analytic) = 1.8080275083121518725237089657771
y1[1] (numeric) = 1.8080275083121518725237089657773
absolute error = 2e-31
relative error = 1.1061778600188778265263196803500e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5891447579422695131181120907946
y2[1] (numeric) = 1.5891447579422695131181120907946
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.58
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4588
Order of pole (three term test) = -9.281
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.64
y1[1] (analytic) = 1.8020957578842926135861107792603
y1[1] (numeric) = 1.8020957578842926135861107792606
absolute error = 3e-31
relative error = 1.6647284068423079729843529839840e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5971954413623920518835462392079
y2[1] (numeric) = 1.5971954413623920518835462392079
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4617
Order of pole (three term test) = -9.511
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=216090404, alloc=4717728, time=11.70
x[1] = 0.65
y1[1] (analytic) = 1.7960837985490558289176045706799
y1[1] (numeric) = 1.7960837985490558289176045706802
absolute error = 3e-31
relative error = 1.6703006855378980889622980697507e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6051864057360395603725216786059
y2[1] (numeric) = 1.6051864057360395603725216786059
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4643
Order of pole (three term test) = -9.743
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=220091192, alloc=4717728, time=11.92
x[1] = 0.66
y1[1] (analytic) = 1.7899922314973650927838170912302
y1[1] (numeric) = 1.7899922314973650927838170912305
absolute error = 3e-31
relative error = 1.6759849273147060944544637298514e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6131168519734337886151454793963
y2[1] (numeric) = 1.6131168519734337886151454793963
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4668
Order of pole (three term test) = -9.977
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.67
y1[1] (analytic) = 1.7838216658808492853029421448381
y1[1] (numeric) = 1.7838216658808492853029421448384
absolute error = 3e-31
relative error = 1.6817824659162905260838480918837e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6209859870365596803574439141266
y2[1] (numeric) = 1.6209859870365596803574439141266
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.05
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4691
Order of pole (three term test) = -10.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=224092596, alloc=4717728, time=12.14
x[1] = 0.68
y1[1] (analytic) = 1.7775727187509279371823940840443
y1[1] (numeric) = 1.7775727187509279371823940840446
absolute error = 3e-31
relative error = 1.6876946683272976088279824975587e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6287930240184685137041781874202
y2[1] (numeric) = 1.6287930240184685137041781874203
absolute error = 1e-31
relative error = 6.1395154894073344668541915317869e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4712
Order of pole (three term test) = -10.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=228093808, alloc=4717728, time=12.36
x[1] = 0.69
y1[1] (analytic) = 1.7712460149971066019735393154978
y1[1] (numeric) = 1.771246014997106601973539315498
absolute error = 2e-31
relative error = 1.1291486236615567354709239226839e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6365371822219679402374292070087
y2[1] (numeric) = 1.6365371822219679402374292070088
absolute error = 1e-31
relative error = 6.1104630610486631158265560320066e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4731
Order of pole (three term test) = -10.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=232096144, alloc=4717728, time=12.58
x[1] = 0.7
y1[1] (analytic) = 1.7648421872844884262558599901919
y1[1] (numeric) = 1.7648421872844884262558599901921
absolute error = 2e-31
relative error = 1.1332458020381652884961903425722e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6442176872376910536726143513987
y2[1] (numeric) = 1.6442176872376910536726143513988
absolute error = 1e-31
relative error = 6.0819197346065175188260274521277e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4749
Order of pole (three term test) = -10.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.71
y1[1] (analytic) = 1.7583618759905081665414579441396
y1[1] (numeric) = 1.7583618759905081665414579441398
absolute error = 2e-31
relative error = 1.1374222947556650864249365164370e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6518337710215366812101279728528
y2[1] (numeric) = 1.6518337710215366812101279728529
absolute error = 1e-31
relative error = 6.0538779236943083185531773730902e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.33
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4764
Order of pole (three term test) = -11.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=236098740, alloc=4717728, time=12.80
x[1] = 0.72
y1[1] (analytic) = 1.751805729140894979445486962252
y1[1] (numeric) = 1.7518057291408949794454869622522
absolute error = 2e-31
relative error = 1.1416791067242497559640900767493e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6593846719714731536180038326482
y2[1] (numeric) = 1.6593846719714731536180038326482
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4777
Order of pole (three term test) = -11.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=240100724, alloc=4717728, time=13.02
x[1] = 0.73
y1[1] (analytic) = 1.7451744023448703887901321585503
y1[1] (numeric) = 1.7451744023448703887901321585506
absolute error = 3e-31
relative error = 1.7190259013478005787652371521656e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6668696350036978737325941307615
y2[1] (numeric) = 1.6668696350036978737325941307616
absolute error = 1e-31
relative error = 5.9992694029595274613422544528161e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4789
Order of pole (three term test) = -11.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=244102212, alloc=4717728, time=13.24
x[1] = 0.74
y1[1] (analytic) = 1.7384685587295879097914245606988
y1[1] (numeric) = 1.7384685587295879097914245606991
absolute error = 3e-31
relative error = 1.7256567482545069417490884219023e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6742879116281450674838811576082
y2[1] (numeric) = 1.6742879116281450674838811576082
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.26
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4799
Order of pole (three term test) = -11.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.75
y1[1] (analytic) = 1.7316888688738208863118387530001
y1[1] (numeric) = 1.7316888688738208863118387530004
absolute error = 3e-31
relative error = 1.7324128219124068957741356444844e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6816387600233341667332419527799
y2[1] (numeric) = 1.6816387600233341667332419527799
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.63
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4806
Order of pole (three term test) = -12.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=248102984, alloc=4717728, time=13.45
x[1] = 0.76
y1[1] (analytic) = 1.724836010740905172339688366667
y1[1] (numeric) = 1.7248360107409051723396883666673
absolute error = 3e-31
relative error = 1.7392957830880089047314622841127e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6889214451105513391477556387697
y2[1] (numeric) = 1.6889214451105513391477556387697
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.01
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.06
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4812
Order of pole (three term test) = -12.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=252105188, alloc=4717728, time=13.67
x[1] = 0.77
y1[1] (analytic) = 1.7179106696109433633712905653243
y1[1] (numeric) = 1.7179106696109433633712905653246
absolute error = 3e-31
relative error = 1.7463073331277536436436098781629e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6961352386273567470198837344522
y2[1] (numeric) = 1.6961352386273567470198837344522
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4816
Order of pole (three term test) = -12.6
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.78
y1[1] (analytic) = 1.7109135380122773572162650237646
y1[1] (numeric) = 1.7109135380122773572162650237648
absolute error = 2e-31
relative error = 1.1689661432707934917780426317918e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7032794192004101843678973251179
y2[1] (numeric) = 1.7032794192004101843678973251179
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.21
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -12.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=256106360, alloc=4717728, time=13.89
x[1] = 0.79
y1[1] (analytic) = 1.703845315652236096912780861085
y1[1] (numeric) = 1.7038453156522360969127808610852
absolute error = 2e-31
relative error = 1.1738154758692957849423038793525e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7103532724176078098140288749692
y2[1] (numeric) = 1.7103532724176078098140288749692
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -13.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=260108956, alloc=4717728, time=14.11
x[1] = 0.8
y1[1] (analytic) = 1.6967067093471654209207499816423
y1[1] (numeric) = 1.6967067093471654209207499816426
absolute error = 3e-31
relative error = 1.7681311587164626470756212777398e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7173560908995227616271746105814
y2[1] (numeric) = 1.7173560908995227616271746105814
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4816
Order of pole (three term test) = -13.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=264110316, alloc=4717728, time=14.33
x[1] = 0.81
y1[1] (analytic) = 1.6894984329517470175496392406801
y1[1] (numeric) = 1.6894984329517470175496392406804
absolute error = 3e-31
relative error = 1.7756749230945759692821379877619e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7242871743701425109281768525145
y2[1] (numeric) = 1.7242871743701425109281768525146
absolute error = 1e-31
relative error = 5.7994979888734933269737662144258e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4812
Order of pole (three term test) = -13.57
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.82
y1[1] (analytic) = 1.6822212072876135516665579784369
y1[1] (numeric) = 1.6822212072876135516665579784372
absolute error = 3e-31
relative error = 1.7833564260179265023530314552991e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7311458297268958793813133646877
y2[1] (numeric) = 1.7311458297268958793813133646878
absolute error = 1e-31
relative error = 5.7765208616639718042472695734813e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4806
Order of pole (three term test) = -13.81
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=268112620, alloc=4717728, time=14.55
x[1] = 0.83
y1[1] (analytic) = 1.6748757600712671021124629178644
y1[1] (numeric) = 1.6748757600712671021124629178647
absolute error = 3e-31
relative error = 1.7911776333023937015518563885435e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7379313711099627187285802261381
y2[1] (numeric) = 1.7379313711099627187285802261382
absolute error = 1e-31
relative error = 5.7539671394580506308555960959128e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4799
Order of pole (three term test) = -14.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=272116140, alloc=4717728, time=14.77
x[1] = 0.84
y1[1] (analytic) = 1.6674628258413081179226710368709
y1[1] (numeric) = 1.6674628258413081179226710368711
absolute error = 2e-31
relative error = 1.1994270390951068400300520586944e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7446431199708593212565726706296
y2[1] (numeric) = 1.7446431199708593212565726706298
absolute error = 2e-31
relative error = 1.1463662551418572589008316556134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4789
Order of pole (three term test) = -14.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.85
y1[1] (analytic) = 1.6599831458849821703954160294615
y1[1] (numeric) = 1.6599831458849821703954160294617
absolute error = 2e-31
relative error = 1.2048315098607495773354058660782e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7512804051402927027120715242355
y2[1] (numeric) = 1.7512804051402927027120715242356
absolute error = 1e-31
relative error = 5.7101078563138000370993153595601e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.69
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4778
Order of pole (three term test) = -14.53
NO COMPLEX POLE (six term test) for Equation 2
bytes used=276118732, alloc=4717728, time=15.00
TOP MAIN SOLVE Loop
x[1] = 0.86
y1[1] (analytic) = 1.6524374681640518462720306642239
y1[1] (numeric) = 1.6524374681640518462720306642241
absolute error = 2e-31
relative error = 1.2103332431829381617794594347584e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7578425628952769722945887295286
y2[1] (numeric) = 1.7578425628952769722945887295288
absolute error = 2e-31
relative error = 1.1377583193263192683296475032920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4764
Order of pole (three term test) = -14.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=280119804, alloc=4717728, time=15.21
x[1] = 0.87
y1[1] (analytic) = 1.6448265472400011947776638054828
y1[1] (numeric) = 1.6448265472400011947776638054831
absolute error = 3e-31
relative error = 1.8239005231487558762563506511973e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7643289370255050781448028237228
y2[1] (numeric) = 1.764328937025505078144802823723
absolute error = 2e-31
relative error = 1.1335754677196500966944005371275e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.03
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4749
Order of pole (three term test) = -15.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=284120752, alloc=4717728, time=15.44
x[1] = 0.88
y1[1] (analytic) = 1.6371511441985802080154986057221
y1[1] (numeric) = 1.6371511441985802080154986057224
absolute error = 3e-31
relative error = 1.8324514572956932853793477648779e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.770738878898969291209645130756
y2[1] (numeric) = 1.7707388788989692912096451307561
absolute error = 1e-31
relative error = 5.6473600479241280545894125024680e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.71
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4732
Order of pole (three term test) = -15.24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.89
y1[1] (analytic) = 1.6294120265736968802035530573802
y1[1] (numeric) = 1.6294120265736968802035530573806
absolute error = 4e-31
relative error = 2.4548732516790979387410939579439e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7770717475268238654903337129732
y2[1] (numeric) = 1.7770717475268238654903337129733
absolute error = 1e-31
relative error = 5.6272348113784054238570141075072e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4712
Order of pole (three term test) = -15.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=288121956, alloc=4717728, time=15.65
x[1] = 0.9
y1[1] (analytic) = 1.6216099682706644564847161514071
y1[1] (numeric) = 1.6216099682706644564847161514075
absolute error = 4e-31
relative error = 2.4666843928356736701397732916790e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7833269096274833884613823157136
y2[1] (numeric) = 1.7833269096274833884613823157137
absolute error = 1e-31
relative error = 5.6074968341552619311245879096031e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4691
Order of pole (three term test) = -15.72
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=292124504, alloc=4717728, time=15.88
x[1] = 0.91
y1[1] (analytic) = 1.6137457494888115465211782261747
y1[1] (numeric) = 1.613745749488811546521178226175
absolute error = 3e-31
relative error = 1.8590289089531694276748317068891e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7895037396899504118789575178716
y2[1] (numeric) = 1.7895037396899504118789575178717
absolute error = 1e-31
relative error = 5.5881414373197124198260167760830e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4668
Order of pole (three term test) = -15.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=296126880, alloc=4717728, time=16.10
x[1] = 0.92
y1[1] (analytic) = 1.6058201566434628417974047066744
y1[1] (numeric) = 1.6058201566434628417974047066747
absolute error = 3e-31
relative error = 1.8682042242331151813099074201194e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7956016200363660302682761024816
y2[1] (numeric) = 1.7956016200363660302682761024818
absolute error = 2e-31
relative error = 1.1138328110661285337217339514262e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4644
Order of pole (three term test) = -16.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.93
y1[1] (analytic) = 1.597833982287298238494907084433
y1[1] (numeric) = 1.5978339822872982384949070844333
absolute error = 3e-31
relative error = 1.8775417429196881134791861746737e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8016199408837771520843192159106
y2[1] (numeric) = 1.8016199408837771520843192159108
absolute error = 2e-31
relative error = 1.1101120467277401119619397346929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4617
Order of pole (three term test) = -16.42
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=300130072, alloc=4717728, time=16.32
x[1] = 0.94
y1[1] (analytic) = 1.589788025031098229960989815224
y1[1] (numeric) = 1.5897880250310982299609898152243
absolute error = 3e-31
relative error = 1.8870440289933095142290138514012e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8075581004051142868702197986342
y2[1] (numeric) = 1.8075581004051142868702197986343
absolute error = 1e-31
relative error = 5.5323256263567825837214471555805e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.88
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4589
Order of pole (three term test) = -16.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=304132624, alloc=4717728, time=16.54
x[1] = 0.95
y1[1] (analytic) = 1.5816830894638834941661809737605
y1[1] (numeric) = 1.5816830894638834941661809737607
absolute error = 2e-31
relative error = 1.2644758063879322064650124534699e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8134155047893737506854221021026
y2[1] (numeric) = 1.8134155047893737506854221021027
absolute error = 1e-31
relative error = 5.5144559940009386778827118227612e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4558
Order of pole (three term test) = -16.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.96
y1[1] (analytic) = 1.5735199860724566621250508003519
y1[1] (numeric) = 1.5735199860724566621250508003521
absolute error = 2e-31
relative error = 1.2710356510895343653297020475909e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8191915683009982716332221464304
y2[1] (numeric) = 1.8191915683009982716332221464306
absolute error = 2e-31
relative error = 1.0993894402599197176082934841730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4526
Order of pole (three term test) = -17.1
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=308133880, alloc=4717728, time=16.76
x[1] = 0.97
y1[1] (analytic) = 1.5652995311603543130365277548499
y1[1] (numeric) = 1.5652995311603543130365277548501
absolute error = 2e-31
relative error = 1.2777107257659515482921316588080e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8248857133384500574766200378563
y2[1] (numeric) = 1.8248857133384500574766200378565
absolute error = 2e-31
relative error = 1.0959590430138200106013713556067e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4492
Order of pole (three term test) = -17.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=312136080, alloc=4717728, time=16.98
x[1] = 0.98
y1[1] (analytic) = 1.5570225467662173008766582673599
y1[1] (numeric) = 1.5570225467662173008766582673602
absolute error = 3e-31
relative error = 1.9267543724596056461225459049805e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8304973704919704680845332877192
y2[1] (numeric) = 1.8304973704919704680845332877193
absolute error = 1e-31
relative error = 5.4629961021535732938417309594081e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4457
Order of pole (three term test) = -17.55
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=316137840, alloc=4717728, time=17.20
x[1] = 0.99
y1[1] (analytic) = 1.5486898605815875753431264086536
y1[1] (numeric) = 1.5486898605815875753431264086539
absolute error = 3e-31
relative error = 1.9371212250807881983288492400645e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8360259786005205167892594115471
y2[1] (numeric) = 1.8360259786005205167892594115473
absolute error = 2e-31
relative error = 1.0893092054854615314046352061738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4419
Order of pole (three term test) = -17.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1
y1[1] (analytic) = 1.540302305868139717400936607443
y1[1] (numeric) = 1.5403023058681397174009366074433
absolute error = 3e-31
relative error = 1.9476696156142872553256497482815e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8414709848078965066525023216303
y2[1] (numeric) = 1.8414709848078965066525023216305
absolute error = 2e-31
relative error = 1.0860882503715589887396722545162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.438
Order of pole (three term test) = -18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=320140088, alloc=4717728, time=17.42
x[1] = 1.01
y1[1] (analytic) = 1.5318607213743554662067313557792
y1[1] (numeric) = 1.5318607213743554662067313557795
absolute error = 3e-31
relative error = 1.9584025872198477020946116726077e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.846831844618015190123098784782
y2[1] (numeric) = 1.8468318446180151901230987847822
absolute error = 2e-31
relative error = 1.0829356261255420139533538002069e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4339
Order of pole (three term test) = -18.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=324141756, alloc=4717728, time=17.64
x[1] = 1.02
y1[1] (analytic) = 1.5233659512516495698896138080338
y1[1] (numeric) = 1.5233659512516495698896138080341
absolute error = 3e-31
relative error = 1.9693232591519440156246480391055e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8521080219493629236165499854554
y2[1] (numeric) = 1.8521080219493629236165499854556
absolute error = 2e-31
relative error = 1.0798506222628306711379488779528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4296
Order of pole (three term test) = -18.43
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=328143860, alloc=4717728, time=17.86
x[1] = 1.03
y1[1] (analytic) = 1.5148188449699553475335022998374
y1[1] (numeric) = 1.5148188449699553475335022998376
absolute error = 2e-31
relative error = 1.3202898859101978301419954888288e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8572989891886033721462743852944
y2[1] (numeric) = 1.8572989891886033721462743852946
absolute error = 2e-31
relative error = 1.0768325464247080094154084022471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4252
Order of pole (three term test) = -18.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.04
y1[1] (analytic) = 1.5062202572327784037344734209922
y1[1] (numeric) = 1.5062202572327784037344734209924
absolute error = 2e-31
relative error = 1.3278270494611403563077827214457e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8624042272433384032807916921162
y2[1] (numeric) = 1.8624042272433384032807916921163
absolute error = 1e-31
relative error = 5.3694036201805817188446247790652e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4205
Order of pole (three term test) = -18.86
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=332146816, alloc=4717728, time=18.09
x[1] = 1.05
y1[1] (analytic) = 1.4975710478917269902908495728121
y1[1] (numeric) = 1.4975710478917269902908495728123
absolute error = 2e-31
relative error = 1.3354959037272989274234396530284e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8674232255940168943814094850003
y2[1] (numeric) = 1.8674232255940168943814094850004
absolute error = 1e-31
relative error = 5.3549724898698611141401121522493e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4158
Order of pole (three term test) = -19.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=336148144, alloc=4717728, time=18.31
x[1] = 1.06
y1[1] (analytic) = 1.4888720818605275619186375399564
y1[1] (numeric) = 1.4888720818605275619186375399566
absolute error = 2e-31
relative error = 1.3432987456523166582740481496900e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8723554823449862622829459219974
y2[1] (numeric) = 1.8723554823449862622829459219975
absolute error = 1e-31
relative error = 5.3408661412285568070262524031186e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4108
Order of pole (three term test) = -19.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.07
y1[1] (analytic) = 1.4801242290285341243650930681759
y1[1] (numeric) = 1.4801242290285341243650930681761
absolute error = 2e-31
relative error = 1.3512379304220170351974605718951e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8772005042746816103070632577768
y2[1] (numeric) = 1.8772005042746816103070632577769
absolute error = 1e-31
relative error = 5.3270814583889269437213141478418e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4057
Order of pole (three term test) = -19.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=340150340, alloc=4717728, time=18.53
x[1] = 1.08
y1[1] (analytic) = 1.471328364173740023913524788526
y1[1] (numeric) = 1.4713283641737400239135247885262
absolute error = 2e-31
relative error = 1.3593158731247244736031450166152e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8819578068849474737353349876248
y2[1] (numeric) = 1.8819578068849474737353349876248
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4004
Order of pole (three term test) = -19.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=344151632, alloc=4717728, time=18.75
x[1] = 1.09
y1[1] (analytic) = 1.4624853668753008770278970738751
y1[1] (numeric) = 1.4624853668753008770278970738753
absolute error = 2e-31
relative error = 1.3675350504690078184058136885999e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.886626914449487231608600628636
y2[1] (numeric) = 1.8866269144494872316086006286361
absolute error = 1e-31
relative error = 5.3004650381116680305033592422926e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.395
Order of pole (three term test) = -19.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=348152996, alloc=4717728, time=18.96
x[1] = 1.1
y1[1] (analytic) = 1.4535961214255773877713700517847
y1[1] (numeric) = 1.4535961214255773877713700517849
absolute error = 2e-31
relative error = 1.3758980025610902976743740015516e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8912073600614353399518025778717
y2[1] (numeric) = 1.8912073600614353399518025778718
absolute error = 1e-31
relative error = 5.2876274760664810486298889444334e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3894
Order of pole (three term test) = -20.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.11
y1[1] (analytic) = 1.4446615167417068486437375119336
y1[1] (numeric) = 1.4446615167417068486437375119338
absolute error = 2e-31
relative error = 1.3844073347442693271740424613815e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8956986856800476292406259593394
y2[1] (numeric) = 1.8956986856800476292406259593395
absolute error = 1e-31
relative error = 5.2750999278203755255959132055767e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3836
Order of pole (three term test) = -20.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=352155640, alloc=4717728, time=19.18
x[1] = 1.12
y1[1] (analytic) = 1.4356824462767121676139887939611
y1[1] (numeric) = 1.4356824462767121676139887939614
absolute error = 3e-31
relative error = 2.0895985792541915969706446406115e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9001004421765049971191032473392
y2[1] (numeric) = 1.9001004421765049971191032473393
absolute error = 1e-31
relative error = 5.2628796762687535009278191791115e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3777
Order of pole (three term test) = -20.46
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=356157016, alloc=4717728, time=19.40
x[1] = 1.13
y1[1] (analytic) = 1.4266598079301573103712158356535
y1[1] (numeric) = 1.4266598079301573103712158356538
absolute error = 3e-31
relative error = 2.1028138476491419984745714892156e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9044121893788259160370815224114
y2[1] (numeric) = 1.9044121893788259160370815224115
absolute error = 1e-31
relative error = 5.2509640800302600469780576938800e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3717
Order of pole (three term test) = -20.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=360157924, alloc=4717728, time=19.63
x[1] = 1.14
y1[1] (analytic) = 1.4175945039583580921751867408226
y1[1] (numeric) = 1.4175945039583580921751867408228
absolute error = 2e-31
relative error = 1.4108406842826967518564790674677e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9086334961158832645942155781022
y2[1] (numeric) = 1.9086334961158832645942155781023
absolute error = 1e-31
relative error = 5.2393505722027037878934821367571e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3655
Order of pole (three term test) = -20.83
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.15
y1[1] (analytic) = 1.4084874408841572981525767188099
y1[1] (numeric) = 1.4084874408841572981525767188101
absolute error = 2e-31
relative error = 1.4199629630666279729823385061215e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9127639402605210809440330497537
y2[1] (numeric) = 1.9127639402605210809440330497538
absolute error = 1e-31
relative error = 5.2280366591593033891786913326237e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3591
Order of pole (three term test) = -21.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=364159892, alloc=4717728, time=19.85
x[1] = 1.16
y1[1] (analytic) = 1.399339529406273154451639623394
y1[1] (numeric) = 1.3993395294062731544516396233942
absolute error = 2e-31
relative error = 1.4292456962525610483894520600656e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9168031087717669266186616668743
y2[1] (numeric) = 1.9168031087717669266186616668745
absolute error = 2e-31
relative error = 1.0434039838768538318447326452046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3526
Order of pole (three term test) = -21.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=368161524, alloc=4783252, time=20.07
x[1] = 1.17
y1[1] (analytic) = 1.3901516843082302153326619350505
y1[1] (numeric) = 1.3901516843082302153326619350507
absolute error = 2e-31
relative error = 1.4386919230294236573160021116968e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.920750597736135639573013008962
y2[1] (numeric) = 1.9207505977361356395730130089622
absolute error = 2e-31
relative error = 1.0412596004693532306875303617753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.346
Order of pole (three term test) = -21.37
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.18
y1[1] (analytic) = 1.3809248243668817730295994667128
y1[1] (numeric) = 1.380924824366881773029599466713
absolute error = 2e-31
relative error = 1.4483047626556703718070567589968e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9246060124080203461075380258748
y2[1] (numeric) = 1.9246060124080203461075380258749
absolute error = 1e-31
relative error = 5.1958686274123412040520623721069e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3392
Order of pole (three term test) = -21.54
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=372162960, alloc=4783252, time=20.29
x[1] = 1.19
y1[1] (analytic) = 1.3716598722605329380656795583505
y1[1] (numeric) = 1.3716598722605329380656795583507
absolute error = 2e-31
relative error = 1.4580874168928958806198104389220e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9283689672491666926020211116027
y2[1] (numeric) = 1.9283689672491666926020211116028
absolute error = 1e-31
relative error = 5.1857295827909311668193449338272e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3323
Order of pole (three term test) = -21.71
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=376163944, alloc=4783252, time=20.51
x[1] = 1.2
y1[1] (analytic) = 1.3623577544766735776383733556231
y1[1] (numeric) = 1.3623577544766735776383733556233
absolute error = 2e-31
relative error = 1.4680431725279574463548072889641e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9320390859672263496701344354948
y2[1] (numeric) = 1.932039085967226349670134435495
absolute error = 2e-31
relative error = 1.0351757449041206860415689159494e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3253
Order of pole (three term test) = -21.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=380166452, alloc=4783252, time=20.73
x[1] = 1.21
y1[1] (analytic) = 1.3530194012193303387030107136648
y1[1] (numeric) = 1.353019401219330338703010713665
absolute error = 2e-31
relative error = 1.4781754039872716414810758633736e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9356160015533859334164648885436
y2[1] (numeric) = 1.9356160015533859334164648885438
absolute error = 2e-31
relative error = 1.0332627950972424843426405252569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3181
Order of pole (three term test) = -22.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.22
y1[1] (analytic) = 1.3436457463160470204755229744352
y1[1] (numeric) = 1.3436457463160470204755229744354
absolute error = 2e-31
relative error = 1.4884875760471227187403854926476e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9390993563190675809352452718884
y2[1] (numeric) = 1.9390993563190675809352452718886
absolute error = 2e-31
relative error = 1.0314066648944375032176755896207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3108
Order of pole (three term test) = -22.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=384169092, alloc=4783252, time=20.95
x[1] = 1.23
y1[1] (analytic) = 1.3342377271245025982395472454977
y1[1] (numeric) = 1.3342377271245025982395472454979
absolute error = 2e-31
relative error = 1.4989832466440013137743254261457e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9424888019316975100238235653892
y2[1] (numeric) = 1.9424888019316975100238235653895
absolute error = 3e-31
relative error = 1.5444104475746095338955611280055e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3034
Order of pole (three term test) = -22.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=388169936, alloc=4783252, time=21.17
x[1] = 1.24
y1[1] (analytic) = 1.3247962844387762365776934156974
y1[1] (numeric) = 1.3247962844387762365776934156976
absolute error = 2e-31
relative error = 1.5096660697891830767007682727402e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9457839994495389862847059630818
y2[1] (numeric) = 1.945783999449538986284705963082
absolute error = 2e-31
relative error = 1.0278633191380948165950190065184e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2959
Order of pole (three term test) = -22.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=392170684, alloc=4783252, time=21.40
x[1] = 1.25
y1[1] (analytic) = 1.315322362395268665447538552438
y1[1] (numeric) = 1.3153223623952686654475385524383
absolute error = 3e-31
relative error = 2.2808096978879367631218237019961e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.948984619355586214348490847036
y2[1] (numeric) = 1.9489846193555862143484908470363
absolute error = 3e-31
relative error = 1.5392630450782737967385088966532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2882
Order of pole (three term test) = -22.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.26
y1[1] (analytic) = 1.3058169083782893268863424891765
y1[1] (numeric) = 1.3058169083782893268863424891767
absolute error = 2e-31
relative error = 1.5316082883961316662083565456501e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9520903415905157638568162214254
y2[1] (numeric) = 1.9520903415905157638568162214257
absolute error = 3e-31
relative error = 1.5368141197582448547984590416573e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2804
Order of pole (three term test) = -22.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=396172968, alloc=4783252, time=21.61
x[1] = 1.27
y1[1] (analytic) = 1.296280872925318733551137016088
y1[1] (numeric) = 1.2962808729253187335511370160882
absolute error = 2e-31
relative error = 1.5428755000346471179595274267252e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9551008555846922350901817421829
y2[1] (numeric) = 1.9551008555846922350901817421832
absolute error = 3e-31
relative error = 1.5344476943123327251491311042914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2725
Order of pole (three term test) = -22.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=400174396, alloc=4783252, time=21.83
x[1] = 1.28
y1[1] (analytic) = 1.2867152096319555127793868935926
y1[1] (numeric) = 1.2867152096319555127793868935928
absolute error = 2e-31
relative error = 1.5543455032074022764459543579423e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9580158602892249637007538591603
y2[1] (numeric) = 1.9580158602892249637007538591606
absolute error = 3e-31
relative error = 1.5321632785736782190165200674150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2645
Order of pole (three term test) = -23.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.29
y1[1] (analytic) = 1.2771208750565576413866060900612
y1[1] (numeric) = 1.2771208750565576413866060900614
absolute error = 2e-31
relative error = 1.5660224799875966808337527131382e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9608350642060726589055612912854
y2[1] (numeric) = 1.9608350642060726589055612912857
absolute error = 3e-31
relative error = 1.5299604004249472112990600227422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2564
Order of pole (three term test) = -23.19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=404177392, alloc=4783252, time=22.05
x[1] = 1.3
y1[1] (analytic) = 1.2674988286245874069979841092929
y1[1] (numeric) = 1.2674988286245874069979841092931
absolute error = 2e-31
relative error = 1.5779107284621937572596305384479e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9635581854171929647013486300396
y2[1] (numeric) = 1.9635581854171929647013486300399
absolute error = 3e-31
relative error = 1.5278386055886581647435587565828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2482
Order of pole (three term test) = -23.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=408178896, alloc=4783252, time=22.27
x[1] = 1.31
y1[1] (analytic) = 1.2578500325326696613381769786162
y1[1] (numeric) = 1.2578500325326696613381769786164
absolute error = 2e-31
relative error = 1.5900146665123648270226575145525e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9661849516127340291692578059375
y2[1] (numeric) = 1.9661849516127340291692578059378
absolute error = 3e-31
relative error = 1.5257974574260140272099709127253e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2399
Order of pole (three term test) = -23.43
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=412180224, alloc=4783252, time=22.49
x[1] = 1.32
y1[1] (analytic) = 1.2481754516523729595739827294274
y1[1] (numeric) = 1.2481754516523729595739827294276
absolute error = 2e-31
relative error = 1.6023388357400705451688301191992e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9687151001182652627358998459728
y2[1] (numeric) = 1.9687151001182652627358998459731
absolute error = 3e-31
relative error = 1.5238365367440840330911248672796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2315
Order of pole (three term test) = -23.55
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.33
y1[1] (analytic) = 1.2384760534337232075157849860106
y1[1] (numeric) = 1.2384760534337232075157849860108
absolute error = 2e-31
relative error = 1.6148879055472424526787374044173e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9711483779210445623376830377638
y2[1] (numeric) = 1.9711483779210445623376830377641
absolute error = 3e-31
relative error = 1.5219554416111878605594024065733e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.223
Order of pole (three term test) = -23.67
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=416182564, alloc=4783252, time=22.71
x[1] = 1.34
y1[1] (analytic) = 1.2287528078084594652326394923001
y1[1] (numeric) = 1.2287528078084594652326394923004
absolute error = 3e-31
relative error = 2.4415000160615268508187564782643e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9734845416953193747878703480896
y2[1] (numeric) = 1.9734845416953193747878703480899
absolute error = 3e-31
relative error = 1.5201537871803413427986673744932e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2145
Order of pole (three term test) = -23.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=420184132, alloc=4783252, time=22.93
x[1] = 1.35
y1[1] (analytic) = 1.2190066870930415814200221730106
y1[1] (numeric) = 1.2190066870930415814200221730109
absolute error = 3e-31
relative error = 2.4610201336582354571266789408816e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9757233578266590692611135392652
y2[1] (numeric) = 1.9757233578266590692611135392656
absolute error = 4e-31
relative error = 2.0245749406941726831426941862872e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2058
Order of pole (three term test) = -23.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.36
y1[1] (analytic) = 1.2092386658914193576759752523919
y1[1] (numeric) = 1.2092386658914193576759752523921
bytes used=424185048, alloc=4783252, time=23.15
absolute error = 2e-31
relative error = 1.6539332196474646398301359132375e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9778646024353161856784924394266
y2[1] (numeric) = 1.977864602435316185678492439427
absolute error = 4e-31
relative error = 2.0223831272751722420754618029620e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.197
Order of pole (three term test) = -23.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.37
y1[1] (analytic) = 1.1994497209975729656881983896453
y1[1] (numeric) = 1.1994497209975729656881983896455
absolute error = 2e-31
relative error = 1.6674312936907564739534081845658e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9799080613986142228876885048919
y2[1] (numeric) = 1.9799080613986142228876885048923
absolute error = 4e-31
relative error = 2.0202958298853460487865628478250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1882
Order of pole (three term test) = -24.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=428187616, alloc=4783252, time=23.37
x[1] = 1.38
y1[1] (analytic) = 1.1896408312978343632091500735982
y1[1] (numeric) = 1.1896408312978343632091500735984
absolute error = 2e-31
relative error = 1.6811796866606429706373023342143e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.981853530372359727878131085206
y2[1] (numeric) = 1.9818535303723597278781310852064
absolute error = 4e-31
relative error = 2.0183126243685938084521885968985e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1793
Order of pole (three term test) = -24.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=432189428, alloc=4783252, time=23.59
x[1] = 1.39
y1[1] (analytic) = 1.179812977672999476596163217804
y1[1] (numeric) = 1.1798129776729994765961632178042
absolute error = 2e-31
relative error = 1.6951839298671674997732875561082e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9837008148112765448400382244429
y2[1] (numeric) = 1.9837008148112765448400382244433
absolute error = 4e-31
relative error = 2.0164331083266446222145378621330e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1703
Order of pole (three term test) = -24.26
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.4
y1[1] (analytic) = 1.1699671429002409386167480352036
y1[1] (numeric) = 1.1699671429002409386167480352038
absolute error = 2e-31
relative error = 1.7094497158631172765647243021492e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9854497299884601806594745788061
y2[1] (numeric) = 1.9854497299884601806594745788065
absolute error = 4e-31
relative error = 2.0146569009446785523348628974165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1613
Order of pole (three term test) = -24.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=436191856, alloc=4783252, time=23.80
x[1] = 1.41
y1[1] (analytic) = 1.1601043115548311901635625493609
y1[1] (numeric) = 1.1601043115548311901635625493611
absolute error = 2e-31
relative error = 1.7239829040196373458189397153398e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9871001010138503414290888619422
y2[1] (numeric) = 1.9871001010138503414290888619426
absolute error = 4e-31
relative error = 2.0129836428266174645298758825995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1522
Order of pole (three term test) = -24.42
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=440192640, alloc=4783252, time=24.02
x[1] = 1.42
y1[1] (analytic) = 1.1502254699116857734869821029759
y1[1] (numeric) = 1.1502254699116857734869821029761
absolute error = 2e-31
relative error = 1.7387895263296159248557909237100e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9886517628517197927362734733357
y2[1] (numeric) = 1.9886517628517197927362734733361
absolute error = 4e-31
relative error = 2.0114129958399623212040984749026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.143
Order of pole (three term test) = -24.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=444194048, alloc=4783252, time=24.25
x[1] = 1.43
y1[1] (analytic) = 1.1403316058467366625338976245749
y1[1] (numeric) = 1.1403316058467366625338976245751
absolute error = 2e-31
relative error = 1.7538757934495107360946728244579e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9901045603371777948572914954818
y2[1] (numeric) = 1.9901045603371777948572914954822
absolute error = 4e-31
relative error = 2.0099446429700614813415274084239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1338
Order of pole (three term test) = -24.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.44
y1[1] (analytic) = 1.1304237087381454929775201561292
y1[1] (numeric) = 1.1304237087381454929775201561293
absolute error = 1e-31
relative error = 8.8462405049542604262797632342193e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.991458348191686462527604463958
y2[1] (numeric) = 1.9914583481916864625276044639584
absolute error = 4e-31
relative error = 2.0085782881837018130937654551087e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1245
Order of pole (three term test) = -24.63
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=448195608, alloc=4783252, time=24.46
x[1] = 1.45
y1[1] (analytic) = 1.120502769367366570532866627248
y1[1] (numeric) = 1.1205027693673665705328666272481
absolute error = 1e-31
relative error = 8.9245651803662906398331279060897e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.992712991037588497665354134323
y2[1] (numeric) = 1.9927129910375884976653541343234
absolute error = 4e-31
relative error = 2.0073136563019215521922904704633e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1152
Order of pole (three term test) = -24.69
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=452196416, alloc=4783252, time=24.69
x[1] = 1.46
y1[1] (analytic) = 1.1105697798200695511746481091234
y1[1] (numeric) = 1.1105697798200695511746481091235
absolute error = 1e-31
relative error = 9.0043869207571660918496856319541e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.99386836341164484228683230125
y2[1] (numeric) = 1.9938683634116448422868323012504
absolute error = 4e-31
relative error = 2.0061504928819508516139480239641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1058
Order of pole (three term test) = -24.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.47
y1[1] (analytic) = 1.1006257333869317009069746014624
y1[1] (numeric) = 1.1006257333869317009069746014625
absolute error = 1e-31
relative error = 9.0857406806464690431127404880792e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9949243497775808978599284627356
y2[1] (numeric) = 1.9949243497775808978599284627359
absolute error = 3e-31
relative error = 1.5038164230811446552372786193594e-29 %
Correct digits = 31
h = 0.01
bytes used=456197260, alloc=4783252, time=24.91
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09641
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.48
y1[1] (analytic) = 1.0906716244643096557762265406478
y1[1] (numeric) = 1.0906716244643096557762265406479
absolute error = 1e-31
relative error = 9.1686624788754029971031479664537e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9958808445376400564840751325627
y2[1] (numeric) = 1.995880844537640056484075132563
absolute error = 3e-31
relative error = 1.5030957425191238120280518218231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08695
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=460199716, alloc=4783252, time=25.13
x[1] = 1.49
y1[1] (analytic) = 1.0807084484548006148683184845637
y1[1] (numeric) = 1.0807084484548006148683184845638
absolute error = 1e-31
relative error = 9.2531894372603662245462113142182e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9967377520431433885532007170437
y2[1] (numeric) = 1.996737752043143388553200717044
absolute error = 3e-31
relative error = 1.5024506833359953352486186796657e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07747
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=464201524, alloc=4783252, time=25.35
x[1] = 1.5
y1[1] (analytic) = 1.0707372016677029100881898514343
y1[1] (numeric) = 1.0707372016677029100881898514344
absolute error = 1e-31
relative error = 9.3393598209016390280655430800655e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9974949866040544309417233711415
y2[1] (numeric) = 1.9974949866040544309417233711418
absolute error = 3e-31
relative error = 1.5018811161575461681971566718162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06795
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.51
y1[1] (analytic) = 1.0607588812193859065815955149162
y1[1] (numeric) = 1.0607588812193859065815955149163
absolute error = 1e-31
relative error = 9.4272130802285522527302635247474e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9981524724975481192427378648367
y2[1] (numeric) = 1.998152472497548119242737864837
absolute error = 3e-31
relative error = 1.5013869268195604235677634524064e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0584
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=468204528, alloc=4783252, time=25.57
x[1] = 1.52
y1[1] (analytic) = 1.0507744849335791967261292701527
y1[1] (numeric) = 1.0507744849335791967261292701528
absolute error = 1e-31
relative error = 9.5167898948670349845863684406231e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9987101439755830071723123941168
y2[1] (numeric) = 1.9987101439755830071723123941171
absolute error = 3e-31
relative error = 1.5009680163191532415062647813725e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04883
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=472205576, alloc=4783252, time=25.80
x[1] = 1.53
y1[1] (analytic) = 1.0407850112415910586889890070761
y1[1] (numeric) = 1.0407850112415910586889890070762
absolute error = 1e-31
relative error = 9.6081322194202517825138776403092e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.999167945271476015924265068709
y2[1] (numeric) = 1.9991679452714760159242650687092
absolute error = 2e-31
relative error = 1.0004162005150652791294527195165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03924
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=476206404, alloc=4783252, time=26.02
x[1] = 1.54
y1[1] (analytic) = 1.0307914590824661576224768070764
y1[1] (numeric) = 1.0307914590824661576224768070765
absolute error = 1e-31
relative error = 9.7012833312581535851318673240320e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.99952583060547905600596353844
y2[1] (numeric) = 1.9995258306054790560059635384403
absolute error = 3e-31
relative error = 1.5003557113796154562307977521650e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02964
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.55
y1[1] (analytic) = 1.0207948278030924736439127746956
y1[1] (numeric) = 1.0207948278030924736439127746957
absolute error = 1e-31
relative error = 9.7962878804172025193735289630128e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9997837641893569638976113476345
y2[1] (numeric) = 1.9997837641893569638976113476347
absolute error = 2e-31
relative error = 1.0001081295960669480714765618937e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02002
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=480208132, alloc=4783252, time=26.24
x[1] = 1.56
y1[1] (analytic) = 1.0107961170582674458239206637609
y1[1] (numeric) = 1.010796117058267445823920663761
absolute error = 1e-31
relative error = 9.8931919417173116965093545801997e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9999417202299662957451700234135
y2[1] (numeric) = 1.9999417202299662957451700234137
absolute error = 2e-31
relative error = 1.0000291407341744952788607126122e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0104
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=484209972, alloc=4783252, time=26.46
x[1] = 1.57
y1[1] (analytic) = 1.0007963267107333254854085336454
y1[1] (numeric) = 1.0007963267107333254854085336454
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9999996829318346202105299238233
y2[1] (numeric) = 1.9999996829318346202105299238235
absolute error = 2e-31
relative error = 1.0000001585341078229540938109805e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0007668
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.58
y1[1] (analytic) = 0.99079645673119173519461094301727
y1[1] (numeric) = 0.99079645673119173519461094301732
absolute error = 5e-32
relative error = 5.0464451765359170751860542073719e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9999576464987400525517942322517
y2[1] (numeric) = 1.9999576464987400525517942322519
absolute error = 2e-31
relative error = 1.0000211771990942379840860928346e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008874
Order of pole (three term test) = -0.8949
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=488213168, alloc=4783252, time=26.68
TOP MAIN SOLVE Loop
x[1] = 1.59
y1[1] (analytic) = 0.9807975070983074319049726537566
y1[1] (numeric) = 0.98079750709830743190497265375664
absolute error = 4e-32
relative error = 4.0783137916347410175888190398334e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9998156151342908719815843437455
y2[1] (numeric) = 1.9998156151342908719815843437457
absolute error = 2e-31
relative error = 1.0000922009330828963822819427239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01851
Order of pole (three term test) = -0.9018
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=492215756, alloc=4783252, time=26.91
x[1] = 1.6
y1[1] (analytic) = 0.9708004776987112737942295370535
y1[1] (numeric) = 0.97080047769871127379422953705354
absolute error = 4e-32
relative error = 4.1203111163295114156406447674942e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9995736030415051643421138255462
y2[1] (numeric) = 1.9995736030415051643421138255464
absolute error = 2e-31
relative error = 1.0002132439425316743056676754077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02814
Order of pole (three term test) = -0.9135
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=496221108, alloc=4783252, time=27.12
x[1] = 1.61
y1[1] (analytic) = 0.96080636822701239041467239039898
y1[1] (numeric) = 0.96080636822701239041467239039902
absolute error = 4e-32
relative error = 4.1631697418713495508345239417076e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9992316344213905321324131478443
y2[1] (numeric) = 1.9992316344213905321324131478445
absolute error = 2e-31
relative error = 1.0003843304424461276096083384889e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03776
Order of pole (three term test) = -0.93
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.62
y1[1] (analytic) = 0.95081617808582955485625572528767
y1[1] (numeric) = 0.95081617808582955485625572528771
absolute error = 4e-32
relative error = 4.2069120111657614378141209755266e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9987897434705240139155188912468
y2[1] (numeric) = 1.998789743470524013915518891247
absolute error = 2e-31
relative error = 1.0006054946666749461619149272934e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04737
Order of pole (three term test) = -0.9513
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=500221928, alloc=4783252, time=27.34
x[1] = 1.63
y1[1] (analytic) = 0.9408309062858517547020283025802
y1[1] (numeric) = 0.94083090628585175470202830258023
absolute error = 3e-32
relative error = 3.1886707589604979116025056843264e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9982479743776324551116699849331
y2[1] (numeric) = 1.9982479743776324551116699849333
absolute error = 2e-31
relative error = 1.0008767808824694166666464553016e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05696
Order of pole (three term test) = -0.9775
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=504222736, alloc=4783252, time=27.56
x[1] = 1.64
y1[1] (analytic) = 0.9308515513459379556355072925434
y1[1] (numeric) = 0.93085155134593795563550729254342
absolute error = 2e-32
relative error = 2.1485703032971881267652406649844e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9976063813191736721375819743679
y2[1] (numeric) = 1.9976063813191736721375819743681
absolute error = 2e-31
relative error = 1.0011982434093175236575055253082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06652
Order of pole (three term test) = -1.008
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=508225232, alloc=4783252, time=27.79
x[1] = 1.65
y1[1] (analytic) = 0.92087911119326604764038540265872
y1[1] (numeric) = 0.92087911119326604764038540265875
absolute error = 3e-32
relative error = 3.2577565975110779315143398436867e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9968650284539188517717030402022
y2[1] (numeric) = 1.9968650284539188517717030402024
absolute error = 2e-31
relative error = 1.0015699466420664460909109164517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07606
Order of pole (three term test) = -1.044
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.66
y1[1] (analytic) = 0.91091458306354095881474206834938
y1[1] (numeric) = 0.9109145830635409588147420683494
absolute error = 2e-32
relative error = 2.1955955445061633774861881719379e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.996023989916536727501000590613
y2[1] (numeric) = 1.9960239899165367275010005906132
absolute error = 2e-31
relative error = 1.0019919650783503500993203269898e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08556
Order of pole (three term test) = -1.085
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=512227640, alloc=4783252, time=28.00
x[1] = 1.67
y1[1] (analytic) = 0.90095896340127191590521765755139
y1[1] (numeric) = 0.90095896340127191590521765755141
absolute error = 2e-32
relative error = 2.2198569316072542984607383810842e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9950833498101801744262972465342
y2[1] (numeric) = 1.9950833498101801744262972465345
absolute error = 3e-31
relative error = 1.5036965750255153107197839891175e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09503
Order of pole (three term test) = -1.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=516228344, alloc=4783252, time=28.23
x[1] = 1.68
y1[1] (analytic) = 0.89101324776012882375199526582718
y1[1] (numeric) = 0.8910132477601288237519952658272
absolute error = 2e-32
relative error = 2.2446355371569327850733656020971e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9940432021980759640604878691936
y2[1] (numeric) = 1.9940432021980759640604878691938
absolute error = 2e-31
relative error = 1.0029872962608622179454201997426e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1045
Order of pole (three term test) = -1.18
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.69
y1[1] (analytic) = 0.88107843070338772792360953016691
y1[1] (numeric) = 0.88107843070338772792360953016693
absolute error = 2e-32
relative error = 2.2699454785237997567942662002762e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9929036510941185200371492939456
y2[1] (numeric) = 1.9929036510941185200371492939458
absolute error = 2e-31
relative error = 1.0035608088238412996445534338997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1139
Order of pole (three term test) = -1.235
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=520229324, alloc=4783252, time=28.45
x[1] = 1.7
y1[1] (analytic) = 0.87115550570447531591235714266513
y1[1] (numeric) = 0.87115550570447531591235714266514
absolute error = 1e-32
relative error = 1.1479006830030102417885126338722e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9916648104524686153461333986479
y2[1] (numeric) = 1.9916648104524686153461333986481
absolute error = 2e-31
relative error = 1.0041850363092160005929222322238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1232
Order of pole (three term test) = -1.294
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=524230388, alloc=4783252, time=28.67
x[1] = 1.71
y1[1] (analytic) = 0.86124546504762240235731021694889
y1[1] (numeric) = 0.8612454650476224023573102169489
absolute error = 1e-32
relative error = 1.1611091617703963089285015727582e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9903268041561580512177522238611
y2[1] (numeric) = 1.9903268041561580512177522238614
absolute error = 3e-31
relative error = 1.5072901564383617206970421469009e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1325
Order of pole (three term test) = -1.358
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=528231064, alloc=4783252, time=28.89
x[1] = 1.72
y1[1] (analytic) = 0.85134929972863633286362171966881
y1[1] (numeric) = 0.85134929972863633286362171966882
absolute error = 1e-32
relative error = 1.1746060052187103378326159677861e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9888897660047014571781706570855
y2[1] (numeric) = 1.9888897660047014571781706570857
absolute error = 2e-31
relative error = 1.0055861487072845040638069990683e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1417
Order of pole (three term test) = -1.427
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.73
y1[1] (analytic) = 0.84146799935580222909505164865743
y1[1] (numeric) = 0.84146799935580222909505164865744
absolute error = 1e-32
relative error = 1.1883993220961037071395011350348e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9873538397007164510856776762221
y2[1] (numeric) = 1.9873538397007164510856776762223
absolute error = 2e-31
relative error = 1.0063633159061337485233998334110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1509
Order of pole (three term test) = -1.5
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=532231740, alloc=4783252, time=29.11
x[1] = 1.74
y1[1] (analytic) = 0.83160255205092298493262268465491
y1[1] (numeric) = 0.83160255205092298493262268465491
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9857191788355534971206826956656
y2[1] (numeric) = 1.9857191788355534971206826956658
absolute error = 2e-31
relative error = 1.0071917627208601197220448435137e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1601
Order of pole (three term test) = -1.578
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=536233600, alloc=4783252, time=29.33
x[1] = 1.75
y1[1] (analytic) = 0.82175394435050790961732305605737
y1[1] (numeric) = 0.82175394435050790961732305605737
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.983985946873936898731662936968
y2[1] (numeric) = 1.9839859468739368987316629369682
absolute error = 2e-31
relative error = 1.0080716565312852184849894533034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1691
Order of pole (three term test) = -1.661
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=540234464, alloc=4783252, time=29.55
x[1] = 1.76
y1[1] (analytic) = 0.8119231611071198989301998234959
y1[1] (numeric) = 0.8119231611071198989301998234959
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.982154317137618462424968099456
y2[1] (numeric) = 1.9821543171376184624249680994562
absolute error = 2e-31
relative error = 1.0090031753371009278629226308623e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1781
Order of pole (three term test) = -1.748
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.77
y1[1] (analytic) = 0.80211118539089099961051415826961
y1[1] (numeric) = 0.8021111853908909996105141582696
absolute error = 1e-32
relative error = 1.2467099551948927122734101620830e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9802244727880454670184814488984
y2[1] (numeric) = 1.9802244727880454670184814488987
absolute error = 3e-31
relative error = 1.5149797617520439703598222929771e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.187
Order of pole (three term test) = -1.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=544236780, alloc=4783252, time=29.77
x[1] = 1.78
y1[1] (analytic) = 0.79231899839121621537344670968737
y1[1] (numeric) = 0.79231899839121621537344670968736
absolute error = 1e-32
relative error = 1.2621179121420473715016888985962e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9781966068080446715477686473056
y2[1] (numeric) = 1.9781966068080446715477686473059
absolute error = 3e-31
relative error = 1.5165327802481194670965803371771e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1959
Order of pole (three term test) = -1.936
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=548237752, alloc=4783252, time=29.99
x[1] = 1.79
y1[1] (analytic) = 0.78254757931863538506482973553539
y1[1] (numeric) = 0.78254757931863538506482973553538
absolute error = 1e-32
relative error = 1.2778775711896017354342768697600e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9760709219825241934086604331086
y2[1] (numeric) = 1.9760709219825241934086604331089
absolute error = 3e-31
relative error = 1.5181641340029450333563199875389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2047
Order of pole (three term test) = -2.036
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.8
y1[1] (analytic) = 0.77279790530691294468332569346942
y1[1] (numeric) = 0.77279790530691294468332569346941
absolute error = 1e-32
relative error = 1.2939993666298239304482617156592e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9738476308781951865323731788434
y2[1] (numeric) = 1.9738476308781951865323731788436
absolute error = 2e-31
relative error = 1.0132494366397315186817884926690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2133
Order of pole (three term test) = -2.141
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=552239984, alloc=4783252, time=30.20
x[1] = 1.81
y1[1] (analytic) = 0.76307095131532536521225014915802
y1[1] (numeric) = 0.76307095131532536521225014915801
absolute error = 1e-32
relative error = 1.3104941267601313273827570299810e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9715269558223153474084512690904
y2[1] (numeric) = 1.9715269558223153474084512690906
absolute error = 2e-31
relative error = 1.0144421277597032241872194621266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2219
Order of pole (three term test) = -2.25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=556241572, alloc=4783252, time=30.43
x[1] = 1.82
y1[1] (analytic) = 0.75336769003116603743582895516913
y1[1] (numeric) = 0.75336769003116603743582895516911
absolute error = 2e-32
relative error = 2.6547461836560339892696380355190e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.969109128880456374587215318498
y2[1] (numeric) = 1.9691091288804563745872153184983
absolute error = 3e-31
relative error = 1.5235316092946357428654503789351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2305
Order of pole (three term test) = -2.363
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=560243168, alloc=4783252, time=30.65
x[1] = 1.83
y1[1] (analytic) = 0.74368909177247735317016241638147
y1[1] (numeric) = 0.74368909177247735317016241638145
absolute error = 2e-32
relative error = 2.6892958658749235944318550045721e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9665943918332976048972389297428
y2[1] (numeric) = 1.9665943918332976048972389297431
absolute error = 3e-31
relative error = 1.5254797900665940344474237527054e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2389
Order of pole (three term test) = -2.481
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.84
y1[1] (analytic) = 0.7340361243910197096197170167184
y1[1] (numeric) = 0.73403612439101970961971701671838
absolute error = 2e-32
relative error = 2.7246615439523023178512681948175e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9639829961524481469948936717271
y2[1] (numeric) = 1.9639829961524481469948936717274
absolute error = 3e-31
relative error = 1.5275081331544961174302181993772e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2472
Order of pole (three term test) = -2.603
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=564243988, alloc=4783252, time=30.87
x[1] = 1.85
y1[1] (analytic) = 0.7244097531754871398780501645252
y1[1] (numeric) = 0.72440975317548713987805016452517
absolute error = 3e-32
relative error = 4.1413026078808945163021176667881e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9612752029752999300124591686361
y2[1] (numeric) = 1.9612752029752999300124591686364
absolute error = 3e-31
relative error = 1.5296170549900036891010390159837e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2554
Order of pole (three term test) = -2.729
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=568246248, alloc=4783252, time=31.09
x[1] = 1.86
y1[1] (analytic) = 0.71481094075497924792906451171088
y1[1] (numeric) = 0.71481094075497924792906451171085
absolute error = 3e-32
relative error = 4.1969139375950472607085202557987e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9584712830789141819789777659032
y2[1] (numeric) = 1.9584712830789141819789777659035
absolute error = 3e-31
relative error = 1.5318069894206963996010683884395e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2636
Order of pole (three term test) = -2.859
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=572247216, alloc=4783252, time=31.31
x[1] = 1.87
y1[1] (analytic) = 0.70524064700273910087485193519011
y1[1] (numeric) = 0.70524064700273910087485193519008
absolute error = 3e-32
relative error = 4.2538671200390243939668968431917e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9555715168529439493442504921726
y2[1] (numeric) = 1.9555715168529439493442504921729
absolute error = 3e-31
relative error = 1.5340783879015739975727742248052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2716
Order of pole (three term test) = -2.993
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.88
y1[1] (analytic) = 0.69569982894016670452068624047776
y1[1] (numeric) = 0.69569982894016670452068624047773
absolute error = 3e-32
relative error = 4.3122045962986910720910849726704e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9525761942715953653314574258151
y2[1] (numeric) = 1.9525761942715953653314574258154
absolute error = 3e-31
relative error = 1.5364317196948844218996088375185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2795
Order of pole (three term test) = -3.131
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=576248340, alloc=4783252, time=31.53
x[1] = 1.89
y1[1] (analytic) = 0.68618944064111766088961758444877
y1[1] (numeric) = 0.68618944064111766088961758444873
absolute error = 4e-32
relative error = 5.8292940157498440313867470590910e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9494856148646304709682016721383
y2[1] (numeric) = 1.9494856148646304709682016721386
absolute error = 3e-31
relative error = 1.5388674720784311942397232278300e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2873
Order of pole (three term test) = -3.273
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=580249824, alloc=4783252, time=31.76
x[1] = 1.9
y1[1] (analytic) = 0.67671043313649657772116630491969
y1[1] (numeric) = 0.67671043313649657772116630491965
absolute error = 4e-32
relative error = 5.9109477320459397490729091256826e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.946300087687414488489709611635
y2[1] (numeric) = 1.9463000876874144884897096116352
absolute error = 2e-31
relative error = 1.0275907670416803606181490885369e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.295
Order of pole (three term test) = -3.419
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.91
y1[1] (analytic) = 0.66726375431915477053366106060247
y1[1] (numeric) = 0.66726375431915477053366106060243
absolute error = 4e-32
relative error = 5.9946310197553228890895568098455e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9430199312900105423618865769482
y2[1] (numeric) = 1.9430199312900105423618865769485
absolute error = 3e-31
relative error = 1.5439882791157159374363902534197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3025
Order of pole (three term test) = -3.569
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=584250680, alloc=4783252, time=31.98
x[1] = 1.92
y1[1] (analytic) = 0.65785034884910176740076339684095
y1[1] (numeric) = 0.6578503488491017674007633968409
absolute error = 5e-32
relative error = 7.6005128046939805592110257325090e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.939645473685324918426371339687
y2[1] (numeric) = 1.9396454736853249184263713396873
absolute error = 3e-31
relative error = 1.5466744003995752334653603471858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.31
Order of pole (three term test) = -3.723
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=588251536, alloc=4783252, time=32.20
x[1] = 1.93
y1[1] (analytic) = 0.64847115805904009521271093528813
y1[1] (numeric) = 0.64847115805904009521271093528807
absolute error = 6e-32
relative error = 9.2525317825372422231928581607912e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9361770523163060466151293727488
y2[1] (numeric) = 1.936177052316306046615129372749
absolute error = 2e-31
relative error = 1.0329633840083687944185628728597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3173
Order of pole (three term test) = -3.88
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=592253068, alloc=4783252, time=32.42
x[1] = 1.94
y1[1] (analytic) = 0.63912711986023279386493231415927
y1[1] (numeric) = 0.63912711986023279386493231415922
absolute error = 5e-32
relative error = 7.8231698274568955701704690982447e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9326150140222004873089793388657
y2[1] (numeric) = 1.9326150140222004873089793388659
absolute error = 2e-31
relative error = 1.0348672578288401119583212477991e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3245
Order of pole (three term test) = -4.041
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.95
y1[1] (analytic) = 0.62981916864871307154417154086931
y1[1] (numeric) = 0.62981916864871307154417154086926
absolute error = 5e-32
relative error = 7.9387866373257241611398599019169e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9289597150038692957132970350915
y2[1] (numeric) = 1.9289597150038692957132970350917
absolute error = 2e-31
relative error = 1.0368282885555171922020502309869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3315
Order of pole (three term test) = -4.205
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=596254852, alloc=4783252, time=32.64
x[1] = 1.96
y1[1] (analytic) = 0.62054823521184548006843478455255
y1[1] (numeric) = 0.6205482352118454800684347845525
absolute error = 5e-32
relative error = 8.0573913779532030341496925580447e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.92521152078816823258555628949
y2[1] (numeric) = 1.9252115207881682325855562894902
absolute error = 2e-31
relative error = 1.0388468894998165620658279075686e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3385
Order of pole (three term test) = -4.373
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=600255776, alloc=4783252, time=32.86
x[1] = 1.97
y1[1] (analytic) = 0.61131524663524795408536018612069
y1[1] (numeric) = 0.61131524663524795408536018612064
absolute error = 5e-32
relative error = 8.1790860403377741483439122286344e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.9213708061913953832639509971532
y2[1] (numeric) = 1.9213708061913953832639509971533
absolute error = 1e-31
relative error = 5.2046174365594374764261221421692e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3453
Order of pole (three term test) = -4.545
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=604257056, alloc=4783252, time=33.08
x[1] = 1.98
y1[1] (analytic) = 0.60212112621008402184752614009281
y1[1] (numeric) = 0.60212112621008402184752614009275
absolute error = 6e-32
relative error = 9.9647724333568069000207150369558e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.917437955281809840204735217402
y2[1] (numeric) = 1.9174379552818098402047352174021
absolute error = 1e-31
relative error = 5.2152926108789158826822515825418e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3519
Order of pole (three term test) = -4.719
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.99
y1[1] (analytic) = 0.59296679334073445826636428386971
y1[1] (numeric) = 0.59296679334073445826636428386965
absolute error = 6e-32
relative error = 1.0118610464165133687485141044742e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9134133613412251971287932710576
y2[1] (numeric) = 1.9134133613412251971287932710577
absolute error = 1e-31
relative error = 5.2262622400579482714762217552780e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3584
Order of pole (three term test) = -4.898
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=608257780, alloc=4783252, time=33.30
x[1] = 2
y1[1] (analytic) = 0.58385316345285761300243177049924
y1[1] (numeric) = 0.58385316345285761300243177049918
absolute error = 6e-32
relative error = 1.0276556462444279282825036800623e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9092974268256816953960198659117
y2[1] (numeric) = 1.9092974268256816953960198659118
absolute error = 1e-31
relative error = 5.2375286634233740665501418840305e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3648
Order of pole (three term test) = -5.079
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=612259108, alloc=4783252, time=33.52
x[1] = 2.01
y1[1] (analytic) = 0.57478114790184760748261765983457
y1[1] (numeric) = 0.57478114790184760748261765983451
absolute error = 6e-32
relative error = 1.0438755727988122619509718940288e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9050905633252009553600997102737
y2[1] (numeric) = 1.9050905633252009553600997102738
absolute error = 1e-31
relative error = 5.2490942911111305115185828638720e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.371
Order of pole (three term test) = -5.263
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.02
y1[1] (analytic) = 0.5657516538816995549482971259098
y1[1] (numeric) = 0.56575165388169955494829712590974
absolute error = 6e-32
relative error = 1.0605360070683273364845328918002e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9007931915226273171970135245537
y2[1] (numeric) = 1.9007931915226273171970135245538
absolute error = 1e-31
relative error = 5.2609616051862623441000162113194e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3771
Order of pole (three term test) = -5.451
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=616261684, alloc=4783252, time=33.74
x[1] = 2.03
y1[1] (analytic) = 0.5567655843342909169364832683039
y1[1] (numeric) = 0.55676558433429091693648326830384
absolute error = 6e-32
relative error = 1.0776528163417343193503462559768e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8964057411515599070388888319676
y2[1] (numeric) = 1.8964057411515599070388888319677
absolute error = 1e-31
relative error = 5.2731331608011644531007003951921e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.383
Order of pole (three term test) = -5.641
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=620262968, alloc=4783252, time=33.96
x[1] = 2.04
y1[1] (analytic) = 0.54782383785908806798272979470864
y1[1] (numeric) = 0.54782383785908806798272979470857
absolute error = 7e-32
relative error = 1.2777830237099957570116634555242e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8919286509533796351715256485842
y2[1] (numeric) = 1.8919286509533796351715256485843
absolute error = 1e-31
relative error = 5.2856115873930053087112286404332e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3888
Order of pole (three term test) = -5.835
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=624265548, alloc=4783252, time=34.18
x[1] = 2.05
y1[1] (analytic) = 0.5389273086232870978140700058326
y1[1] (numeric) = 0.53892730862328709781407000583253
absolute error = 7e-32
relative error = 1.2988764696080812717677203345394e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8873623686333754235599666046803
y2[1] (numeric) = 1.8873623686333754235599666046804
absolute error = 1e-31
relative error = 5.2983995899213160085343150742371e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3944
Order of pole (three term test) = -6.031
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.06
y1[1] (analytic) = 0.5300768862723978368768903735121
y1[1] (numeric) = 0.53007688627239783687689037351203
absolute error = 7e-32
relative error = 1.3205631449477717009092215845660e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8827073508159740500427975851999
y2[1] (numeric) = 1.8827073508159740500427975852
absolute error = 1e-31
relative error = 5.3114999501467680964206275448477e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3999
Order of pole (three term test) = -6.23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=628266516, alloc=4783252, time=34.41
x[1] = 2.07
y1[1] (analytic) = 0.52127345584128004672267286098827
y1[1] (numeric) = 0.5212734558412800467226728609882
absolute error = 7e-32
relative error = 1.3428652315899613097040294089005e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8779640629990780861734511204438
y2[1] (numeric) = 1.8779640629990780861734511204439
absolute error = 1e-31
relative error = 5.3249155279522029454566958678987e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4052
Order of pole (three term test) = -6.432
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=632269016, alloc=4783252, time=34.63
x[1] = 2.08
y1[1] (analytic) = 0.51251789766564067155843115022765
y1[1] (numeric) = 0.51251789766564067155843115022758
absolute error = 7e-32
relative error = 1.3658059614859927566157851270601e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8731329795075164948766768050246
y2[1] (numeric) = 1.8731329795075164948766768050247
absolute error = 1e-31
relative error = 5.3386492627070165095923924006010e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4103
Order of pole (three term test) = -6.636
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=636269816, alloc=4783252, time=34.85
x[1] = 2.09
y1[1] (analytic) = 0.50381108729400100116293368812955
y1[1] (numeric) = 0.50381108729400100116293368812948
absolute error = 7e-32
relative error = 1.3894096768686477198846348172216e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8682145834456125428216220587275
y2[1] (numeric) = 1.8682145834456125428216220587276
absolute error = 1e-31
relative error = 5.3527041746760457022675405506926e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4153
Order of pole (three term test) = -6.843
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.1
y1[1] (analytic) = 0.49515389540014254837906147628083
y1[1] (numeric) = 0.49515389540014254837906147628076
absolute error = 7e-32
relative error = 1.4137018945076009576445347769865e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.863209366648873770680759313269
y2[1] (numeric) = 1.8632093666488737706807593132691
absolute error = 1e-31
relative error = 5.3670833664741466195688589559233e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4201
Order of pole (three term test) = -7.053
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=640271484, alloc=4783252, time=35.07
x[1] = 2.11
y1[1] (analytic) = 0.48654718769604039652158984292831
y1[1] (numeric) = 0.48654718769604039652158984292823
absolute error = 8e-32
relative error = 1.6442392849669132628553339786179e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8581178296348088522373755083107
y2[1] (numeric) = 1.8581178296348088522373755083108
absolute error = 1e-31
relative error = 5.3817900245677003573499542569469e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4247
Order of pole (three term test) = -7.265
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=644273228, alloc=4783252, time=35.29
x[1] = 2.12
y1[1] (analytic) = 0.47799182484529272329309811701611
y1[1] (numeric) = 0.47799182484529272329309811701603
absolute error = 8e-32
relative error = 1.6736687918437281660527851552696e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8529404815528762606147273336542
y2[1] (numeric) = 1.8529404815528762606147273336543
absolute error = 1e-31
relative error = 5.3968274208243293468159819123348e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4292
Order of pole (three term test) = -7.479
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.13
y1[1] (analytic) = 0.46948866237705515818347379039028
y1[1] (numeric) = 0.46948866237705515818347379039019
absolute error = 9e-32
relative error = 1.9169791991210920975147376791752e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8476778401335697467185299963159
y2[1] (numeric) = 1.847677840133569746718529996316
absolute error = 1e-31
relative error = 5.4121989141121560249116459817596e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4335
Order of pole (three term test) = -7.695
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=648274472, alloc=4783252, time=35.51
x[1] = 2.14
y1[1] (analytic) = 0.4610385506004885798455500879914
y1[1] (numeric) = 0.46103855060048857984555008799131
absolute error = 9e-32
relative error = 1.9521144139200021080431334863534e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8423304316366457213025066370689
y2[1] (numeric) = 1.842330431636645721302506637069
absolute error = 1e-31
relative error = 5.4279079519499863413845924845852e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4376
Order of pole (three term test) = -7.913
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=652275356, alloc=4783252, time=35.73
x[1] = 2.15
y1[1] (analytic) = 0.45264233451972890859584611773597
y1[1] (numeric) = 0.45264233451972890859584611773588
absolute error = 9e-32
relative error = 1.9883248458298425483614882967232e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8368987907984977178756481370438
y2[1] (numeric) = 1.8368987907984977178756481370439
absolute error = 1e-31
relative error = 5.4439580722098531640546833609281e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4415
Order of pole (three term test) = -8.133
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=656276792, alloc=4783252, time=35.96
x[1] = 2.16
y1[1] (analytic) = 0.44430085374938739699030125601663
y1[1] (numeric) = 0.44430085374938739699030125601653
absolute error = 1.0e-31
relative error = 2.2507271628248110298256594206240e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8313834607786831989610381203463
y2[1] (numeric) = 1.8313834607786831989610381203464
absolute error = 1e-31
relative error = 5.4603529048734091617148145897672e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4453
Order of pole (three term test) = -8.356
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.17
y1[1] (analytic) = 0.43601494243058986837553000558349
y1[1] (numeric) = 0.43601494243058986837553000558339
absolute error = 1.0e-31
relative error = 2.2934993796897043128857967076157e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8257849931056080529810564239434
y2[1] (numeric) = 1.8257849931056080529810564239435
absolute error = 1e-31
relative error = 5.4770961738437153082079098280508e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4489
Order of pole (three term test) = -8.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=660278088, alloc=4783252, time=36.18
x[1] = 2.18
y1[1] (analytic) = 0.42778542914756329942177513233751
y1[1] (numeric) = 0.42778542914756329942177513233741
absolute error = 1.0e-31
relative error = 2.3376205262359532174541561676584e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8201039476213742132740097460839
y2[1] (numeric) = 1.8201039476213742132740097460841
absolute error = 2e-31
relative error = 1.0988383397628059707265540141167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4523
Order of pole (three term test) = -8.806
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=664279944, alloc=4783252, time=36.40
x[1] = 2.19
y1[1] (analytic) = 0.41961313684477808790979483620305
y1[1] (numeric) = 0.41961313684477808790979483620295
absolute error = 1.0e-31
relative error = 2.3831475046738508391086818491592e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.814340892425795914434327645905
y2[1] (numeric) = 1.8143408924257959144343276459052
absolute error = 2e-31
relative error = 1.1023286794390527091372329186661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4555
Order of pole (three term test) = -9.033
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.2
y1[1] (analytic) = 0.41149888274465429147585738734507
y1[1] (numeric) = 0.41149888274465429147585738734497
absolute error = 1.0e-31
relative error = 2.4301402553759201463543345717732e-29 %
bytes used=668280724, alloc=4783252, time=36.62
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8084964038195901843040369104161
y2[1] (numeric) = 1.8084964038195901843040369104163
absolute error = 2e-31
relative error = 1.1058910572207660313451262858026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4586
Order of pole (three term test) = -9.262
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.21
y1[1] (analytic) = 0.40344347826584006662239082248137
y1[1] (numeric) = 0.40344347826584006662239082248126
absolute error = 1.1e-31
relative error = 2.7265281489447688512062121403292e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.802571066246747252518974042556
y2[1] (numeric) = 1.8025710662467472525189740425561
absolute error = 1e-31
relative error = 5.5476314844116870858691896016497e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = -9.493
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=672281564, alloc=4783252, time=36.84
x[1] = 2.22
y1[1] (analytic) = 0.39544772894207048008228556249985
y1[1] (numeric) = 0.39544772894207048008228556249974
absolute error = 1.1e-31
relative error = 2.7816571432659310148297156950592e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7965654722360866385208567496092
y2[1] (numeric) = 1.7965654722360866385208567496093
absolute error = 1e-31
relative error = 5.5661762148604290709750739383974e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4641
Order of pole (three term test) = -9.725
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=676282524, alloc=4783252, time=37.06
x[1] = 2.23
y1[1] (analytic) = 0.38751243434161480658809608931437
y1[1] (numeric) = 0.38751243434161480658809608931426
absolute error = 1.1e-31
relative error = 2.8386185900560957468028311846929e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7904802223420047633777101271885
y2[1] (numeric) = 1.7904802223420047633777101271887
absolute error = 2e-31
relative error = 1.1170187612482737957162540709450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4666
Order of pole (three term test) = -9.958
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.24
y1[1] (analytic) = 0.37963838798732036824923773368956
y1[1] (numeric) = 0.37963838798732036824923773368945
absolute error = 1.1e-31
relative error = 2.8974941281141968144287979636889e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7843159250844200106020886706045
y2[1] (numeric) = 1.7843159250844200106020886706047
absolute error = 2e-31
relative error = 1.1208777391287226724600959064138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4689
Order of pole (three term test) = -10.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=680283720, alloc=4783252, time=37.28
x[1] = 2.25
y1[1] (analytic) = 0.3718263772772609110866109426036
y1[1] (numeric) = 0.37182637727726091108661094260349
absolute error = 1.1e-31
relative error = 2.9583700006838397004823053942106e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7780731968879212414109666755878
y2[1] (numeric) = 1.778073196887921241410966675588
absolute error = 2e-31
relative error = 1.1248130861544434238164208751652e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4711
Order of pole (three term test) = -10.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=684285324, alloc=4783252, time=37.50
x[1] = 2.26
y1[1] (analytic) = 0.36407718340599745382087343125516
y1[1] (numeric) = 0.36407718340599745382087343125505
absolute error = 1.1e-31
relative error = 3.0213373705798660840844883773265e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7717526620201258495250616377403
y2[1] (numeric) = 1.7717526620201258495250616377406
absolute error = 3e-31
relative error = 1.6932386017015743784964768054637e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.473
Order of pole (three term test) = -10.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=688286608, alloc=4783252, time=37.72
x[1] = 2.27
y1[1] (analytic) = 0.3563915812864594827638656518757
y1[1] (numeric) = 0.35639158128645948276386565187558
absolute error = 1.2e-31
relative error = 3.3670829026555124299702425027534e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7653549525292535196507426019347
y2[1] (numeric) = 1.765354952529253519650742601935
absolute error = 3e-31
relative error = 1.6993749589576022113004233810382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = -10.9
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.28
y1[1] (analytic) = 0.3487703394724543046286016495393
y1[1] (numeric) = 0.34877033947245430462860164953919
absolute error = 1.1e-31
relative error = 3.1539379227713181534491112498274e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7588807081809219322166535763009
y2[1] (numeric) = 1.7588807081809219322166535763012
absolute error = 3e-31
relative error = 1.7056301692584225525149988219156e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = -11.14
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=692288036, alloc=4783252, time=37.94
x[1] = 2.29
y1[1] (analytic) = 0.34121422008181230625796898181105
y1[1] (numeric) = 0.34121422008181230625796898181093
absolute error = 1.2e-31
relative error = 3.5168522569554053347774748499358e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7523305763941707347419082779736
y2[1] (numeric) = 1.7523305763941707347419082779739
absolute error = 3e-31
relative error = 1.7120057370528798218855619258085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = -11.38
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=696289008, alloc=4783252, time=38.16
x[1] = 2.3
y1[1] (analytic) = 0.33372397872017580668211942883398
y1[1] (numeric) = 0.33372397872017580668211942883386
absolute error = 1.2e-31
relative error = 3.5957859683981171396459860882399e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7457052121767201773854062116435
y2[1] (numeric) = 1.7457052121767201773854062116437
absolute error = 2e-31
relative error = 1.1456688025272030899982595398474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4788
Order of pole (three term test) = -11.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.31
bytes used=700290644, alloc=4783252, time=38.38
y1[1] (analytic) = 0.32630036440543912255583567652897
y1[1] (numeric) = 0.32630036440543912255583567652884
absolute error = 1.3e-31
relative error = 3.9840592957006523441717853701029e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7390052780594708867587641920983
y2[1] (numeric) = 1.7390052780594708867587641920985
absolute error = 2e-31
relative error = 1.1500827658394280952087812218683e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = -11.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.32
y1[1] (analytic) = 0.31894411949284740290636383399177
y1[1] (numeric) = 0.31894411949284740290636383399164
absolute error = 1.3e-31
relative error = 4.0759491100419978796890635615474e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7322314440302513279708986777247
y2[1] (numeric) = 1.7322314440302513279708986777249
absolute error = 2e-31
relative error = 1.1545801266294715857384298405282e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -12.1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=704291552, alloc=4783252, time=38.61
x[1] = 2.33
y1[1] (analytic) = 0.311655979600761723245819572184
y1[1] (numeric) = 0.31165597960076172324581957218386
absolute error = 1.4e-31
relative error = 4.4921326450833104379202326093125e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7253843874668195801028441924754
y2[1] (numeric) = 1.7253843874668195801028441924756
absolute error = 2e-31
relative error = 1.1591619899472757235409221573002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.34
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=708292504, alloc=4783252, time=38.83
x[1] = 2.34
y1[1] (analytic) = 0.30443667353709786247689442793865
y1[1] (numeric) = 0.30443667353709786247689442793851
absolute error = 1.4e-31
relative error = 4.5986575261583904920582457000222e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.718464793069126124879428686794
y2[1] (numeric) = 1.7184647930691261248794286867942
absolute error = 2e-31
relative error = 1.1638294878465682814164913705365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.35
y1[1] (analytic) = 0.29728692322644611865287088774108
y1[1] (numeric) = 0.29728692322644611865287088774094
absolute error = 1.4e-31
relative error = 4.7092552366778925890009106112970e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7114733527908444222024911820132
y2[1] (numeric) = 1.7114733527908444222024911820134
absolute error = 2e-31
relative error = 1.1685837800154261681419958387265e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=712294704, alloc=4783252, time=39.05
x[1] = 2.36
y1[1] (analytic) = 0.2902074436378794515496369653549
y1[1] (numeric) = 0.29020744363787945154963696535476
absolute error = 1.4e-31
relative error = 4.8241353924295565419934518332240e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7044107657701761194310307129327
y2[1] (numeric) = 1.7044107657701761194310307129329
absolute error = 2e-31
relative error = 1.1734260544266483056168790209376e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.07
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.86
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=716295740, alloc=4783252, time=39.27
x[1] = 2.37
y1[1] (analytic) = 0.28319894271345717117528339117765
y1[1] (numeric) = 0.28319894271345717117528339117751
absolute error = 1.4e-31
relative error = 4.9435212807857498682526330463051e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6972777382599378138296964202892
y2[1] (numeric) = 1.6972777382599378138296964202894
absolute error = 2e-31
relative error = 1.1783575280085953264648784681268e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.48
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=720296808, alloc=4783252, time=39.49
x[1] = 2.38
y1[1] (analytic) = 0.27626212129743132178885239263247
y1[1] (numeric) = 0.27626212129743132178885239263233
absolute error = 1.4e-31
relative error = 5.0676509447805255977507015649474e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6900749835569363594511131070202
y2[1] (numeric) = 1.6900749835569363594511131070204
absolute error = 2e-31
relative error = 1.1833794473371794526768408186209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.55
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.12
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.39
y1[1] (analytic) = 0.26939767306616284073084170738194
y1[1] (numeric) = 0.2693976730661628407308417073818
absolute error = 1.4e-31
relative error = 5.1967783688174855930193774745584e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.682803221930639780862500311013
y2[1] (numeric) = 1.6828032219306397808625003110132
absolute error = 2e-31
relative error = 1.1884930893497149134414363654770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -13.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=724297624, alloc=4783252, time=39.71
x[1] = 2.4
y1[1] (analytic) = 0.26260628445875450039117777266522
y1[1] (numeric) = 0.26260628445875450039117777266508
absolute error = 1.4e-31
relative error = 5.3311747770449376552569514043235e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6754631805511509265657715253413
y2[1] (numeric) = 1.6754631805511509265657715253414
absolute error = 1e-31
relative error = 5.9684988104068370815749986399565e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -14.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=728300264, alloc=4783252, time=39.93
x[1] = 2.41
y1[1] (analytic) = 0.25588863460840756996265560443205
y1[1] (numeric) = 0.25588863460840756996265560443191
absolute error = 1.4e-31
relative error = 5.4711300568016751271244306576809e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6680555934164910646857498006547
y2[1] (numeric) = 1.6680555934164910646857498006548
absolute error = 1e-31
relative error = 5.9950040271248527805796052913975e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = -14.27
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=732302544, alloc=4783252, time=40.15
x[1] = 2.42
y1[1] (analytic) = 0.24924539527450906125646743108926
y1[1] (numeric) = 0.24924539527450906125646743108912
absolute error = 1.4e-31
relative error = 5.6169543210942578987104533123125e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6605812012792006925063341065602
y2[1] (numeric) = 1.6605812012792006925063341065603
absolute error = 1e-31
relative error = 6.0219879595750384454833072308559e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4779
Order of pole (three term test) = -14.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.72
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.43
y1[1] (analytic) = 0.2426772307754563497986447558221
y1[1] (numeric) = 0.24267723077545634979864475582196
absolute error = 1.4e-31
relative error = 5.7689796258446172196698543365891e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6530407515722648997124970471899
y2[1] (numeric) = 1.65304075157226489971249704719
absolute error = 1e-31
relative error = 6.0494576376829488891749456671227e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4765
Order of pole (three term test) = -14.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=736304840, alloc=4783252, time=40.37
x[1] = 2.44
y1[1] (analytic) = 0.2361847979222258886893249074626
y1[1] (numeric) = 0.23618479792222588868932490746246
absolute error = 1.4e-31
relative error = 5.9275618596799395017610738374469e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6454349983343706927400610729825
y2[1] (numeric) = 1.6454349983343706927400610729826
absolute error = 1e-31
relative error = 6.0774202628014654497184761948944e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.475
Order of pole (three term test) = -14.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.06
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=740307036, alloc=4783252, time=40.59
x[1] = 2.45
y1[1] (analytic) = 0.22976874595269265829809693266351
y1[1] (numeric) = 0.22976874595269265829809693266337
absolute error = 1.4e-31
relative error = 6.0930828263659825661619481242199e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6377647021345037544385328556338
y2[1] (numeric) = 1.6377647021345037544385328556338
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4733
Order of pole (three term test) = -15.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.46
y1[1] (analytic) = 0.2234297164667069197957236853138
y1[1] (numeric) = 0.22342971646670691979572368531366
absolute error = 1.4e-31
relative error = 6.2659525426583659499872931345508e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6300306299958921793081937186159
y2[1] (numeric) = 1.6300306299958921793081937186159
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4714
Order of pole (three term test) = -15.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=744309352, alloc=4783252, time=40.81
x[1] = 2.47
y1[1] (analytic) = 0.21716834336193476479278441593845
y1[1] (numeric) = 0.21716834336193476479278441593831
absolute error = 1.4e-31
relative error = 6.4466117774207407505468249347982e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6222335553193047898745424048558
y2[1] (numeric) = 1.6222335553193047898745424048557
absolute error = 1e-31
relative error = 6.1643404966011176812438993960883e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = -15.7
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=748310260, alloc=4783252, time=41.03
x[1] = 2.48
y1[1] (analytic) = 0.21098525277046887697680796640967
y1[1] (numeric) = 0.21098525277046887697680796640953
absolute error = 1.4e-31
relative error = 6.6355348614012457477156891030084e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6143742578057117043045348806656
y2[1] (numeric) = 1.6143742578057117043045348806655
absolute error = 1e-31
relative error = 6.1943505055588478063216065453407e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = -15.93
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=752312456, alloc=4783252, time=41.26
x[1] = 2.49
y1[1] (analytic) = 0.20488106299621584461890866742843
y1[1] (numeric) = 0.20488106299621584461890866742829
absolute error = 1.4e-31
relative error = 6.8332328011489183589149841491894e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6064535233783148891434102397918
y2[1] (numeric) = 1.6064535233783148891434102397917
absolute error = 1e-31
relative error = 6.2248921954308108540006066531960e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4646
Order of pole (three term test) = -16.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.5
y1[1] (analytic) = 0.19885638445306628516649720953265
y1[1] (numeric) = 0.19885638445306628516649720953251
absolute error = 1.4e-31
relative error = 7.0402567352843800796774741612230e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5984721441039564940518547021862
y2[1] (numeric) = 1.5984721441039564940518547021861
absolute error = 1e-31
relative error = 6.2559738916223809323680023061471e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4619
Order of pole (three term test) = -16.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=756313252, alloc=4783252, time=41.48
x[1] = 2.51
y1[1] (analytic) = 0.19291181960385396485808249212159
y1[1] (numeric) = 0.19291181960385396485808249212145
absolute error = 1.4e-31
relative error = 7.2572017768269031421447195481734e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.590430918113912827644537155024
y2[1] (numeric) = 1.590430918113912827644537155024
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4591
Order of pole (three term test) = -16.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=760315736, alloc=4783252, time=41.70
x[1] = 2.52
y1[1] (analytic) = 0.18704796290011001739733573954815
y1[1] (numeric) = 0.18704796290011001739733573954801
absolute error = 1.4e-31
relative error = 7.4847112916575717037326922556863e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5823306495240818949664275822971
y2[1] (numeric) = 1.5823306495240818949664275822971
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4561
Order of pole (three term test) = -16.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.53
bytes used=764317068, alloc=4783252, time=41.92
y1[1] (analytic) = 0.18126540072261828621434482744501
y1[1] (numeric) = 0.18126540072261828621434482744487
absolute error = 1.4e-31
relative error = 7.7234816706269972734102279806096e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5741721483545724777866405874022
y2[1] (numeric) = 1.5741721483545724777866405874022
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4529
Order of pole (three term test) = -17.08
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.54
y1[1] (analytic) = 0.17556471132277773473029564419343
y1[1] (numeric) = 0.1755647113227777347302956441933
absolute error = 1.3e-31
relative error = 7.4046771142404300979153572532063e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.565956230448702798734765747982
y2[1] (numeric) = 1.565956230448702798734765747982
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4495
Order of pole (three term test) = -17.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=768318140, alloc=4783252, time=42.14
x[1] = 2.55
y1[1] (analytic) = 0.16994646476477778833568952416771
y1[1] (numeric) = 0.16994646476477778833568952416758
absolute error = 1.3e-31
relative error = 7.6494677414992110616142703285276e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5576837173914168693457702817662
y2[1] (numeric) = 1.5576837173914168693457702817662
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = -17.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=772320024, alloc=4783252, time=42.36
x[1] = 2.56
y1[1] (analytic) = 0.16441122286859239049971187661756
y1[1] (numeric) = 0.16441122286859239049971187661742
absolute error = 1.4e-31
relative error = 8.5152337874097957189917983292244e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5493554364271266803106833831373
y2[1] (numeric) = 1.5493554364271266803106833831372
absolute error = 1e-31
relative error = 6.4542969062414659438401251231488e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4422
Order of pole (three term test) = -17.76
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.57
y1[1] (analytic) = 0.15895953915379847355763627843287
y1[1] (numeric) = 0.15895953915379847355763627843274
absolute error = 1.3e-31
relative error = 8.1781817368142224695369421739338e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5409722203769884496455725487458
y2[1] (numeric) = 1.5409722203769884496455725487458
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4383
Order of pole (three term test) = -17.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=776321348, alloc=4783252, time=42.58
x[1] = 2.58
y1[1] (analytic) = 0.15359195878422446228236750543077
y1[1] (numeric) = 0.15359195878422446228236750543063
absolute error = 1.4e-31
relative error = 9.1150605219301036810672622435278e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5325349075556212010850587644716
y2[1] (numeric) = 1.5325349075556212010850587644716
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4342
Order of pole (three term test) = -18.2
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=780323276, alloc=4783252, time=42.80
x[1] = 2.59
y1[1] (analytic) = 0.14830901851343434534364025459169
y1[1] (numeric) = 0.14830901851343434534364025459155
absolute error = 1.4e-31
relative error = 9.4397496122137922701715252795718e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5240443416872760007731302488759
y2[1] (numeric) = 1.5240443416872760007731302488759
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.43
Order of pole (three term test) = -18.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=784324184, alloc=4783252, time=43.02
x[1] = 2.6
y1[1] (analytic) = 0.1431112466310527662022978483548
y1[1] (numeric) = 0.14311124663105276620229784835466
absolute error = 1.4e-31
relative error = 9.7825994319598305210250306423408e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5155013718214642352577269352094
y2[1] (numeric) = 1.5155013718214642352577269352094
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4255
Order of pole (three term test) = -18.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.61
y1[1] (analytic) = 0.13799916290993650088583255127735
y1[1] (numeric) = 0.13799916290993650088583255127721
absolute error = 1.4e-31
relative error = 1.0144989074417018127254841086481e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.5069068522480533678909866995555
y2[1] (numeric) = 1.5069068522480533678909866995555
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4209
Order of pole (three term test) = -18.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=788324944, alloc=4783252, time=43.24
x[1] = 2.62
y1[1] (analytic) = 0.13297327855419760545338632325165
y1[1] (numeric) = 0.13297327855419760545338632325151
absolute error = 1.4e-31
relative error = 1.0528431089479261397388473608442e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4982616424118386639887600099976
y2[1] (numeric) = 1.4982616424118386639887600099976
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4161
Order of pole (three term test) = -19.05
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=792325960, alloc=4783252, time=43.46
x[1] = 2.63
y1[1] (analytic) = 0.12803409614808343079215160980507
y1[1] (numeric) = 0.12803409614808343079215160980493
absolute error = 1.4e-31
relative error = 1.0934587286661271856013687898544e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4895666068265994275056870536116
y2[1] (numeric) = 1.4895666068265994275056870536116
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4112
Order of pole (three term test) = -19.26
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.64
y1[1] (analytic) = 0.12318210960571861670109268373401
y1[1] (numeric) = 0.12318210960571861670109268373387
absolute error = 1.4e-31
relative error = 1.1365286765108350452315550746286e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4808226149886483435305502695329
y2[1] (numeric) = 1.4808226149886483435305502695328
absolute error = 1e-31
relative error = 6.7530032961285223035000128588586e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4061
Order of pole (three term test) = -19.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=796327304, alloc=4783252, time=43.68
TOP MAIN SOLVE Loop
x[1] = 2.65
y1[1] (analytic) = 0.11841780412171409102069763394619
y1[1] (numeric) = 0.11841780412171409102069763394605
absolute error = 1.4e-31
relative error = 1.1822546536676440096275811634186e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4720305412898825715956107783974
y2[1] (numeric) = 1.4720305412898825715956107783973
absolute error = 1e-31
relative error = 6.7933373116276463929622807634632e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4008
Order of pole (three term test) = -19.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=800328432, alloc=4783252, time=43.90
x[1] = 2.66
y1[1] (analytic) = 0.11374165612264801286768899611741
y1[1] (numeric) = 0.11374165612264801286768899611727
absolute error = 1.4e-31
relative error = 1.2308595177217881022599201551891e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4631912649303452846181405937964
y2[1] (numeric) = 1.4631912649303452846181405937963
absolute error = 1e-31
relative error = 6.8343765027028414840271986631591e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3954
Order of pole (three term test) = -19.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=804330872, alloc=4783252, time=44.13
x[1] = 2.67
y1[1] (analytic) = 0.10915413321942351183993714157026
y1[1] (numeric) = 0.10915413321942351183993714157012
absolute error = 1.4e-31
relative error = 1.2825900025111243144427275681052e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4543056698303063972473913211913
y2[1] (numeric) = 1.4543056698303063972473913211912
absolute error = 1e-31
relative error = 6.8761335443097295179643921677375e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3898
Order of pole (three term test) = -20.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.68
y1[1] (analytic) = 0.10465569416050798737795418137934
y1[1] (numeric) = 0.1046556941605079873779541813792
absolute error = 1.4e-31
relative error = 1.3377198548345136235490750031355e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4453746445418712754708988319294
y2[1] (numeric) = 1.4453746445418712754708988319294
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3841
Order of pole (three term test) = -20.25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=808333376, alloc=4783252, time=44.35
x[1] = 2.69
y1[1] (analytic) = 0.10024678878605864431406511567113
y1[1] (numeric) = 0.10024678878605864431406511567099
absolute error = 1.4e-31
relative error = 1.3965534626628344284421263970088e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.436399082160126266535504118761
y2[1] (numeric) = 1.4363990821601262665355041187609
absolute error = 1e-31
relative error = 6.9618535156410134689666493987095e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3782
Order of pole (three term test) = -20.44
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=812335416, alloc=4783252, time=44.56
x[1] = 2.7
y1[1] (analytic) = 0.09592785798293885201747271805667
y1[1] (numeric) = 0.095927857982938852017472718056533
absolute error = 1.37e-31
relative error = 1.4281565634913477425081617435858e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4273798802338299345560530858579
y2[1] (numeric) = 1.4273798802338299345560530858578
absolute error = 1e-31
relative error = 7.0058434607904267797675710847523e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3722
Order of pole (three term test) = -20.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=816336412, alloc=4783252, time=44.79
x[1] = 2.71
y1[1] (analytic) = 0.09169933364062982546181540628392
y1[1] (numeric) = 0.091699333640629825461815406283787
absolute error = 1.33e-31
relative error = 1.4503922190015873494940028591286e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4183179406756589326137906811086
y2[1] (numeric) = 1.4183179406756589326137906811085
absolute error = 1e-31
relative error = 7.0506053073235437914383616903355e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.366
Order of pole (three term test) = -20.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.72
y1[1] (analytic) = 0.08756163860804203701037120001294
y1[1] (numeric) = 0.087561638608042037010371200012802
absolute error = 1.38e-31
relative error = 1.5760326347675897333155458705836e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4092141696720174866824446740074
y2[1] (numeric) = 1.4092141696720174866824446740073
absolute error = 1e-31
relative error = 7.0961534557429366788879393526631e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3596
Order of pole (three term test) = -21
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=820338532, alloc=4783252, time=45.01
x[1] = 2.73
y1[1] (analytic) = 0.08351518665123067774173887510721
y1[1] (numeric) = 0.08351518665123067774173887510708
absolute error = 1.30e-31
relative error = 1.5566031186985837047051170884282e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4000694775924195103584479578944
y2[1] (numeric) = 1.4000694775924195103584479578943
absolute error = 1e-31
relative error = 7.1425026829355283900967676110507e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3532
Order of pole (three term test) = -21.18
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=824340800, alloc=4783252, time=45.23
x[1] = 2.74
y1[1] (analytic) = 0.07956038241201939673462674822072
y1[1] (numeric) = 0.079560382412019396734626748220592
absolute error = 1.28e-31
relative error = 1.6088409346391314293590496623375e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3908847788984524121083117016403
y2[1] (numeric) = 1.3908847788984524121083117016401
absolute error = 2e-31
relative error = 1.4379336306950977797316343373181e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3465
Order of pole (three term test) = -21.35
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.75
y1[1] (analytic) = 0.07569762136753645590334051047329
y1[1] (numeric) = 0.075697621367536455903340510473156
absolute error = 1.34e-31
relative error = 1.7702009333871486226245080790084e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3816609920523316985765613723778
y2[1] (numeric) = 1.3816609920523316985765613723776
absolute error = 2e-31
relative error = 1.4475330862668287119521462972938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3398
Order of pole (three term test) = -21.52
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=828343028, alloc=4783252, time=45.45
TOP MAIN SOLVE Loop
x[1] = 2.76
y1[1] (analytic) = 0.0719272897906673467347668028599
y1[1] (numeric) = 0.071927289790667346734766802859768
absolute error = 1.32e-31
relative error = 1.8351866222704134255124437601203e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3723990394250555184177005924498
y2[1] (numeric) = 1.3723990394250555184177005924496
absolute error = 2e-31
relative error = 1.4573020984027122311852859218502e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3329
Order of pole (three term test) = -21.69
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=832343992, alloc=4783252, time=45.67
x[1] = 2.77
y1[1] (analytic) = 0.06824976471142782363222279217093
y1[1] (numeric) = 0.068249764711427823632222792170799
absolute error = 1.31e-31
relative error = 1.9194205365233325212115333435933e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3630998472041683311212820091725
y2[1] (numeric) = 1.3630998472041683311212820091723
absolute error = 2e-31
relative error = 1.4672439470242529137252962894959e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3258
Order of pole (three term test) = -21.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=836345020, alloc=4783252, time=45.89
x[1] = 2.78
y1[1] (analytic) = 0.06466541387926121653064833088241
y1[1] (numeric) = 0.06466541387926121653064833088228
absolute error = 1.30e-31
relative error = 2.0103482248289170315311693577974e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3537643453011429243863393172273
y2[1] (numeric) = 1.3537643453011429243863393172272
absolute error = 1e-31
relative error = 7.3868099974043225636108880988959e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3187
Order of pole (three term test) = -22.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.79
y1[1] (analytic) = 0.06117459572626379302046038037591
y1[1] (numeric) = 0.061174595726263793020460380375785
absolute error = 1.25e-31
relative error = 2.0433318523155250727496206708957e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3443934672583900417662615955623
y2[1] (numeric) = 1.3443934672583900417662615955621
absolute error = 2e-31
relative error = 1.4876597132523878476707375692431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3114
Order of pole (three term test) = -22.18
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=840345984, alloc=4783252, time=46.11
x[1] = 2.8
y1[1] (analytic) = 0.05777765933134184741321188263385
y1[1] (numeric) = 0.057777659331341847413211882633724
absolute error = 1.26e-31
relative error = 2.1807737014304856653654785626447e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3349881501559049195438537527124
y2[1] (numeric) = 1.3349881501559049195438537527122
absolute error = 2e-31
relative error = 1.4981406387513121402988476048624e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.304
Order of pole (three term test) = -22.33
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=844347656, alloc=4783252, time=46.33
x[1] = 2.81
y1[1] (analytic) = 0.05447494438530410101027952164116
y1[1] (numeric) = 0.054474944385304101010279521641045
absolute error = 1.15e-31
relative error = 2.1110622745495442478650728540365e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3255493345175600681051012812063
y2[1] (numeric) = 1.3255493345175600681051012812061
absolute error = 2e-31
relative error = 1.5088084222288938287329434848217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2965
Order of pole (three term test) = -22.48
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=848348600, alloc=4783252, time=46.56
x[1] = 2.82
y1[1] (analytic) = 0.05126678115689290430546393623996
y1[1] (numeric) = 0.051266781156892904305463936239844
absolute error = 1.16e-31
relative error = 2.2626737505715941825387027618442e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3160779642170536684554128560246
y2[1] (numeric) = 1.3160779642170536684554128560243
absolute error = 3e-31
relative error = 2.2795002131843506168479856380455e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2888
Order of pole (three term test) = -22.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.83
y1[1] (analytic) = 0.04815349045975763797297488727547
y1[1] (numeric) = 0.048153490459757637972974887275355
absolute error = 1.15e-31
relative error = 2.3881965544347542227547838075219e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3065749863835229889603130778681
y2[1] (numeric) = 1.3065749863835229889603130778678
absolute error = 3e-31
relative error = 2.2960794682773765725803158632272e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.281
Order of pole (three term test) = -22.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=852349328, alloc=4783252, time=46.77
x[1] = 2.84
y1[1] (analytic) = 0.04513538362037361527318050641376
y1[1] (numeric) = 0.04513538362037361527318050641365
absolute error = 1.10e-31
relative error = 2.4371123313184206765929529813561e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2970413513068322608902560680973
y2[1] (numeric) = 1.297041351306832260890256068097
absolute error = 3e-31
relative error = 2.3129563270880716746085794943971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2732
Order of pole (three term test) = -22.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=856351244, alloc=4783252, time=47.00
x[1] = 2.85
y1[1] (analytic) = 0.04221276244690969395914589282507
y1[1] (numeric) = 0.042212762446909693959145892824965
absolute error = 1.05e-31
relative error = 2.4873994004077983622485503413616e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2874780123425444839030789266917
y2[1] (numeric) = 1.2874780123425444839030789266914
absolute error = 3e-31
relative error = 2.3301368809720879836539577894521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2652
Order of pole (three term test) = -23.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.86
y1[1] (analytic) = 0.03938591919904771089682683360723
y1[1] (numeric) = 0.039385919199047710896826833607127
absolute error = 1.03e-31
relative error = 2.6151478014125001494054856947860e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2778859258165866642043569097532
y2[1] (numeric) = 1.2778859258165866642043569097529
absolute error = 3e-31
relative error = 2.3476273894189411165786211289924e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2571
Order of pole (three term test) = -23.17
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=860354144, alloc=4783252, time=47.22
x[1] = 2.87
y1[1] (analytic) = 0.03665513655875675743030624126206
y1[1] (numeric) = 0.03665513655875675743030624126196
absolute error = 1.00e-31
relative error = 2.7281306083720051514660789750988e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2682660509296180187823989209871
y2[1] (numeric) = 1.2682660509296180187823989209868
absolute error = 3e-31
relative error = 2.3654342854963670011957727083442e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2489
Order of pole (three term test) = -23.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=864356272, alloc=4783252, time=47.44
x[1] = 2.88
y1[1] (analytic) = 0.03402068760202521804018209523448
y1[1] (numeric) = 0.034020687602025218040182095234375
absolute error = 1.05e-31
relative error = 3.0863573725579095400366543351518e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2586193496611107088177669201177
y2[1] (numeric) = 1.2586193496611107088177669201173
absolute error = 4e-31
relative error = 3.1780855753385796650456475741914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2406
Order of pole (three term test) = -23.42
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=868357256, alloc=4783252, time=47.66
x[1] = 2.89
y1[1] (analytic) = 0.03148283577155339906768449279072
y1[1] (numeric) = 0.031482835771553399067684492790621
absolute error = 9.9e-32
relative error = 3.1445706072466427934625345769856e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2489467866731526941140458405805
y2[1] (numeric) = 1.2489467866731526941140458405801
absolute error = 4e-31
relative error = 3.2026984997934850976340977751985e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2322
Order of pole (three term test) = -23.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.9
y1[1] (analytic) = 0.02904183485040947821889333065447
y1[1] (numeric) = 0.029041834850409478218893330654376
absolute error = 9.4e-32
relative error = 3.2367100937038293816947344350961e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2392493292139823281842569187396
y2[1] (numeric) = 1.2392493292139823281842569187392
absolute error = 4e-31
relative error = 3.2277604721699359494621608101687e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2237
Order of pole (three term test) = -23.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=872359820, alloc=4783252, time=47.88
x[1] = 2.91
y1[1] (analytic) = 0.02669792893665140923215289339725
y1[1] (numeric) = 0.02669792893665140923215289339716
absolute error = 9.0e-32
relative error = 3.3710480020210983533143408054110e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.229527947021264340453018223827
y2[1] (numeric) = 1.2295279470212643404530182238266
absolute error = 4e-31
relative error = 3.2532810740013387622925457247450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2151
Order of pole (three term test) = -23.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=876360536, alloc=4783252, time=48.10
x[1] = 2.92
y1[1] (analytic) = 0.02445135241891731949706826484173
y1[1] (numeric) = 0.024451352418917319497068264841651
absolute error = 7.9e-32
relative error = 3.2309051314020542832857790857207e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2197836122251168778956290930646
y2[1] (numeric) = 1.2197836122251168778956290930642
absolute error = 4e-31
relative error = 3.2792701589942175252235791894286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2065
Order of pole (three term test) = -23.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=880361696, alloc=4783252, time=48.33
x[1] = 2.93
y1[1] (analytic) = 0.02230232995298684156498039532367
y1[1] (numeric) = 0.022302329952986841564980395323594
absolute error = 7.6e-32
relative error = 3.4077157032564524988510103620528e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2100172992508993033291040342591
y2[1] (numeric) = 1.2100172992508993033291040342587
absolute error = 4e-31
relative error = 3.3057378621581117357198114099627e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1977
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.94
y1[1] (analytic) = 0.02025107643931572239823661867168
y1[1] (numeric) = 0.020251076439315722398236618671602
absolute error = 7.8e-32
relative error = 3.8516471079319868413797051230950e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.2002299847217704714943170944231
y2[1] (numeric) = 1.2002299847217704714943170944227
absolute error = 4e-31
relative error = 3.3326946092979455514922821192404e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1889
Order of pole (three term test) = -24.07
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=884362664, alloc=4783252, time=48.55
x[1] = 2.95
y1[1] (analytic) = 0.01829779700154595687861059529803
y1[1] (numeric) = 0.01829779700154595687861059529796
absolute error = 7.0e-32
relative error = 3.8255971466994519491208103156076e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1904226473610272270204473140574
y2[1] (numeric) = 1.190422647361027227020447314057
absolute error = 4e-31
relative error = 3.3601511268853523048700450715492e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.18
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=888363708, alloc=4783252, time=48.77
x[1] = 2.96
y1[1] (analytic) = 0.01644268696599359454361267702384
y1[1] (numeric) = 0.016442686965993594543612677023774
absolute error = 6.6e-32
relative error = 4.0139424983580698262874449253270e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1805962678942328903405445088014
y2[1] (numeric) = 1.180596267894232890340544508801
absolute error = 4e-31
relative error = 3.3881184523262879701788275698032e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1711
Order of pole (three term test) = -24.25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.97
y1[1] (analytic) = 0.01468593184211627075292362519386
y1[1] (numeric) = 0.014685931842116270752923625193793
absolute error = 6.7e-32
relative error = 4.5621892243744182034248839569915e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.170751828951145518628064498668
y2[1] (numeric) = 1.1707518289511455186280644986676
absolute error = 4e-31
relative error = 3.4166079446431653699229679897348e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.162
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=892365348, alloc=4783252, time=48.99
x[1] = 2.98
y1[1] (analytic) = 0.0130277073039624155155580356046
y1[1] (numeric) = 0.013027707303962415515558035604538
absolute error = 6.2e-32
relative error = 4.7590875779917558894699724799269e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1608903149674557488465539545413
y2[1] (numeric) = 1.160890314967455748846553954541
absolute error = 3e-31
relative error = 2.5842234716930183173243269372778e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1529
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=896368292, alloc=4783252, time=49.21
x[1] = 2.99
y1[1] (analytic) = 0.01146817917260399504141581278916
y1[1] (numeric) = 0.011468179172603995041415812789103
absolute error = 5.7e-32
relative error = 4.9702746305329505509999270286152e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1510127120863440490462950356105
y2[1] (numeric) = 1.1510127120863440490462950356102
absolute error = 3e-31
relative error = 2.6064004059191944315529243141445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1438
Order of pole (three term test) = -24.49
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=900370584, alloc=4783252, time=49.43
x[1] = 3
y1[1] (analytic) = 0.01000750339955454272842720526874
y1[1] (numeric) = 0.010007503399554542728427205268684
absolute error = 5.6e-32
relative error = 5.5958012467417888017542157769939e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1411200080598672221007448028081
y2[1] (numeric) = 1.1411200080598672221007448028078
absolute error = 3e-31
relative error = 2.6289960554636154528328783203420e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1345
Order of pole (three term test) = -24.56
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.01
y1[1] (analytic) = 0.00864582605117413776837442581758
y1[1] (numeric) = 0.0086458260511741377683744258175313
absolute error = 4.87e-32
relative error = 5.6327758286770464412436016572122e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1312131921501840231502181246848
y2[1] (numeric) = 1.1312131921501840231502181246845
absolute error = 3e-31
relative error = 2.6520199912959545544553436322264e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1253
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=904371356, alloc=4783252, time=49.65
x[1] = 3.02
y1[1] (analytic) = 0.00738328329406289086053346673696
y1[1] (numeric) = 0.0073832832940628908605334667369159
absolute error = 4.41e-32
relative error = 5.9729524445394192781514909276202e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1212932550306297681087579963391
y2[1] (numeric) = 1.1212932550306297681087579963388
absolute error = 3e-31
relative error = 2.6754820708504579425038196999236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1159
Order of pole (three term test) = -24.68
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=908373156, alloc=4783252, time=49.88
x[1] = 3.03
y1[1] (analytic) = 0.00622000138144439767239269129157
y1[1] (numeric) = 0.0062200013814443976723926912915284
absolute error = 4.16e-32
relative error = 6.6881014084822794513370212993405e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1113611886866498256909050329173
y2[1] (numeric) = 1.1113611886866498256909050329169
absolute error = 4e-31
relative error = 3.5991899309773420495461350994889e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1066
Order of pole (three term test) = -24.74
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=912374948, alloc=4783252, time=50.10
x[1] = 3.04
y1[1] (analytic) = 0.00515609664054052169075504515681
y1[1] (numeric) = 0.0051560966405405216907550451567735
absolute error = 3.65e-32
relative error = 7.0789984254782408039210449605178e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.1014179863166018995266083126088
y2[1] (numeric) = 1.1014179863166018995266083126084
absolute error = 4e-31
relative error = 3.6316821131430139406694916077635e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09716
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.05
y1[1] (analytic) = 0.00419167546093876897441779843508
y1[1] (numeric) = 0.0041916754609387689744177984350455
absolute error = 3.45e-32
relative error = 8.2305990340848976380265847726778e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.0914646422324370200534015886964
y2[1] (numeric) = 1.091464642232437020053401588696
absolute error = 4e-31
relative error = 3.6648003473741156043474375626958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08771
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=916377224, alloc=4783252, time=50.32
x[1] = 3.06
y1[1] (analytic) = 0.00332683428395341806126072820685
y1[1] (numeric) = 0.0033268342839534180612607282068144
absolute error = 3.56e-32
relative error = 1.0700863632346307446607778535730e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0815021517602691780038900888357
y2[1] (numeric) = 1.0815021517602691780038900888353
absolute error = 4e-31
relative error = 3.6985594466821354012012967012881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07822
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=920378596, alloc=4783252, time=50.54
x[1] = 3.07
y1[1] (analytic) = 0.00256165959298146890788633727323
y1[1] (numeric) = 0.0025616595929814689078863372732003
absolute error = 2.97e-32
relative error = 1.1594046328939713396373838579515e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0715315111408435424423407903189
y2[1] (numeric) = 1.0715315111408435424423407903185
absolute error = 4e-31
relative error = 3.7329746800831456110202306009587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06871
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.08
y1[1] (analytic) = 0.00189622790485437525888146264021
y1[1] (numeric) = 0.0018962279048543752588814626401805
absolute error = 2.95e-32
relative error = 1.5557201707916809436070530055748e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0615537174299132164456296371357
y2[1] (numeric) = 1.0615537174299132164456296371353
absolute error = 4e-31
relative error = 3.7680617893593230538051602323753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05916
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=924379852, alloc=4783252, time=50.76
x[1] = 3.09
y1[1] (analytic) = 0.00133060576218642526525648191424
y1[1] (numeric) = 0.0013306057621864252652564819142208
absolute error = 1.92e-32
relative error = 1.4429518153033500279399442972715e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0515697683985344926699585105746
y2[1] (numeric) = 1.0515697683985344926699585105742
absolute error = 4e-31
relative error = 3.8038370065466162663557389723232e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04959
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=928381736, alloc=4783252, time=50.98
x[1] = 3.1
y1[1] (analytic) = 0.00086484972672053550762394545853
y1[1] (numeric) = 0.00086484972672053550762394545851694
absolute error = 1.306e-32
relative error = 1.5100889318104811482135260651958e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0415806624332905791946982715967
y2[1] (numeric) = 1.0415806624332905791946982715963
absolute error = 4e-31
relative error = 3.8403170721846857708863738592162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04001
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=932382608, alloc=4783252, time=51.20
x[1] = 3.11
y1[1] (analytic) = 0.00049900637367212383916916328317
y1[1] (numeric) = 0.00049900637367212383916916328315265
absolute error = 1.735e-32
relative error = 3.4769094976329816132572590594481e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0315873984364537731876268727034
y2[1] (numeric) = 1.031587398436453773187626872703
absolute error = 4e-31
relative error = 3.8775192543672795921686194180398e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0304
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.12
y1[1] (analytic) = 0.00023311228707162665641502602441
y1[1] (numeric) = 0.00023311228707162665641502602439925
absolute error = 1.075e-32
relative error = 4.6115115316495215370977391285957e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0215909757260960660909981042019
y2[1] (numeric) = 1.0215909757260960660909981042015
absolute error = 4e-31
relative error = 3.9154613686333700268877518867403e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02079
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=936384148, alloc=4783252, time=51.42
x[1] = 3.13
y1[1] (analytic) = 6.719405610612634217276086079e-05
y1[1] (numeric) = 6.7194056106126342172760860787360e-05
absolute error = 2.640e-33
relative error = 3.9289189446018588863893057913300e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.0115923939361581691846814831183
y2[1] (numeric) = 1.0115923939361581691846814831179
absolute error = 4e-31
relative error = 3.9541617987416786850333532636119e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01116
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=940386432, alloc=4783252, time=51.65
x[1] = 3.14
y1[1] (analytic) = 1.26827246045471488569365495e-06
y1[1] (numeric) = 1.2682724604547148856936549485990e-06
absolute error = 1.4010e-33
relative error = 1.1046522286683558421743442916377e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 1.0015926529164869525405414363244
y2[1] (numeric) = 1.001592652916486952540541436324
absolute error = 4e-31
relative error = 3.9936395183736646345327266444476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001534
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=944388880, alloc=4783252, time=51.87
x[1] = 3.15
y1[1] (analytic) = 3.534152865803837180534320527e-05
y1[1] (numeric) = 3.5341528658038371805343205277823e-05
absolute error = 7.823e-33
relative error = 2.2135431875895022116133343830567e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.99159275263285129354085848342893
y2[1] (numeric) = 0.99159275263285129354085848342849
absolute error = 4.4e-31
relative error = 4.4373055251939210004885439927396e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.008107
Order of pole (three term test) = -0.8946
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.16
y1[1] (analytic) = 0.00016941041740165184008290572605
y1[1] (numeric) = 0.0001694104174016518400829057260557
absolute error = 5.70e-33
relative error = 3.3646100915305471774810746581447e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.98159369306694633329262072881263
y2[1] (numeric) = 0.98159369306694633329262072881219
absolute error = 4.4e-31
relative error = 4.4825063884145317479488930755361e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01775
Order of pole (three term test) = -0.901
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=948391344, alloc=4783252, time=52.09
x[1] = 3.17
y1[1] (analytic) = 0.00040346153191414445991164986472
y1[1] (numeric) = 0.00040346153191414445991164986473483
absolute error = 1.483e-32
relative error = 3.6756911940630276808255262606181e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.97159647411639614042871472510327
y2[1] (numeric) = 0.97159647411639614042871472510283
absolute error = 4.4e-31
relative error = 4.5286290319255368759710430872690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02738
Order of pole (three term test) = -0.9124
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=952393404, alloc=4783252, time=52.30
x[1] = 3.18
y1[1] (analytic) = 0.00073747146727910692731584613969
y1[1] (numeric) = 0.00073747146727910692731584613970798
absolute error = 1.798e-32
relative error = 2.4380604264375159151298573581197e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.96160209549476478194630475327388
y2[1] (numeric) = 0.96160209549476478194630475327344
absolute error = 4.4e-31
relative error = 4.5756971834967832310669968290697e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.037
Order of pole (three term test) = -0.9285
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.19
y1[1] (analytic) = 0.00117140682278134343104917030052
y1[1] (numeric) = 0.00117140682278134343104917030054
absolute error = 2.00e-32
relative error = 1.7073487716686477114838181724227e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.95161155663158579989199285154883
y2[1] (numeric) = 0.95161155663158579989199285154839
absolute error = 4.4e-31
relative error = 4.6237353564459177357974584759506e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04661
Order of pole (three term test) = -0.9495
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=956395000, alloc=4783252, time=52.52
x[1] = 3.2
y1[1] (analytic) = 0.00170522420524691533833927771642
y1[1] (numeric) = 0.0017052242052469153383392777164423
absolute error = 2.23e-32
relative error = 1.3077459217024763457899792524171e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.9416258565724200908627825853809
y2[1] (numeric) = 0.94162585657242009086278258538046
absolute error = 4.4e-31
relative error = 4.6727688808549594592273188529471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05619
Order of pole (three term test) = -0.9752
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=960396492, alloc=4783252, time=52.74
x[1] = 3.21
y1[1] (analytic) = 0.00233887023338242242789333479576
y1[1] (numeric) = 0.0023388702333824224278933347957894
absolute error = 2.94e-32
relative error = 1.2570171521436813500946582719218e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.93164599387895218245161163932314
y2[1] (numeric) = 0.93164599387895218245161163932269
absolute error = 4.5e-31
relative error = 4.8301608438888220331470922256761e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06576
Order of pole (three term test) = -1.006
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=964398864, alloc=4783252, time=52.97
x[1] = 3.22
y1[1] (analytic) = 0.00307228154311308774565726252414
y1[1] (numeric) = 0.003072281543113087745657262524169
absolute error = 2.90e-32
relative error = 9.4392390778791778628221594243232e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.92167296652913489692655585208396
y2[1] (numeric) = 0.92167296652913489692655585208351
absolute error = 4.5e-31
relative error = 4.8824259400232186624363588292243e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0753
Order of pole (three term test) = -1.041
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.23
y1[1] (analytic) = 0.00390538479391911227929150541505
y1[1] (numeric) = 0.003905384793919112279291505415091
absolute error = 4.10e-32
relative error = 1.0498325303012173710280741798755e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.91170777181739238759412427147028
y2[1] (numeric) = 0.91170777181739238759412427146983
absolute error = 4.5e-31
relative error = 4.9357920806463336885743435540541e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08481
Order of pole (three term test) = -1.081
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=968400532, alloc=4783252, time=53.19
x[1] = 3.24
y1[1] (analytic) = 0.00483809667616966582117615625753
y1[1] (numeric) = 0.0048380966761696658211761562575696
absolute error = 3.96e-32
relative error = 8.1850369371600541755481796671122e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.90175140625489152745984504056236
y2[1] (numeric) = 0.90175140625489152745984504056192
absolute error = 4.4e-31
relative error = 4.8793935551194293603994503288698e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09428
Order of pole (three term test) = -1.126
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=972402232, alloc=4783252, time=53.41
x[1] = 3.25
y1[1] (analytic) = 0.0058703239194537806269707748284
y1[1] (numeric) = 0.0058703239194537806269707748284477
absolute error = 4.77e-32
relative error = 8.1256163466424811982673486384663e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.89180486546989162296416915743917
y2[1] (numeric) = 0.89180486546989162296416915743873
absolute error = 4.4e-31
relative error = 4.9338147506984521545413936187389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1037
Order of pole (three term test) = -1.176
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=976404260, alloc=4783252, time=53.63
x[1] = 3.26
y1[1] (analytic) = 0.00700196330190731478730543282834
y1[1] (numeric) = 0.007001963301907314787305432828396
absolute error = 5.60e-32
relative error = 7.9977568555301853816020254205073e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.88186914410818241773927688966392
y2[1] (numeric) = 0.88186914410818241773927688966348
absolute error = 4.4e-31
relative error = 4.9894023726724635103575052408843e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1131
Order of pole (three term test) = -1.23
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.27
y1[1] (analytic) = 0.00823290166053505262403825950526
y1[1] (numeric) = 0.0082329016605350526240382595053157
absolute error = 5.57e-32
relative error = 6.7655369026210476716935459995424e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.87194523573362034250344310924638
y2[1] (numeric) = 0.87194523573362034250344310924594
absolute error = 4.4e-31
relative error = 5.0461884756994095874845530100089e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1225
Order of pole (three term test) = -1.289
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=980409344, alloc=4783252, time=53.85
x[1] = 3.28
y1[1] (analytic) = 0.00956301590252690990964158386829
y1[1] (numeric) = 0.0095630159025269099096415838683488
absolute error = 5.88e-32
relative error = 6.1486878824976982061091668556915e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.86203413272877295738508592941475
y2[1] (numeric) = 0.86203413272877295738508592941431
absolute error = 4.4e-31
relative error = 5.1042062407340879198931845679909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1318
Order of pole (three term test) = -1.353
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=984410960, alloc=4783252, time=54.08
x[1] = 3.29
y1[1] (analytic) = 0.01099217301756711229862487446052
y1[1] (numeric) = 0.010992173017567112298624874460582
absolute error = 6.2e-32
relative error = 5.6403770119806942288802155434389e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.85213682619568152214947021625736
y2[1] (numeric) = 0.85213682619568152214947021625692
absolute error = 4.4e-31
relative error = 5.1634900226569957120511496645365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.141
Order of pole (three term test) = -1.421
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.3
y1[1] (analytic) = 0.01252023009113511606340894889715
y1[1] (numeric) = 0.012520230091135116063408948897216
absolute error = 6.6e-32
relative error = 5.2714686167573675393502740216258e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.84225430585675161798834572239752
y2[1] (numeric) = 0.84225430585675161798834572239708
absolute error = 4.4e-31
relative error = 5.2240754002726824273379813880667e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1502
Order of pole (three term test) = -1.494
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=988411988, alloc=4783252, time=54.29
x[1] = 3.31
y1[1] (analytic) = 0.01414703431879694105366192941447
y1[1] (numeric) = 0.014147034318796941053661929414544
absolute error = 7.4e-32
relative error = 5.2307782912265483653376098265741e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.83238755995578173172775000568302
y2[1] (numeric) = 0.83238755995578173172775000568259
absolute error = 4.3e-31
relative error = 5.1658628827038519302295407078665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1593
Order of pole (three term test) = -1.572
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=992414684, alloc=4783252, time=54.51
x[1] = 3.32
y1[1] (analytic) = 0.01587242302148548675771041526881
y1[1] (numeric) = 0.015872423021485486757710415268883
absolute error = 7.3e-32
relative error = 4.5991717774396861575188709273826e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.82253757515913969951307944769159
y2[1] (numeric) = 0.82253757515913969951307944769116
absolute error = 4.3e-31
relative error = 5.2277247020211343679749267165640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1684
Order of pole (three term test) = -1.654
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=996416284, alloc=4783252, time=54.73
x[1] = 3.33
y1[1] (analytic) = 0.01769622366176830344715328514073
y1[1] (numeric) = 0.017696223661768303447153285140815
absolute error = 8.5e-32
relative error = 4.8032846795238987809865490419912e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.81270533645709689224470717586405
y2[1] (numeric) = 0.81270533645709689224470717586362
absolute error = 4.3e-31
relative error = 5.2909705487420520704096066478282e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1774
Order of pole (three term test) = -1.741
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.34
y1[1] (analytic) = 0.01961825386110119164112009893009
y1[1] (numeric) = 0.019618253861101191641120098930172
absolute error = 8.2e-32
relative error = 4.1797807582961545165391006948088e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.80289182706533000926338308940728
y2[1] (numeric) = 0.80289182706533000926338308940685
absolute error = 4.3e-31
relative error = 5.3556405172500478764952038449259e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1863
Order of pole (three term test) = -1.832
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1000418388, alloc=4783252, time=54.95
x[1] = 3.35
y1[1] (analytic) = 0.02163832141806590454460562472847
y1[1] (numeric) = 0.021638321418065904544605624728556
absolute error = 8.6e-32
relative error = 3.9744302868242969077556403197381e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.79309802832660033002396588397449
y2[1] (numeric) = 0.79309802832660033002396588397406
absolute error = 4.3e-31
relative error = 5.4217761820348973426413875756893e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1952
Order of pole (three term test) = -1.928
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1004419856, alloc=4783252, time=55.18
x[1] = 3.36
y1[1] (analytic) = 0.02375622432759012970583469222168
y1[1] (numeric) = 0.023756224327590129705834692221774
absolute error = 9.4e-32
relative error = 3.9568577356305640642741944110259e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.78332491961262025575038601809447
y2[1] (numeric) = 0.78332491961262025575038601809404
absolute error = 4.3e-31
relative error = 5.4894206635561784153719234086793e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.204
Order of pole (three term test) = -2.028
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1008422864, alloc=4783252, time=55.40
x[1] = 3.37
y1[1] (analytic) = 0.02597175080114782791050823402915
y1[1] (numeric) = 0.02597175080114782791050823402925
absolute error = 1.00e-31
relative error = 3.8503372670424850765170070879704e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.77357347822611695433589651569143
y2[1] (numeric) = 0.773573478226116954335896515691
absolute error = 4.3e-31
relative error = 5.5586186975545483602973234604070e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2127
Order of pole (three term test) = -2.132
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.38
y1[1] (analytic) = 0.02828467928793790929587465000943
y1[1] (numeric) = 0.028284679287937909295874650009532
absolute error = 1.02e-31
relative error = 3.6061925596412267524254532731765e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.76384467930310290204250822241037
y2[1] (numeric) = 0.76384467930310290204250822240994
absolute error = 4.3e-31
relative error = 5.6294167080186042102323499937925e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2213
Order of pole (three term test) = -2.241
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1012424108, alloc=4783252, time=55.61
x[1] = 3.39
y1[1] (analytic) = 0.03069477849703912883466392532752
y1[1] (numeric) = 0.030694778497039128834663925327633
absolute error = 1.13e-31
relative error = 3.6814078984443616198222243770451e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.75413949571536309486399862844206
y2[1] (numeric) = 0.75413949571536309486399862844163
absolute error = 4.3e-31
relative error = 5.7018628840292971538251515258835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2298
Order of pole (three term test) = -2.354
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1016427064, alloc=4783252, time=55.84
x[1] = 3.4
y1[1] (analytic) = 0.03320180742053898571779846023431
y1[1] (numeric) = 0.033201807420538985717798460234418
absolute error = 1.08e-31
relative error = 3.2528349626288739076358255928212e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.74445889797316868075009757063626
y2[1] (numeric) = 0.74445889797316868075009757063583
absolute error = 4.3e-31
relative error = 5.7760072607191510723297311684589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2382
Order of pole (three term test) = -2.472
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.41
y1[1] (analytic) = 0.03580551535763431376521635904704
y1[1] (numeric) = 0.035805515357634313765216359047155
absolute error = 1.15e-31
relative error = 3.2117956926845390016785727688583e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.73480385412822674124755569242589
y2[1] (numeric) = 0.73480385412822674124755569242546
absolute error = 4.3e-31
relative error = 5.8519018045999928866669396922807e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2465
Order of pole (three term test) = -2.593
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1020429304, alloc=4783252, time=56.05
x[1] = 3.42
y1[1] (analytic) = 0.03850564193970115282584985439859
y1[1] (numeric) = 0.038505641939701152825849854398712
absolute error = 1.22e-31
relative error = 3.1683668640312209137003856159090e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.7251753296768759274990566423338
y2[1] (numeric) = 0.72517532967687592749905664233337
absolute error = 4.3e-31
relative error = 5.9296005035306381189283757785919e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2548
Order of pole (three term test) = -2.719
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1024430820, alloc=4783252, time=56.28
x[1] = 3.43
y1[1] (analytic) = 0.04130191715633139420051035877444
y1[1] (numeric) = 0.041301917156331394200510358774568
absolute error = 1.28e-31
relative error = 3.0991297453701416836902046817463e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.71557428746353763095570308540863
y2[1] (numeric) = 0.7155742874635376309557030854082
absolute error = 4.3e-31
relative error = 6.0091594616150991729638389297957e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2629
Order of pole (three term test) = -2.849
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1028431768, alloc=4783252, time=56.51
x[1] = 3.44
y1[1] (analytic) = 0.04419406138233359644483498702751
y1[1] (numeric) = 0.044194061382333596444834987027644
absolute error = 1.34e-31
relative error = 3.0320815921563157582801550260809e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.70600168758443234360554818943968
y2[1] (numeric) = 0.70600168758443234360554818943925
absolute error = 4.3e-31
relative error = 6.0906369993425167897985337895305e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2709
Order of pole (three term test) = -2.982
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.45
y1[1] (analytic) = 0.04718178540569527149321486005225
y1[1] (numeric) = 0.047181785405695271493214860052387
absolute error = 1.37e-31
relative error = 2.9036629034276191557643595969170e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.69645848729157083600191363378011
y2[1] (numeric) = 0.69645848729157083600191363377968
absolute error = 4.3e-31
relative error = 6.1740937593022889260103651902949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2789
Order of pole (three term test) = -3.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1032433608, alloc=4783252, time=56.72
x[1] = 3.46
y1[1] (analytic) = 0.05026479045650384489839462421797
y1[1] (numeric) = 0.050264790456503844898394624218108
absolute error = 1.38e-31
relative error = 2.7454605648742727487367618766883e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.68694564089702975389368422402507
y2[1] (numeric) = 0.68694564089702975389368422402465
absolute error = 4.2e-31
relative error = 6.1140208918358392144328238498409e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2867
Order of pole (three term test) = -3.262
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1036434588, alloc=4783252, time=56.95
x[1] = 3.47
y1[1] (analytic) = 0.05344276823682339811481994647332
y1[1] (numeric) = 0.053442768236823398114819946473462
absolute error = 1.42e-31
relative error = 2.6570479914279302620680234054722e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.67746409967752120581814601284274
y2[1] (numeric) = 0.67746409967752120581814601284231
absolute error = 4.3e-31
relative error = 6.3471998029812020133563966288301e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2944
Order of pole (three term test) = -3.408
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1040436440, alloc=4783252, time=57.17
x[1] = 3.48
y1[1] (analytic) = 0.05671540095152420517640185261772
y1[1] (numeric) = 0.056715400951524205176401852617864
absolute error = 1.44e-31
relative error = 2.5389928940655766251444922119285e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.66801481177926588461808356455725
y2[1] (numeric) = 0.66801481177926588461808356455682
absolute error = 4.3e-31
relative error = 6.4369830192041636233545801547531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3019
Order of pole (three term test) = -3.557
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.49
y1[1] (analytic) = 0.06008236134006198084072132723323
y1[1] (numeric) = 0.06008236134006198084072132723338
absolute error = 1.50e-31
relative error = 2.4965729817277061818567726425865e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.6585987221231792354917125192625
y2[1] (numeric) = 0.65859872212317923549171251926207
absolute error = 4.3e-31
relative error = 6.5290135792212501420501037601781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3094
Order of pole (three term test) = -3.71
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1044437592, alloc=4783252, time=57.39
x[1] = 3.5
y1[1] (analytic) = 0.06354331270920366230134237332824
y1[1] (numeric) = 0.063543312709203662301342373328396
absolute error = 1.56e-31
relative error = 2.4550183701298412158126748578633e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.64921677231038015187963119995636
y2[1] (numeric) = 0.64921677231038015187963119995594
absolute error = 4.2e-31
relative error = 6.4693337867002105064592493762007e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3167
Order of pole (three term test) = -3.867
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1048438536, alloc=4783252, time=57.61
x[1] = 3.51
y1[1] (analytic) = 0.06709790896669645191733369424242
y1[1] (numeric) = 0.067097908966696451917333694242579
absolute error = 1.59e-31
relative error = 2.3696714614298706008238174719260e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.63986990052803164824046007658263
y2[1] (numeric) = 0.6398699005280316482404600765822
absolute error = 4.3e-31
relative error = 6.7201160680500302268013275331826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3239
Order of pole (three term test) = -4.028
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.52
y1[1] (analytic) = 0.07074579465587675408378348772776
y1[1] (numeric) = 0.070745794655876754083783487727927
absolute error = 1.67e-31
relative error = 2.3605643390158392104604764309909e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.63055904145552292556942567856704
y2[1] (numeric) = 0.63055904145552292556942567856661
absolute error = 4.3e-31
relative error = 6.8193455605271890151199653398013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.331
Order of pole (three term test) = -4.192
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1052439812, alloc=4783252, time=57.83
x[1] = 3.53
y1[1] (analytic) = 0.07448660499121554537846098531599
y1[1] (numeric) = 0.074486604991215545378460985316154
absolute error = 1.64e-31
relative error = 2.2017381517031292926043188883248e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.62128512617100221137515574599336
y2[1] (numeric) = 0.62128512617100221137515574599294
absolute error = 4.2e-31
relative error = 6.7601811520657490739607838089915e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3379
Order of pole (three term test) = -4.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1056441392, alloc=4783252, time=58.05
x[1] = 3.54
y1[1] (analytic) = 0.07831996589479662347723111387023
y1[1] (numeric) = 0.078319965894796623477231113870407
absolute error = 1.77e-31
relative error = 2.2599601261031629670635365984953e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.61204908205826972075279889951549
y2[1] (numeric) = 0.61204908205826972075279889951507
absolute error = 4.2e-31
relative error = 6.8621947538516883649892322499788e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3447
Order of pole (three term test) = -4.531
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1060443292, alloc=4783252, time=58.28
x[1] = 3.55
y1[1] (analytic) = 0.08224549403372408704372917728953
y1[1] (numeric) = 0.082245494033724087043729177289704
absolute error = 1.74e-31
relative error = 2.1156174212857513377368669064541e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.60285183271404004917977257656305
y2[1] (numeric) = 0.60285183271404004917977257656263
absolute error = 4.2e-31
relative error = 6.9668860109317281963977497113805e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3514
Order of pole (three term test) = -4.705
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.56
y1[1] (analytic) = 0.08626279685845530587647938689634
y1[1] (numeric) = 0.08626279685845530587647938689652
absolute error = 1.80e-31
relative error = 2.0866469272420392427138505180829e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.59369429785558327071757857731409
y2[1] (numeric) = 0.59369429785558327071757857731366
absolute error = 4.3e-31
relative error = 7.2427847387646281266272573584303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3579
Order of pole (three term test) = -4.883
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1064444288, alloc=4783252, time=58.49
x[1] = 3.57
y1[1] (analytic) = 0.09037147264205554804838656396326
y1[1] (numeric) = 0.090371472642055548048386563963449
absolute error = 1.89e-31
relative error = 2.0913679336464234553114708795254e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.58457739322875397743290054393371
y2[1] (numeric) = 0.58457739322875397743290054393329
absolute error = 4.2e-31
relative error = 7.1846774244936913983170404883802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3643
Order of pole (three term test) = -5.064
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1068445956, alloc=4783252, time=58.71
x[1] = 3.58
y1[1] (analytic) = 0.09457111052037033860859914545098
y1[1] (numeric) = 0.094571110520370338608599145451172
absolute error = 1.92e-31
relative error = 2.0302183081443647171058862685311e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.57550203051641745705739905165624
y2[1] (numeric) = 0.57550203051641745705739905165581
absolute error = 4.3e-31
relative error = 7.4717373214851464774811976881278e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3705
Order of pole (three term test) = -5.249
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.59
y1[1] (analytic) = 0.09886129053311153264435016065217
y1[1] (numeric) = 0.09886129053311153264435016065236
bytes used=1072447420, alloc=4783252, time=58.94
absolute error = 1.90e-31
relative error = 1.9218846828260192758249469561801e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.56646911724728216619212706795597
y2[1] (numeric) = 0.56646911724728216619212706795555
absolute error = 4.2e-31
relative error = 7.4143494713526697022363174326705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3766
Order of pole (three term test) = -5.436
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.6
y1[1] (analytic) = 0.10324158366585299412970827473406
y1[1] (numeric) = 0.10324158366585299412970827473426
absolute error = 2.0e-31
relative error = 1.9372039143385371512357974086129e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.55747955670514761573327265250731
y2[1] (numeric) = 0.55747955670514761573327265250689
absolute error = 4.2e-31
relative error = 7.5339085523119745528115820273110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3826
Order of pole (three term test) = -5.626
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1076449188, alloc=4783252, time=59.16
x[1] = 3.61
y1[1] (analytic) = 0.10771155189293168102835030646159
y1[1] (numeric) = 0.10771155189293168102835030646179
absolute error = 2.0e-31
relative error = 1.8568110521590631059020581654406e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.54853424783857674365505981360747
y2[1] (numeric) = 0.54853424783857674365505981360706
absolute error = 4.1e-31
relative error = 7.4744649329654116125769084249483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3883
Order of pole (three term test) = -5.819
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1080450472, alloc=4783252, time=59.38
x[1] = 3.62
y1[1] (analytic) = 0.112270748221249846577595727932
y1[1] (numeric) = 0.11227074822124984657759572793221
absolute error = 2.1e-31
relative error = 1.8704783153859183310522332542914e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.53963408517100180783725645920515
y2[1] (numeric) = 0.53963408517100180783725645920474
absolute error = 4.1e-31
relative error = 7.5977409742395581960428563209555e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.394
Order of pole (three term test) = -6.015
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.63
y1[1] (analytic) = 0.11691871673497397657007645560199
y1[1] (numeric) = 0.1169187167349739765700764556022
absolute error = 2.1e-31
relative error = 1.7961196108234615511650190212631e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.53077995871127278827309518546809
y2[1] (numeric) = 0.53077995871127278827309518546768
absolute error = 4.1e-31
relative error = 7.7244815534383580992743688451508e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3994
Order of pole (three term test) = -6.214
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1084452856, alloc=4783252, time=59.59
x[1] = 3.64
y1[1] (analytic) = 0.12165499264112599277656275586591
y1[1] (numeric) = 0.12165499264112599277656275586612
absolute error = 2.1e-31
relative error = 1.7261930270259093175891529780780e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.52197275386465724374284336112709
y2[1] (numeric) = 0.52197275386465724374284336112668
absolute error = 4.1e-31
relative error = 7.8548161175920160446689553586286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4048
Order of pole (three term test) = -6.416
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1088454464, alloc=4783252, time=59.81
x[1] = 3.65
y1[1] (analytic) = 0.12647910231606216342759552547173
y1[1] (numeric) = 0.12647910231606216342759552547194
absolute error = 2.1e-31
relative error = 1.6603533402318521460730028762443e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.51321335134430052289318861170468
y2[1] (numeric) = 0.51321335134430052289318861170427
absolute error = 4.1e-31
relative error = 7.9888802371577904586030773401186e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4099
Order of pole (three term test) = -6.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1092455708, alloc=4783252, time=60.04
x[1] = 3.66
y1[1] (analytic) = 0.13139056335283507290160907984007
y1[1] (numeric) = 0.13139056335283507290160907984029
absolute error = 2.2e-31
relative error = 1.6743972655723677714625419349646e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.50450262708315518362754885358965
y2[1] (numeric) = 0.50450262708315518362754885358924
absolute error = 4.1e-31
relative error = 8.1268159567466694812858458666712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4149
Order of pole (three term test) = -6.827
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.67
y1[1] (analytic) = 0.13638888460943391446204381352019
y1[1] (numeric) = 0.13638888460943391446204381352041
absolute error = 2.2e-31
relative error = 1.6130346738298845862309964674857e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.49584145214638842779197594108609
y2[1] (numeric) = 0.49584145214638842779197594108568
absolute error = 4.1e-31
relative error = 8.2687721695150800791351374428014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4197
Order of pole (three term test) = -7.036
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1096456788, alloc=4783252, time=60.25
x[1] = 3.68
y1[1] (analytic) = 0.14147356625789828205437513146384
y1[1] (numeric) = 0.14147356625789828205437513146406
absolute error = 2.2e-31
relative error = 1.5550608203298733980230507572888e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.48723069264427631034019077495596
y2[1] (numeric) = 0.48723069264427631034019077495555
absolute error = 4.1e-31
relative error = 8.4149050170642288760879179749677e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4244
Order of pole (three term test) = -7.248
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1100458072, alloc=4783252, time=60.47
x[1] = 3.69
y1[1] (analytic) = 0.14664409983430054982480697162784
y1[1] (numeric) = 0.14664409983430054982480697162806
absolute error = 2.2e-31
relative error = 1.5002308326662131248966956816554e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.47867120964559343348424545187534
y2[1] (numeric) = 0.47867120964559343348424545187494
absolute error = 4.0e-31
relative error = 8.3564666505879613144861729446830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4288
Order of pole (three term test) = -7.461
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.7
y1[1] (analytic) = 0.1518999682895918411643298936456
y1[1] (numeric) = 0.15189996828959184116432989364582
absolute error = 2.2e-31
relative error = 1.4483215663388282675999810825621e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.47016385909150678678922237429879
y2[1] (numeric) = 0.47016385909150678678922237429839
absolute error = 4.0e-31
relative error = 8.5076722139578368839378799270553e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
bytes used=1104459464, alloc=4783252, time=60.70
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4331
Order of pole (three term test) = -7.677
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.71
y1[1] (analytic) = 0.15724064604130650272361082739025
y1[1] (numeric) = 0.15724064604130650272361082739048
absolute error = 2.3e-31
relative error = 1.4627261194257615779831067534823e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.46170949170998234375620595674963
y2[1] (numeric) = 0.46170949170998234375620595674923
absolute error = 4.0e-31
relative error = 8.6634562897670626362795229888497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4373
Order of pole (three term test) = -7.896
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1108462012, alloc=4783252, time=60.92
x[1] = 3.72
y1[1] (analytic) = 0.16266559902611991299439991051033
y1[1] (numeric) = 0.16266559902611991299439991051056
absolute error = 2.3e-31
relative error = 1.4139437064567531172240682653813e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.45330895293071297416254103294378
y2[1] (numeric) = 0.45330895293071297416254103294338
absolute error = 4.0e-31
relative error = 8.8240039693444770569395995691338e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4412
Order of pole (three term test) = -8.116
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1112463092, alloc=4783252, time=61.14
x[1] = 3.73
y1[1] (analytic) = 0.16817428475325436972039430207837
y1[1] (numeric) = 0.1681742847532543697203943020786
absolute error = 2.3e-31
relative error = 1.3676288282566888107581684997021e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.44496308280057617929725076783427
y2[1] (numeric) = 0.44496308280057617929725076783387
absolute error = 4.0e-31
relative error = 8.9895098146664054678118942372193e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.445
Order of pole (three term test) = -8.338
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.74
y1[1] (analytic) = 0.17376615235872771559332264379747
y1[1] (numeric) = 0.1737661523587277155933226437977
absolute error = 2.3e-31
relative error = 1.3236179594123805716875255875596e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.43667271589963010424763888032052
y2[1] (numeric) = 0.43667271589963010424763888032012
absolute error = 4.0e-31
relative error = 9.1601784456792261682450736080407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4486
Order of pole (three term test) = -8.562
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1116464224, alloc=4783252, time=61.36
x[1] = 3.75
y1[1] (analytic) = 0.17944064266043927741688759770929
y1[1] (numeric) = 0.17944064266043927741688759770953
absolute error = 2.4e-31
relative error = 1.3374896369166429455942148381823e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.42843868125765622756584442664971
y2[1] (numeric) = 0.42843868125765622756584442664931
absolute error = 4.0e-31
relative error = 9.3362251705617202263018467213337e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.452
Order of pole (three term test) = -8.788
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1120466880, alloc=4783252, time=61.58
x[1] = 3.76
y1[1] (analytic) = 0.18519718821408761019055486243691
y1[1] (numeric) = 0.18519718821408761019055486243715
absolute error = 2.4e-31
relative error = 1.2959160034468797647962271081071e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.42026180227125707397683496224605
y2[1] (numeric) = 0.42026180227125707397683496224566
absolute error = 3.9e-31
relative error = 9.2799297459890333083196114778390e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4553
Order of pole (three term test) = -9.015
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1124468960, alloc=4783252, time=61.80
x[1] = 3.77
y1[1] (analytic) = 0.19103521336991445438537825380378
y1[1] (numeric) = 0.19103521336991445438537825380403
absolute error = 2.5e-31
relative error = 1.3086592549610632555198222857158e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.41214289662151724028748227352559
y2[1] (numeric) = 0.4121428966215172402874822735252
absolute error = 3.9e-31
relative error = 9.4627373951357530340886139859666e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.81
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4584
Order of pole (three term test) = -9.244
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.78
y1[1] (analytic) = 0.19695413433026923206341974076229
y1[1] (numeric) = 0.19695413433026923206341974076254
absolute error = 2.5e-31
relative error = 1.2693310594880887635931620717644e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.40408277619223596832551418909979
y2[1] (numeric) = 0.4040827761922359683255141890994
absolute error = 3.9e-31
relative error = 9.6514878380875033625865936071682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4612
Order of pole (three term test) = -9.474
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1128470068, alloc=4783252, time=62.02
x[1] = 3.79
y1[1] (analytic) = 0.20295335920798832543912274815984
y1[1] (numeric) = 0.2029533592079883254391227481601
absolute error = 2.6e-31
relative error = 1.2810825157791539325730264395304e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.39608224698873944158290927976732
y2[1] (numeric) = 0.39608224698873944158290927976693
absolute error = 3.9e-31
relative error = 9.8464397979212544977933818698717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4639
Order of pole (three term test) = -9.706
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1132470824, alloc=4783252, time=62.25
x[1] = 3.8
y1[1] (analytic) = 0.20903228808558330000343182564927
y1[1] (numeric) = 0.20903228808558330000343182564954
absolute error = 2.7e-31
relative error = 1.2916664811584271614471406759581e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.38814210905728092426641391388112
y2[1] (numeric) = 0.38814210905728092426641391388073
absolute error = 3.9e-31
relative error = 1.0047866255666810255751182866613e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4664
Order of pole (three term test) = -9.939
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.81
y1[1] (analytic) = 0.21519031307523215343766962563504
y1[1] (numeric) = 0.21519031307523215343766962563531
absolute error = 2.7e-31
relative error = 1.2547033188506304528562865828438e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.38026315640503680267411028948219
y2[1] (numeric) = 0.38026315640503680267411028948181
absolute error = 3.8e-31
relative error = 9.9930796239234783510244517033441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4688
Order of pole (three term test) = -10.17
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1136473016, alloc=4783252, time=62.47
TOP MAIN SOLVE Loop
x[1] = 3.82
y1[1] (analytic) = 0.2214268183795675912422723433438
y1[1] (numeric) = 0.22142681837956759124227234334407
absolute error = 2.7e-31
relative error = 1.2193644924128781761588054809686e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.37244617692070652922722804311009
y2[1] (numeric) = 0.37244617692070652922722804310971
absolute error = 3.8e-31
relative error = 1.0202816502017731093807678885123e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.12
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.31
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4709
Order of pole (three term test) = -10.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1140474440, alloc=4783252, time=62.69
x[1] = 3.83
y1[1] (analytic) = 0.22774118035325625030347747297652
y1[1] (numeric) = 0.22774118035325625030347747297679
absolute error = 2.7e-31
relative error = 1.1855563389159343654539698047059e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.36469195229572440909662976137772
y2[1] (numeric) = 0.36469195229572440909662976137734
absolute error = 3.8e-31
relative error = 1.0419752824484113521228723385706e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4728
Order of pole (three term test) = -10.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1144476824, alloc=4783252, time=62.91
x[1] = 3.84
y1[1] (analytic) = 0.23413276756536271252692305975232
y1[1] (numeric) = 0.2341327675653627125269230597526
absolute error = 2.8e-31
relative error = 1.1959026620305616047164964929122e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.35700125794609110817965112113726
y2[1] (numeric) = 0.35700125794609110817965112113688
absolute error = 3.8e-31
relative error = 1.0644220196484064252468914570540e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4746
Order of pole (three term test) = -10.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.85
y1[1] (analytic) = 0.24060094086249207218876492604721
y1[1] (numeric) = 0.24060094086249207218876492604749
absolute error = 2.8e-31
relative error = 1.1637527226463558402117112738584e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.349374862934832699211357781338
y2[1] (numeric) = 0.34937486293483269921135778133763
absolute error = 3.7e-31
relative error = 1.0590344047419759949912052340568e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4762
Order of pole (three term test) = -11.12
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1148478416, alloc=4783252, time=63.13
x[1] = 3.86
y1[1] (analytic) = 0.24714505343270474280019539063516
y1[1] (numeric) = 0.24714505343270474280019539063545
absolute error = 2.9e-31
relative error = 1.1733999769449735446425060397461e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.3418135298950950000409906547043
y2[1] (numeric) = 0.34181352989509500004099065470393
absolute error = 3.7e-31
relative error = 1.0824615401080104342875486157253e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4775
Order of pole (three term test) = -11.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1152479516, alloc=4783252, time=63.34
x[1] = 3.87
y1[1] (analytic) = 0.25376445087019711205793919067272
y1[1] (numeric) = 0.25376445087019711205793919067301
absolute error = 2.9e-31
relative error = 1.1427920617152861569562630730983e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.33431801495388089457568407689649
y2[1] (numeric) = 0.33431801495388089457568407689613
absolute error = 3.6e-31
relative error = 1.0768190282825827686500048894455e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4787
Order of pole (three term test) = -11.6
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1156481680, alloc=4783252, time=63.57
x[1] = 3.88
y1[1] (analytic) = 0.26045847124074157686913192295872
y1[1] (numeric) = 0.26045847124074157686913192295901
absolute error = 2.9e-31
relative error = 1.1134212629696087305721609290673e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.32688906765643826259581048063146
y2[1] (numeric) = 0.3268890676564382625958104806311
absolute error = 3.6e-31
relative error = 1.1012910360720948359783902398117e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4797
Order of pole (three term test) = -11.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.89
y1[1] (analytic) = 0.26722644514787941450161169736831
y1[1] (numeric) = 0.26722644514787941450161169736861
absolute error = 3.0e-31
relative error = 1.1226433814736567485061822061565e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.31952743089130607958596019184132
y2[1] (numeric) = 0.31952743089130607958596019184096
absolute error = 3.6e-31
relative error = 1.1266638328853259205311066454488e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4805
Order of pole (three term test) = -12.08
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1160483788, alloc=4783252, time=63.79
x[1] = 3.9
y1[1] (analytic) = 0.27406769579985987062766951538565
y1[1] (numeric) = 0.27406769579985987062766951538595
absolute error = 3.0e-31
relative error = 1.0946200686821456044917964425869e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.31223384081602618190911187462131
y2[1] (numeric) = 0.31223384081602618190911187462096
absolute error = 3.5e-31
relative error = 1.1209547276658788601832670535714e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4811
Order of pole (three term test) = -12.32
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1164484924, alloc=4783252, time=64.01
x[1] = 3.91
y1[1] (analytic) = 0.28098153907731877040823638612561
y1[1] (numeric) = 0.28098153907731877040823638612591
absolute error = 3.0e-31
relative error = 1.0676858023667093893263740277045e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.30500902678352812608556955192351
y2[1] (numeric) = 0.30500902678352812608556955192316
absolute error = 3.5e-31
relative error = 1.1475070219754610586558002943360e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4815
Order of pole (three term test) = -12.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.92
y1[1] (analytic) = 0.28796728360168988481279741570741
y1[1] (numeric) = 0.28796728360168988481279741570771
absolute error = 3.0e-31
relative error = 1.0417850119909923799761690996621e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.29785371126919450362939256217935
y2[1] (numeric) = 0.297853711269194503629392562179
absolute error = 3.5e-31
relative error = 1.1750734899645976717104663757944e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -12.8
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1168486328, alloc=4783252, time=64.23
TOP MAIN SOLVE Loop
x[1] = 3.93
y1[1] (analytic) = 0.29502423080434221109541016047305
y1[1] (numeric) = 0.29502423080434221109541016047335
absolute error = 3.0e-31
relative error = 1.0168656289081478211369132386118e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.29076860979861400485005610714845
y2[1] (numeric) = 0.2907686097986140048500561071481
absolute error = 3.5e-31
relative error = 1.2037062743547509682326538319983e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -13.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1172487888, alloc=4783252, time=64.45
x[1] = 3.94
y1[1] (analytic) = 0.30215167499643625375639385056441
y1[1] (numeric) = 0.30215167499643625375639385056471
absolute error = 3.0e-31
relative error = 9.9287882486019105531171254904653e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.28375443087602945625275664545921
y2[1] (numeric) = 0.28375443087602945625275664545887
absolute error = 3.4e-31
relative error = 1.1982191747643365703914171380541e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4816
Order of pole (three term test) = -13.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1176489304, alloc=4783252, time=64.67
x[1] = 3.95
y1[1] (analytic) = 0.30934890343949232041980668835977
y1[1] (numeric) = 0.30934890343949232041980668836008
absolute error = 3.1e-31
relative error = 1.0021047320784669664568549056888e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.27681187591348798667399566455718
y2[1] (numeric) = 0.27681187591348798667399566455683
absolute error = 3.5e-31
relative error = 1.2643966189853266886244917064324e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4813
Order of pole (three term test) = -13.53
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.96
y1[1] (analytic) = 0.31661519641666377585593019124849
y1[1] (numeric) = 0.3166151964166637758559301912488
absolute error = 3.1e-31
relative error = 9.7910651007427257075598872351453e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.26994163916070040707678694126831
y2[1] (numeric) = 0.26994163916070040707678694126797
absolute error = 3.4e-31
relative error = 1.2595315085776476812661438072664e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4807
Order of pole (three term test) = -13.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1180491260, alloc=4783252, time=64.89
x[1] = 3.97
y1[1] (analytic) = 0.32394982730470812688275251068066
y1[1] (numeric) = 0.32394982730470812688275251068097
absolute error = 3.1e-31
relative error = 9.5693830917962836346113297661520e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.26314440763561681800905744824866
y2[1] (numeric) = 0.26314440763561681800905744824832
absolute error = 3.4e-31
relative error = 1.2920662196659987563365009114063e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.48
Order of pole (three term test) = -14.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1184493064, alloc=4783252, time=65.11
x[1] = 3.98
y1[1] (analytic) = 0.33135206264664874109793628332516
y1[1] (numeric) = 0.33135206264664874109793628332548
absolute error = 3.2e-31
relative error = 9.6574017811757371708335468928135e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.2564208610557253871066425986234
y2[1] (numeric) = 0.25642086105572538710664259862307
absolute error = 3.3e-31
relative error = 1.2869467743043121316726535848888e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4791
Order of pole (three term test) = -14.25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1188495804, alloc=4783252, time=65.33
x[1] = 3.99
y1[1] (analytic) = 0.33882116222511993332994904798987
y1[1] (numeric) = 0.3388211622251199333299490479902
absolute error = 3.3e-31
relative error = 9.7396513792943379694693106231727e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.24977167177008116670587470137992
y2[1] (numeric) = 0.24977167177008116670587470137959
absolute error = 3.3e-31
relative error = 1.3212066751259538242806403568086e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.478
Order of pole (three term test) = -14.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4
y1[1] (analytic) = 0.34635637913638808536083181690225
y1[1] (numeric) = 0.34635637913638808536083181690258
absolute error = 3.3e-31
relative error = 9.5277586866691640604810665471333e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.24319750469207174862736090548817
y2[1] (numeric) = 0.24319750469207174862736090548784
absolute error = 3.3e-31
relative error = 1.3569218171783241049825129334081e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.41
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4766
Order of pole (three term test) = -14.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1192496572, alloc=4783252, time=65.55
x[1] = 4.01
y1[1] (analytic) = 0.35395695986504139687031758531497
y1[1] (numeric) = 0.35395695986504139687031758531531
absolute error = 3.4e-31
relative error = 9.6056876556301370316432742228926e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.2366990172329264795094438207023
y2[1] (numeric) = 0.23669901723292647950944382070198
absolute error = 3.2e-31
relative error = 1.3519278776096488770703692755694e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4751
Order of pole (three term test) = -14.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1196500500, alloc=4783252, time=65.77
x[1] = 4.02
y1[1] (analytic) = 0.36162214435934079868844661923465
y1[1] (numeric) = 0.36162214435934079868844661923499
absolute error = 3.4e-31
relative error = 9.4020790845746697204942160082402e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.23027685923597588571440266645551
y2[1] (numeric) = 0.23027685923597588571440266645519
absolute error = 3.2e-31
relative error = 1.3896315985102109314632946880031e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4734
Order of pole (three term test) = -15.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.03
y1[1] (analytic) = 0.36935116610722449332814547814755
y1[1] (numeric) = 0.3693511661072244933281454781479
absolute error = 3.5e-31
relative error = 9.4760767561349257283373953423003e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.2239316729116678818101206987675
y2[1] (numeric) = 0.22393167291166788181012069876719
absolute error = 3.1e-31
relative error = 1.3843508422423238101436767365080e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.44
Order of pole (ratio test) Not computed
bytes used=1200501388, alloc=4783252, time=65.99
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4716
Order of pole (three term test) = -15.44
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.04
y1[1] (analytic) = 0.37714325221295852240705342082732
y1[1] (numeric) = 0.37714325221295852240705342082768
absolute error = 3.6e-31
relative error = 9.5454445462734044455530900642727e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.21766409277334726095221776933351
y2[1] (numeric) = 0.2176640927733472609522177693332
absolute error = 3.1e-31
relative error = 1.4242128595955500368836945257968e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4695
Order of pole (three term test) = -15.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1204503376, alloc=4783252, time=66.21
x[1] = 4.05
y1[1] (analytic) = 0.38499762347442569596572927151763
y1[1] (numeric) = 0.38499762347442569596572927151799
absolute error = 3.6e-31
relative error = 9.3507070706350420512656114658011e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.21147474557380488916409289058062
y2[1] (numeric) = 0.21147474557380488916409289058032
absolute error = 3.0e-31
relative error = 1.4186091071347321332075953148276e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4672
Order of pole (three term test) = -15.91
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1208504296, alloc=4783252, time=66.43
x[1] = 4.06
y1[1] (analytic) = 0.39291349446104515485371415221066
y1[1] (numeric) = 0.39291349446104515485371415221102
absolute error = 3.6e-31
relative error = 9.1623221160629209165826223691078e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.20536425024260294854257330725366
y2[1] (numeric) = 0.20536425024260294854257330725337
absolute error = 2.9e-31
relative error = 1.4121250395695175849235542699607e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4648
Order of pole (three term test) = -16.15
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.07
y1[1] (analytic) = 0.40089007359231477429214422696039
y1[1] (numeric) = 0.40089007359231477429214422696075
absolute error = 3.6e-31
relative error = 8.9800178082259541976266602087294e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.19933321782418249681262071972431
y2[1] (numeric) = 0.19933321782418249681262071972402
absolute error = 2.9e-31
relative error = 1.4548503413805728783891840148020e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.22
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4621
Order of pole (three term test) = -16.38
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1212505056, alloc=4783252, time=66.65
x[1] = 4.08
y1[1] (analytic) = 0.40892656321696855443800898175208
y1[1] (numeric) = 0.40892656321696855443800898175245
absolute error = 3.7e-31
relative error = 9.0480793688055214425136116047793e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.19338225141675953242356232661989
y2[1] (numeric) = 0.1933822514167595324235623266196
absolute error = 2.9e-31
relative error = 1.4996205591536879822251521282150e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4593
Order of pole (three term test) = -16.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1216506852, alloc=4783252, time=66.87
x[1] = 4.09
y1[1] (analytic) = 0.41702215969274108227696288635572
y1[1] (numeric) = 0.41702215969274108227696288635609
absolute error = 3.7e-31
relative error = 8.8724301910625883719922468838380e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.18751194611201567552941728764728
y2[1] (numeric) = 0.187511946112015675529417287647
absolute error = 2.8e-31
relative error = 1.4932381952493518190719216765739e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4563
Order of pole (three term test) = -16.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1220509304, alloc=4783252, time=67.09
x[1] = 4.1
y1[1] (analytic) = 0.42517605346673108846497132034021
y1[1] (numeric) = 0.42517605346673108846497132034058
absolute error = 3.7e-31
relative error = 8.7022774914803975431728603699651e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.18172288893558949573496297564155
y2[1] (numeric) = 0.18172288893558949573496297564126
absolute error = 2.9e-31
relative error = 1.5958363951763315128553036109532e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4531
Order of pole (three term test) = -17.07
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.11
y1[1] (analytic) = 0.43338742915635606283007600612553
y1[1] (numeric) = 0.4333874291563560628300760061259
absolute error = 3.7e-31
relative error = 8.5373957597305537262972735264238e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.17601565878837443742517601630396
y2[1] (numeric) = 0.17601565878837443742517601630367
absolute error = 2.9e-31
relative error = 1.6475806868334946820757192198711e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4498
Order of pole (three term test) = -17.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1224512204, alloc=4783252, time=67.31
x[1] = 4.12
y1[1] (analytic) = 0.4416554656308898331401917272407
y1[1] (numeric) = 0.44165546563088983314019172724108
absolute error = 3.8e-31
relative error = 8.6039917893279754971248773889396e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.17039082638862921283659693902778
y2[1] (numeric) = 0.1703908263886292128365969390275
absolute error = 2.8e-31
relative error = 1.6432809555214728273358986397609e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4462
Order of pole (three term test) = -17.52
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1228512956, alloc=4783252, time=67.53
x[1] = 4.13
y1[1] (analytic) = 0.44997933609357495344700530792948
y1[1] (numeric) = 0.44997933609357495344700530792986
absolute error = 3.8e-31
relative error = 8.4448322293843627016410109333337e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.16484895421490645178307012404365
y2[1] (numeric) = 0.16484895421490645178307012404337
absolute error = 2.8e-31
relative error = 1.6985245756243992314698909283482e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4425
Order of pole (three term test) = -17.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.14
y1[1] (analytic) = 0.45835820816430169083556922640269
y1[1] (numeric) = 0.45835820816430169083556922640308
absolute error = 3.9e-31
relative error = 8.5086291257208550914643867005897e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.15939059644980531512332717185912
y2[1] (numeric) = 0.15939059644980531512332717185885
absolute error = 2.7e-31
relative error = 1.6939518767973704185998985376723e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4386
Order of pole (three term test) = -17.96
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1232513736, alloc=4783252, time=67.75
TOP MAIN SOLVE Loop
x[1] = 4.15
y1[1] (analytic) = 0.46679124396284534274981382833728
y1[1] (numeric) = 0.46679124396284534274981382833767
absolute error = 3.9e-31
relative error = 8.3549125019800583713741735547117e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.15401629892455369666219427078778
y2[1] (numeric) = 0.15401629892455369666219427078751
absolute error = 2.7e-31
relative error = 1.7530612142047510707722802451133e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4345
Order of pole (three term test) = -18.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1236515020, alloc=4783252, time=67.98
x[1] = 4.16
y1[1] (analytic) = 0.47527760019265356123160978929078
y1[1] (numeric) = 0.47527760019265356123160978929118
absolute error = 4.0e-31
relative error = 8.4161340622377360117692175940059e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.14872659906442555521905209735327
y2[1] (numeric) = 0.148726599064425555219052097353
absolute error = 2.7e-31
relative error = 1.8154116459224694350760464244585e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4303
Order of pole (three term test) = -18.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1240517664, alloc=4783252, time=68.20
x[1] = 4.17
y1[1] (analytic) = 0.48381642822517530541077945724221
y1[1] (numeric) = 0.48381642822517530541077945724261
absolute error = 4.0e-31
relative error = 8.2675985490479065992038214279867e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.14352202583499883508485599858706
y2[1] (numeric) = 0.1435220258349988350848559985868
absolute error = 2.6e-31
relative error = 1.8115686319736800161906228019214e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4259
Order of pole (three term test) = -18.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.18
y1[1] (analytic) = 0.49240687418472298942108196695328
y1[1] (numeric) = 0.49240687418472298942108196695368
absolute error = 4.0e-31
relative error = 8.1233634413061179583939073332217e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.13840309968925934903088583719909
y2[1] (numeric) = 0.13840309968925934903088583719884
absolute error = 2.5e-31
relative error = 1.8063179261251836716180478632131e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4213
Order of pole (three term test) = -18.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1244518420, alloc=4783252, time=68.42
x[1] = 4.19
y1[1] (analytic) = 0.50104807903385933959809874850755
y1[1] (numeric) = 0.50104807903385933959809874850796
absolute error = 4.1e-31
relative error = 8.1828474582834079462273378125174e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.13337033251555591343684467407746
y2[1] (numeric) = 0.13337033251555591343684467407721
absolute error = 2.5e-31
relative error = 1.8744798433402777474359859883854e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4165
Order of pole (three term test) = -19.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1248519572, alloc=4783252, time=68.64
x[1] = 4.2
y1[1] (analytic) = 0.50973917865930042234445511862287
y1[1] (numeric) = 0.50973917865930042234445511862328
absolute error = 4.1e-31
relative error = 8.0433291605791181453482779819878e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.12842422758641193998142290209118
y2[1] (numeric) = 0.12842422758641193998142290209093
absolute error = 2.5e-31
relative error = 1.9466731838568715055974511445170e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4116
Order of pole (three term test) = -19.24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1252522136, alloc=4783252, time=68.86
x[1] = 4.21
y1[1] (analytic) = 0.51847930395832625243117705051315
y1[1] (numeric) = 0.51847930395832625243117705051356
absolute error = 4.1e-31
relative error = 7.9077409044075271291637418482172e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.1235652795081986026935019100478
y2[1] (numeric) = 0.12356527950819860269350191004756
absolute error = 2.4e-31
relative error = 1.9422931826417785093200288305506e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4065
Order of pole (three term test) = -19.44
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.22
y1[1] (analytic) = 0.52726758092569034074636158684479
y1[1] (numeric) = 0.52726758092569034074636158684521
absolute error = 4.2e-31
relative error = 7.9655949880823806030981670370110e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.11879397417167461300535326877877
y2[1] (numeric) = 0.11879397417167461300535326877853
absolute error = 2.4e-31
relative error = 2.0203044950172725736486774120930e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4013
Order of pole (three term test) = -19.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1256524052, alloc=4783252, time=69.08
x[1] = 4.23
y1[1] (analytic) = 0.53610313074101949060881041045516
y1[1] (numeric) = 0.53610313074101949060881041045558
absolute error = 4.2e-31
relative error = 7.8343135101535799528651749112202e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.11411078870339754878911140270074
y2[1] (numeric) = 0.1141107887033975487891114027005
absolute error = 2.4e-31
relative error = 2.1032191848556928798552565715362e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3959
Order of pole (three term test) = -19.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1260525260, alloc=4783252, time=69.30
x[1] = 4.24
y1[1] (analytic) = 0.54498506985669510273982813029406
y1[1] (numeric) = 0.54498506985669510273982813029448
absolute error = 4.2e-31
relative error = 7.7066331397012367151759248952173e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.10951619141801159620312567541779
y2[1] (numeric) = 0.10951619141801159620312567541756
absolute error = 2.3e-31
relative error = 2.1001460790588908012045204111776e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3903
Order of pole (three term test) = -20.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.25
y1[1] (analytic) = 0.55391251008620720083592227945516
y1[1] (numeric) = 0.55391251008620720083592227945558
absolute error = 4.2e-31
relative error = 7.5824248839339995682845419390173e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.10501064177141647553424717156172
y2[1] (numeric) = 0.1050106417714164755342471715615
absolute error = 2.2e-31
relative error = 2.0950257639496040122310348196034e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3846
Order of pole (three term test) = -20.24
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1264529400, alloc=4783252, time=69.52
TOP MAIN SOLVE Loop
x[1] = 4.26
y1[1] (analytic) = 0.56288455869297234241347586451402
y1[1] (numeric) = 0.56288455869297234241347586451444
absolute error = 4.2e-31
relative error = 7.4615654935578131135330933900657e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.10059459031482223410444018114688
y2[1] (numeric) = 0.10059459031482223410444018114667
absolute error = 2.1e-31
relative error = 2.0875874074617836654494539897547e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3787
Order of pole (three term test) = -20.43
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1268531728, alloc=4783252, time=69.75
x[1] = 4.27
y1[1] (analytic) = 0.57190031847960653320832267790571
y1[1] (numeric) = 0.57190031847960653320832267790613
absolute error = 4.2e-31
relative error = 7.3439371587791279374287098785601e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.09626847864969450072414018033867
y2[1] (numeric) = 0.096268478649694500724140180338464
absolute error = 2.06e-31
relative error = 2.1398489192874943422126235835263e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3727
Order of pole (three term test) = -20.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1272533004, alloc=4783252, time=69.97
x[1] = 4.28
y1[1] (analytic) = 0.58095888787764421791317926316396
y1[1] (numeric) = 0.58095888787764421791317926316438
absolute error = 4.2e-31
relative error = 7.2294272239184026770966441643116e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.09203273938359470712936747670058
y2[1] (numeric) = 0.09203273938359470712936747670037
absolute error = 2.10e-31
relative error = 2.2817966889447337580106622156532e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3665
Order of pole (three term test) = -20.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.29
y1[1] (analytic) = 0.59005936103769437542862536622075
y1[1] (numeric) = 0.59005936103769437542862536622117
absolute error = 4.2e-31
relative error = 7.1179279193431763092296473156832e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.08788779608691969234365311475198
y2[1] (numeric) = 0.087887796086919692343653114751774
absolute error = 2.06e-31
relative error = 2.3438976646572083353073097065253e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3601
Order of pole (three term test) = -20.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1276535412, alloc=4783252, time=70.19
x[1] = 4.3
y1[1] (analytic) = 0.59920082792002470309323760366397
y1[1] (numeric) = 0.59920082792002470309323760366438
absolute error = 4.1e-31
relative error = 6.8424471545410260059808363242554e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.08383406325054501596829063971536
y2[1] (numeric) = 0.083834063250545015968290639715166
absolute error = 1.94e-31
relative error = 2.3140951598661631277394736129995e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3537
Order of pole (three term test) = -21.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1280537300, alloc=4783252, time=70.41
x[1] = 4.31
y1[1] (analytic) = 0.60838237438556483154993990315575
y1[1] (numeric) = 0.60838237438556483154993990315617
absolute error = 4.2e-31
relative error = 6.9035530561545044511886461757627e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.07987194624437621603428757300901
y2[1] (numeric) = 0.079871946244376216034287573008812
absolute error = 1.98e-31
relative error = 2.4789680145541862337148671006393e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3471
Order of pole (three term test) = -21.34
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1284539528, alloc=4783252, time=70.63
x[1] = 4.32
y1[1] (analytic) = 0.61760308228731947000291984056992
y1[1] (numeric) = 0.61760308228731947000291984057034
absolute error = 4.2e-31
relative error = 6.8004841951972132245167517172568e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.07600184127681215625569090101602
y2[1] (numeric) = 0.076001841276812156255690901015829
absolute error = 1.91e-31
relative error = 2.5130970091151370665759427822845e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3403
Order of pole (three term test) = -21.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.33
y1[1] (analytic) = 0.62686202956218234062676254933714
y1[1] (numeric) = 0.62686202956218234062676254933756
absolute error = 4.2e-31
relative error = 6.7000389271198885036651632026841e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.07222413535512451631578081322702
y2[1] (numeric) = 0.072224135355124516315780813226838
absolute error = 1.82e-31
relative error = 2.5199332481463422733131484737321e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3334
Order of pole (three term test) = -21.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1288540484, alloc=4783252, time=70.85
x[1] = 4.34
y1[1] (analytic) = 0.63615829032314172081087264557633
y1[1] (numeric) = 0.63615829032314172081087264557675
absolute error = 4.2e-31
relative error = 6.6021304192492346760206398294526e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.06853920624675738720408708901116
y2[1] (numeric) = 0.06853920624675738720408708901098
absolute error = 1.80e-31
relative error = 2.6262340907765598798106125209627e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3264
Order of pole (three term test) = -21.84
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1292541340, alloc=4783252, time=71.07
x[1] = 4.35
y1[1] (analytic) = 0.64549093495186837276179742256413
y1[1] (numeric) = 0.64549093495186837276179742256455
absolute error = 4.2e-31
relative error = 6.5066754195598066390416899856545e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.06494742244155084161244420165858
y2[1] (numeric) = 0.064947422441550841612444201658405
absolute error = 1.75e-31
relative error = 2.6944872239924611408309682996957e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3193
Order of pole (three term test) = -22.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.36
y1[1] (analytic) = 0.65485903019167660174764743303657
y1[1] (numeric) = 0.654859030191676601747647433037
absolute error = 4.3e-31
relative error = 6.5662987020907296318770483799885e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.06144914311489225700156528111504
y2[1] (numeric) = 0.061449143114892257001565281114867
absolute error = 1.73e-31
relative error = 2.8153362476762233166727956686143e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.312
Order of pole (three term test) = -22.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1296544084, alloc=4783252, time=71.29
x[1] = 4.37
y1[1] (analytic) = 0.66426163924084914695625730757717
y1[1] (numeric) = 0.6642616392408491469562573075776
absolute error = 4.3e-31
relative error = 6.4733528868447850851381286449989e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.05804471809179907617512114959174
y2[1] (numeric) = 0.058044718091799076175121149591568
absolute error = 1.72e-31
relative error = 2.9632325843667288772617957631019e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3046
Order of pole (three term test) = -22.32
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1300545068, alloc=4783252, time=71.51
x[1] = 4.38
y1[1] (analytic) = 0.67369782184631657255577147615592
y1[1] (numeric) = 0.67369782184631657255577147615635
absolute error = 4.3e-31
relative error = 6.3826835423269524583332788278400e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.05473448781193659705533608906184
y2[1] (numeric) = 0.054734487811936597055336089061672
absolute error = 1.68e-31
relative error = 3.0693627859866855866884197699121e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2971
Order of pole (three term test) = -22.47
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1304547372, alloc=4783252, time=71.73
x[1] = 4.39
y1[1] (analytic) = 0.68316663439768179109661463324426
y1[1] (numeric) = 0.68316663439768179109661463324469
absolute error = 4.3e-31
relative error = 6.2942183992798804536187439574710e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.05151878329557428985197103638587
y2[1] (numeric) = 0.051518783295574289851971036385708
absolute error = 1.62e-31
relative error = 3.1444841985217569303061251035447e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2894
Order of pole (three term test) = -22.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.4
y1[1] (analytic) = 0.69266713002158031688086025778229
y1[1] (numeric) = 0.69266713002158031688086025778272
absolute error = 4.3e-31
relative error = 6.2078880513155457639396060811148e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.04839792611048404596460766661961
y2[1] (numeric) = 0.048397926110484045964607666619457
absolute error = 1.53e-31
relative error = 3.1612924828788658425991785533416e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2817
Order of pole (three term test) = -22.76
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1308548480, alloc=4783252, time=71.95
x[1] = 4.41
y1[1] (analytic) = 0.70219835867636681335229353350936
y1[1] (numeric) = 0.7021983586763668133522935335098
absolute error = 4.4e-31
relative error = 6.2660357228603223047942938833405e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.04537222833978366876575843546385
y2[1] (numeric) = 0.045372228339783668765758435463695
absolute error = 1.55e-31
relative error = 3.4161866337980046379817954074430e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2738
Order of pole (three term test) = -22.9
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1312549612, alloc=4783252, time=72.18
x[1] = 4.42
y1[1] (analytic) = 0.71175936724711846593133485650678
y1[1] (numeric) = 0.71175936724711846593133485650722
absolute error = 4.4e-31
relative error = 6.1818645492758890744428228894235e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.04244199255072882188892726816111
y2[1] (numeric) = 0.042441992550728821888927268160961
absolute error = 1.49e-31
relative error = 3.5106740057481430366945102182752e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2658
Order of pole (three term test) = -23.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1316550884, alloc=4783252, time=72.40
x[1] = 4.43
y1[1] (analytic) = 0.72134919964094568003670965106636
y1[1] (numeric) = 0.72134919964094568003670965106679
absolute error = 4.3e-31
relative error = 5.9610518763177964676708345697616e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03960751176445655580078546569952
y2[1] (numeric) = 0.039607511764456555800785465699381
absolute error = 1.39e-31
relative error = 3.5094353017332792366399151783206e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2577
Order of pole (three term test) = -23.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.44
y1[1] (analytic) = 0.73096689688260057330348764383661
y1[1] (numeric) = 0.73096689688260057330348764383705
absolute error = 4.4e-31
relative error = 6.0194244346289144988031004923516e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03686906942668343827959196692216
y2[1] (numeric) = 0.03686906942668343827959196692202
absolute error = 1.40e-31
relative error = 3.7972208731332147807823851637306e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2495
Order of pole (three term test) = -23.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1320551776, alloc=4783252, time=72.62
x[1] = 4.45
y1[1] (analytic) = 0.74061149721037370122794327025554
y1[1] (numeric) = 0.74061149721037370122794327025598
absolute error = 4.4e-31
relative error = 5.9410365847320381856552541821785e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03422693937936121896239198130831
y2[1] (numeric) = 0.034226939379361218962391981308172
absolute error = 1.38e-31
relative error = 4.0319117777505325043449875769916e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2413
Order of pole (three term test) = -23.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1324553988, alloc=4783252, time=72.84
x[1] = 4.46
y1[1] (analytic) = 0.75028203617226942664658639888734
y1[1] (numeric) = 0.75028203617226942664658639888778
absolute error = 4.4e-31
relative error = 5.8644613463592677651042958050628e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03168138583329286237091907175356
y2[1] (numeric) = 0.03168138583329286237091907175343
absolute error = 1.30e-31
relative error = 4.1033558533095335216321412618200e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2329
Order of pole (three term test) = -23.53
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.47
y1[1] (analytic) = 0.75997754672245031559256134466984
y1[1] (numeric) = 0.75997754672245031559256134467028
absolute error = 4.4e-31
relative error = 5.7896447322369565587489086313026e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02923266334171168779007820072841
y2[1] (numeric) = 0.029232663341711687790078200728287
absolute error = 1.23e-31
relative error = 4.2076220891065023514485241837420e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2244
Order of pole (three term test) = -23.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1328555956, alloc=4783252, time=73.06
x[1] = 4.48
y1[1] (analytic) = 0.76969705931794091517019859315115
y1[1] (numeric) = 0.76969705931794091517019859315159
absolute error = 4.4e-31
relative error = 5.7165347674564515965399282909592e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02688101677482625806300458146732
y2[1] (numeric) = 0.026881016774826258063004581467194
absolute error = 1.26e-31
relative error = 4.6873226952485462493966643605897e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2158
Order of pole (three term test) = -23.76
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1332557916, alloc=4783252, time=73.28
x[1] = 4.49
y1[1] (analytic) = 0.7794396020155812431505179934839
y1[1] (numeric) = 0.77943960201558124315051799348435
absolute error = 4.5e-31
relative error = 5.7733787048583189420744622027995e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02462668129533356279260630634082
y2[1] (numeric) = 0.0246266812953335627926063063407
absolute error = 1.20e-31
relative error = 4.8727637541132448928485309732809e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2072
Order of pole (three term test) = -23.86
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1336558560, alloc=4783252, time=73.50
x[1] = 4.5
y1[1] (analytic) = 0.78920420056922029401951817520617
y1[1] (numeric) = 0.78920420056922029401951817520662
absolute error = 4.5e-31
relative error = 5.7019463362642221493349440092524e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02246988233490294461086498550137
y2[1] (numeric) = 0.022469882334902944610864985501257
absolute error = 1.13e-31
relative error = 5.0289537931613778104520405686489e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1984
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.51
y1[1] (analytic) = 0.79898987852713984220964167825923
y1[1] (numeric) = 0.79898987852713984220964167825968
absolute error = 4.5e-31
relative error = 5.6321113958230766066083989270203e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02041083557163312010367080295234
y2[1] (numeric) = 0.020410835571633120103670802952228
absolute error = 1.12e-31
relative error = 5.4872814788463170350451079444087e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1896
Order of pole (three term test) = -24.06
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1340561228, alloc=4783252, time=73.72
x[1] = 4.52
y1[1] (analytic) = 0.80879565732969880021527888180112
y1[1] (numeric) = 0.80879565732969880021527888180156
absolute error = 4.4e-31
relative error = 5.4401874690165116929146189017453e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01844974690848454967031375325789
y2[1] (numeric) = 0.018449746908484549670313753257788
absolute error = 1.02e-31
relative error = 5.5285311232693876727786110089430e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1807
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1344564012, alloc=4783252, time=73.94
x[1] = 4.53
y1[1] (analytic) = 0.8186205564071883672378692086186
y1[1] (numeric) = 0.81862055640718836723786920861904
absolute error = 4.4e-31
relative error = 5.3748955673810432019545480321644e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01658681245268931306267214456304
y2[1] (numeric) = 0.016586812452689313062672144562942
absolute error = 9.8e-32
relative error = 5.9083081984272818846321847533861e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1718
Order of pole (three term test) = -24.24
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1348566848, alloc=4783252, time=74.16
x[1] = 4.54
y1[1] (analytic) = 0.8284635932778881829272807804022
y1[1] (numeric) = 0.82846359327788818292728078040264
absolute error = 4.4e-31
relative error = 5.3110360379157009570151396499770e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01482221849614054959938606921746
y2[1] (numeric) = 0.014822218496140549599386069217364
absolute error = 9.6e-32
relative error = 6.4767632473503711006330107070854e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1627
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.55
y1[1] (analytic) = 0.83832378364631368068580757499206
y1[1] (numeric) = 0.8383237836463136806858075749925
absolute error = 4.4e-31
relative error = 5.2485687342211287629103230865803e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01315614149676342409465234597491
y2[1] (numeric) = 0.013156141496763424094652345974816
absolute error = 9.4e-32
relative error = 7.1449520380367738984241266513188e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1536
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1352568688, alloc=4783252, time=74.38
x[1] = 4.56
y1[1] (analytic) = 0.8482001415016448158813262073901
y1[1] (numeric) = 0.84820014150164481588132620739054
absolute error = 4.4e-31
relative error = 5.1874549233277481029027235742575e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01158874806086948138952391096191
y2[1] (numeric) = 0.011588748060869481389523910961824
absolute error = 8.6e-32
relative error = 7.4209914261910001401057656147251e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1445
Order of pole (three term test) = -24.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1356570212, alloc=4783252, time=74.60
x[1] = 4.57
y1[1] (analytic) = 0.85809167921632632617881468562541
y1[1] (numeric) = 0.85809167921632632617881468562585
absolute error = 4.4e-31
relative error = 5.1276572265779455836794602739520e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01012019492649615403555587193493
y2[1] (numeric) = 0.010120194926496154035555871934845
absolute error = 8.5e-32
relative error = 8.3990477078121823703045430642831e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1353
Order of pole (three term test) = -24.55
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.58
y1[1] (analytic) = 0.8679974076448296640463665993177
y1[1] (numeric) = 0.86799740764482966404636659931814
absolute error = 4.4e-31
relative error = 5.0691395633757560733637833810330e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00875062894773308916614616390269
y2[1] (numeric) = 0.0087506289477330891661461639026128
absolute error = 7.72e-32
relative error = 8.8222230037532551195514679146174e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.126
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1360572592, alloc=4783252, time=74.82
x[1] = 4.59
y1[1] (analytic) = 0.8779163362225667253247514756035
y1[1] (numeric) = 0.87791633622256672532475147560393
absolute error = 4.3e-31
relative error = 4.8979610272451711769921848316377e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00748018708003686190982232131219
y2[1] (numeric) = 0.0074801870800368619098223213121139
absolute error = 7.61e-32
relative error = 1.0173542344027174224035704588322e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1167
Order of pole (three term test) = -24.68
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1364573260, alloc=4783252, time=75.05
x[1] = 4.6
y1[1] (analytic) = 0.88784747306494548257009217877081
y1[1] (numeric) = 0.88784747306494548257009217877125
absolute error = 4.4e-31
relative error = 4.9558061868563123968825762260306e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00630899636653554386189534009117
y2[1] (numeric) = 0.0063089963665355438618953400911031
absolute error = 6.69e-32
relative error = 1.0603905298607227570752324932856e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1073
Order of pole (three term test) = -24.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1368576584, alloc=4783252, time=75.27
x[1] = 4.61
y1[1] (analytic) = 0.89778982506655761768887117182731
y1[1] (numeric) = 0.89778982506655761768887117182775
absolute error = 4.4e-31
relative error = 4.9009243334583416022693216929191e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00523717392532449614622064259686
y2[1] (numeric) = 0.0052371739253244961462206425968008
absolute error = 5.92e-32
relative error = 1.1303806374223471754175158213830e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09791
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.62
y1[1] (analytic) = 0.90774239800048823518465822438418
y1[1] (numeric) = 0.90774239800048823518465822438462
absolute error = 4.4e-31
relative error = 4.8471901386252462245655675308211e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00426482693775465747717316554853
y2[1] (numeric) = 0.0042648269377546574771731655484757
absolute error = 5.43e-32
relative error = 1.2732052388645767331202731273528e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08846
Order of pole (three term test) = -24.83
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1372577372, alloc=4783252, time=75.49
x[1] = 4.63
y1[1] (analytic) = 0.91770419661773772512799271259738
y1[1] (numeric) = 0.91770419661773772512799271259782
absolute error = 4.4e-31
relative error = 4.7945732581549743971616731949714e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.0033920526377144983832706460193
y2[1] (numeric) = 0.0033920526377144983832706460192417
absolute error = 5.83e-32
relative error = 1.7187233285177275273763802350198e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07898
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1376579172, alloc=4783252, time=75.71
x[1] = 4.64
y1[1] (analytic) = 0.92767422474674583374597479923988
y1[1] (numeric) = 0.92767422474674583374597479924032
absolute error = 4.4e-31
relative error = 4.7430443604285715117353767985177e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00261893830190671338809106811717
y2[1] (numeric) = 0.0026189383019067133880910681171192
absolute error = 5.08e-32
relative error = 1.9397173260254031205527662248560e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06947
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1380581020, alloc=4783252, time=75.93
x[1] = 4.65
y1[1] (analytic) = 0.93765148539300798930744298382293
y1[1] (numeric) = 0.93765148539300798930744298382336
absolute error = 4.3e-31
relative error = 4.5859256525335685680531490822209e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00194556124112062347116344910397
y2[1] (numeric) = 0.0019455612411206234711634491039292
absolute error = 4.08e-32
relative error = 2.0970812502668697953779931606214e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05992
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.66
y1[1] (analytic) = 0.94763498083877392175416283320404
y1[1] (numeric) = 0.94763498083877392175416283320448
absolute error = 4.4e-31
relative error = 4.6431380109094927261376758092147e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00137198879250116156131290216748
y2[1] (numeric) = 0.0013719887925011615613129021674358
absolute error = 4.42e-32
relative error = 3.2216006604122882536646122148595e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05036
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1384581956, alloc=4783252, time=76.15
x[1] = 4.67
y1[1] (analytic) = 0.95762371274281860629914567989472
y1[1] (numeric) = 0.95762371274281860629914567989516
absolute error = 4.4e-31
relative error = 4.5947066070425023496110046093238e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00089827831281521415746815072662
y2[1] (numeric) = 0.00089827831281521415746815072658099
absolute error = 3.901e-32
relative error = 4.3427520673122151838761111124668e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04077
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1388582896, alloc=4783252, time=76.38
x[1] = 4.68
y1[1] (analytic) = 0.96761668224027555398087963205543
y1[1] (numeric) = 0.96761668224027555398087963205587
absolute error = 4.4e-31
relative error = 4.5472552104133791021447932829057e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00052447717271599243715805024033
y2[1] (numeric) = 0.00052447717271599243715805024029498
absolute error = 3.502e-32
relative error = 6.6771256828299640639840157891958e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03117
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.69
y1[1] (analytic) = 0.97761289004252246592761160355799
y1[1] (numeric) = 0.97761289004252246592761160355843
absolute error = 4.4e-31
relative error = 4.5007589863188246519088614301831e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00025062275200600641080659305708
y2[1] (numeric) = 0.00025062275200600641080659305705549
absolute error = 2.451e-32
relative error = 9.7796388411745613246629416672938e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02155
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1392584924, alloc=4783252, time=76.59
x[1] = 4.7
y1[1] (analytic) = 0.98761133653710926284949170367289
y1[1] (numeric) = 0.98761133653710926284949170367333
absolute error = 4.4e-31
relative error = 4.4551938978625434587635146898843e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 7.674243589911582046345842503e-05
y2[1] (numeric) = 7.6742435899115820463458425004950e-05
absolute error = 2.5050e-32
relative error = 3.2641653482214539427303416338765e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01193
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1396586548, alloc=4783252, time=76.81
x[1] = 4.71
y1[1] (analytic) = 0.9976110218877184970389038522753
y1[1] (numeric) = 0.99761102188771849703890385227575
absolute error = 4.5e-31
relative error = 4.5107761454809555273093822891541e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 2.85361228203157476528740643e-06
y2[1] (numeric) = 2.8536122820315747652874064070820e-06
absolute error = 2.29180e-32
relative error = 8.0312241940884721707618150165526e-25 %
Correct digits = 27
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0023
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1400587464, alloc=4783252, time=77.03
x[1] = 4.72
y1[1] (analytic) = 1.0076109461341481509210826531746
y1[1] (numeric) = 1.0076109461341481509210826531751
absolute error = 5e-31
relative error = 4.9622327141078176188871323475169e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 2.896366997554156770211203836e-05
y2[1] (numeric) = 2.8963669975541567702112038345742e-05
absolute error = 1.4258e-32
relative error = 4.9227187065866301544864890041506e-26 %
Correct digits = 28
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007339
Order of pole (three term test) = -0.8943
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.73
y1[1] (analytic) = 1.0176101092923068239584801849428
y1[1] (numeric) = 1.0176101092923068239584801849433
absolute error = 5e-31
relative error = 4.9134731999441627543022091838329e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00015506999799563475715808844232
y2[1] (numeric) = 0.00015506999799563475715808844230866
absolute error = 1.134e-32
relative error = 7.3128265599895233363911888809881e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01698
Order of pole (three term test) = -0.9004
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1404589200, alloc=4783252, time=77.24
x[1] = 4.74
y1[1] (analytic) = 1.027607511454211308473521317219
y1[1] (numeric) = 1.0276075114542113084735213172195
absolute error = 5e-31
relative error = 4.8656709339583225744690083100827e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00038115998581459739020295192723
y2[1] (numeric) = 0.00038115998581459739020295192722415
absolute error = 5.85e-33
relative error = 1.5347885973648708535690781425278e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02661
Order of pole (three term test) = -0.9113
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1408590400, alloc=4783252, time=77.47
x[1] = 4.75
y1[1] (analytic) = 1.0376021528879765547154963123733
y1[1] (numeric) = 1.0376021528879765547154963123738
absolute error = 5e-31
relative error = 4.8188026461620293829220241435298e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00070721102462205526572924440292
y2[1] (numeric) = 0.00070721102462205526572924440292029
absolute error = 2.9e-34
relative error = 4.1006148080762821450430809075312e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03623
Order of pole (three term test) = -0.927
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1412591980, alloc=4783252, time=77.69
x[1] = 4.76
y1[1] (analytic) = 1.0475930341377880262584087164105
y1[1] (numeric) = 1.047593034137788026258408716411
absolute error = 5e-31
relative error = 4.7728457875010640814403009420407e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00113319050958583593125991543056
y2[1] (numeric) = 0.0011331905095858359312599154305679
absolute error = 7.9e-33
relative error = 6.9714667861870207942824880661780e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04584
Order of pole (three term test) = -0.9476
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.77
y1[1] (analytic) = 1.0575791561238464485775487727873
y1[1] (numeric) = 1.0575791561238464485775487727877
absolute error = 4e-31
relative error = 3.7822228027455423281346723107060e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00165905584311242472959066170051
y2[1] (numeric) = 0.0016590558431124247295906617005233
absolute error = 1.33e-32
relative error = 8.0166077924471256249930463996881e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05543
Order of pole (three term test) = -0.973
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1416594300, alloc=4783252, time=77.91
x[1] = 4.78
y1[1] (analytic) = 1.0675595202422749564132217146596
y1[1] (numeric) = 1.06755952024227495641322171466
absolute error = 4e-31
relative error = 3.7468636868998449506310026169618e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00228475443910668865237937835233
y2[1] (numeric) = 0.0022847544391066886523793783523408
absolute error = 1.08e-32
relative error = 4.7269850164828520281841680006276e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.065
Order of pole (three term test) = -1.003
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1420596484, alloc=4783252, time=78.13
x[1] = 4.79
y1[1] (analytic) = 1.0775331284649786492901502413476
y1[1] (numeric) = 1.077533128464978649290150241348
absolute error = 4e-31
relative error = 3.7121828501906757454238376321981e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00301022372823044203184712123726
y2[1] (numeric) = 0.0030102237282304420318471212372798
absolute error = 1.98e-32
relative error = 6.5775841889464529976137641968191e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07454
Order of pole (three term test) = -1.038
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.8
y1[1] (analytic) = 1.0874989834394465693202152576495
y1[1] (numeric) = 1.0874989834394465693202152576499
absolute error = 4e-31
relative error = 3.6781643577717656510041120214023e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00383539116415932821840353349637
y2[1] (numeric) = 0.0038353911641593282184035334963873
absolute error = 1.73e-32
relative error = 4.5106220616201353440439825113456e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08405
Order of pole (three term test) = -1.078
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1424597196, alloc=4783252, time=78.35
x[1] = 4.81
y1[1] (analytic) = 1.0974560885884861211739226395384
y1[1] (numeric) = 1.0974560885884861211739226395388
absolute error = 4e-31
relative error = 3.6447927544369229007899929081408e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00476017423083739156124302459597
y2[1] (numeric) = 0.0047601742308373915612430245959988
absolute error = 2.88e-32
relative error = 6.0501987119353012956380719744231e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09353
Order of pole (three term test) = -1.122
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1428598548, alloc=4783252, time=78.57
x[1] = 4.82
y1[1] (analytic) = 1.1074034482098799608617106191698
y1[1] (numeric) = 1.1074034482098799608617106191702
absolute error = 4e-31
relative error = 3.6120530475735907657611268381448e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00578448045072861424075909870166
y2[1] (numeric) = 0.0057844804507286142407590987016902
absolute error = 3.02e-32
relative error = 5.2208664645406489955090219257734e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.103
Order of pole (three term test) = -1.172
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1432599200, alloc=4783252, time=78.79
x[1] = 4.83
y1[1] (analytic) = 1.1173400675759553877192667889538
y1[1] (numeric) = 1.1173400675759553877192667889543
absolute error = 5e-31
relative error = 4.4749133635271754187434660667638e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.0069082073940645928059698487306
y2[1] (numeric) = 0.0069082073940645928059698487306335
absolute error = 3.35e-32
relative error = 4.8493043258635511987917523623896e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1124
Order of pole (three term test) = -1.226
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.84
y1[1] (analytic) = 1.1272649530330562827406304097327
y1[1] (numeric) = 1.1272649530330562827406304097332
absolute error = 5e-31
relative error = 4.4355144605062323621209495972152e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00813124268908742965700724495948
y2[1] (numeric) = 0.0081312426890874296570072449595232
absolute error = 4.32e-32
relative error = 5.3128410566292347603406893111553e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1217
Order of pole (three term test) = -1.284
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1436600496, alloc=4783252, time=79.01
x[1] = 4.85
y1[1] (analytic) = 1.1371771121009076461481397184653
y1[1] (numeric) = 1.1371771121009076461481397184658
absolute error = 5e-31
relative error = 4.3968524751281873902806729849140e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.00945346403328681519205768370882
y2[1] (numeric) = 0.0094534640332868151920576837088641
absolute error = 4.41e-32
relative error = 4.6649566597723807682769034270286e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.131
Order of pole (three term test) = -1.348
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1440601908, alloc=4783252, time=79.23
x[1] = 4.86
y1[1] (analytic) = 1.1470755535718627978282707459854
y1[1] (numeric) = 1.1470755535718627978282707459859
absolute error = 5e-31
relative error = 4.3589107835404291663434573502654e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01087473920563017691990330595709
y2[1] (numeric) = 0.01087473920563017691990330595714
absolute error = 5.0e-32
relative error = 4.5978114099613081587802828122255e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1403
Order of pole (three term test) = -1.416
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1444602736, alloc=4783252, time=79.45
x[1] = 4.87
y1[1] (analytic) = 1.156959287610023315996029785628
y1[1] (numeric) = 1.1569592876100233159960297856285
absolute error = 5e-31
relative error = 4.3216732460212133253836905413410e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01239492607978467253334458870749
y2[1] (numeric) = 0.012394926079784672533344588707546
absolute error = 5.6e-32
relative error = 4.5179777305273646859150951794440e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1495
Order of pole (three term test) = -1.488
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.88
y1[1] (analytic) = 1.1668273258502218021766327470316
y1[1] (numeric) = 1.1668273258502218021766327470321
absolute error = 5e-31
relative error = 4.2851241903824064013091106717644e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01401387263832970475521515768158
y2[1] (numeric) = 0.014013872638329704755215157681636
absolute error = 5.6e-32
relative error = 3.9960403127136288240374723786773e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1586
Order of pole (three term test) = -1.566
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1448605056, alloc=4783252, time=79.67
x[1] = 4.89
y1[1] (analytic) = 1.1766786814968575743104585897138
y1[1] (numeric) = 1.1766786814968575743104585897143
absolute error = 5e-31
relative error = 4.2492483960357642863617610448281e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.0157314169879585367173479427511
y2[1] (numeric) = 0.015731416987958536717347942751164
absolute error = 6.4e-32
relative error = 4.0682921347128609179482733013644e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1677
Order of pole (three term test) = -1.648
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1452606164, alloc=4783252, time=79.89
x[1] = 4.9
y1[1] (analytic) = 1.1865123694225754044943291441219
y1[1] (numeric) = 1.1865123694225754044943291441224
absolute error = 5e-31
relative error = 4.2140310786926605670891027960234e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01754738737566748772362275008167
y2[1] (numeric) = 0.017547387375667487723622750081738
absolute error = 6.8e-32
relative error = 3.8752207690071205093208261215615e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1767
Order of pole (three term test) = -1.734
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.91
y1[1] (analytic) = 1.1963274062667774335675731995194
y1[1] (numeric) = 1.1963274062667774335675731995199
absolute error = 5e-31
relative error = 4.1794578756687071617795244809446e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.01946160220593109049100989773031
y2[1] (numeric) = 0.019461602205931090491009897730382
absolute error = 7.2e-32
relative error = 3.6995926254240969614894705893939e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1856
Order of pole (three term test) = -1.825
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1456606852, alloc=4783252, time=80.12
x[1] = 4.92
y1[1] (analytic) = 1.2061228105339584114335092408118
y1[1] (numeric) = 1.2061228105339584114335092408123
absolute error = 5e-31
relative error = 4.1455148317661511482865452331360e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02147387005886149236719839365887
y2[1] (numeric) = 0.021473870058861492367198393658951
absolute error = 8.1e-32
relative error = 3.7720261777673474752559620323968e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1945
Order of pole (three term test) = -1.92
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1460608256, alloc=4783252, time=80.34
x[1] = 4.93
y1[1] (analytic) = 1.2158976026918544296742604464858
y1[1] (numeric) = 1.2158976026918544296742604464863
absolute error = 5e-31
relative error = 4.1121883857082927692891949371220e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02358398970935028459981967725086
y2[1] (numeric) = 0.023583989709350284599819677250947
absolute error = 8.7e-32
relative error = 3.6889432649941892825587654175736e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2033
Order of pole (three term test) = -2.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1464609176, alloc=4783252, time=80.56
x[1] = 4.94
y1[1] (analytic) = 1.2256508052693953316674308040397
y1[1] (numeric) = 1.2256508052693953316674308040403
absolute error = 6e-31
relative error = 4.8953584285217462836141418821301e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02579175014719084549029147317684
y2[1] (numeric) = 0.025791750147190845490291473176932
absolute error = 9.2e-32
relative error = 3.5670320732391378347318039674276e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.212
Order of pole (three term test) = -2.124
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.95
y1[1] (analytic) = 1.2353814429544510050452574116347
y1[1] (numeric) = 1.2353814429544510050452574116353
absolute error = 6e-31
relative error = 4.8567995206815020426559199643075e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.02809693059817918521473493662265
y2[1] (numeric) = 0.02809693059817918521473493662274
absolute error = 9.0e-32
relative error = 3.2031968647077922529863330700693e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2206
Order of pole (three term test) = -2.232
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1468610576, alloc=4783252, time=80.78
x[1] = 4.96
y1[1] (analytic) = 1.2450885426913617819484480229353
y1[1] (numeric) = 1.2450885426913617819484480229359
absolute error = 6e-31
relative error = 4.8189343924332514910852705673234e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03049930054619118224506697690327
y2[1] (numeric) = 0.030499300546191182245066976903365
absolute error = 9.5e-32
relative error = 3.1148255303797057989786881840664e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2291
Order of pole (three term test) = -2.345
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1472613464, alloc=4783252, time=81.01
x[1] = 4.97
y1[1] (analytic) = 1.2547711337782431941159535140125
y1[1] (numeric) = 1.2547711337782431941159535140131
absolute error = 6e-31
relative error = 4.7817485105298774559121332554296e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03299861975623400366502328592209
y2[1] (numeric) = 0.0329986197562340036650232859222
absolute error = 1.10e-31
relative error = 3.3334727577270597389478458271213e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2375
Order of pole (three term test) = -2.462
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1476614856, alloc=4783252, time=81.23
x[1] = 4.98
y1[1] (analytic) = 1.2644282479640553524162533206808
y1[1] (numeric) = 1.2644282479640553524162533206813
absolute error = 5e-31
relative error = 3.9543564516617299972528736922544e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03559463829846940425828992207108
y2[1] (numeric) = 0.035594638298469404258289922071189
absolute error = 1.09e-31
relative error = 3.0622589583860746948991827418206e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2459
Order of pole (three term test) = -2.583
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.99
y1[1] (analytic) = 1.274058919545427243963091597697
y1[1] (numeric) = 1.2740589195454272439630915976975
absolute error = 5e-31
relative error = 3.9244652843715854210949373177312e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.03828709657320650205885398558889
y2[1] (numeric) = 0.03828709657320650205885398558901
absolute error = 1.20e-31
relative error = 3.1342151988609287359174902862106e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2541
Order of pole (three term test) = -2.709
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1480617184, alloc=4783252, time=81.45
x[1] = 5
y1[1] (analytic) = 1.2836621854632262644666391715136
y1[1] (numeric) = 1.2836621854632262644666391715141
absolute error = 5e-31
relative error = 3.8951057814293132730758830428766e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.04107572533686153110684559384401
y2[1] (numeric) = 0.041075725336861531106845593844128
absolute error = 1.18e-31
relative error = 2.8727429408070926193838448159792e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2623
Order of pole (three term test) = -2.838
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1484619148, alloc=4783252, time=81.67
x[1] = 5.01
y1[1] (analytic) = 1.2932370853988633289473205124347
y1[1] (numeric) = 1.2932370853988633289473205124352
absolute error = 5e-31
relative error = 3.8662671032650504548376666572480e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.0439602457288819754562286275313
y2[1] (numeric) = 0.04396024572888197545622862753143
absolute error = 1.30e-31
relative error = 2.9572173186145254412224780396633e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2703
Order of pole (three term test) = -2.972
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.02
y1[1] (analytic) = 1.3027826618703239303814883348922
y1[1] (numeric) = 1.3027826618703239303814883348927
absolute error = 5e-31
relative error = 3.8379387033151112096107023167685e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.0469403692996323920433761822583
y2[1] (numeric) = 0.046940369299632392043376182258432
absolute error = 1.32e-31
relative error = 2.8120784299205277536129013553710e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2782
Order of pole (three term test) = -3.109
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1488621592, alloc=4783252, time=81.89
x[1] = 5.03
y1[1] (analytic) = 1.3122979603279155432531068738344
y1[1] (numeric) = 1.3122979603279155432531068738349
absolute error = 5e-31
relative error = 3.8101103188109852772710456218954e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.0500157980392391338574819762391
y2[1] (numeric) = 0.05001579803923913385748197623924
absolute error = 1.40e-31
relative error = 2.7991155892417257585529153533839e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.286
Order of pole (three term test) = -3.251
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1492622792, alloc=4783252, time=82.11
x[1] = 5.04
y1[1] (analytic) = 1.3217820292497217973508779058944
y1[1] (numeric) = 1.321782029249721797350877905895
absolute error = 6e-31
relative error = 4.5393263542898654919180527042144e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.05318622440739108896452786213993
y2[1] (numeric) = 0.053186224407391088964527862140075
absolute error = 1.45e-31
relative error = 2.7262698493004872329781342977945e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2937
Order of pole (three term test) = -3.396
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1496624844, alloc=4783252, time=82.34
x[1] = 5.05
y1[1] (analytic) = 1.3312339202367538764729746824182
y1[1] (numeric) = 1.3312339202367538764729746824187
absolute error = 5e-31
relative error = 3.7559139111410057984689836519205e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.05645133136409345533573891273199
y2[1] (numeric) = 0.056451331364093455335738912732141
absolute error = 1.51e-31
relative error = 2.6748704831440938605413837941484e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3013
Order of pole (three term test) = -3.545
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.06
y1[1] (analytic) = 1.3406526881077896269788058689017
y1[1] (numeric) = 1.3406526881077896269788058689022
absolute error = 5e-31
relative error = 3.7295267031889139865400928720905e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.05981079240137147612867129510649
y2[1] (numeric) = 0.059810792401371476128671295106643
absolute error = 1.53e-31
relative error = 2.5580667611501444094148981951943e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3088
Order of pole (three term test) = -3.698
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1500626028, alloc=4783252, time=82.56
x[1] = 5.07
y1[1] (analytic) = 1.3500373909938908923559866414642
y1[1] (numeric) = 1.3500373909938908923559866414648
absolute error = 6e-31
relative error = 4.4443213499315226281249853422689e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.06326427157592096507382451599952
y2[1] (numeric) = 0.063264271575920965073824515999677
absolute error = 1.57e-31
relative error = 2.4816534844883256496334889128487e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3161
Order of pole (three term test) = -3.855
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1504627640, alloc=4783252, time=82.78
x[1] = 5.08
y1[1] (analytic) = 1.359387090432589622147824426171
y1[1] (numeric) = 1.3593870904325896221478244261716
absolute error = 6e-31
relative error = 4.4137538470301758501029385064361e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.06681142354270235694144805746205
y2[1] (numeric) = 0.066811423542702356941448057462216
absolute error = 1.66e-31
relative error = 2.4846050450324787423291537558153e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3233
Order of pole (three term test) = -4.015
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.09
y1[1] (analytic) = 1.3687008514617333367089146951106
y1[1] (numeric) = 1.3687008514617333367089146951112
absolute error = 6e-31
relative error = 4.3837190527003557584565438920484e-29 %
Correct digits = 31
h = 0.01
bytes used=1508628956, alloc=4783252, time=83.00
y2[1] (analytic) = 0.07045189358947492371149067095049
y2[1] (numeric) = 0.070451893589474923711490670950663
absolute error = 1.73e-31
relative error = 2.4555762973253160062911952399451e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3304
Order of pole (three term test) = -4.179
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.1
y1[1] (analytic) = 1.377977742712980563320575552929
y1[1] (numeric) = 1.3779777427129805633205755529296
absolute error = 6e-31
relative error = 4.3542067582217414457401342162547e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.07418531767226770305385375245514
y2[1] (numeric) = 0.074185317672267703053853752455314
absolute error = 1.74e-31
relative error = 2.3454775885531522225493825482253e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3374
Order of pole (three term test) = -4.346
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1512629908, alloc=4783252, time=83.22
x[1] = 5.11
y1[1] (analytic) = 1.3872168365049368942004221740824
y1[1] (numeric) = 1.387216836504936894200422174083
absolute error = 6e-31
relative error = 4.3252070203508137067983205634490e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.07801132245178359205565978186573
y2[1] (numeric) = 0.078011322451783592055659781865911
absolute error = 1.81e-31
relative error = 2.3201760246004104558644155287595e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3442
Order of pole (three term test) = -4.517
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1516632076, alloc=4783252, time=83.44
x[1] = 5.12
y1[1] (analytic) = 1.3964172089359223528778932563282
y1[1] (numeric) = 1.3964172089359223528778932563289
absolute error = 7e-31
relative error = 5.0128285122854070015216058822684e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.08192952533073296581649974338058
y2[1] (numeric) = 0.081929525330732965816499743380773
absolute error = 1.93e-31
relative error = 2.3556831218159501669018580610545e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3509
Order of pole (three term test) = -4.691
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.13
y1[1] (analytic) = 1.4055779399763607922763978187695
y1[1] (numeric) = 1.4055779399763607922763978187702
absolute error = 7e-31
relative error = 4.9801578417755524718309527606857e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.08593953449209308758091124734233
y2[1] (numeric) = 0.085939534492093087580911247342525
absolute error = 1.95e-31
relative error = 2.2690371917006494647749358249609e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3574
Order of pole (three term test) = -4.869
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1520633292, alloc=4783252, time=83.66
x[1] = 5.14
y1[1] (analytic) = 1.4146981135607820856392650382033
y1[1] (numeric) = 1.414698113560782085639265038204
absolute error = 7e-31
relative error = 4.9480521200251441999912476419366e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.09004094893828948449895684118915
y2[1] (numeric) = 0.090040948938289484498956841189355
absolute error = 2.05e-31
relative error = 2.2767418870773887058249846832453e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3638
Order of pole (three term test) = -5.05
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1524634088, alloc=4783252, time=83.88
x[1] = 5.15
y1[1] (analytic) = 1.4237768176794279101570727656681
y1[1] (numeric) = 1.4237768176794279101570727656688
absolute error = 7e-31
relative error = 4.9165008961229575006219556173388e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.09423335853129537090997748932069
y2[1] (numeric) = 0.094233358531295370909977489320898
absolute error = 2.08e-31
relative error = 2.2072862863199570348021733001731e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.37
Order of pole (three term test) = -5.234
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1528636164, alloc=4783252, time=84.10
x[1] = 5.16
y1[1] (analytic) = 1.4328131444694519627943298888998
y1[1] (numeric) = 1.4328131444694519627943298889005
absolute error = 7e-31
relative error = 4.8854939857436813541492294296509e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.09851634403364510924060892121324
y2[1] (numeric) = 0.098516344033645109240608921213462
absolute error = 2.22e-31
relative error = 2.2534331960611834514698087230675e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3761
Order of pole (three term test) = -5.421
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.17
y1[1] (analytic) = 1.4418061903057054883699297989835
y1[1] (numeric) = 1.4418061903057054883699297989842
absolute error = 7e-31
relative error = 4.8550214634019523057285632240264e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.10288947715035760720514881630516
y2[1] (numeric) = 0.10288947715035760720514881630538
absolute error = 2.2e-31
relative error = 2.1382167165501565414067420962254e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3821
Order of pole (three term test) = -5.611
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1532638432, alloc=4783252, time=84.32
x[1] = 5.18
y1[1] (analytic) = 1.4507550558910990414142212704052
y1[1] (numeric) = 1.4507550558910990414142212704059
absolute error = 7e-31
relative error = 4.8250736549736726516523819940802e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.10735232057176545900349083681378
y2[1] (numeric) = 0.10735232057176545900349083681401
absolute error = 2.3e-31
relative error = 2.1424781390379360541814991237059e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3879
Order of pole (three term test) = -5.804
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1536639232, alloc=4783252, time=84.54
x[1] = 5.19
y1[1] (analytic) = 1.4596588463465314457018122646263
y1[1] (numeric) = 1.459658846346531445701812264627
absolute error = 7e-31
relative error = 4.7956411304742365436188296242167e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.1119044280172455476381965471094
y2[1] (numeric) = 0.11190442801724554763819654710964
absolute error = 2.4e-31
relative error = 2.1446872501150150542667422849700e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3935
Order of pole (three term test) = -6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.2
y1[1] (analytic) = 1.4685166713003769586390939266086
y1[1] (numeric) = 1.4685166713003769586390939266093
absolute error = 7e-31
relative error = 4.7667146970837409966248289158113e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.1165453442798467353269155595782
y2[1] (numeric) = 0.11654534427984673532691555957844
absolute error = 2.4e-31
relative error = 2.0592843196182595337735803277755e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.399
Order of pole (three term test) = -6.198
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
bytes used=1540640080, alloc=4783252, time=84.77
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.21
y1[1] (analytic) = 1.4773276449775216918646184103044
y1[1] (numeric) = 1.4773276449775216918646184103051
absolute error = 7e-31
relative error = 4.7382853924096902952655180899275e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.12127460527181017927830228300415
y2[1] (numeric) = 0.1212746052718101792783022830044
absolute error = 2.5e-31
relative error = 2.0614373424648989487422267575926e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4043
Order of pole (three term test) = -6.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1544640856, alloc=4783252, time=84.98
x[1] = 5.22
y1[1] (analytic) = 1.4860908862879403844944672651737
y1[1] (numeric) = 1.4860908862879403844944672651744
absolute error = 7e-31
relative error = 4.7103444779781131097722050194478e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.12609173807097772083778515183022
y2[1] (numeric) = 0.12609173807097772083778515183047
absolute error = 2.5e-31
relative error = 1.9826834321157001487725554788542e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4095
Order of pole (three term test) = -6.604
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1548642780, alloc=4783252, time=85.20
x[1] = 5.23
y1[1] (analytic) = 1.4948055189148046714090995785478
y1[1] (numeric) = 1.4948055189148046714090995785485
absolute error = 7e-31
relative error = 4.6828834329444028449714214630752e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.13099626096808370720294728808506
y2[1] (numeric) = 0.13099626096808370720294728808532
absolute error = 2.6e-31
relative error = 1.9847894747419326878068068044452e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4145
Order of pole (three term test) = -6.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.24
y1[1] (analytic) = 1.5034706714021140358282745011865
y1[1] (numeric) = 1.5034706714021140358282745011872
absolute error = 7e-31
relative error = 4.6558939480155643782259207952980e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.13598768351492551656575677797294
y2[1] (numeric) = 0.1359876835149255165657567779732
absolute error = 2.6e-31
relative error = 1.9119378555445673127035219408218e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4193
Order of pole (three term test) = -7.019
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1552643816, alloc=4783252, time=85.42
x[1] = 5.25
y1[1] (analytic) = 1.5120854772418406831518162141691
y1[1] (numeric) = 1.5120854772418406831518162141698
absolute error = 7e-31
relative error = 4.6293679195759053638266382641296e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.14106550657340796966927431057729
y2[1] (numeric) = 0.14106550657340796966927431057756
absolute error = 2.7e-31
relative error = 1.9140043980878970097364377524983e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.424
Order of pole (three term test) = -7.231
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1556645380, alloc=4783252, time=85.64
x[1] = 5.26
y1[1] (analytic) = 1.5206490749605796216514577467554
y1[1] (numeric) = 1.5206490749605796216514577467561
absolute error = 7e-31
relative error = 4.6032974440085486040845383637867e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.14622922236545672337855271464404
y2[1] (numeric) = 0.14622922236545672337855271464431
absolute error = 2.7e-31
relative error = 1.8464161651986003062597641132833e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4285
Order of pole (three term test) = -7.444
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1560646824, alloc=4783252, time=85.86
x[1] = 5.27
y1[1] (analytic) = 1.5291606082056952850779026207164
y1[1] (numeric) = 1.5291606082056952850779026207171
absolute error = 7e-31
relative error = 4.5776748122054644730355639935523e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.1514783145237956549679656594851
y2[1] (numeric) = 0.15147831452379565496796565948538
absolute error = 2.8e-31
relative error = 1.8484494026768097937091874311698e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4328
Order of pole (three term test) = -7.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.28
y1[1] (analytic) = 1.5376192258309560825926322278478
y1[1] (numeric) = 1.5376192258309560825926322278485
absolute error = 7e-31
relative error = 4.5524925042590298405176317144077e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.15681225814358315942885113299026
y2[1] (numeric) = 0.15681225814358315942885113299055
absolute error = 2.9e-31
relative error = 1.8493452197752625338130437644105e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.437
Order of pole (three term test) = -7.878
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1564648720, alloc=4783252, time=86.08
x[1] = 5.29
y1[1] (analytic) = 1.5460240819816483126408276469977
y1[1] (numeric) = 1.5460240819816483126408276469983
absolute error = 6e-31
relative error = 3.8809227294243541289129166266754e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.16223051983490219621076903672188
y2[1] (numeric) = 0.16223051983490219621076903672218
absolute error = 3.0e-31
relative error = 1.8492204814809336752083787814922e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4409
Order of pole (three term test) = -8.098
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1568650364, alloc=4783252, time=86.30
x[1] = 5.3
y1[1] (analytic) = 1.5543743361791609294449466335608
y1[1] (numeric) = 1.5543743361791609294449466335615
absolute error = 7e-31
relative error = 4.5034196956743649823373705361909e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.16773255777609883643544033214541
y2[1] (numeric) = 0.16773255777609883643544033214571
absolute error = 3.0e-31
relative error = 1.7885615290053646439417508899519e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4447
Order of pole (three term test) = -8.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.31
y1[1] (analytic) = 1.562669153405032703712793494195
y1[1] (numeric) = 1.5626691534050327037127934941956
absolute error = 6e-31
relative error = 3.8395843335910802203134807437258e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.17331782176796397677309498526352
y2[1] (numeric) = 0.17331782176796397677309498526382
absolute error = 3.0e-31
relative error = 1.7309241308238731030433707717558e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4483
Order of pole (three term test) = -8.544
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1572652472, alloc=4783252, time=86.51
TOP MAIN SOLVE Loop
x[1] = 5.32
y1[1] (analytic) = 1.5709077041844533729140501068966
y1[1] (numeric) = 1.5709077041844533729140501068972
absolute error = 6e-31
relative error = 3.8194478160732796098478367970987e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.17898575328875280185499235258526
y2[1] (numeric) = 0.17898575328875280185499235258557
absolute error = 3.1e-31
relative error = 1.7319814248002493853693832908149e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4518
Order of pole (three term test) = -8.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1576653260, alloc=4783252, time=86.74
x[1] = 5.33
y1[1] (analytic) = 1.5790891646692104310798244932856
y1[1] (numeric) = 1.5790891646692104310798244932861
absolute error = 5e-31
relative error = 3.1663823119496904660265380234817e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.18473578555003649332172215557053
y2[1] (numeric) = 0.18473578555003649332172215557085
absolute error = 3.2e-31
relative error = 1.7322036390904165353538909114412e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.455
Order of pole (three term test) = -8.997
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1580655364, alloc=4783252, time=86.95
x[1] = 5.34
y1[1] (analytic) = 1.5872127167200732635153590826657
y1[1] (numeric) = 1.5872127167200732635153590826662
absolute error = 5e-31
relative error = 3.1501763735438988368420215483635e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.19056734355338060038292414918256
y2[1] (numeric) = 0.19056734355338060038292414918289
absolute error = 3.3e-31
relative error = 1.7316713023685631962104037795176e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4581
Order of pole (three term test) = -9.226
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.35
y1[1] (analytic) = 1.5952775479886063880810806137854
y1[1] (numeric) = 1.5952775479886063880810806137859
absolute error = 5e-31
relative error = 3.1342508432493218025058850823574e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.19647984414784440409860233060843
y2[1] (numeric) = 0.19647984414784440409860233060877
absolute error = 3.4e-31
relative error = 1.7304573986946037939239141066363e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.461
Order of pole (three term test) = -9.456
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1584656572, alloc=4783252, time=87.17
x[1] = 5.36
y1[1] (analytic) = 1.6032828519984036217860410431167
y1[1] (numeric) = 1.6032828519984036217860410431172
absolute error = 5e-31
relative error = 3.1186013084140305313929572647327e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.20247269608829552549352153390762
y2[1] (numeric) = 0.20247269608829552549352153390796
absolute error = 3.4e-31
relative error = 1.6792387643800166066340848418128e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.37
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4637
Order of pole (three term test) = -9.688
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1588658856, alloc=4783252, time=87.40
x[1] = 5.37
y1[1] (analytic) = 1.611227828225735049344785028739
y1[1] (numeric) = 1.6112278282257350493447850287395
absolute error = 5e-31
relative error = 3.1032234625105380805043351278785e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.20854530009453394609247031570643
y2[1] (numeric) = 0.20854530009453394609247031570677
absolute error = 3.4e-31
relative error = 1.6303412248843652220138712983874e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4662
Order of pole (three term test) = -9.921
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1592661236, alloc=4783252, time=87.62
x[1] = 5.38
y1[1] (analytic) = 1.6191116821795987290679938861927
y1[1] (numeric) = 1.6191116821795987290679938861932
absolute error = 5e-31
relative error = 3.0881131024075822902927943730723e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.21469704891121952852360645852928
y2[1] (numeric) = 0.21469704891121952852360645852963
absolute error = 3.5e-31
relative error = 1.6302040562501177401679826090879e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = -10.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.39
y1[1] (analytic) = 1.6269336254811691309830264844484
y1[1] (numeric) = 1.6269336254811691309830264844488
absolute error = 4e-31
relative error = 2.4586129005828319315748979435276e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.2209273273685970444877641912544
y2[1] (numeric) = 0.22092732736859704448776419125475
absolute error = 3.5e-31
relative error = 1.5842313586497020507421640293691e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.29
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4707
Order of pole (three term test) = -10.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1596661932, alloc=4783252, time=87.84
x[1] = 5.4
y1[1] (analytic) = 1.6346928759426343624067518389807
y1[1] (numeric) = 1.6346928759426343624067518389812
absolute error = 5e-31
relative error = 3.0586785282934474866876042775751e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.22723551244401263764153021726577
y2[1] (numeric) = 0.22723551244401263764153021726612
absolute error = 3.5e-31
relative error = 1.5402522089773915005800457464444e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4727
Order of pole (three term test) = -10.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1600663188, alloc=4783252, time=88.06
x[1] = 5.41
y1[1] (analytic) = 1.6423886576454142973138135876736
y1[1] (numeric) = 1.642388657645414297313813587674
absolute error = 4e-31
relative error = 2.4354771213133799943941376849681e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.23362097332421556979906379088919
y2[1] (numeric) = 0.23362097332421556979906379088955
absolute error = 3.6e-31
relative error = 1.5409575385185882845074577697857e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.93
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4745
Order of pole (three term test) = -10.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.42
y1[1] (analytic) = 1.6500202010177517877525710803082
y1[1] (numeric) = 1.6500202010177517877525710803086
absolute error = 4e-31
relative error = 2.4242127445062509812826511015435e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.24008307146843902032995860887945
y2[1] (numeric) = 0.24008307146843902032995860887982
absolute error = 3.7e-31
relative error = 1.5411332324971511980163406128571e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.476
Order of pole (three term test) = -11.1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1604664176, alloc=4783252, time=88.27
TOP MAIN SOLVE Loop
x[1] = 5.43
y1[1] (analytic) = 1.6575867429116691982522346148438
y1[1] (numeric) = 1.6575867429116691982522346148442
absolute error = 4e-31
relative error = 2.4131467128976400023520417076753e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.24662116067225363072577388837689
y2[1] (numeric) = 0.24662116067225363072577388837726
absolute error = 3.7e-31
relative error = 1.5002767767025079671516340248723e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4774
Order of pole (three term test) = -11.34
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1608665936, alloc=4783252, time=88.49
x[1] = 5.44
y1[1] (analytic) = 1.6650875266792825676318843385363
y1[1] (numeric) = 1.6650875266792825676318843385367
absolute error = 4e-31
relative error = 2.4022761181673615578395238362166e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.25323458713218740903398908799371
y2[1] (numeric) = 0.25323458713218740903398908799408
absolute error = 3.7e-31
relative error = 1.4610958328802910619045731005535e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4786
Order of pole (three term test) = -11.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1612667088, alloc=4783252, time=88.72
x[1] = 5.45
y1[1] (analytic) = 1.6725218022484657668587868348645
y1[1] (numeric) = 1.6725218022484657668587868348649
absolute error = 4e-31
relative error = 2.3915981212457580500864758658746e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.25992268951110553222278861742014
y2[1] (numeric) = 0.25992268951110553222278861742051
absolute error = 3.7e-31
relative error = 1.4235001980625137871285022007013e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.27
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4796
Order of pole (three term test) = -11.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.46
y1[1] (analytic) = 1.6798888261978570866032768193071
y1[1] (numeric) = 1.6798888261978570866032768193075
absolute error = 4e-31
relative error = 2.3811099506229351645724166071324e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.2666847990043435085509230441066
y2[1] (numeric) = 0.26668479900434350855092304410697
absolute error = 3.7e-31
relative error = 1.3874056615951844771072320209952e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -12.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1616669256, alloc=4783252, time=88.93
x[1] = 5.47
y1[1] (analytic) = 1.6871878618312007538939537370804
y1[1] (numeric) = 1.6871878618312007538939537370808
absolute error = 4e-31
relative error = 2.3708089007104241217575946976021e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.27352023940658708668152059583978
y2[1] (numeric) = 0.27352023940658708668152059584016
absolute error = 3.8e-31
relative error = 1.3892938995096850615648515715512e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.97
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -12.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1620669912, alloc=4783252, time=89.16
x[1] = 5.48
y1[1] (analytic) = 1.6944181792510159437834788005517
y1[1] (numeric) = 1.6944181792510159437834788005521
absolute error = 4e-31
relative error = 2.3606923302535156445220090772211e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.2804283271794922236046706498801
y2[1] (numeric) = 0.28042832717949222360467064988049
absolute error = 3.9e-31
relative error = 1.3907296881258890648563261712534e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -12.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1624670608, alloc=4783252, time=89.38
x[1] = 5.49
y1[1] (analytic) = 1.7015790554315859191851965250435
y1[1] (numeric) = 1.701579055431585919185196525044
absolute error = 5e-31
relative error = 2.9384470759907229921394929220408e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.28740837152003834942833673574752
y2[1] (numeric) = 0.28740837152003834942833673574791
absolute error = 3.9e-31
relative error = 1.3569542109625323748180376613249e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.5
y1[1] (analytic) = 1.7086697742912600000274211813258
y1[1] (numeric) = 1.7086697742912600000274211813263
absolute error = 5e-31
relative error = 2.9262529689646745984862886461862e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.29445967442960809376808082447793
y2[1] (numeric) = 0.29445967442960809376808082447833
absolute error = 4.0e-31
relative error = 1.3584203024568031116059478298815e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1628672912, alloc=4783252, time=89.59
x[1] = 5.51
y1[1] (analytic) = 1.7156896267640611315887241762732
y1[1] (numeric) = 1.7156896267640611315887241762736
absolute error = 4e-31
relative error = 2.3314240160933685846338345314485e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.30158153078378656582052617869171
y2[1] (numeric) = 0.30158153078378656582052617869211
absolute error = 4.0e-31
relative error = 1.3263411687062918285258131790502e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -13.27
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1632676088, alloc=4848776, time=89.81
x[1] = 5.52
y1[1] (analytic) = 1.7226379108705918913170616076532
y1[1] (numeric) = 1.7226379108705918913170616076536
absolute error = 4e-31
relative error = 2.3220201847168613952719494519517e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.30877322840287320825071729003055
y2[1] (numeric) = 0.30877322840287320825071729003095
absolute error = 4.0e-31
relative error = 1.2954490972841021892340296308975e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.53
y1[1] (analytic) = 1.7295139317882318435911482223455
y1[1] (numeric) = 1.7295139317882318435911482223458
absolute error = 3e-31
relative error = 1.7345914044752148454207174173503e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.31603404812309917376674785034254
y2[1] (numeric) = 0.31603404812309917376674785034295
absolute error = 4.1e-31
relative error = 1.2973285708769579308779119300629e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.75
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4808
Order of pole (three term test) = -13.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1636678296, alloc=4848776, time=90.03
TOP MAIN SOLVE Loop
x[1] = 5.54
y1[1] (analytic) = 1.7363170019206192227470992412368
y1[1] (numeric) = 1.7363170019206192227470992412371
absolute error = 3e-31
relative error = 1.7277950954126254173531406978970e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.32336326386854310270334690980483
y2[1] (numeric) = 0.32336326386854310270334690980524
absolute error = 4.1e-31
relative error = 1.2679238670929463947284150278235e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4801
Order of pole (three term test) = -13.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1640679240, alloc=4848776, time=90.25
x[1] = 5.55
y1[1] (analytic) = 1.7430464409664099962599385961293
y1[1] (numeric) = 1.7430464409664099962599385961296
absolute error = 3e-31
relative error = 1.7211245377585510813480506603140e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.33076014272373811009659447825526
y2[1] (numeric) = 0.33076014272373811009659447825567
absolute error = 4.1e-31
relative error = 1.2395689414804904665885459460060e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.01
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4792
Order of pole (three term test) = -14.23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.11
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1644680160, alloc=4848776, time=90.47
x[1] = 5.56
y1[1] (analytic) = 1.7497015759873074322309544561574
y1[1] (numeric) = 1.7497015759873074322309544561577
absolute error = 3e-31
relative error = 1.7145780978720238626009912595748e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.33822394500696272161156471904958
y2[1] (numeric) = 0.33822394500696272161156471904999
absolute error = 4.1e-31
relative error = 1.2122145875613853634559561703149e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.478
Order of pole (three term test) = -14.47
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.57
y1[1] (analytic) = 1.7562817414753553682808444254304
y1[1] (numeric) = 1.7562817414753553682808444254308
absolute error = 4e-31
relative error = 2.2775389082162983402051374926983e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.3457539243442084292903795474788
y2[1] (numeric) = 0.34575392434420842929037954747921
absolute error = 4.1e-31
relative error = 1.1858144510655869530171425480187e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4767
Order of pole (three term test) = -14.71
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.44
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1648681460, alloc=4848776, time=90.69
x[1] = 5.58
y1[1] (analytic) = 1.7627862794194884525778386345335
y1[1] (numeric) = 1.7627862794194884525778386345338
absolute error = 3e-31
relative error = 1.7018512312155868899293173960808e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.35334932774381647042673725271193
y2[1] (numeric) = 0.35334932774381647042673725271235
absolute error = 4.2e-31
relative error = 1.1886254395381396068240192593121e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4753
Order of pole (three term test) = -14.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.11
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1652683260, alloc=4848776, time=90.91
x[1] = 5.59
y1[1] (analytic) = 1.7692145393713327020321562629051
y1[1] (numeric) = 1.7692145393713327020321562629054
absolute error = 3e-31
relative error = 1.6956677289493736861386368646763e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.36100939567177636595122579880666
y2[1] (numeric) = 0.36100939567177636595122579880708
absolute error = 4.2e-31
relative error = 1.1634046233573845633300529753541e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.61
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4736
Order of pole (three term test) = -15.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.78
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1656684676, alloc=4848776, time=91.13
x[1] = 5.6
y1[1] (analytic) = 1.7755658785102497976558096621573
y1[1] (numeric) = 1.7755658785102497976558096621576
absolute error = 3e-31
relative error = 1.6896021917908701912551036171017e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.36873336212767868853633084628333
y2[1] (numeric) = 0.36873336212767868853633084628375
absolute error = 4.2e-31
relative error = 1.1390344436871692017721820537495e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4717
Order of pole (three term test) = -15.42
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.61
y1[1] (analytic) = 1.7818396617076186127124234987124
y1[1] (numeric) = 1.7818396617076186127124234987127
absolute error = 3e-31
relative error = 1.6836531728814266625064053619441e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.37652045472131446520762175590142
y2[1] (numeric) = 0.37652045472131446520762175590184
absolute error = 4.2e-31
relative error = 1.1154772462783393080936556406935e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4697
Order of pole (three term test) = -15.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1660686000, alloc=4848776, time=91.35
x[1] = 5.62
y1[1] (analytic) = 1.788035261590347545557821695409
y1[1] (numeric) = 1.7880352615903475455578216954093
absolute error = 3e-31
relative error = 1.6778192603045670684844278887291e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.38436989474991355458468707877178
y2[1] (numeric) = 0.3843698947499135545846870787722
absolute error = 4.2e-31
relative error = 1.0926974399836095870097036233844e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.62
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4674
Order of pole (three term test) = -15.89
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1664687012, alloc=4848776, time=91.58
x[1] = 5.63
y1[1] (analytic) = 1.7941520586036113059910248809931
y1[1] (numeric) = 1.7941520586036113059910248809933
absolute error = 2e-31
relative error = 1.1147327175582877649959575777762e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.39228089727601427497846053907225
y2[1] (numeric) = 0.39228089727601427497846053907268
absolute error = 4.3e-31
relative error = 1.0961532998060979800624162859149e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.465
Order of pole (three term test) = -16.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.64
y1[1] (analytic) = 1.8001894410728058814893037287734
y1[1] (numeric) = 1.8001894410728058814893037287736
absolute error = 2e-31
relative error = 1.1109941844832280010408129366131e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.4002526712059564964470189172122
y2[1] (numeric) = 0.40025267120595649644701891721263
absolute error = 4.3e-31
relative error = 1.0743213748066069335154707327859e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.99
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4624
Order of pole (three term test) = -16.36
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.24
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1668688100, alloc=4848776, time=91.80
TOP MAIN SOLVE Loop
x[1] = 5.65
y1[1] (analytic) = 1.8061468052647154878822936455404
y1[1] (numeric) = 1.8061468052647154878822936455406
absolute error = 2e-31
relative error = 1.1073296999835363206936571986305e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.40828441936899034756605694566804
y2[1] (numeric) = 0.40828441936899034756605694566846
absolute error = 4.2e-31
relative error = 1.0286946551845310600601557136015e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4596
Order of pole (three term test) = -16.59
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1672689032, alloc=4848776, time=92.02
x[1] = 5.66
y1[1] (analytic) = 1.8120235554478853878210756882658
y1[1] (numeric) = 1.812023555447885387821075688266
absolute error = 2e-31
relative error = 1.1037384111188619143987952479432e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.4163753385969926261092858725629
y2[1] (numeric) = 0.41637533859699262610928587256332
absolute error = 4.2e-31
relative error = 1.0087052739848160495843727094265e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4566
Order of pole (three term test) = -16.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1676690256, alloc=4848776, time=92.24
x[1] = 5.67
y1[1] (analytic) = 1.8178191039521945398106873148475
y1[1] (numeric) = 1.8178191039521945398106873148477
absolute error = 2e-31
relative error = 1.1002194858947837852805672547205e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.42452461980478294206411777393379
y2[1] (numeric) = 0.42452461980478294206411777393421
absolute error = 4.2e-31
relative error = 9.8934191424077222609783492987148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4534
Order of pole (three term test) = -17.05
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.68
y1[1] (analytic) = 1.8235328712276221205908034265397
y1[1] (numeric) = 1.8235328712276221205908034265398
absolute error = 1e-31
relative error = 5.4838605641739221652662230381298e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.43273144807103156143526394233455
y2[1] (numeric) = 0.43273144807103156143526394233498
absolute error = 4.3e-31
relative error = 9.9368789099288387638390706812012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4501
Order of pole (three term test) = -17.27
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1680694028, alloc=4848776, time=92.46
x[1] = 5.69
y1[1] (analytic) = 1.8291642859022020442613215727059
y1[1] (numeric) = 1.829164285902202044261321572706
absolute error = 1e-31
relative error = 5.4669775028259321830241120464934e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.44099500271975086011928997036201
y2[1] (numeric) = 0.44099500271975086011928997036244
absolute error = 4.3e-31
relative error = 9.7506773851871036970751719241310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4465
Order of pole (three term test) = -17.5
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1684695240, alloc=4848776, time=92.69
x[1] = 5.7
y1[1] (analytic) = 1.8347127848391596827492340309974
y1[1] (numeric) = 1.8347127848391596827492340309975
absolute error = 1e-31
relative error = 5.4504443870633687246981978669675e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.44931445740236223877264939212753
y2[1] (numeric) = 0.44931445740236223877264939212796
absolute error = 4.3e-31
relative error = 9.5701349670779435198322660693544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4428
Order of pole (three term test) = -17.72
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1688696100, alloc=4848776, time=92.91
x[1] = 5.71
y1[1] (analytic) = 1.840177813193225073992353850756
y1[1] (numeric) = 1.8401778131932250739923538507561
absolute error = 1e-31
relative error = 5.4342574550701667443430731653777e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.45768898018033029205009794707004
y2[1] (numeric) = 0.45768898018033029205009794707047
absolute error = 4.3e-31
relative error = 9.3950262868592382667206151016002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4389
Order of pole (three term test) = -17.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.72
y1[1] (analytic) = 1.8455588244661169865660040040995
y1[1] (numeric) = 1.8455588244661169865660040040996
absolute error = 1e-31
relative error = 5.4184130396888317453978372312479e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.46611773360835596886542620284383
y2[1] (numeric) = 0.46611773360835596886542620284426
absolute error = 4.3e-31
relative error = 9.2251371058389507314903020422525e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4349
Order of pole (three term test) = -18.16
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1692698556, alloc=4848776, time=93.13
x[1] = 5.73
y1[1] (analytic) = 1.8508552805611922923924435421742
y1[1] (numeric) = 1.8508552805611922923924435421743
absolute error = 1e-31
relative error = 5.4029075665861514127258177039982e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.47459987481812040442781186647779
y2[1] (numeric) = 0.47459987481812040442781186647822
absolute error = 4.3e-31
relative error = 9.0602636624122100552532274521124e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4306
Order of pole (three term test) = -18.38
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1696700308, alloc=4848776, time=93.35
x[1] = 5.74
y1[1] (analytic) = 1.8560666518372551826413008060802
y1[1] (numeric) = 1.8560666518372551826413008060803
absolute error = 1e-31
relative error = 5.3877375524749347007577927552173e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.48313455560257104974037444265051
y2[1] (numeric) = 0.48313455560257104974037444265094
absolute error = 4.3e-31
relative error = 8.9002120633598436652276196478772e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4262
Order of pole (three term test) = -18.59
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.75
y1[1] (analytic) = 1.8611924171615208459442645129289
y1[1] (numeric) = 1.861192417161520845944264512929
absolute error = 1e-31
relative error = 5.3728996033902091225244929260809e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.49172092250074167001822059073657
y2[1] (numeric) = 0.49172092250074167001822059073699
absolute error = 4.2e-31
relative error = 8.5414303272679333208839517818073e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4217
Order of pole (three term test) = -18.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1700701680, alloc=4848776, time=93.57
x[1] = 5.76
y1[1] (analytic) = 1.8662320639617283126003474993147
y1[1] (numeric) = 1.8662320639617283126003474993147
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.50035811688309773009682147249262
y2[1] (numeric) = 0.50035811688309773009682147249304
absolute error = 4.2e-31
relative error = 8.3939879424026136943967604749367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4169
Order of pole (three term test) = -19.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1704702624, alloc=4848776, time=93.80
x[1] = 5.77
y1[1] (analytic) = 1.8711850882773972535307298212406
y1[1] (numeric) = 1.8711850882773972535307298212406
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.50904527503739863236330217008544
y2[1] (numeric) = 0.50904527503739863236330217008586
absolute error = 4.2e-31
relative error = 8.2507395824299393087016816704661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.412
Order of pole (three term test) = -19.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1708703416, alloc=4848776, time=94.02
x[1] = 5.78
y1[1] (analytic) = 1.8760509948102236083459995829373
y1[1] (numeric) = 1.8760509948102236083459995829373
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.51778152825506822105840167195699
y2[1] (numeric) = 0.51778152825506822105840167195742
absolute error = 4.3e-31
relative error = 8.3046608759703473312646560409350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4069
Order of pole (three term test) = -19.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.79
y1[1] (analytic) = 1.8808292969736090030049809872269
y1[1] (numeric) = 1.880829296973609003004980987227
absolute error = 1e-31
relative error = 5.3168036121570025438366731729952e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.52656600291806491597064841086205
y2[1] (numeric) = 0.52656600291806491597064841086248
absolute error = 4.3e-31
relative error = 8.1661177823306825729287477877476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4017
Order of pole (three term test) = -19.63
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1712707704, alloc=4848776, time=94.23
x[1] = 5.8
y1[1] (analytic) = 1.8855195169413190041646581017615
y1[1] (numeric) = 1.8855195169413190041646581017615
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.53539782058624278858177347329741
y2[1] (numeric) = 0.53539782058624278858177347329784
absolute error = 4.3e-31
relative error = 8.0314111015462169038770698756160e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3963
Order of pole (three term test) = -19.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1716710980, alloc=4848776, time=94.46
x[1] = 5.81
y1[1] (analytic) = 1.8901211856952653444363077588889
y1[1] (numeric) = 1.8901211856952653444363077588889
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.54427609808519484462854759312049
y2[1] (numeric) = 0.54427609808519484462854759312092
absolute error = 4.3e-31
relative error = 7.9004020480188833774875266149099e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3907
Order of pole (three term test) = -20.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1720713060, alloc=4848776, time=94.68
x[1] = 5.82
y1[1] (analytic) = 1.8946338430724073403651343641758
y1[1] (numeric) = 1.8946338430724073403651343641758
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.55319994759456972882598823711744
y2[1] (numeric) = 0.55319994759456972882598823711786
absolute error = 4.2e-31
relative error = 7.5921916085901445216255856685019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.385
Order of pole (three term test) = -20.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.83
y1[1] (analytic) = 1.8990570378107678130306930348074
y1[1] (numeric) = 1.8990570378107678130306930348074
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.56216847673685302015506147042438
y2[1] (numeric) = 0.56216847673685302015506147042481
absolute error = 4.3e-31
relative error = 7.6489525434788809063616855480330e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3792
Order of pole (three term test) = -20.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1724715056, alloc=4848776, time=94.90
x[1] = 5.84
y1[1] (analytic) = 1.903390327594558909714387498229
y1[1] (numeric) = 1.903390327594558909714387498229
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.57118078866660423965933399774091
y2[1] (numeric) = 0.57118078866660423965933399774134
absolute error = 4.3e-31
relative error = 7.5282644047573025696941502780326e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3731
Order of pole (three term test) = -20.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1728717320, alloc=4848776, time=95.12
x[1] = 5.85
y1[1] (analytic) = 1.90763327909841331408948072728
y1[1] (numeric) = 1.90763327909841331408948072728
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.58023598216014064712415964041523
y2[1] (numeric) = 0.58023598216014064712415964041566
absolute error = 4.3e-31
relative error = 7.4107779114140377967334121338072e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.367
Order of pole (three term test) = -20.79
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.86
y1[1] (analytic) = 1.9117854680307164218494585297175
y1[1] (numeric) = 1.9117854680307164218494585297176
absolute error = 1e-31
relative error = 5.2307124241825920347489552300375e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.5893331517056588583334685788649
y2[1] (numeric) = 0.58933315170565885833346857886533
absolute error = 4.3e-31
relative error = 7.2963823391826182344999470659179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3607
Order of pole (three term test) = -20.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1732718912, alloc=4848776, time=95.34
x[1] = 5.87
y1[1] (analytic) = 1.9158464791760351485932932817607
y1[1] (numeric) = 1.9158464791760351485932932817608
absolute error = 1e-31
relative error = 5.2196249066369803600317103433371e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.59847138759378527081753477878537
y2[1] (numeric) = 0.5984713875937852708175347787858
absolute error = 4.3e-31
relative error = 7.1849717282033896410028695234949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3542
Order of pole (three term test) = -21.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1736721004, alloc=4848776, time=95.56
x[1] = 5.88
y1[1] (analytic) = 1.9198159064366391271221765013287
y1[1] (numeric) = 1.9198159064366391271221765013288
absolute error = 1e-31
relative error = 5.2088327669713659551814502842530e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.60764977600854624312460526099845
y2[1] (numeric) = 0.60764977600854624312460526099888
absolute error = 4.3e-31
relative error = 7.0764446392876198207548395819711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3476
Order of pole (three term test) = -21.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1740722536, alloc=4848776, time=95.78
x[1] = 5.89
y1[1] (analytic) = 1.9236933528731101420625914701266
y1[1] (numeric) = 1.9236933528731101420625914701268
absolute error = 2e-31
relative error = 1.0396667415900371752974540956322e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.6168673991187489306742722820455
y2[1] (numeric) = 0.61686739911874893067427228204593
absolute error = 4.3e-31
relative error = 6.9707039246083360662504503343727e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3409
Order of pole (three term test) = -21.5
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.9
y1[1] (analytic) = 1.9274784307440357409061046800325
y1[1] (numeric) = 1.9274784307440357409061046800326
absolute error = 1e-31
relative error = 5.1881255014303061220920881218789e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.62612333516976364018515353101662
y2[1] (numeric) = 0.62612333516976364018515353101705
absolute error = 4.3e-31
relative error = 6.8676565118502117973402701203178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.334
Order of pole (three term test) = -21.67
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1744723756, alloc=4848776, time=95.99
x[1] = 5.91
y1[1] (analytic) = 1.9311707615447830521378500235795
y1[1] (numeric) = 1.9311707615447830521378500235797
absolute error = 2e-31
relative error = 1.0356411974672602385802630395445e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.63541665857569852451792261500197
y2[1] (numeric) = 0.63541665857569852451792261500241
absolute error = 4.4e-31
relative error = 6.9245902521074976428624315771116e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.327
Order of pole (three term test) = -21.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1748724532, alloc=4848776, time=96.22
x[1] = 5.92
y1[1] (analytic) = 1.9347699760453489331042042875189
y1[1] (numeric) = 1.9347699760453489331042042875191
absolute error = 2e-31
relative error = 1.0337146145341683476158365186911e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.64474644001195740054101751977893
y2[1] (numeric) = 0.64474644001195740054101751977937
absolute error = 4.4e-31
relative error = 6.8243882043278874975927841303354e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3198
Order of pole (three term test) = -21.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1752726800, alloc=4848776, time=96.43
x[1] = 5.93
y1[1] (analytic) = 1.938275714327282662636408866662
y1[1] (numeric) = 1.9382757143272826626364088666622
absolute error = 2e-31
relative error = 1.0318449461118796428404211063347e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 0.65411174650817143431437173267238
y2[1] (numeric) = 0.65411174650817143431437173267282
absolute error = 4.4e-31
relative error = 6.7266793838948944502109844835458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3126
Order of pole (three term test) = -22.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.94
y1[1] (analytic) = 1.9416876258196774861916441437897
y1[1] (numeric) = 1.9416876258196774861916441437898
absolute error = 1e-31
relative error = 5.1501589993284994119191247881999e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.66351164154149540050009246731935
y2[1] (numeric) = 0.66351164154149540050009246731979
absolute error = 4.4e-31
relative error = 6.6313832712531662419818093631161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3052
Order of pole (three term test) = -22.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1756728844, alloc=4848776, time=96.65
x[1] = 5.95
y1[1] (analytic) = 1.9450053693342274143870352824965
y1[1] (numeric) = 1.9450053693342274143870352824966
absolute error = 1e-31
relative error = 5.1413739816168146874289864012752e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.67294518513025918645189154620177
y2[1] (numeric) = 0.67294518513025918645189154620221
absolute error = 4.4e-31
relative error = 6.5384225895728942511172954056618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2977
Order of pole (three term test) = -22.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1760731440, alloc=4848776, time=96.88
x[1] = 5.96
y1[1] (analytic) = 1.9482286130993457692759499337911
y1[1] (numeric) = 1.9482286130993457692759499337912
absolute error = 1e-31
relative error = 5.1328678435183578198960999117550e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.68241143392796517591090265779117
y2[1] (numeric) = 0.68241143392796517591090265779161
absolute error = 4.4e-31
relative error = 6.4477231494694747492276547975442e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.29
Order of pole (three term test) = -22.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 5.97
y1[1] (analytic) = 1.9513570347933420665403922538039
y1[1] (numeric) = 1.951357034793342066540392253804
absolute error = 1e-31
relative error = 5.1246388137571386401760895235829e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.69190944131762211264784629855594
y2[1] (numeric) = 0.69190944131762211264784629855638
absolute error = 4.4e-31
relative error = 6.3592137023321424936101320185809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2823
Order of pole (three term test) = -22.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1764733172, alloc=4848776, time=97.09
x[1] = 5.98
y1[1] (analytic) = 1.9543903215766539159389213028699
y1[1] (numeric) = 1.95439032157665391593892130287
absolute error = 1e-31
relative error = 5.1166851828926159794762497969549e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.70143825750640601074378947433419
y2[1] (numeric) = 0.70143825750640601074378947433463
absolute error = 4.4e-31
relative error = 6.2728258017204261353256157792637e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2744
Order of pole (three term test) = -22.89
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1768736020, alloc=4848776, time=97.32
x[1] = 5.99
y1[1] (analytic) = 1.9573281701231307168469088616542
y1[1] (numeric) = 1.9573281701231307168469088616543
absolute error = 1e-31
relative error = 5.1090053025553321059706116952282e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.71099692962063864549735591405603
y2[1] (numeric) = 0.71099692962063864549735591405648
absolute error = 4.5e-31
relative error = 6.3291412557871826530024417523346e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2665
Order of pole (three term test) = -23.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1772739400, alloc=4848776, time=97.54
x[1] = 6
y1[1] (analytic) = 1.9601702866503660205456522979229
y1[1] (numeric) = 1.960170286650366020545652297923
absolute error = 1e-31
relative error = 5.1015975847121346886927851693977e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.72058450180107412718844455338811
y2[1] (numeric) = 0.72058450180107412718844455338855
absolute error = 4.4e-31
relative error = 6.1061540860265019009313463032524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2584
Order of pole (three term test) = -23.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.01
y1[1] (analytic) = 1.9629163869490755260493904569901
y1[1] (numeric) = 1.9629163869490755260493904569902
absolute error = 1e-31
relative error = 5.0944605009604174857161493669980e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.73020001529848402912048512990378
y2[1] (numeric) = 0.73020001529848402912048512990422
absolute error = 4.4e-31
relative error = 6.0257462446113630694060831987420e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2502
Order of pole (three term test) = -23.28
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1776740348, alloc=4848776, time=97.76
x[1] = 6.02
y1[1] (analytic) = 1.9655661964115177716951214558362
y1[1] (numeric) = 1.9655661964115177716951214558363
absolute error = 1e-31
relative error = 5.0875925818508354309447609093763e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.73984250856953151150808067207442
y2[1] (numeric) = 0.73984250856953151150808067207487
absolute error = 4.5e-31
relative error = 6.0823755703097495553495070739274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2419
Order of pole (three term test) = -23.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1780742772, alloc=4848776, time=97.98
x[1] = 6.03
y1[1] (analytic) = 1.9681194500589546804497472298303
y1[1] (numeric) = 1.9681194500589546804497472298304
absolute error = 1e-31
relative error = 5.0809924162379736228576477902417e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.74951101737292485387754295475596
y2[1] (numeric) = 0.7495110173729248538775429547564
absolute error = 4.4e-31
relative error = 5.8704940928316559331399069018439e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2335
Order of pole (three term test) = -23.52
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.04
y1[1] (analytic) = 1.9705758925681492129028978290782
y1[1] (numeric) = 1.9705758925681492129028978290783
absolute error = 1e-31
relative error = 5.0746586506584729302460719663391e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.75920457486584078070720854419957
y2[1] (numeric) = 0.75920457486584078070720854420001
absolute error = 4.4e-31
relative error = 5.7955393653647635574877518841691e-29 %
Correct digits = 31
h = 0.01
bytes used=1784743432, alloc=4848776, time=98.20
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2251
Order of pole (three term test) = -23.64
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.05
y1[1] (analytic) = 1.9729352782968974782022174858561
y1[1] (numeric) = 1.9729352782968974782022174858561
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.76892221170060793805532390450696
y2[1] (numeric) = 0.76892221170060793805532390450741
absolute error = 4.5e-31
relative error = 5.8523475216660100745384654281500e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2165
Order of pole (three term test) = -23.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1788746096, alloc=4848776, time=98.42
x[1] = 6.06
y1[1] (analytic) = 1.9751973713085927497412956127139
y1[1] (numeric) = 1.975197371308592749741295612714
absolute error = 1e-31
relative error = 5.0627851906135719520857181136263e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.77866295612164085290840607231132
y2[1] (numeric) = 0.77866295612164085290840607231177
absolute error = 4.5e-31
relative error = 5.7791371281017005651198241164596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2079
Order of pole (three term test) = -23.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1792749056, alloc=4848776, time=98.65
x[1] = 6.07
y1[1] (analytic) = 1.9773619453958189292191438829884
y1[1] (numeric) = 1.9773619453958189292191438829885
absolute error = 1e-31
relative error = 5.0572430724099160623209898434290e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.78842583406261468193492209381295
y2[1] (numeric) = 0.78842583406261468193492209381339
absolute error = 4.4e-31
relative error = 5.5807405210552292827492451523437e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1991
Order of pole (three term test) = -23.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.08
y1[1] (analytic) = 1.9794287841029710997444746005297
y1[1] (numeric) = 1.9794287841029710997444746005298
absolute error = 1e-31
relative error = 5.0519625057042688053180194149383e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.79820986924387103225039054359125
y2[1] (numeric) = 0.79820986924387103225039054359169
absolute error = 4.4e-31
relative error = 5.5123347499674941182864888236783e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1903
Order of pole (three term test) = -24.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1796750512, alloc=4848776, time=98.86
x[1] = 6.09
y1[1] (analytic) = 1.9813976807479009059483203288902
y1[1] (numeric) = 1.9813976807479009059483203288903
absolute error = 1e-31
relative error = 5.0469424170444103851093032242593e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.80801408327004511369299986177423
y2[1] (numeric) = 0.80801408327004511369299986177467
absolute error = 4.4e-31
relative error = 5.4454496414135927040209285927861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1814
Order of pole (three term test) = -24.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1800753072, alloc=4848776, time=99.08
x[1] = 6.1
y1[1] (analytic) = 1.983268438442584596585021274648
y1[1] (numeric) = 1.9832684384425845965850212746481
absolute error = 1e-31
relative error = 5.0421817874804540239850384699054e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.81783749572790445997587163677534
y2[1] (numeric) = 0.81783749572790445997587163677578
absolute error = 4.4e-31
relative error = 5.3800419068385260340199296014215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1725
Order of pole (three term test) = -24.24
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1804755124, alloc=4848776, time=99.31
x[1] = 6.11
y1[1] (analytic) = 1.9850408701128116628345436375483
y1[1] (numeric) = 1.9850408701128116628345436375484
absolute error = 1e-31
relative error = 5.0376796521230774364944185275886e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.82767912428438943492538560312259
y2[1] (numeric) = 0.82767912428438943492538560312303
absolute error = 4.4e-31
relative error = 5.3160698039886359540702471756242e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1635
Order of pole (three term test) = -24.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.12
y1[1] (analytic) = 1.9867147985168921034587058395238
y1[1] (numeric) = 1.9867147985168921034587058395239
absolute error = 1e-31
relative error = 5.0334350997260036232335675139481e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.83753798478484571983664267141119
y2[1] (numeric) = 0.83753798478484571983664267141162
absolute error = 4.3e-31
relative error = 5.1340955014770137522899548923326e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1544
Order of pole (three term test) = -24.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1808755904, alloc=4848776, time=99.53
x[1] = 6.13
y1[1] (analytic) = 1.9882900562633804461003863456359
y1[1] (numeric) = 1.988290056263380446100386345636
absolute error = 1e-31
relative error = 5.0294472722924194586351898388872e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.84741309135143895877919057733864
y2[1] (numeric) = 0.84741309135143895877919057733908
absolute error = 4.4e-31
relative error = 5.1922728653896061070999344214847e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1452
Order of pole (three term test) = -24.48
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1812757548, alloc=4848776, time=99.75
x[1] = 6.14
y1[1] (analytic) = 1.9897664858278147523383531246708
y1[1] (numeric) = 1.9897664858278147523383531246709
absolute error = 1e-31
relative error = 5.0257153647050390840428906008731e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.85730345648174172047049350830549
y2[1] (numeric) = 0.85730345648174172047049350830592
absolute error = 4.3e-31
relative error = 5.0157268905069188224024589878460e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.136
Order of pole (three term test) = -24.55
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.15
y1[1] (analytic) = 1.9911439395684689326111583908272
y1[1] (numeric) = 1.9911439395684689326111583908272
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.86720809114748291810311388832781
y2[1] (numeric) = 0.86720809114748291810311388832825
absolute error = 4.4e-31
relative error = 5.0737533988848681567442470469554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1267
Order of pole (three term test) = -24.61
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1816759144, alloc=4848776, time=99.97
TOP MAIN SOLVE Loop
x[1] = 6.16
y1[1] (analytic) = 1.9924222797411167957917331223665
y1[1] (numeric) = 1.9924222797411167957917331223665
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.87712600489344981226591451196916
y2[1] (numeric) = 0.8771260048934498122659145119696
absolute error = 4.4e-31
relative error = 5.0163830230235809196527491303881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1174
Order of pole (three term test) = -24.67
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1820760068, alloc=4848776, time=100.19
x[1] = 6.17
y1[1] (analytic) = 1.9936013785128063570200272314103
y1[1] (numeric) = 1.9936013785128063570200272314103
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.88705620593653270684140696811863
y2[1] (numeric) = 0.88705620593653270684140696811907
absolute error = 4.4e-31
relative error = 4.9602268385627101637076880311924e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1081
Order of pole (three term test) = -24.73
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1824764232, alloc=4848776, time=100.41
x[1] = 6.18
y1[1] (analytic) = 1.9946811179746430263743906724648
y1[1] (numeric) = 1.9946811179746430263743906724647
absolute error = 1e-31
relative error = 5.0133326624928340772007230591739e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.89699770126490243349219359023036
y2[1] (numeric) = 0.8969977012649024334921935902308
absolute error = 4.4e-31
relative error = 4.9052522585011471950583822674041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09866
Order of pole (three term test) = -24.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.19
y1[1] (analytic) = 1.9956613901535804000734809732792
y1[1] (numeric) = 1.9956613901535804000734809732791
absolute error = 1e-31
relative error = 5.0108701051887507652432289476065e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.90694949673731070707070191707552
y2[1] (numeric) = 0.90694949673731070707070191707596
absolute error = 4.4e-31
relative error = 4.8514277981615310802654252460421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08922
Order of pole (three term test) = -24.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1828766216, alloc=4848776, time=100.63
x[1] = 6.2
y1[1] (analytic) = 1.9965420970232174751394026238693
y1[1] (numeric) = 1.9965420970232174751394026238692
absolute error = 1e-31
relative error = 5.0086597296945006851233404593310e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.91691059718250342199942071090163
y2[1] (numeric) = 0.91691059718250342199942071090207
absolute error = 4.4e-31
relative error = 4.7987230309262273970954351598773e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07974
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1832768036, alloc=4848776, time=100.85
x[1] = 6.21
y1[1] (analytic) = 1.9973231505136012078096096586582
y1[1] (numeric) = 1.9973231505136012078096096586581
absolute error = 1e-31
relative error = 5.0067010926241716427742466632367e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.92688000649873694837484364690016
y2[1] (numeric) = 0.9268800064987369483748436469006
absolute error = 4.4e-31
relative error = 4.7471085460359380868400081343706e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07022
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1836769824, alloc=4848776, time=101.08
x[1] = 6.22
y1[1] (analytic) = 1.9980044725200334354498990129263
y1[1] (numeric) = 1.9980044725200334354498990129262
absolute error = 1e-31
relative error = 5.0049938013338119691090102871090e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.93685672775338747624844024993293
y2[1] (numeric) = 0.93685672775338747624844024993337
absolute error = 4.4e-31
relative error = 4.6965559083418670880233962238862e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06068
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.23
y1[1] (analytic) = 1.9985859949108812812836424313629
y1[1] (numeric) = 1.9985859949108812812836424313628
absolute error = 1e-31
relative error = 5.0035375137540223042916838827539e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.9468397632826434472332334916325
y2[1] (numeric) = 0.94683976328264344723323349163294
absolute error = 4.4e-31
relative error = 4.6470376199088137236231092394832e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05112
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1840772264, alloc=4848776, time=101.30
x[1] = 6.24
y1[1] (analytic) = 1.9990676595343902609032926544429
y1[1] (numeric) = 1.9990676595343902609032926544428
absolute error = 1e-31
relative error = 5.0023319382442185416780825501388e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.95682811479127110427590013953252
y2[1] (numeric) = 0.95682811479127110427590013953296
absolute error = 4.4e-31
relative error = 4.5985270833725924536296959831260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04153
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1844774472, alloc=4848776, time=101.52
x[1] = 6.25
y1[1] (analytic) = 1.999449418224499409259190301842
y1[1] (numeric) = 1.999449418224499409259190301842
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.96682078345244318312255432921071
y2[1] (numeric) = 0.96682078345244318312255432921115
absolute error = 4.4e-31
relative error = 4.5509985669608135864597630273115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03193
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.26
y1[1] (analytic) = 1.999731232805657846617818495209
y1[1] (numeric) = 1.999731232805657846617818495209
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.97681677000762076269225808000719
y2[1] (numeric) = 0.97681677000762076269225808000763
absolute error = 4.4e-31
relative error = 4.5044271710913325428110264419769e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02232
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1848776660, alloc=4848776, time=101.74
x[1] = 6.27
y1[1] (analytic) = 1.999913075096642301836923186416
y1[1] (numeric) = 1.9999130750966423018369231864159
absolute error = 1e-31
relative error = 5.0002173217037282924637595280909e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.9868150748664782862564560011288
y2[1] (numeric) = 0.98681507486647828625645600112924
absolute error = 4.4e-31
relative error = 4.4587887964676108351150486828239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0127
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1852777400, alloc=4848776, time=101.96
x[1] = 6.28
y1[1] (analytic) = 1.9999949269133752112083529380473
y1[1] (numeric) = 1.9999949269133752112083529380472
absolute error = 1e-31
relative error = 5.0000126827487323134588458603357e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 0.99681469820686176100548681808265
y2[1] (numeric) = 0.99681469820686176100548681808308
absolute error = 4.3e-31
relative error = 4.3137405655586069920567542626436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003067
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1856779188, alloc=4848776, time=102.18
x[1] = 6.29
y1[1] (analytic) = 1.9999767800707431110610822800232
y1[1] (numeric) = 1.9999767800707431110610822800231
absolute error = 1e-31
relative error = 5.0000580504971064404166855616864e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0068146400747701402655132902638
y2[1] (numeric) = 1.0068146400747701402655132902643
absolute error = 5e-31
relative error = 4.9661574245967258807264488770086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.006571
Order of pole (three term test) = -0.894
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.3
y1[1] (analytic) = 1.9998586363834151422866736621397
y1[1] (numeric) = 1.9998586363834151422866736621396
absolute error = 1e-31
relative error = 5.0003534340228179891263494178970e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0168139004843498903109663674941
y2[1] (numeric) = 1.0168139004843498903109663674946
absolute error = 5e-31
relative error = 4.9173206597768738977832840008288e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01621
Order of pole (three term test) = -0.8997
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1860781904, alloc=4848776, time=102.40
x[1] = 6.31
y1[1] (analytic) = 1.9996405076656615849374075411613
y1[1] (numeric) = 1.9996405076656615849374075411612
absolute error = 1e-31
relative error = 5.0008988924083111290802420740934e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0268114795178927423991508690108
y2[1] (numeric) = 1.0268114795178927423991508690113
absolute error = 5e-31
relative error = 4.8694430279914613189448741337292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02584
Order of pole (three term test) = -0.9102
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1864783412, alloc=4848776, time=102.62
x[1] = 6.32
y1[1] (analytic) = 1.9993224157301724410434695687937
y1[1] (numeric) = 1.9993224157301724410434695687936
absolute error = 1e-31
relative error = 5.0016945347696211829813776301372e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0368063774258266303351404065955
y2[1] (numeric) = 1.0368063774258266303351404065961
absolute error = 6e-31
relative error = 5.7870014408058956959106579027517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03547
Order of pole (three term test) = -0.9256
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1868785584, alloc=4848776, time=102.84
x[1] = 6.33
y1[1] (analytic) = 1.9989043923858761837899286507793
y1[1] (numeric) = 1.9989043923858761837899286507791
absolute error = 2e-31
relative error = 1.0005481040605529450989697033971e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.0467975947266898145565305659031
y2[1] (numeric) = 1.0467975947266898145565305659037
absolute error = 6e-31
relative error = 5.7317670868039683692750241369258e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04508
Order of pole (three term test) = -0.9458
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.34
y1[1] (analytic) = 1.9983864794347588911767704763508
y1[1] (numeric) = 1.9983864794347588911767704763507
absolute error = 1e-31
relative error = 5.0040370583514393349253940443680e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0567841323070781954089533630368
y2[1] (numeric) = 1.0567841323070781954089533630373
absolute error = 5e-31
relative error = 4.7313352340789217248052384397171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05467
Order of pole (three term test) = -0.9708
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1872787568, alloc=4848776, time=103.06
x[1] = 6.35
y1[1] (analytic) = 1.9977687286676840822459698015753
y1[1] (numeric) = 1.9977687286676840822459698015752
absolute error = 1e-31
relative error = 5.0055844084960824194603959209837e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0667649915215558209643145750232
y2[1] (numeric) = 1.0667649915215558209643145750237
absolute error = 5e-31
relative error = 4.6870679481788809737683248460587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06424
Order of pole (three term test) = -1.001
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1876789404, alloc=4848776, time=103.28
x[1] = 6.36
y1[1] (analytic) = 1.9970512018592136738884953211603
y1[1] (numeric) = 1.9970512018592136738884953211602
absolute error = 1e-31
relative error = 5.0073828806643541627143406019027e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0767391742925185984142305994414
y2[1] (numeric) = 1.0767391742925185984142305994419
absolute error = 5e-31
relative error = 4.6436501237965044766365843199248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07378
Order of pole (three term test) = -1.035
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.37
y1[1] (analytic) = 1.9962339707614305761312505732947
y1[1] (numeric) = 1.9962339707614305761312505732946
absolute error = 1e-31
relative error = 5.0094328352631253290188195914006e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0867056832100012227507449816142
y2[1] (numeric) = 1.0867056832100012227507449816147
absolute error = 5e-31
relative error = 4.6010617936869401624119477699882e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08329
Order of pole (three term test) = -1.075
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1880791660, alloc=4848776, time=103.51
x[1] = 6.38
y1[1] (analytic) = 1.9953171170967635436392743633319
y1[1] (numeric) = 1.9953171170967635436392743633318
absolute error = 1e-31
relative error = 5.0117346833320664548085128793318e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.0966635216314173421246287010364
y2[1] (numeric) = 1.0966635216314173421246287010369
absolute error = 5e-31
relative error = 4.5592835918914360172425933420973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09277
Order of pole (three term test) = -1.119
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1884793780, alloc=4848776, time=103.73
x[1] = 6.39
y1[1] (analytic) = 1.9943007325498150009420712157889
y1[1] (numeric) = 1.9943007325498150009420712157888
absolute error = 1e-31
relative error = 5.0142888867189508462883133578572e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1066116937812229859478449144211
y2[1] (numeric) = 1.1066116937812229859478449144216
absolute error = 5e-31
relative error = 4.5182967323572305098980132637313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1022
Order of pole (three term test) = -1.168
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1888795752, alloc=4848776, time=103.95
x[1] = 6.4
y1[1] (analytic) = 1.9931849187581926585947390986722
y1[1] (numeric) = 1.9931849187581926585947390986721
absolute error = 1e-31
relative error = 5.0170959582767998232310490090278e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.116549204850493289480420488799
y2[1] (numeric) = 1.1165492048504932894804204887994
absolute error = 4e-31
relative error = 3.5824663907540042228847243027606e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1116
Order of pole (three term test) = -1.221
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.41
y1[1] (analytic) = 1.9919697873023458371046380129593
y1[1] (numeric) = 1.9919697873023458371046380129592
absolute error = 1e-31
relative error = 5.0201564620830148123502903943088e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1264750610964025573122459647381
y2[1] (numeric) = 1.1264750610964025573122459647386
absolute error = 5e-31
relative error = 4.4386246732648306987668306127310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.121
Order of pole (three term test) = -1.28
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1892796820, alloc=4848776, time=104.17
x[1] = 6.42
y1[1] (analytic) = 1.9906554596944075149827370785494
y1[1] (numeric) = 1.9906554596944075149827370785493
absolute error = 1e-31
relative error = 5.0234710136806572195486107986128e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1363882699415977178163555462574
y2[1] (numeric) = 1.1363882699415977178163555462579
absolute error = 5e-31
relative error = 4.3999046208537197161039158739513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1303
Order of pole (three term test) = -1.343
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1896799756, alloc=4848776, time=104.39
x[1] = 6.43
y1[1] (analytic) = 1.989242067366043216705536719677
y1[1] (numeric) = 1.9892420673660432167055367196769
absolute error = 1e-31
relative error = 5.0270402803420535170470490766568e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1462878400734552313110527254404
y2[1] (numeric) = 1.1462878400734552313110527254409
absolute error = 5e-31
relative error = 4.3619061680699632768217389636150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1395
Order of pole (three term test) = -1.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1900802652, alloc=4848776, time=104.61
x[1] = 6.44
y1[1] (analytic) = 1.9877297516553079556886438646254
y1[1] (numeric) = 1.9877297516553079556886438646253
absolute error = 1e-31
relative error = 5.0308649813549196878337210876750e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.156172781543211526322779143611
y2[1] (numeric) = 1.1561727815432115263227791436116
absolute error = 6e-31
relative error = 5.1895357647076318399736798980141e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1487
Order of pole (three term test) = -1.483
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.45
y1[1] (analytic) = 1.9861186637925125465667502912062
y1[1] (numeric) = 1.9861186637925125465667502912061
absolute error = 1e-31
relative error = 5.0349458883312160952252424369257e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1660421058649570509887088237076
y2[1] (numeric) = 1.1660421058649570509887088237081
absolute error = 5e-31
relative error = 4.2880098195862795810791294267241e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1579
Order of pole (three term test) = -1.559
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1904803952, alloc=4848776, time=104.83
x[1] = 6.46
y1[1] (analytic) = 1.9844089648851007001370080863308
y1[1] (numeric) = 1.9844089648851007001370080863307
absolute error = 1e-31
relative error = 5.0392838255389610091613983961542e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1758948261144840402764222822845
y2[1] (numeric) = 1.175894826114484040276422282285
absolute error = 5e-31
relative error = 4.2520809590782267735076164029025e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.167
Order of pole (three term test) = -1.641
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1908804972, alloc=4848776, time=105.05
x[1] = 6.47
y1[1] (analytic) = 1.9826008259015384132437055032545
y1[1] (numeric) = 1.9826008259015384132437055032544
absolute error = 1e-31
relative error = 5.0438796702572484430818774139681e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.1857299570279781143263114185045
y2[1] (numeric) = 1.185729957027978114326311418505
absolute error = 5e-31
relative error = 4.2168117372461911739679477438738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.176
Order of pole (three term test) = -1.727
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.48
y1[1] (analytic) = 1.9806944276542172646518292852309
y1[1] (numeric) = 1.9806944276542172646518292852307
absolute error = 2e-31
relative error = 1.0097468706309467312420915368232e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.1955465151005438388391236641071
y2[1] (numeric) = 1.1955465151005438388391236641076
absolute error = 5e-31
relative error = 4.1821877583571115073082595357528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1849
Order of pole (three term test) = -1.817
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1912806092, alloc=4848776, time=105.27
x[1] = 6.49
y1[1] (analytic) = 1.9786899607813733265656788933949
y1[1] (numeric) = 1.9786899607813733265656788933948
absolute error = 1e-31
relative error = 5.0538488586918676765933434637827e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.205343518684554395034710999914
y2[1] (numeric) = 1.2053435186845543950347109999145
absolute error = 5e-31
relative error = 4.1481950352682237240404435877610e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1938
Order of pole (three term test) = -1.912
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1916808816, alloc=4848776, time=105.49
x[1] = 6.5
y1[1] (analytic) = 1.9765876257280234998863132539441
y1[1] (numeric) = 1.9765876257280234998863132539439
absolute error = 2e-31
relative error = 1.0118448451094361043171581084156e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2151199880878155242969457490747
y2[1] (numeric) = 1.2151199880878155242969457490752
absolute error = 5e-31
relative error = 4.1148199758184332709997020091988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2026
Order of pole (three term test) = -2.012
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1920811244, alloc=4848776, time=105.71
x[1] = 6.51
y1[1] (analytic) = 1.9743876327259211795584179456101
y1[1] (numeric) = 1.97438763272592117955841794561
absolute error = 1e-31
relative error = 5.0648615470679314564569626640187e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2248749456715339311921416700011
y2[1] (numeric) = 1.2248749456715339311921416700016
absolute error = 5e-31
relative error = 4.0820493697491423007366308762054e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2113
Order of pole (three term test) = -2.115
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.52
y1[1] (analytic) = 1.9720902017725332544233545841722
y1[1] (numeric) = 1.9720902017725332544233545841721
absolute error = 1e-31
relative error = 5.0707619717454636607472756122881e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.2346074159480803481023185705953
y2[1] (numeric) = 1.2346074159480803481023185705958
absolute error = 5e-31
relative error = 4.0498703761311829510016997801529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2199
Order of pole (three term test) = -2.223
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1924813580, alloc=4848776, time=105.93
x[1] = 6.53
y1[1] (analytic) = 1.9696955626090405438608879906796
y1[1] (numeric) = 1.9696955626090405438608879906794
absolute error = 2e-31
relative error = 1.0153853407431240177843456393666e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2443164256785374852483160662742
y2[1] (numeric) = 1.2443164256785374852483160662747
absolute error = 5e-31
relative error = 4.0182705112756611182975806467334e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2284
Order of pole (three term test) = -2.336
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1928814956, alloc=4848776, time=106.15
x[1] = 6.54
y1[1] (analytic) = 1.9672039546973638711575940623119
y1[1] (numeric) = 1.9672039546973638711575940623117
absolute error = 2e-31
relative error = 1.0166714006569194280618436316166e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2540010039700231113890438578016
y2[1] (numeric) = 1.2540010039700231113890438578021
absolute error = 5e-31
relative error = 3.9872376371076055203166222181320e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2369
Order of pole (three term test) = -2.453
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1932817112, alloc=4848776, time=106.38
x[1] = 6.55
y1[1] (analytic) = 1.9646156271962180709754666300476
y1[1] (numeric) = 1.9646156271962180709754666300474
absolute error = 2e-31
relative error = 1.0180108374961266035141798270846e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2636601823727785329699009008071
y2[1] (numeric) = 1.2636601823727785329699009008076
absolute error = 5e-31
relative error = 3.9567599499823480475319129974475e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2452
Order of pole (three term test) = -2.573
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.56
y1[1] (analytic) = 1.9619308389361963255000215151936
y1[1] (numeric) = 1.9619308389361963255000215151933
absolute error = 3e-31
relative error = 1.5291058891895845133967295878128e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2732929949770127629533554213434
y2[1] (numeric) = 1.2732929949770127629533554213439
absolute error = 5e-31
relative error = 3.9268259699255369573533217570367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2535
Order of pole (three term test) = -2.698
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1936818336, alloc=4848776, time=106.59
x[1] = 6.57
y1[1] (analytic) = 1.9591498583938873208135199903714
y1[1] (numeric) = 1.9591498583938873208135199903712
absolute error = 2e-31
relative error = 1.0208509529942756186929505133145e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2828984785094926949955059244941
y2[1] (numeric) = 1.2828984785094926949955059244945
absolute error = 4e-31
relative error = 3.1179396242228861214857616546180e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2616
Order of pole (three term test) = -2.828
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1940819496, alloc=4848776, time=106.82
x[1] = 6.58
y1[1] (analytic) = 1.9562729636650278117561053581556
y1[1] (numeric) = 1.9562729636650278117561053581554
absolute error = 2e-31
relative error = 1.0223522162536309319635795691783e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.2924756724298696240316970834387
y2[1] (numeric) = 1.2924756724298696240316970834392
absolute error = 5e-31
relative error = 3.8685447677324096783038560223549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2697
Order of pole (three term test) = -2.961
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.59
y1[1] (analytic) = 1.9533004424366932799959937456649
y1[1] (numeric) = 1.9533004424366932799959937456647
absolute error = 2e-31
relative error = 1.0239080258974652122444013703585e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.302023619026732480699403780303
y2[1] (numeric) = 1.3020236190267324806994037803035
absolute error = 5e-31
relative error = 3.8401761127325160805581873075471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2776
Order of pole (three term test) = -3.098
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1944822104, alloc=4848776, time=107.04
x[1] = 6.6
y1[1] (analytic) = 1.9502325919585294662197377216682
y1[1] (numeric) = 1.950232591958529466219737721668
absolute error = 2e-31
relative error = 1.0255187038954627459390687778687e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3115413635133781743549851055926
y2[1] (numeric) = 1.3115413635133781743549851055931
absolute error = 5e-31
relative error = 3.8123082802405250066152327167510e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2854
Order of pole (three term test) = -3.239
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1948823272, alloc=4848776, time=107.26
x[1] = 6.61
y1[1] (analytic) = 1.9470697190130276532653700665807
y1[1] (numeric) = 1.9470697190130276532653700665805
absolute error = 2e-31
relative error = 1.0271845843372279343612560788600e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.321027954123289467729814993965
y2[1] (numeric) = 1.3210279541232894677298149939655
absolute error = 5e-31
relative error = 3.7849312608364060700698404268138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2931
Order of pole (three term test) = -3.384
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1952825112, alloc=4848776, time=107.48
x[1] = 6.62
y1[1] (analytic) = 1.9438121398848466726453438661522
y1[1] (numeric) = 1.943812139884846672645343866152
absolute error = 2e-31
relative error = 1.0289060135813751790844923758817e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3304824422053108355178885136054
y2[1] (numeric) = 1.330482442205310835517888513606
absolute error = 6e-31
relative error = 4.5096423745771772884385684908617e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3007
Order of pole (three term test) = -3.533
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.63
y1[1] (analytic) = 1.9404601803291847022330517254913
y1[1] (numeric) = 1.9404601803291847022330517254911
absolute error = 2e-31
relative error = 1.0306833504105787979625170703049e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3399038823185127893883579996919
y2[1] (numeric) = 1.3399038823185127893883579996924
absolute error = 5e-31
relative error = 3.7316109505916292189792446716778e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3082
Order of pole (three term test) = -3.686
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1956825996, alloc=4848776, time=107.70
x[1] = 6.64
y1[1] (analytic) = 1.9370141755392040179067987040978
y1[1] (numeric) = 1.9370141755392040179067987040976
absolute error = 2e-31
relative error = 1.0325169661927036250377238268722e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3492913323267351830695511189999
y2[1] (numeric) = 1.3492913323267351830695511190004
absolute error = 5e-31
relative error = 3.7056489434182729294230298355059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3155
Order of pole (three term test) = -3.842
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1960826632, alloc=4848776, time=107.92
x[1] = 6.65
y1[1] (analytic) = 1.9334744701125119566489186248007
y1[1] (numeric) = 1.9334744701125119566489186248005
absolute error = 2e-31
relative error = 1.0344072450481421753077588258766e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3586438534928000432527482887922
y2[1] (numeric) = 1.3586438534928000432527482887927
absolute error = 5e-31
relative error = 3.6801403010406338624718258113102e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3228
Order of pole (three term test) = -4.002
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.66
y1[1] (analytic) = 1.9298414180167014429757914073278
y1[1] (numeric) = 1.9298414180167014429757914073276
absolute error = 2e-31
relative error = 1.0363545840234896352567719961663e-29 %
Correct digits = 31
bytes used=1964827404, alloc=4848776, time=108.14
h = 0.01
y2[1] (analytic) = 1.3679605105723845051111395029691
y2[1] (numeric) = 1.3679605105723845051111395029696
absolute error = 5e-31
relative error = 3.6550762696416514086782325837308e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3299
Order of pole (three term test) = -4.166
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.67
y1[1] (analytic) = 1.9261153825539545246174022925197
y1[1] (numeric) = 1.9261153825539545246174022925195
absolute error = 2e-31
relative error = 1.0383593932716934794294502789363e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3772403719075444652186358553043
y2[1] (numeric) = 1.3772403719075444652186358553047
absolute error = 4e-31
relative error = 2.9043586592366637601272782758542e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3368
Order of pole (three term test) = -4.333
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1968828476, alloc=4848776, time=108.36
x[1] = 6.68
y1[1] (analytic) = 1.922296736324712457063378045988
y1[1] (numeric) = 1.9222967363247124570633780459877
absolute error = 3e-31
relative error = 1.5606331443582303294931534765634e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3864825095198795995811799962591
y2[1] (numeric) = 1.3864825095198795995811799962596
absolute error = 5e-31
relative error = 3.6062481608451254902556216570287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3437
Order of pole (three term test) = -4.503
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1972829864, alloc=4848776, time=108.58
x[1] = 6.69
y1[1] (analytic) = 1.9183858611904159699367707089692
y1[1] (numeric) = 1.9183858611904159699367707089689
absolute error = 3e-31
relative error = 1.5638146947863815120616530211414e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.3956859992033304303563896485654
y2[1] (numeric) = 1.3956859992033304303563896485658
absolute error = 4e-31
relative error = 2.8659741534150477939958390613928e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3503
Order of pole (three term test) = -4.677
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.7
y1[1] (analytic) = 1.9143831482353194411379018434766
y1[1] (numeric) = 1.9143831482353194411379018434764
absolute error = 2e-31
relative error = 1.0447229447478172120317894418132e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4048499206165981616321928483868
y2[1] (numeric) = 1.4048499206165981616321928483873
absolute error = 5e-31
relative error = 3.5590990372875318073418123562199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3569
Order of pole (three term test) = -4.855
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1976831052, alloc=4848776, time=108.80
x[1] = 6.71
y1[1] (analytic) = 1.9102889977273827973090314718501
y1[1] (numeric) = 1.9102889977273827973090314718498
absolute error = 3e-31
relative error = 1.5704430081359500034473907488979e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4139733573751780423578933216319
y2[1] (numeric) = 1.4139733573751780423578933216324
absolute error = 5e-31
relative error = 3.5361345204422546789941438664684e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3633
Order of pole (three term test) = -5.035
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1980831916, alloc=4848776, time=109.02
x[1] = 6.72
y1[1] (analytic) = 1.9061038190782450513972152694962
y1[1] (numeric) = 1.9061038190782450513972152694959
absolute error = 3e-31
relative error = 1.5738911857648666739679849104672e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4230553971429970531680671023396
y2[1] (numeric) = 1.4230553971429970531680671023401
absolute error = 5e-31
relative error = 3.5135666608891476073600011545389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3696
Order of pole (three term test) = -5.219
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1984834656, alloc=4848776, time=109.24
x[1] = 6.73
y1[1] (analytic) = 1.9018280308022834799282384509219
y1[1] (numeric) = 1.9018280308022834799282384509216
absolute error = 3e-31
relative error = 1.5774296894417179346192400352367e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.432095131723646753406972487949
y2[1] (numeric) = 1.4320951317236467534069724879495
absolute error = 5e-31
relative error = 3.4913881691519194799285298142926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3757
Order of pole (three term test) = -5.406
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.74
y1[1] (analytic) = 1.8974620604747625340397817171234
y1[1] (numeric) = 1.8974620604747625340397817171231
absolute error = 3e-31
relative error = 1.5810592804418826111075432616398e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4410916571512021651447980095527
y2[1] (numeric) = 1.4410916571512021651447980095532
absolute error = 5e-31
relative error = 3.4695919410734540019204006285175e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3816
Order of pole (three term test) = -5.596
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1988837080, alloc=4848776, time=109.47
x[1] = 6.75
y1[1] (analytic) = 1.8930063446890766693478401565171
y1[1] (numeric) = 1.8930063446890766693478401565168
absolute error = 3e-31
relative error = 1.5847807422392687789593412410525e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4500440737806176123730289434098
y2[1] (numeric) = 1.4500440737806176123730289434103
absolute error = 5e-31
relative error = 3.4481710524589668427103642737770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3874
Order of pole (three term test) = -5.788
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=1992839688, alloc=4848776, time=109.69
x[1] = 6.76
y1[1] (analytic) = 1.8884613290130913703277776011807
y1[1] (numeric) = 1.8884613290130913703277776011803
absolute error = 4e-31
relative error = 2.1181265078329124850641180477917e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4589514863776904758703424419645
y2[1] (numeric) = 1.458951486377690475870342441965
absolute error = 5e-31
relative error = 3.4271187539032465723634814494904e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3931
Order of pole (three term test) = -5.984
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.77
y1[1] (analytic) = 1.883827467944586735071195974561
y1[1] (numeric) = 1.8838274679445867350711959745606
absolute error = 4e-31
relative error = 2.1233367004486533047595491471835e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4678130042085838674385142406797
y2[1] (numeric) = 1.4678130042085838674385142406802
absolute error = 5e-31
relative error = 3.4064284657948663169439137648872e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3986
Order of pole (three term test) = -6.182
NO COMPLEX POLE (six term test) for Equation 2
bytes used=1996841068, alloc=4848776, time=109.91
TOP MAIN SOLVE Loop
x[1] = 6.78
y1[1] (analytic) = 1.8791052248658080760230137214455
y1[1] (numeric) = 1.8791052248658080760230137214451
absolute error = 4e-31
relative error = 2.1286727039384666101701657135094e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4766277411288992713155153298713
y2[1] (numeric) = 1.4766277411288992713155153298717
absolute error = 4e-31
relative error = 2.7088750187924499950139093995284e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4039
Order of pole (three term test) = -6.384
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2000843628, alloc=4848776, time=110.13
x[1] = 6.79
y1[1] (analytic) = 1.874295071997128081600805239217
y1[1] (numeric) = 1.8742950719971280816008052392166
absolute error = 4e-31
relative error = 2.1341356864038796680697677479147e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4853948156722902455758842356298
y2[1] (numeric) = 1.4853948156722902455758842356302
absolute error = 4e-31
relative error = 2.6928867381226172608657609868054e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4091
Order of pole (three term test) = -6.587
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2004845352, alloc=4848776, time=110.35
x[1] = 6.8
y1[1] (analytic) = 1.8693974903498251724416246398463
y1[1] (numeric) = 1.8693974903498251724416246398459
absolute error = 4e-31
relative error = 2.1397268481683206316713002815590e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.4941133511386083222220793776203
y2[1] (numeric) = 1.4941133511386083222220793776207
absolute error = 4e-31
relative error = 2.6771730517980770891271585503182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4141
Order of pole (three term test) = -6.794
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.81
y1[1] (analytic) = 1.864412969677982774401337921625
y1[1] (numeric) = 1.8644129696779827744013379216246
absolute error = 4e-31
relative error = 2.1454474223545393092896203824638e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.502782475681572291450257040417
y2[1] (numeric) = 1.5027824756815722914502570404174
absolute error = 4e-31
relative error = 2.6617292021493923320279431865551e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4189
Order of pole (three term test) = -7.003
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2008847368, alloc=4848776, time=110.57
x[1] = 6.82
y1[1] (analytic) = 1.8593420084295143183390798118649
y1[1] (numeric) = 1.8593420084295143183390798118645
absolute error = 4e-31
relative error = 2.1512986754806791929681130530927e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5114013223959521032351058739392
y2[1] (numeric) = 1.5114013223959521032351058739396
absolute error = 4e-31
relative error = 2.6465505493001631393879220431824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4236
Order of pole (three term test) = -7.214
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2012848984, alloc=4848776, time=110.79
x[1] = 6.83
y1[1] (analytic) = 1.8541851136963188641460444707435
y1[1] (numeric) = 1.8541851136963188641460444707431
absolute error = 4e-31
relative error = 2.1572819080755093475535038503897e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.519969029404258667916232448682
y2[1] (numeric) = 1.5199690294042586679162324486824
absolute error = 4e-31
relative error = 2.6316325679134214277798591450549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4281
Order of pole (three term test) = -7.427
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2016851548, alloc=4848776, time=111.01
x[1] = 6.84
y1[1] (analytic) = 1.8489428011635723334146703357036
y1[1] (numeric) = 1.8489428011635723334146703357032
absolute error = 4e-31
relative error = 2.1633984553133441506386020902778e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.52848473994293088687828048687
y2[1] (numeric) = 1.5284847399429308868782804868705
absolute error = 5e-31
relative error = 3.2712135550575959668520368656127e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4325
Order of pole (three term test) = -7.643
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.85
y1[1] (analytic) = 1.8436155950581594215826950226731
y1[1] (numeric) = 1.8436155950581594215826950226727
absolute error = 4e-31
relative error = 2.1696496876691989737307925485437e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5369476024480112946935380437703
y2[1] (numeric) = 1.5369476024480112946935380437707
absolute error = 4e-31
relative error = 2.6025610721074037269399114066682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4366
Order of pole (three term test) = -7.861
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2020852764, alloc=4848776, time=111.23
x[1] = 6.86
y1[1] (analytic) = 1.8382040280962513463178926153106
y1[1] (numeric) = 1.8382040280962513463178926153102
absolute error = 4e-31
relative error = 2.1760370115947507367753638381334e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5453567706403017452342145089099
y2[1] (numeric) = 1.5453567706403017452342145089104
absolute error = 5e-31
relative error = 3.2354988148971609074570625586995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4406
Order of pole (three term test) = -8.081
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2024854088, alloc=4848776, time=111.46
x[1] = 6.87
y1[1] (analytic) = 1.8327086414300346743249698044871
y1[1] (numeric) = 1.8327086414300346743249698044868
absolute error = 3e-31
relative error = 1.6369214026617704137898331651175e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.553711403609990626256739034717
y2[1] (numeric) = 1.5537114036099906262567390347175
absolute error = 5e-31
relative error = 3.2181008573295440007015271027040e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4444
Order of pole (three term test) = -8.302
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.88
y1[1] (analytic) = 1.8271299845935965536475476920373
y1[1] (numeric) = 1.827129984593596553647547692037
absolute error = 3e-31
relative error = 1.6419193080383285732237657310654e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5620106659007431398071444064856
y2[1] (numeric) = 1.562010665900743139807144406486
absolute error = 4e-31
relative error = 2.5608019761461585075552407140251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4481
Order of pole (three term test) = -8.526
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2028857248, alloc=4848776, time=111.67
TOP MAIN SOLVE Loop
x[1] = 6.89
y1[1] (analytic) = 1.8214686154479717628969035711689
y1[1] (numeric) = 1.8214686154479717628969035711686
absolute error = 3e-31
relative error = 1.6470226138165879823065285550419e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5702537275932462394895708153654
y2[1] (numeric) = 1.5702537275932462394895708153659
absolute error = 5e-31
relative error = 3.1841987776482354748602333664093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4515
Order of pole (three term test) = -8.752
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2032859648, alloc=4848776, time=111.89
x[1] = 6.9
y1[1] (analytic) = 1.8157251001253570726567558363581
y1[1] (numeric) = 1.8157251001253570726567558363577
absolute error = 4e-31
relative error = 2.2029766508839037891330630590699e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5784397643881998701737832329889
y2[1] (numeric) = 1.5784397643881998701737832329893
absolute error = 4e-31
relative error = 2.5341480177106359749079287523152e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4548
Order of pole (three term test) = -8.979
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2036861676, alloc=4848776, time=112.12
x[1] = 6.91
y1[1] (analytic) = 1.8099000129724984975814636670357
y1[1] (numeric) = 1.8099000129724984975814636670353
absolute error = 4e-31
relative error = 2.2100668386816460885395497466827e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5865679576887462110868907718869
y2[1] (numeric) = 1.5865679576887462110868907718874
absolute error = 5e-31
relative error = 3.1514565611698196133992415684150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4579
Order of pole (three term test) = -9.207
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.92
y1[1] (analytic) = 1.8039939364932571004152545324359
y1[1] (numeric) = 1.8039939364932571004152545324356
absolute error = 3e-31
relative error = 1.6629767646734068085022954709376e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5946374946823286794336496667012
y2[1] (numeric) = 1.5946374946823286794336496667017
absolute error = 5e-31
relative error = 3.1355088643491737547443655574927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.05
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4608
Order of pole (three term test) = -9.438
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2040862988, alloc=4848776, time=112.33
x[1] = 6.93
y1[1] (analytic) = 1.7980074612903590913042159244115
y1[1] (numeric) = 1.7980074612903590913042159244112
absolute error = 3e-31
relative error = 1.6685136544689409892608458885800e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6026475684219725087132034548561
y2[1] (numeric) = 1.6026475684219725087132034548567
absolute error = 6e-31
relative error = 3.7438050125442284430706762808992e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.35
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4635
Order of pole (three term test) = -9.669
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2044864264, alloc=4848776, time=112.56
x[1] = 6.94
y1[1] (analytic) = 1.7919411860063360473425786969406
y1[1] (numeric) = 1.7919411860063360473425786969403
absolute error = 3e-31
relative error = 1.6741620893741723673639447094270e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6105973779069787737421622721598
y2[1] (numeric) = 1.6105973779069787737421622721604
absolute error = 6e-31
relative error = 3.7253258215266598901220840308304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.466
Order of pole (three term test) = -9.902
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2048866000, alloc=4848776, time=112.78
x[1] = 6.95
y1[1] (analytic) = 1.7857957172636611582821210643353
y1[1] (numeric) = 1.785795717263661158282121064335
absolute error = 3e-31
relative error = 1.6799233926917685918370123297032e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6184861281630237930487637521055
y2[1] (numeric) = 1.6184861281630237930487637521061
absolute error = 6e-31
relative error = 3.7071680106458369406768717515920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4684
Order of pole (three term test) = -10.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.96
y1[1] (analytic) = 1.7795716696040874847302360221301
y1[1] (numeric) = 1.7795716696040874847302360221298
absolute error = 3e-31
relative error = 1.6857989207410954631288666173306e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6263130303216558987646253922822
y2[1] (numeric) = 1.6263130303216558987646253922828
absolute error = 6e-31
relative error = 3.6893266475355647377126810588395e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.07
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.26
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4706
Order of pole (three term test) = -10.37
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2052868032, alloc=4848776, time=113.00
x[1] = 6.97
y1[1] (analytic) = 1.7732696654271942949602911009115
y1[1] (numeric) = 1.7732696654271942949602911009112
absolute error = 3e-31
relative error = 1.6917900635700983113430442570157e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6340773016991816244033463000763
y2[1] (numeric) = 1.6340773016991816244033463000769
absolute error = 6e-31
relative error = 3.6717969179064846862216732153770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4725
Order of pole (three term test) = -10.61
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2056869924, alloc=4848776, time=113.22
x[1] = 6.98
y1[1] (analytic) = 1.7668903349281476256493882018266
y1[1] (numeric) = 1.7668903349281476256493882018263
absolute error = 3e-31
relative error = 1.6978982456893670315755728239991e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6417781658749334219729187281771
y2[1] (numeric) = 1.6417781658749334219729187281776
absolute error = 5e-31
relative error = 3.0454784354714628153848192303930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4743
Order of pole (three term test) = -10.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 6.99
y1[1] (analytic) = 1.7604343160346812904355837112889
y1[1] (numeric) = 1.7604343160346812904355837112886
absolute error = 3e-31
relative error = 1.7041249268290784377519046783563e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6494148527689110817154610389165
y2[1] (numeric) = 1.649414852768911081715461038917
absolute error = 5e-31
relative error = 3.0313780621087434073713846184171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4759
Order of pole (three term test) = -11.08
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2060870592, alloc=4848776, time=113.44
TOP MAIN SOLVE Loop
x[1] = 7
y1[1] (analytic) = 1.7539022543433046381411975217192
y1[1] (numeric) = 1.7539022543433046381411975217189
absolute error = 3e-31
relative error = 1.7104716027195362538017329211926e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6569865987187890903969990915936
y2[1] (numeric) = 1.6569865987187890903969990915941
absolute error = 5e-31
relative error = 3.0175259135264504374506407158066e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4773
Order of pole (three term test) = -11.32
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2064871452, alloc=4848776, time=113.66
x[1] = 7.01
y1[1] (analytic) = 1.7472948030547434398332286031403
y1[1] (numeric) = 1.74729480305474343983322860314
absolute error = 3e-31
relative error = 1.7169398058960568024070601084219e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6644926465562822274756396593097
y2[1] (numeric) = 1.6644926465562822274756396593102
absolute error = 5e-31
relative error = 3.0039183473382396731765084728548e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.78
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.89
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4785
Order of pole (three term test) = -11.56
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2068872772, alloc=4848776, time=113.88
x[1] = 7.02
y1[1] (analytic) = 1.7406126229086203605783720026158
y1[1] (numeric) = 1.7406126229086203605783720026154
absolute error = 4e-31
relative error = 2.2980414753719697696317560334243e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6719322456828617626521568426536
y2[1] (numeric) = 1.6719322456828617626521568426541
absolute error = 5e-31
relative error = 2.9905518078921113942390640851614e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4796
Order of pole (three term test) = -11.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.03
y1[1] (analytic) = 1.7338563821173815477910290110704
y1[1] (numeric) = 1.73385638211738154779102901107
absolute error = 4e-31
relative error = 2.3069961510394585963135681488193e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6793046521448146832463330425656
y2[1] (numeric) = 1.679304652144814683246333042566
absolute error = 4e-31
relative error = 2.3819382593213112622664624261331e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.59
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4804
Order of pole (three term test) = -12.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2072873940, alloc=4848776, time=114.10
x[1] = 7.04
y1[1] (analytic) = 1.7270267562994759434604147036375
y1[1] (numeric) = 1.7270267562994759434604147036371
absolute error = 4e-31
relative error = 2.3161192989104900629529718387340e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6866091287076384455388660059318
y2[1] (numeric) = 1.6866091287076384455388660059322
absolute error = 4e-31
relative error = 2.3716224061143281130944476118529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.481
Order of pole (three term test) = -12.28
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2076874904, alloc=4848776, time=114.32
x[1] = 7.05
y1[1] (analytic) = 1.7201244284117940022698564219134
y1[1] (numeric) = 1.720124428411794002269856421913
absolute error = 4e-31
relative error = 2.3254131700770246858926345523629e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6938449449297638106657031726717
y2[1] (numeric) = 1.6938449449297638106657031726721
absolute error = 4e-31
relative error = 2.3614912403719823043602435575079e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.31
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4815
Order of pole (three term test) = -12.52
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2080877860, alloc=4848776, time=114.55
x[1] = 7.06
y1[1] (analytic) = 1.7131500886813725716801703877066
y1[1] (numeric) = 1.7131500886813725716801703877063
absolute error = 3e-31
relative error = 1.7511600529461651998003388486956e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7010113772355983928426493826761
y2[1] (numeric) = 1.7010113772355983928426493826765
absolute error = 4e-31
relative error = 2.3515421786893671329037106556524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 2 = 0.4817
Order of pole (three term test) = -12.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.07
y1[1] (analytic) = 1.7061044345363727634321957003992
y1[1] (numeric) = 1.7061044345363727634321957003989
absolute error = 3e-31
relative error = 1.7583917720811963765240253022327e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7081077089878836156262949024486
y2[1] (numeric) = 1.708107708987883615626294902449
absolute error = 4e-31
relative error = 2.3417726990823936490634567612299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4818
Order of pole (three term test) = -13.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2084879220, alloc=4848776, time=114.77
x[1] = 7.08
y1[1] (analytic) = 1.6989881705363377186238172158325
y1[1] (numeric) = 1.6989881705363377186238172158322
absolute error = 3e-31
relative error = 1.7657568498861048570383562112350e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7151332305593578405759349412061
y2[1] (numeric) = 1.7151332305593578405759349412064
absolute error = 3e-31
relative error = 1.7491352546540116193081361983980e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4817
Order of pole (three term test) = -13.25
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2088882428, alloc=4848776, time=114.99
x[1] = 7.09
y1[1] (analytic) = 1.6918020083017372405268512690559
y1[1] (numeric) = 1.6918020083017372405268512690556
absolute error = 3e-31
relative error = 1.7732571455045478833424676587574e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7220872394037185020633335393084
y2[1] (numeric) = 1.7220872394037185020633335393087
absolute error = 3e-31
relative error = 1.7420720224596550143799922410581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4814
Order of pole (three term test) = -13.49
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.1
y1[1] (analytic) = 1.6845466664428063406217999420893
y1[1] (numeric) = 1.684546666442806340621799942089
absolute error = 3e-31
relative error = 1.7808945633634399982622843576322e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7289690401258761520759857678532
y2[1] (numeric) = 1.7289690401258761520759857678535
absolute error = 3e-31
relative error = 1.7351380680486837963700447386936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4808
Order of pole (three term test) = -13.73
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2092884152, alloc=4848776, time=115.21
TOP MAIN SOLVE Loop
x[1] = 7.11
y1[1] (analytic) = 1.6772228704876848139365693873049
y1[1] (numeric) = 1.6772228704876848139365693873046
absolute error = 3e-31
relative error = 1.7886710542694259169652794065945e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.735777944551493389667942755402
y2[1] (numeric) = 1.7357779445514933896679427554023
absolute error = 3e-31
relative error = 1.7283316736549318124217235807059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4801
Order of pole (three term test) = -13.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2096886288, alloc=4848776, time=115.43
x[1] = 7.12
y1[1] (analytic) = 1.6698313528098650296717348469898
y1[1] (numeric) = 1.6698313528098650296717348469895
absolute error = 3e-31
relative error = 1.7965886165401245303470808159384e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7425132717958017212232033740469
y2[1] (numeric) = 1.7425132717958017212232033740473
absolute error = 4e-31
relative error = 2.2955348832882486487251014199457e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4792
Order of pole (three term test) = -14.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2100888384, alloc=4848776, time=115.65
x[1] = 7.13
y1[1] (analytic) = 1.6623728525549551922728298696433
y1[1] (numeric) = 1.662372852554955192272829869643
absolute error = 3e-31
relative error = 1.8046492971713306722740301929411e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7491743483316894699029934380455
y2[1] (numeric) = 1.7491743483316894699029934380459
absolute error = 4e-31
relative error = 2.2867931969246411431676758703628e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4781
Order of pole (three term test) = -14.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.14
y1[1] (analytic) = 1.6548481155667653965625220817479
y1[1] (numeric) = 1.6548481155667653965625220817476
absolute error = 3e-31
relative error = 1.8128551930414087625228726451513e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7557605080570539255427274225094
y2[1] (numeric) = 1.7557605080570539255427274225098
absolute error = 4e-31
relative error = 2.2782150422248926039806901536998e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4769
Order of pole (three term test) = -14.69
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2104889232, alloc=4848776, time=115.87
x[1] = 7.15
y1[1] (analytic) = 1.6472578943127238682655675486971
y1[1] (numeric) = 1.6472578943127238682655675486968
absolute error = 3e-31
relative error = 1.8212084521541619930002312466959e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7622710923614109998397896104677
y2[1] (numeric) = 1.7622710923614109998397896104681
absolute error = 4e-31
relative error = 2.2697983399591905196619171866340e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4754
Order of pole (three term test) = -14.93
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2108892296, alloc=4848776, time=116.09
x[1] = 7.16
y1[1] (analytic) = 1.6396029478086308482403383037247
y1[1] (numeric) = 1.6396029478086308482403383037244
absolute error = 3e-31
relative error = 1.8297112749215124579336990808531e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.768705450191755725922123751153
y2[1] (numeric) = 1.7687054501917557259221237511534
absolute error = 4e-31
relative error = 2.2615410607607595443272540239482e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4737
Order of pole (three term test) = -15.17
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2112893436, alloc=4848776, time=116.31
x[1] = 7.17
y1[1] (analytic) = 1.6318840415427576449657950046256
y1[1] (numeric) = 1.6318840415427576449657950046252
absolute error = 4e-31
relative error = 2.4511545539831755281151793621343e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.77506293811766701630255793724
y2[1] (numeric) = 1.7750629381176670163025579372403
absolute error = 3e-31
relative error = 1.6900809180215857907042347250532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4719
Order of pole (three term test) = -15.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.18
y1[1] (analytic) = 1.6241019473992984453154054422433
y1[1] (numeric) = 1.6241019473992984453154054422429
absolute error = 4e-31
relative error = 2.4628995774589561696724385613321e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7813429203956501687973230526633
y2[1] (numeric) = 1.7813429203956501687973230526636
absolute error = 3e-31
relative error = 1.6841226726483840518990403119699e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4698
Order of pole (three term test) = -15.64
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2116895600, alloc=4848776, time=116.53
x[1] = 7.19
y1[1] (analytic) = 1.6162574435811825383731415638198
y1[1] (numeric) = 1.6162574435811825383731415638194
absolute error = 4e-31
relative error = 2.4748532579915602600070597853375e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7875447690327106862117915153751
y2[1] (numeric) = 1.7875447690327106862117915153754
absolute error = 3e-31
relative error = 1.6782796447796840164980364907247e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.87
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4676
Order of pole (three term test) = -15.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2120896272, alloc=4848776, time=116.75
x[1] = 7.2
y1[1] (analytic) = 1.6083513145322546710048504790937
y1[1] (numeric) = 1.6083513145322546710048504790933
absolute error = 4e-31
relative error = 2.4870188272039877304714736147521e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7936678638491530524644457476436
y2[1] (numeric) = 1.7936678638491530524644457476439
absolute error = 3e-31
relative error = 1.6725504539965929448042959987178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.56
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4652
Order of pole (three term test) = -16.11
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.21
y1[1] (analytic) = 1.600384350858831317084592824522
y1[1] (numeric) = 1.6003843508588313170845928245216
absolute error = 4e-31
relative error = 2.4993995960116939115510456591918e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7997115925405981853237961160432
y2[1] (numeric) = 1.7997115925405981853237961160435
absolute error = 3e-31
relative error = 1.6669337534048947981962710094748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.26
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4626
Order of pole (three term test) = -16.34
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2124897472, alloc=4848776, time=116.97
TOP MAIN SOLVE Loop
x[1] = 7.22
y1[1] (analytic) = 1.5923573492506407046836562940431
y1[1] (numeric) = 1.5923573492506407046836562940427
absolute error = 4e-31
relative error = 2.5119989566929745813795113408907e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8056753507392133640646556876854
y2[1] (numeric) = 1.8056753507392133640646556876856
absolute error = 2e-31
relative error = 1.1076188192862207298195164701170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.97
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4598
Order of pole (three term test) = -16.57
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2128899912, alloc=4848776, time=117.19
x[1] = 7.23
y1[1] (analytic) = 1.5842711124011545071536423439622
y1[1] (numeric) = 1.5842711124011545071536423439618
absolute error = 4e-31
relative error = 2.5248203850271031911569583146412e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8115585420741485091020309448447
y2[1] (numeric) = 1.8115585420741485091020309448449
absolute error = 2e-31
relative error = 1.1040217324194750944597707506465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4568
Order of pole (three term test) = -16.8
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2132902168, alloc=4848776, time=117.41
x[1] = 7.24
y1[1] (analytic) = 1.5761264489273191648681277271593
y1[1] (numeric) = 1.5761264489273191648681277271589
absolute error = 4e-31
relative error = 2.5378674425026759545071775684155e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8173605782311727700250284673932
y2[1] (numeric) = 1.8173605782311727700250284673934
absolute error = 2e-31
relative error = 1.1004970746898170269650882412467e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4537
Order of pole (three term test) = -17.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.25
y1[1] (analytic) = 1.5679241732886948644238363482182
y1[1] (numeric) = 1.5679241732886948644238363482177
absolute error = 5e-31
relative error = 3.1889297232484037771701987177072e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8230808790115054584216711834121
y2[1] (numeric) = 1.8230808790115054584216711834122
absolute error = 1e-31
relative error = 5.4852201650110609423257260165343e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4503
Order of pole (three term test) = -17.26
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2136903816, alloc=4848776, time=117.63
x[1] = 7.26
y1[1] (analytic) = 1.5596651057060102613360173629058
y1[1] (numeric) = 1.5596651057060102613360173629053
absolute error = 5e-31
relative error = 3.2058164164265640309003302750709e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.82871887238983544245036732029
y2[1] (numeric) = 1.8287188723898354424503673202902
absolute error = 2e-31
relative error = 1.0936618143970528580477477540529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4468
Order of pole (three term test) = -17.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2140905460, alloc=4848776, time=117.85
x[1] = 7.27
y1[1] (analytic) = 1.5513500720791410906878891460087
y1[1] (numeric) = 1.5513500720791410906878891460082
absolute error = 5e-31
relative error = 3.2229991734224951453311812878083e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8342739945715232012669242437266
y2[1] (numeric) = 1.8342739945715232012669242437268
absolute error = 2e-31
relative error = 1.0903496456466906001501904947052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4431
Order of pole (three term test) = -17.7
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2144906204, alloc=4848776, time=118.08
x[1] = 7.28
y1[1] (analytic) = 1.5429799039045208678047332531733
y1[1] (numeric) = 1.5429799039045208678047332531728
absolute error = 5e-31
relative error = 3.2404829041178481191539678788709e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8397456900489798191493327030497
y2[1] (numeric) = 1.8397456900489798191493327030498
absolute error = 1e-31
relative error = 5.4355338643210891470252497404783e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4393
Order of pole (three term test) = -17.93
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.29
y1[1] (analytic) = 1.5345554381919919378137467806639
y1[1] (numeric) = 1.5345554381919919378137467806634
absolute error = 5e-31
relative error = 3.2582726407662294711921496365585e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8451334116572172814678913429188
y2[1] (numeric) = 1.8451334116572172814678913429189
absolute error = 1e-31
relative error = 5.4196623056207312225760454425609e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4352
Order of pole (three term test) = -18.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2148907852, alloc=4848776, time=118.30
x[1] = 7.3
y1[1] (analytic) = 1.5260775173811051889154065767377
y1[1] (numeric) = 1.5260775173811051889154065767372
absolute error = 5e-31
relative error = 3.2763735413522621489256279187456e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8504366206285645175173662279669
y2[1] (numeric) = 1.850436620628564517517366227967
absolute error = 1e-31
relative error = 5.4041299704732149391360213418594e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.431
Order of pole (three term test) = -18.36
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2152910360, alloc=4848776, time=118.52
x[1] = 7.31
y1[1] (analytic) = 1.5175469892568767993252681617755
y1[1] (numeric) = 1.517546989256876799325268161775
absolute error = 5e-31
relative error = 3.2947908930638355745462324117377e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8556547866465437186524987147974
y2[1] (numeric) = 1.8556547866465437186524987147975
absolute error = 1e-31
relative error = 5.3889333684049889764468845556093e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4266
Order of pole (three term test) = -18.58
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.32
y1[1] (analytic) = 1.5089647068650104421413027004031
y1[1] (numeric) = 1.5089647068650104421413027004026
absolute error = 5e-31
relative error = 3.3135301158818235801815644400499e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8607873878989015441399449026743
y2[1] (numeric) = 1.8607873878989015441399449026744
absolute error = 1e-31
relative error = 5.3740690984000317652268404695759e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.422
Order of pole (three term test) = -18.79
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2156912440, alloc=4848776, time=118.74
x[1] = 7.33
y1[1] (analytic) = 1.5003315284265934258456373647886
y1[1] (numeric) = 1.5003315284265934258456373647881
absolute error = 5e-31
relative error = 3.3325967662917339750161647653245e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8658339111297899116502539931945
y2[1] (numeric) = 1.8658339111297899116502539931946
absolute error = 1e-31
relative error = 5.3595338472248329586084701874053e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4173
Order of pole (three term test) = -19
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2160913412, alloc=4848776, time=118.96
x[1] = 7.34
y1[1] (analytic) = 1.4916483172522753007555626024528
y1[1] (numeric) = 1.4916483172522753007555626024523
absolute error = 5e-31
relative error = 3.3519965411219473554079404122087e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.870793851691091154354320208236
y2[1] (numeric) = 1.870793851691091154354320208236
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4124
Order of pole (three term test) = -19.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2164914412, alloc=4848776, time=119.18
x[1] = 7.35
y1[1] (analytic) = 1.4829159416559375134916436182999
y1[1] (numeric) = 1.4829159416559375134916436182994
absolute error = 5e-31
relative error = 3.3717352815134059869763376338206e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8756667135928824121513694426684
y2[1] (numeric) = 1.8756667135928824121513694426684
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4073
Order of pole (three term test) = -19.41
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.36
y1[1] (analytic) = 1.4741352748678627424255475449175
y1[1] (numeric) = 1.474135274867862742425547544917
absolute error = 5e-31
relative error = 3.3918189770258266547574322789779e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8804520095530342106314113723386
y2[1] (numeric) = 1.8804520095530342106314113723386
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4021
Order of pole (three term test) = -19.62
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2168916112, alloc=4848776, time=119.40
x[1] = 7.37
y1[1] (analytic) = 1.4653071949474125971016828724968
y1[1] (numeric) = 1.4653071949474125971016828724964
absolute error = 4e-31
relative error = 2.7298030159085878582822533051552e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8851492610459382679555927834817
y2[1] (numeric) = 1.8851492610459382679555927834817
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3967
Order of pole (three term test) = -19.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2172917164, alloc=4848776, time=119.62
x[1] = 7.38
y1[1] (analytic) = 1.4564325846952224137899406331777
y1[1] (numeric) = 1.4564325846952224137899406331773
absolute error = 4e-31
relative error = 2.7464367675054814628985238272664e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8897579983503596569143704586037
y2[1] (numeric) = 1.8897579983503596569143704586037
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3912
Order of pole (three term test) = -20.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2176919112, alloc=4848776, time=119.84
x[1] = 7.39
y1[1] (analytic) = 1.447512331564921927616811305895
y1[1] (numeric) = 1.4475123315649219276168113058946
absolute error = 4e-31
relative error = 2.7633616051308902012574093504972e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8942777605964085369871744703402
y2[1] (numeric) = 1.8942777605964085369871744703402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3855
Order of pole (three term test) = -20.21
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.4
y1[1] (analytic) = 1.4385473275743906491340984687003
y1[1] (numeric) = 1.4385473275743906491340984686999
absolute error = 4e-31
relative error = 2.7805828305590805376290833686806e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8987080958116267592694988965346
y2[1] (numeric) = 1.8987080958116267592694988965345
absolute error = 1e-31
relative error = 5.2667390116780292570636128301751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3796
Order of pole (three term test) = -20.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2180921240, alloc=4848776, time=120.07
x[1] = 7.41
y1[1] (analytic) = 1.4295384692165568197136187208456
y1[1] (numeric) = 1.4295384692165568197136187208452
absolute error = 4e-31
relative error = 2.7981058825175631484597901172432e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9030485609661847356453326235512
y2[1] (numeric) = 1.9030485609661847356453326235512
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3736
Order of pole (three term test) = -20.59
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2184923372, alloc=4848776, time=120.29
x[1] = 7.42
y1[1] (analytic) = 1.4204866573697488657980144485792
y1[1] (numeric) = 1.4204866573697488657980144485788
absolute error = 4e-31
relative error = 2.8159363407232699770851559366022e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.907298722017184052555676926842
y2[1] (numeric) = 1.907298722017184052555676926842
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3675
Order of pole (three term test) = -20.77
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.43
y1[1] (analytic) = 1.4113927972076083167875474809437
y1[1] (numeric) = 1.4113927972076083167875474809433
absolute error = 4e-31
relative error = 2.8340799300618943403028291283865e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9114581539520613991386916987506
y2[1] (numeric) = 1.9114581539520613991386916987506
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3612
Order of pole (three term test) = -20.96
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2188925552, alloc=4848776, time=120.50
x[1] = 7.44
y1[1] (analytic) = 1.4022577981085731951960126380232
y1[1] (numeric) = 1.4022577981085731951960126380228
absolute error = 4e-31
relative error = 2.8525425249161569245467311355243e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.915526440831089469384826128484
y2[1] (numeric) = 1.915526440831089469384826128484
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3547
Order of pole (three term test) = -21.13
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2192928420, alloc=4848776, time=120.73
x[1] = 7.45
y1[1] (analytic) = 1.3930825735649409306613253235169
y1[1] (numeric) = 1.3930825735649409306613253235165
absolute error = 4e-31
relative error = 2.8713301536490242712709564501959e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9195031758289705882521356215873
y2[1] (numeric) = 1.9195031758289705882521356215873
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3481
Order of pole (three term test) = -21.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2196929644, alloc=4848776, time=120.95
x[1] = 7.46
y1[1] (analytic) = 1.3838680410915198914436014504911
y1[1] (numeric) = 1.3838680410915198914436014504907
absolute error = 4e-31
relative error = 2.8904490032481835607326235118702e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9233879612755189024138346667882
y2[1] (numeric) = 1.9233879612755189024138346667881
absolute error = 1e-31
relative error = 5.1991590887198723577749314577032e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3414
Order of pole (three term test) = -21.48
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.47
y1[1] (analytic) = 1.3746151221338786681814564223101
y1[1] (numeric) = 1.3746151221338786681814564223097
absolute error = 4e-31
relative error = 2.9099054241383689195893765919359e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9271804086954270674529126075413
y2[1] (numeric) = 1.9271804086954270674529126075413
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3345
Order of pole (three term test) = -21.65
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2200930892, alloc=4848776, time=121.17
x[1] = 7.48
y1[1] (analytic) = 1.3653247419762022849016888635084
y1[1] (numeric) = 1.3653247419762022849016888635079
absolute error = 5e-31
relative error = 3.6621324189605511330861915869381e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9308801388471134548682316522293
y2[1] (numeric) = 1.9308801388471134548682316522293
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3275
Order of pole (three term test) = -21.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2204933580, alloc=4848776, time=121.39
x[1] = 7.49
y1[1] (analytic) = 1.3559978296487645515844618973593
y1[1] (numeric) = 1.3559978296487645515844618973588
absolute error = 5e-31
relative error = 3.6873215359755539086228806052210e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9344867817606459942037790778139
y2[1] (numeric) = 1.9344867817606459942037790778139
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3204
Order of pole (three term test) = -21.98
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.5
y1[1] (analytic) = 1.3466353178350258109716193361719
y1[1] (numeric) = 1.3466353178350258109716193361714
absolute error = 5e-31
relative error = 3.7129577204602487552087167596485e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.937999976774738857948463798149
y2[1] (numeric) = 1.937999976774738857948463798149
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
bytes used=2208934856, alloc=4848776, time=121.62
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3132
Order of pole (three term test) = -22.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.51
y1[1] (analytic) = 1.3372381427783653697660376664312
y1[1] (numeric) = 1.3372381427783653697660376664307
absolute error = 5e-31
relative error = 3.7390497922917106905624265951740e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9414193725728182895687977852796
y2[1] (numeric) = 1.9414193725728182895687977852796
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3058
Order of pole (three term test) = -22.29
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2212936832, alloc=4848776, time=121.84
x[1] = 7.52
y1[1] (analytic) = 1.3278072441884579409011711786588
y1[1] (numeric) = 1.3278072441884579409011711786583
absolute error = 5e-31
relative error = 3.7656068091840757381029468754692e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9447446272181539681217138320954
y2[1] (numeric) = 1.9447446272181539681217138320953
absolute error = 1e-31
relative error = 5.1420633126028626297485592068471e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2983
Order of pole (three term test) = -22.45
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2216938724, alloc=4848776, time=122.06
x[1] = 7.53
y1[1] (analytic) = 1.3183435651473034591585439161043
y1[1] (numeric) = 1.3183435651473034591585439161038
absolute error = 5e-31
relative error = 3.7926380741588641139534830648339e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9479754081880523963403344141535
y2[1] (numeric) = 1.9479754081880523963403344141534
absolute error = 1e-31
relative error = 5.1335350323039737447641236850873e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2906
Order of pole (three term test) = -22.59
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.54
y1[1] (analytic) = 1.3088480520149196670733184671152
y1[1] (numeric) = 1.3088480520149196670733184671147
absolute error = 5e-31
relative error = 3.8201531432947455591529209387524e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.951111392407108892882377468875
y2[1] (numeric) = 1.9511113924071088928823774688749
absolute error = 1e-31
relative error = 5.1252839991174892926930923448901e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2829
Order of pole (three term test) = -22.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2220940300, alloc=4848776, time=122.28
x[1] = 7.55
y1[1] (analytic) = 1.2993216543347069017907617945243
y1[1] (numeric) = 1.2993216543347069017907617945237
absolute error = 6e-31
relative error = 4.6177942005224153757048018379397e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.954152266279514863569684152709
y2[1] (numeric) = 1.954152266279514863569684152709
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2751
Order of pole (three term test) = -22.88
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2224941884, alloc=4848776, time=122.50
x[1] = 7.56
y1[1] (analytic) = 1.2897653247384945463160600407277
y1[1] (numeric) = 1.2897653247384945463160600407272
absolute error = 5e-31
relative error = 3.8766742322009404725441401844031e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9570977257204171209186672597821
y2[1] (numeric) = 1.957097725720417120918667259782
absolute error = 1e-31
relative error = 5.1096068778675585676338329841038e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2671
Order of pole (three term test) = -23.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2228944096, alloc=4848776, time=122.72
x[1] = 7.57
y1[1] (analytic) = 1.2801800188512786404332296334417
y1[1] (numeric) = 1.2801800188512786404332296334411
absolute error = 6e-31
relative error = 4.6868408439805787520183605871058e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9599474761863261160558599363545
y2[1] (numeric) = 1.9599474761863261160558599363544
absolute error = 1e-31
relative error = 5.1021775437870617073815551310957e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.259
Order of pole (three term test) = -23.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.58
y1[1] (analytic) = 1.270566695195660177452647741408
y1[1] (numeric) = 1.2705666951956601774526477414074
absolute error = 6e-31
relative error = 4.7223022787292826829203056943533e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9627012327045700422207132450104
y2[1] (numeric) = 1.9627012327045700422207132450102
absolute error = 2e-31
relative error = 1.0190037926679410444150991660076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2509
Order of pole (three term test) = -23.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2232945792, alloc=4848776, time=122.94
x[1] = 7.59
y1[1] (analytic) = 1.2609263150959936428778928397435
y1[1] (numeric) = 1.260926315095993642877892839743
absolute error = 5e-31
relative error = 3.9653387673326118873796439473621e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9653587199017918644698373032588
y2[1] (numeric) = 1.9653587199017918644698373032587
absolute error = 1e-31
relative error = 5.0881296624056985014321354049747e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2426
Order of pole (three term test) = -23.4
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2236948296, alloc=4848776, time=123.16
x[1] = 7.6
y1[1] (analytic) = 1.2512598425822553800581527493518
y1[1] (numeric) = 1.2512598425822553800581527493513
absolute error = 5e-31
relative error = 3.9959725628862014391210231882770e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9679196720314864259034630180288
y2[1] (numeric) = 1.9679196720314864259034630180287
absolute error = 1e-31
relative error = 5.0815082252198764888350465623730e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2342
Order of pole (three term test) = -23.51
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.61
y1[1] (analytic) = 1.2415682442936413959095254813347
y1[1] (numeric) = 1.2415682442936413959095254813342
absolute error = 5e-31
relative error = 4.0271648562054054034472077690615e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9703838330005748767264492819134
y2[1] (numeric) = 1.9703838330005748767264492819133
absolute error = 1e-31
relative error = 5.0751532937476565321008001065750e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2257
Order of pole (three term test) = -23.63
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2240951120, alloc=4848776, time=123.38
TOP MAIN SOLVE Loop
x[1] = 7.62
y1[1] (analytic) = 1.2318524893819042468443058622056
y1[1] (numeric) = 1.231852489381904246844305862205
absolute error = 6e-31
relative error = 4.8707130534846481929008110119072e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9727509563950137687230748141779
y2[1] (numeric) = 1.9727509563950137687230748141778
absolute error = 1e-31
relative error = 5.0690635670880141732739479848208e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2172
Order of pole (three term test) = -23.74
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2244951904, alloc=4848776, time=123.60
x[1] = 7.63
y1[1] (analytic) = 1.2221135494144386711391126846887
y1[1] (numeric) = 1.2221135494144386711391126846882
absolute error = 5e-31
relative error = 4.0912728628167907755244893064892e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9750208055044362542575080082731
y2[1] (numeric) = 1.975020805504436254257508008273
absolute error = 1e-31
relative error = 5.0632378009030235452620746969957e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2086
Order of pole (three term test) = -23.85
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2248955840, alloc=4848776, time=123.82
x[1] = 7.64
y1[1] (analytic) = 1.2123523982771256590978578675718
y1[1] (numeric) = 1.2123523982771256590978578675713
absolute error = 5e-31
relative error = 4.1242133946412787519803477380049e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9771931533458229257005890029222
y2[1] (numeric) = 1.9771931533458229257005890029221
absolute error = 1e-31
relative error = 5.0576748068735296197158308345525e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1998
Order of pole (three term test) = -23.95
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.65
y1[1] (analytic) = 1.2025700120769446765215783227058
y1[1] (numeric) = 1.2025700120769446765215783227053
absolute error = 5e-31
relative error = 4.1577620843584467673931620302621e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9792677826861999282187069323438
y2[1] (numeric) = 1.9792677826861999282187069323437
absolute error = 1e-31
relative error = 5.0523734521805406216527867898368e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.191
Order of pole (three term test) = -24.05
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2252957524, alloc=4848776, time=124.04
x[1] = 7.66
y1[1] (analytic) = 1.1927673690443637801816273360472
y1[1] (numeric) = 1.1927673690443637801816273360467
absolute error = 5e-31
relative error = 4.1919322491241207313440369845350e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9812444860643620761324084988271
y2[1] (numeric) = 1.981244486064362076132408498827
absolute error = 1e-31
relative error = 5.0473326590119495182459178234592e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1822
Order of pole (three term test) = -24.14
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2256959412, alloc=4848776, time=124.26
x[1] = 7.67
y1[1] (analytic) = 1.1829454494355173862033368443022
y1[1] (numeric) = 1.1829454494355173862033368443016
absolute error = 6e-31
relative error = 5.0720851099795885433942992445884e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9831230658116188005512045434252
y2[1] (numeric) = 1.9831230658116188005512045434251
absolute error = 1e-31
relative error = 5.0425514040942136274791710943717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1732
Order of pole (three term test) = -24.23
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2260961456, alloc=4848776, time=124.48
x[1] = 7.68
y1[1] (analytic) = 1.173105235434181473501793986326
y1[1] (numeric) = 1.1731052354341814735017939863254
absolute error = 6e-31
relative error = 5.1146306561144296021411835173259e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9849033340715608537070993661777
y2[1] (numeric) = 1.9849033340715608537070993661776
absolute error = 1e-31
relative error = 5.0380287182486411017944532623804e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1642
Order of pole (three term test) = -24.31
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.69
y1[1] (analytic) = 1.1632477110535560246677012934441
y1[1] (numeric) = 1.1632477110535560246677012934435
absolute error = 6e-31
relative error = 5.1579727542002096266671462144835e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9865851128188457933328816416347
y2[1] (numeric) = 1.9865851128188457933328816416346
absolute error = 1e-31
relative error = 5.0337636859719523464897718339957e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1551
Order of pole (three term test) = -24.39
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2264962548, alloc=4848776, time=124.70
x[1] = 7.7
y1[1] (analytic) = 1.153373862037864525977384239572
y1[1] (numeric) = 1.1533738620378645259773842395715
absolute error = 5e-31
relative error = 4.3351077777726275532102945132069e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9881682338770003685523936187237
y2[1] (numeric) = 1.9881682338770003685523936187235
absolute error = 2e-31
relative error = 1.0059510890081606711770458984385e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.146
Order of pole (three term test) = -24.47
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2268965712, alloc=4848776, time=124.93
x[1] = 7.71
y1[1] (analytic) = 1.1434846757637803664949450070563
y1[1] (numeric) = 1.1434846757637803664949450070557
absolute error = 6e-31
relative error = 5.2471188527230184695082840346312e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9896525389352380270590248501636
y2[1] (numeric) = 1.9896525389352380270590248501634
absolute error = 2e-31
relative error = 1.0052006372279953029871264420101e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1367
Order of pole (three term test) = -24.54
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.72
y1[1] (analytic) = 1.1335811411416899935445078592584
y1[1] (numeric) = 1.1335811411416899935445078592579
absolute error = 5e-31
relative error = 4.4108002669877107091396095549036e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9910378795642898618457271446539
y2[1] (numeric) = 1.9910378795642898618457271446537
absolute error = 2e-31
relative error = 1.0045012305027925284467761180833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1275
Order of pole (three term test) = -24.61
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2272968664, alloc=4848776, time=125.14
TOP MAIN SOLVE Loop
x[1] = 7.73
y1[1] (analytic) = 1.1236642485168026981547284658424
y1[1] (numeric) = 1.1236642485168026981547284658418
absolute error = 6e-31
relative error = 5.3396733124861710691736365042923e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9923241172312474144050701519763
y2[1] (numeric) = 1.992324117231247414405070151976
absolute error = 3e-31
relative error = 1.5057790918925027891607077295763e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1182
Order of pole (three term test) = -24.67
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2276970584, alloc=4848776, time=125.36
x[1] = 7.74
y1[1] (analytic) = 1.1137349895701169194146144923951
y1[1] (numeric) = 1.1137349895701169194146144923946
absolute error = 5e-31
relative error = 4.4893983279899614029466772306856e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9935111233134158501313865368873
y2[1] (numeric) = 1.9935111233134158501313865368871
absolute error = 2e-31
relative error = 1.0032549989868122655034641083791e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1088
Order of pole (three term test) = -24.73
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2280971752, alloc=4848776, time=125.58
x[1] = 7.75
y1[1] (analytic) = 1.1037943572192529710276940677138
y1[1] (numeric) = 1.1037943572192529710276940677133
absolute error = 5e-31
relative error = 4.5298292814218667651695660992755e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9945987791111761206190108016398
y2[1] (numeric) = 1.9945987791111761206190108016396
absolute error = 2e-31
relative error = 1.0027079234908740626238700463870e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09941
Order of pole (three term test) = -24.78
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.76
y1[1] (analytic) = 1.0938433455191621067092375928365
y1[1] (numeric) = 1.093843345519162106709237592836
absolute error = 5e-31
relative error = 4.5710384585526641788078464196465e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9955869758598548266511003661026
y2[1] (numeric) = 1.9955869758598548266511003661024
absolute error = 2e-31
relative error = 1.0022113915321799981513405550014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08997
Order of pole (three term test) = -24.82
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2284972584, alloc=4848776, time=125.80
x[1] = 7.77
y1[1] (analytic) = 1.083882949562721853437250999942
y1[1] (numeric) = 1.0838829495627218534372509999415
absolute error = 5e-31
relative error = 4.6130442424776433990059391437462e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9964756147406005949026315428916
y2[1] (numeric) = 1.9964756147406005949026315428914
absolute error = 2e-31
relative error = 1.0017653034344009875412720303522e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08049
Order of pole (three term test) = -24.87
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2288973284, alloc=4848776, time=126.02
x[1] = 7.78
y1[1] (analytic) = 1.073914165381227552941078415626
y1[1] (numeric) = 1.0739141653812275529410784156255
absolute error = 5e-31
relative error = 4.6558655814220084875888534542433e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9972646068902658807289637249532
y2[1] (numeric) = 1.997264606890265880728963724953
absolute error = 2e-31
relative error = 1.0013695697106419549129945894878e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07098
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2292976604, alloc=4848776, time=126.25
x[1] = 7.79
y1[1] (analytic) = 1.0639379898447900621905419292717
y1[1] (numeric) = 1.0639379898447900621905419292712
absolute error = 5e-31
relative error = 4.6995220094823501121770592876975e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9979538734102932088679277373902
y2[1] (numeric) = 1.99795387341029320886792773739
absolute error = 2e-31
relative error = 1.0010241110252531867802956576208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06144
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.8
y1[1] (analytic) = 1.0539554205626495730325679129525
y1[1] (numeric) = 1.053955420562649573032567912952
absolute error = 5e-31
relative error = 4.7440336682653726303702306149576e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9985433453746049634387733205961
y2[1] (numeric) = 1.9985433453746049634387733205959
absolute error = 2e-31
relative error = 1.0007288581600025305815155486860e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05188
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2296978824, alloc=4848776, time=126.47
x[1] = 7.81
y1[1] (analytic) = 1.043967455783415519510264690171
y1[1] (numeric) = 1.0439674557834155195102646901705
absolute error = 5e-31
relative error = 4.7894213294684488042981498834906e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9990329638364959382655506530315
y2[1] (numeric) = 1.9990329638364959382655506530313
absolute error = 2e-31
relative error = 1.0004837519845836604967565088052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0423
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2300981084, alloc=4848776, time=126.68
x[1] = 7.82
y1[1] (analytic) = 1.0339750942952425487905865122099
y1[1] (numeric) = 1.0339750942952425487905865122095
absolute error = 4e-31
relative error = 3.8685651347592662318530425394862e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.999422679834527958275637348282
y2[1] (numeric) = 1.9994226798345279582756373482818
absolute error = 2e-31
relative error = 1.0002887434314388294772655741586e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0327
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.83
y1[1] (analytic) = 1.0239793353259525380203046620934
y1[1] (numeric) = 1.023979335325952538020304662093
absolute error = 4e-31
relative error = 3.9063288310664220613124090005152e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9997124543974259825161832418216
y2[1] (numeric) = 1.9997124543974259825161832418214
absolute error = 2e-31
relative error = 1.0001437934748776987017674855467e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02308
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2304982636, alloc=4848776, time=126.91
x[1] = 7.84
y1[1] (analytic) = 1.0139811784431126448253687138652
y1[1] (numeric) = 1.0139811784431126448253687138648
absolute error = 4e-31
relative error = 3.9448463985709098427657535076082e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9999022585479751991822513952502
y2[1] (numeric) = 1.99990225854797519918225139525
absolute error = 2e-31
relative error = 1.0000488731144769873864047712938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01346
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2308985076, alloc=4848776, time=127.13
x[1] = 7.85
y1[1] (analytic) = 1.0039816234540793835653399973692
y1[1] (numeric) = 1.0039816234540793835653399973688
absolute error = 4e-31
relative error = 3.9841366679984397261773394340007e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9999920733059187229504000722697
y2[1] (numeric) = 1.9999920733059187229504000722695
absolute error = 2e-31
relative error = 1.0000039633627488205463148449996e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.003834
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2312987724, alloc=4848776, time=127.35
x[1] = 7.86
y1[1] (analytic) = 0.99398167030601872285197549971847
y1[1] (numeric) = 0.99398167030601872285197549971808
absolute error = 3.9e-31
relative error = 3.9236136002380212676261114333298e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9999818896898556048503870679297
y2[1] (numeric) = 1.9999818896898556048503870679295
absolute error = 2e-31
relative error = 1.0000090552370687734480618537827e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005803
Order of pole (three term test) = -0.8937
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.87
y1[1] (analytic) = 0.98398231898591220223889403738306
y1[1] (numeric) = 0.98398231898591220223889403738267
absolute error = 3.9e-31
relative error = 3.9634858520825075791967996823270e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9998717087181389648755908903309
y2[1] (numeric) = 1.9998717087181389648755908903307
absolute error = 2e-31
relative error = 1.0000641497558577225920436006756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01544
Order of pole (three term test) = -0.8991
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2316988520, alloc=4848776, time=127.57
x[1] = 7.88
y1[1] (analytic) = 0.97398456942055906738732777394789
y1[1] (numeric) = 0.97398456942055906738732777394751
absolute error = 3.8e-31
relative error = 3.9014991811016968411369639999902e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9996615414087741575196361940153
y2[1] (numeric) = 1.9996615414087741575196361940151
absolute error = 2e-31
relative error = 1.0001692579390147175956211255841e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02508
Order of pole (three term test) = -0.9092
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2320989860, alloc=4848776, time=127.79
x[1] = 7.89
y1[1] (analytic) = 0.96398942137658442341111123213176
y1[1] (numeric) = 0.96398942137658442341111123213138
absolute error = 3.8e-31
relative error = 3.9419519713956718719402499246341e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9993514087783169804225849407293
y2[1] (numeric) = 1.9993514087783169804225849407291
absolute error = 2e-31
relative error = 1.0003244008126011897736911831577e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0347
Order of pole (three term test) = -0.9242
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2324991684, alloc=4848776, time=128.01
x[1] = 7.9
y1[1] (analytic) = 0.95399787436046340550224704004151
y1[1] (numeric) = 0.95399787436046340550224704004114
absolute error = 3.7e-31
relative error = 3.8784153502232785844828065743389e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9989413418397720363049105120439
y2[1] (numeric) = 1.9989413418397720363049105120437
absolute error = 2e-31
relative error = 1.0005296094177799149914495618334e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04431
Order of pole (three term test) = -0.944
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.91
y1[1] (analytic) = 0.94401092751857136433667294165175
y1[1] (numeric) = 0.94401092751857136433667294165138
absolute error = 3.7e-31
relative error = 3.9194461548510099608569309295945e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.998431381599491458351310017202
y2[1] (numeric) = 1.9984313815994914583513100172018
absolute error = 2e-31
relative error = 1.0007849248240152539524422794472e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0539
Order of pole (three term test) = -0.9686
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2328993340, alloc=4848776, time=128.23
x[1] = 7.92
y1[1] (analytic) = 0.93402957953727006115839826028491
y1[1] (numeric) = 0.93402957953727006115839826028454
absolute error = 3.7e-31
relative error = 3.9613306484715679868496361910274e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.997821579053074309169232028065
y2[1] (numeric) = 1.9978215790530743091692320280648
absolute error = 2e-31
relative error = 1.0010903981465443059479640958815e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06348
Order of pole (three term test) = -0.9981
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2332995592, alloc=4848776, time=128.45
x[1] = 7.93
y1[1] (analytic) = 0.92405482854303986383924017488675
y1[1] (numeric) = 0.92405482854303986383924017488639
absolute error = 3.6e-31
relative error = 3.8958727218341916477710893519297e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9971119951802670633788067322389
y2[1] (numeric) = 1.9971119951802670633788067322387
absolute error = 2e-31
relative error = 1.0014460905681317357072387768245e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07302
Order of pole (three term test) = -1.032
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.94
y1[1] (analytic) = 0.91408767200266793061133094292942
y1[1] (numeric) = 0.91408767200266793061133094292906
absolute error = 3.6e-31
relative error = 3.9383530817265991387913959869253e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9963027009388656837816699276909
y2[1] (numeric) = 1.9963027009388656837816699276906
absolute error = 3e-31
relative error = 1.5027781100476862562666240063814e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08254
Order of pole (three term test) = -1.071
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2336998348, alloc=4848776, time=128.67
x[1] = 7.95
y1[1] (analytic) = 0.90412910662350236257084658291809
y1[1] (numeric) = 0.90412910662350236257084658291773
absolute error = 3.6e-31
relative error = 3.9817322256600160267116815541104e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9953937772576199008959823902
y2[1] (numeric) = 1.9953937772576199008959823901997
absolute error = 3e-31
relative error = 1.5034626419067348345204221367742e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09202
Order of pole (three term test) = -1.115
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2341000440, alloc=4848776, time=128.89
x[1] = 7.96
y1[1] (analytic) = 0.89418012825378229945458538112409
y1[1] (numeric) = 0.89418012825378229945458538112373
absolute error = 3.6e-31
relative error = 4.0260344490436536740372816860517e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9943853150281404054237780310308
y2[1] (numeric) = 1.9943853150281404054237780310305
absolute error = 3e-31
relative error = 1.5042228687677990442008221858471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1015
Order of pole (three term test) = -1.164
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2345001864, alloc=4848776, time=129.12
x[1] = 7.97
y1[1] (analytic) = 0.8842417317830539255967605880346
y1[1] (numeric) = 0.88424173178305392559676058803425
absolute error = 3.5e-31
relative error = 3.9581936411690582504417373890931e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.993277415095809762924650126215
y2[1] (numeric) = 1.9932774150958097629246501262146
absolute error = 4e-31
relative error = 2.0067452576879441603519859998639e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1109
Order of pole (three term test) = -1.217
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 7.98
y1[1] (analytic) = 0.87431491104268234438242524016836
y1[1] (numeric) = 0.87431491104268234438242524016801
absolute error = 3.5e-31
relative error = 4.0031342892528306012809331914833e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9920701882496979595967340362938
y2[1] (numeric) = 1.9920701882496979595967340362935
absolute error = 3e-31
relative error = 1.5059710333981274889440303989368e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1202
Order of pole (three term test) = -1.275
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2349004372, alloc=4848776, time=129.34
x[1] = 7.99
y1[1] (analytic) = 0.86440065870646926992717726984173
y1[1] (numeric) = 0.86440065870646926992717726984138
absolute error = 3.5e-31
relative error = 4.0490482795762423147390511736799e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9907637552114835876020046344142
y2[1] (numeric) = 1.9907637552114835876020046344139
absolute error = 3e-31
relative error = 1.5069593225949117383279571621265e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1295
Order of pole (three term test) = -1.337
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2353005492, alloc=4848776, time=129.56
x[1] = 8
y1[1] (analytic) = 0.85449996619138647413115861816881
y1[1] (numeric) = 0.85449996619138647413115861816846
absolute error = 3.5e-31
relative error = 4.0959627132578354463467456843756e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9893582466233817778081235982453
y2[1] (numeric) = 1.9893582466233817778081235982449
absolute error = 4e-31
relative error = 2.0106986797322009755261012046511e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1388
Order of pole (three term test) = -1.405
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2357006828, alloc=4848776, time=129.77
x[1] = 8.01
y1[1] (analytic) = 0.84461382355843491567992109966912
y1[1] (numeric) = 0.84461382355843491567992109966878
absolute error = 3.4e-31
relative error = 4.0255083508762507945712399823699e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.987853803035080087143502358473
y2[1] (numeric) = 1.9878538030350800871435023584726
absolute error = 4e-31
relative error = 2.0122204127349556060734731378044e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.148
Order of pole (three term test) = -1.477
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.02
y1[1] (analytic) = 0.83474321941363946499664181478805
y1[1] (numeric) = 0.83474321941363946499664181478772
absolute error = 3.3e-31
relative error = 3.9533115373109180426198350160359e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9862505748896836469659584733293
y2[1] (numeric) = 1.9862505748896836469659584733289
absolute error = 4e-31
relative error = 2.0138446027748336798620726272162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1572
Order of pole (three term test) = -1.553
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2361008552, alloc=4848776, time=129.99
x[1] = 8.03
y1[1] (analytic) = 0.82488914080918912559068876792971
y1[1] (numeric) = 0.82488914080918912559068876792938
absolute error = 3.3e-31
relative error = 4.0005375713429910118010129448483e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9845487225086709779184162261999
y2[1] (numeric) = 1.9845487225086709779184162261995
absolute error = 4e-31
relative error = 2.0155715778767044220831639193635e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1662
Order of pole (three term test) = -1.634
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2365009880, alloc=4848776, time=130.21
x[1] = 8.04
y1[1] (analytic) = 0.81505257314473263769801896017425
y1[1] (numeric) = 0.81505257314473263769801896017392
absolute error = 3.3e-31
relative error = 4.0488185777606321447438238089233e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9827484160758619756776290970863
y2[1] (numeric) = 1.9827484160758619756776290970859
absolute error = 4e-31
relative error = 2.0174016872582163859709820523118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1753
Order of pole (three term test) = -1.72
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.05
y1[1] (analytic) = 0.80523450006883933457079152741579
y1[1] (numeric) = 0.80523450006883933457079152741546
absolute error = 3.3e-31
relative error = 4.0981850625102174178439187010711e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9808498356203996707839892683332
y2[1] (numeric) = 1.9808498356203996707839892683328
absolute error = 4e-31
relative error = 2.0193353014804401080504152602682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1842
Order of pole (three term test) = -1.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2369012332, alloc=4848776, time=130.43
x[1] = 8.06
y1[1] (analytic) = 0.79543590338063510524845128323445
y1[1] (numeric) = 0.79543590338063510524845128323412
absolute error = 3.3e-31
relative error = 4.1486686557331207987780162615416e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9788531709987474643622593641338
y2[1] (numeric) = 1.9788531709987474643622593641334
absolute error = 4e-31
relative error = 2.0213728126080011428422202758502e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1931
Order of pole (three term test) = -1.905
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2373013880, alloc=4848776, time=130.66
x[1] = 8.07
y1[1] (analytic) = 0.7856577629316233001320358003571
y1[1] (numeric) = 0.78565776293162330013203580035678
absolute error = 3.2e-31
relative error = 4.0730202780144866780956489562031e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9767586218757036399946520970817
y2[1] (numeric) = 1.9767586218757036399946520970813
absolute error = 4e-31
relative error = 2.0235146343788227592062780894616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2019
Order of pole (three term test) = -2.004
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2377016048, alloc=4848776, time=130.88
x[1] = 8.08
y1[1] (analytic) = 0.77590105652770039718933296069646
y1[1] (numeric) = 0.77590105652770039718933296069614
absolute error = 3.2e-31
relative error = 4.1242371989034106844103176187709e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9745663977044350502792493264352
y2[1] (numeric) = 1.9745663977044350502792493264348
absolute error = 4e-31
relative error = 2.0257612023836050348552308604932e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2106
Order of pole (three term test) = -2.107
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.09
y1[1] (analytic) = 0.76616675983137622714261511889606
y1[1] (numeric) = 0.76616675983137622714261511889574
absolute error = 3.2e-31
relative error = 4.1766364292602307525785329128685e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9722767177055319746884661471166
y2[1] (numeric) = 1.9722767177055319746884661471163
absolute error = 3e-31
relative error = 1.5210847306913810138979784064963e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2192
Order of pole (three term test) = -2.215
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2381017072, alloc=4848776, time=131.10
x[1] = 8.1
y1[1] (analytic) = 0.75645584626420853553494823189785
y1[1] (numeric) = 0.75645584626420853553494823189753
absolute error = 3.2e-31
relative error = 4.2302535115609786889913223314903e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9698898108450862432243199360998
y2[1] (numeric) = 1.9698898108450862432243199360995
absolute error = 3e-31
relative error = 1.5229278224008857875484117145228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2278
Order of pole (three term test) = -2.327
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2385019192, alloc=4848776, time=131.32
x[1] = 8.11
y1[1] (analytic) = 0.74676928690946163813756506302267
y1[1] (numeric) = 0.74676928690946163813756506302236
absolute error = 3.1e-31
relative error = 4.1512151802995136062187710906825e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.967405915811794818039870659888
y2[1] (numeric) = 1.9674059158117948180398706598876
absolute error = 4e-31
relative error = 2.0331340715469549131338655961929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2362
Order of pole (three term test) = -2.443
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2389020984, alloc=4848776, time=131.54
x[1] = 8.12
y1[1] (analytic) = 0.73710805041499890375164420647488
y1[1] (numeric) = 0.73710805041499890375164420647457
absolute error = 3.1e-31
relative error = 4.2056249395928727958925192889086e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9648252809930911226495900140035
y2[1] (numeric) = 1.9648252809930911226495900140031
absolute error = 4e-31
relative error = 2.0358044242886882536385852617917e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2446
Order of pole (three term test) = -2.564
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.13
y1[1] (analytic) = 0.72747310289641877507529209311262
y1[1] (numeric) = 0.72747310289641877507529209311232
absolute error = 3.0e-31
relative error = 4.1238638075491223551238402328077e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9621481644503065055758478648868
y2[1] (numeric) = 1.9621481644503065055758478648864
absolute error = 4e-31
relative error = 2.0385820359904346382699823741690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2528
Order of pole (three term test) = -2.688
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2393023964, alloc=4848776, time=131.75
x[1] = 8.14
y1[1] (analytic) = 0.71786540784044401395292156573867
y1[1] (numeric) = 0.71786540784044401395292156573837
absolute error = 3.0e-31
relative error = 4.1790563624244079172191330689261e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.95937483389286432226445263426
y2[1] (numeric) = 1.9593748338928643222644526342595
absolute error = 5e-31
relative error = 2.5518343471147147040712593883951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.261
Order of pole (three term test) = -2.817
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2397025128, alloc=4848776, time=131.98
x[1] = 8.15
y1[1] (analytic) = 0.70828592600857383200199339212464
y1[1] (numeric) = 0.70828592600857383200199339212435
absolute error = 2.9e-31
relative error = 4.0943916764553858629342741422664e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9565055666515092158395492118634
y2[1] (numeric) = 1.9565055666515092158395492118629
absolute error = 5e-31
relative error = 2.5555766797828870788588456698778e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.269
Order of pole (three term test) = -2.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.16
y1[1] (analytic) = 0.69873561534100854132376841810555
y1[1] (numeric) = 0.69873561534100854132376841810526
absolute error = 2.9e-31
relative error = 4.1503537766350923913504448708913e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9535406496505742737474900484332
y2[1] (numeric) = 1.9535406496505742737474900484328
absolute error = 4e-31
relative error = 2.0475642524845703241307513306837e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.277
Order of pole (three term test) = -3.087
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2401027048, alloc=4848776, time=132.19
x[1] = 8.17
y1[1] (analytic) = 0.6892154308608563327529367613304
y1[1] (numeric) = 0.68921543086085633275293676133012
absolute error = 2.8e-31
relative error = 4.0625904102331158168781435825635e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9504803793792888335509044160486
y2[1] (numeric) = 1.9504803793792888335509044160482
absolute error = 4e-31
relative error = 2.0507768456881068898595441011335e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2848
Order of pole (three term test) = -3.228
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2405028304, alloc=4848776, time=132.41
x[1] = 8.18
y1[1] (analytic) = 0.67972632457863176088847166404938
y1[1] (numeric) = 0.6797263245786317608884716640491
absolute error = 2.8e-31
relative error = 4.1193049301654519041722470755194e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9473250618621298070684763467843
y2[1] (numeric) = 1.9473250618621298070684763467839
absolute error = 4e-31
relative error = 2.0540997896750733310816417346135e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2925
Order of pole (three term test) = -3.373
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2409030488, alloc=4848776, time=132.64
x[1] = 8.19
y1[1] (analytic) = 0.67026924539705548597762058902613
y1[1] (numeric) = 0.67026924539705548597762058902586
absolute error = 2.7e-31
relative error = 4.0282319657984134408394719526169e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9440750126282194877033101243501
y2[1] (numeric) = 1.9440750126282194877033101243497
absolute error = 4e-31
relative error = 2.0575337751974650584178131713015e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3001
Order of pole (three term test) = -3.521
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.2
y1[1] (analytic) = 0.66084513901616479259951187548036
y1[1] (numeric) = 0.66084513901616479259951187548009
absolute error = 2.7e-31
relative error = 4.0856773252802210192368787472063e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9407305566797729011536487499456
y2[1] (numeric) = 1.9407305566797729011536487499452
absolute error = 4e-31
relative error = 2.0610795178302608209442548111800e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3076
Order of pole (three term test) = -3.673
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2413032796, alloc=4848776, time=132.86
x[1] = 8.21
y1[1] (analytic) = 0.65145494783874437401743429021275
y1[1] (numeric) = 0.65145494783874437401743429021249
absolute error = 2.6e-31
relative error = 3.9910664714815888115670484402578e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9372920284595978547445805237238
y2[1] (numeric) = 1.9372920284595978547445805237233
absolute error = 5e-31
relative error = 2.5809221978658829718769546315053e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.315
Order of pole (three term test) = -3.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2417033492, alloc=4848776, time=133.08
x[1] = 8.22
y1[1] (analytic) = 0.64209961087608683904254682894266
y1[1] (numeric) = 0.64209961087608683904254682894241
absolute error = 2.5e-31
relative error = 3.8934768961921284037687735000581e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9337597718176509353487173692576
y2[1] (numeric) = 1.9337597718176509353487173692572
absolute error = 4e-31
relative error = 2.0685092627819908590438969084020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3222
Order of pole (three term test) = -3.989
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.23
y1[1] (analytic) = 0.63278006365409236527979974770724
y1[1] (numeric) = 0.632780063654092365279799747707
absolute error = 2.4e-31
bytes used=2421034744, alloc=4848776, time=133.31
relative error = 3.7927870011276998457359809309757e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9301341399766528002681829243461
y2[1] (numeric) = 1.9301341399766528002681829243457
absolute error = 4e-31
relative error = 2.0723948233195774755132956381564e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3293
Order of pole (three term test) = -4.153
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.24
y1[1] (analytic) = 0.62349723811971688871249220409109
y1[1] (numeric) = 0.62349723811971688871249220409085
absolute error = 2.4e-31
relative error = 3.8492552224251860132713925192002e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9264154954967661995201683705964
y2[1] (numeric) = 1.926415495496766199520168370596
absolute error = 4e-31
relative error = 2.0763952581104612735305926787544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3363
Order of pole (three term test) = -4.319
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2425035608, alloc=4848776, time=133.53
x[1] = 8.25
y1[1] (analytic) = 0.61425206254777818472854847037505
y1[1] (numeric) = 0.61425206254777818472854847037481
absolute error = 2.4e-31
relative error = 3.9071907875170081610988967729197e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9226042102393402616943925628889
y2[1] (numeric) = 1.9226042102393402616943925628885
absolute error = 4e-31
relative error = 2.0805114119156380367095633431868e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3431
Order of pole (three term test) = -4.49
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2429037704, alloc=4848776, time=133.75
x[1] = 8.26
y1[1] (analytic) = 0.60504546144812915990274875070963
y1[1] (numeric) = 0.6050454614481291599027487507094
absolute error = 2.3e-31
relative error = 3.8013672468431202547115175899884e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9187006653297246689236677183023
y2[1] (numeric) = 1.9187006653297246689236677183019
absolute error = 4e-31
relative error = 2.0847441564380801542214001788396e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3498
Order of pole (three term test) = -4.663
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.27
y1[1] (analytic) = 0.59587835547320763712838104690138
y1[1] (numeric) = 0.59587835547320763712838104690115
absolute error = 2.3e-31
relative error = 3.8598482037050839879063759715256e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9147052511191574395190855236994
y2[1] (numeric) = 1.914705251119157439519085523699
absolute error = 4e-31
relative error = 2.0890943907225273815723293390283e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3564
Order of pole (three term test) = -4.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2433038940, alloc=4848776, time=133.97
x[1] = 8.28
y1[1] (analytic) = 0.58675166132597187904275931870762
y1[1] (numeric) = 0.5867516613259718790427593187074
absolute error = 2.2e-31
relative error = 3.7494567889732527320595997569208e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9106183671457301294598000680928
y2[1] (numeric) = 1.9106183671457301294598000680924
absolute error = 4e-31
relative error = 2.0935630415694128972642900731401e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3628
Order of pole (three term test) = -5.021
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2437039944, alloc=4848776, time=134.19
x[1] = 8.29
y1[1] (analytic) = 0.57766629166823105611754524541246
y1[1] (numeric) = 0.57766629166823105611754524541224
absolute error = 2.2e-31
relative error = 3.8084271693379641750405319602891e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.9064404220944343561847297311685
y2[1] (numeric) = 1.9064404220944343561847297311681
absolute error = 4e-31
relative error = 2.0981510639632579376227284206219e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3691
Order of pole (three term test) = -5.204
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2441041752, alloc=4848776, time=134.42
x[1] = 8.3
y1[1] (analytic) = 0.56862315502937982629067353455349
y1[1] (numeric) = 0.56862315502937982629067353455327
absolute error = 2.2e-31
relative error = 3.8689947472967920316310226610220e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.902171833756293640000504405253
y2[1] (numeric) = 1.9021718337562936400005044052525
absolute error = 5e-31
relative error = 2.6285743018948519848091755590945e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3752
Order of pole (three term test) = -5.391
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.31
y1[1] (analytic) = 0.55962315571554615260586332180965
y1[1] (numeric) = 0.55962315571554615260586332180944
absolute error = 2.1e-31
relative error = 3.7525252101387674413305792937461e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8978130289865846498874605706974
y2[1] (numeric) = 1.8978130289865846498874605706969
absolute error = 5e-31
relative error = 2.6346114836559825490921750639402e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3812
Order of pole (three term test) = -5.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2445042440, alloc=4848776, time=134.64
x[1] = 8.32
y1[1] (analytic) = 0.55066719371916144400224181130983
y1[1] (numeric) = 0.55066719371916144400224181130963
absolute error = 2.0e-31
relative error = 3.6319577828709254453721644300959e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8933644436621520315442881127292
y2[1] (numeric) = 1.8933644436621520315442881127286
absolute error = 6e-31
relative error = 3.1689620136706377160803738181857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.387
Order of pole (three term test) = -5.773
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2449043964, alloc=4848776, time=134.86
x[1] = 8.33
y1[1] (analytic) = 0.54175616462896206216464322918317
y1[1] (numeric) = 0.54175616462896206216464322918298
absolute error = 1.9e-31
relative error = 3.5071128379337813629547824983337e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8888265226378210861529535570277
y2[1] (numeric) = 1.8888265226378210861529535570271
absolute error = 6e-31
relative error = 3.1765754705841181443899738895132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3926
Order of pole (three term test) = -5.968
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.34
y1[1] (analytic) = 0.53289095954043119420889956615966
y1[1] (numeric) = 0.53289095954043119420889956615947
absolute error = 1.9e-31
relative error = 3.5654573716892720161856647847451e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8841997197019126585597005850824
y2[1] (numeric) = 1.8841997197019126585597005850818
absolute error = 6e-31
relative error = 3.1843758054211058464570781440593e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
bytes used=2453045320, alloc=4848776, time=135.08
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3981
Order of pole (three term test) = -6.167
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.35
y1[1] (analytic) = 0.52407246496669004694022305615659
y1[1] (numeric) = 0.52407246496669004694022305615641
absolute error = 1.8e-31
relative error = 3.4346395209189394852466913040885e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8794844975308646833462389263335
y2[1] (numeric) = 1.8794844975308646833462389263329
absolute error = 6e-31
relative error = 3.1923647190931239239016313034555e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4035
Order of pole (three term test) = -6.367
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2457046988, alloc=4848776, time=135.30
x[1] = 8.36
y1[1] (analytic) = 0.51530156274984727349099746200915
y1[1] (numeric) = 0.51530156274984727349099746200897
absolute error = 1.8e-31
relative error = 3.4931002157154499896799356894065e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8746813276429649265986992559849
y2[1] (numeric) = 1.8746813276429649265986992559844
absolute error = 5e-31
relative error = 2.6671199666166704216787599614913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4087
Order of pole (three term test) = -6.571
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2461049148, alloc=4848776, time=135.52
x[1] = 8.37
y1[1] (analytic) = 0.5065791299728154973214391576657
y1[1] (numeric) = 0.50657912997281549732143915766552
absolute error = 1.8e-31
relative error = 3.5532454724232188780905229538886e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8697906903511995500616212829926
y2[1] (numeric) = 1.869790690351199550061621282992
absolute error = 6e-31
relative error = 3.2089153245666392647544709220322e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4137
Order of pole (three term test) = -6.777
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.38
y1[1] (analytic) = 0.49790603887160375185724195569388
y1[1] (numeric) = 0.49790603887160375185724195569371
absolute error = 1.7e-31
relative error = 3.4142988180112897933156079937372e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.86481307471522221278126689719
y2[1] (numeric) = 1.8648130747152222127812668971894
absolute error = 6e-31
relative error = 3.2174806587069146447322217331809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4186
Order of pole (three term test) = -6.986
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2465050272, alloc=4848776, time=135.74
x[1] = 8.39
y1[1] (analytic) = 0.48928315674809460644715252561116
y1[1] (numeric) = 0.489283156748094606447152525611
absolute error = 1.6e-31
relative error = 3.2700900857369045507544819908545e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8597489784924485132880684290261
y2[1] (numeric) = 1.8597489784924485132880684290256
absolute error = 5e-31
relative error = 2.6885348817629703757539650064674e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4233
Order of pole (three term test) = -7.197
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2469051136, alloc=4848776, time=135.97
x[1] = 8.4
y1[1] (analytic) = 0.48071134588331470085519515941454
y1[1] (numeric) = 0.48071134588331470085519515941438
absolute error = 1.6e-31
relative error = 3.3284007413221643330527233681750e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8545989080882806628332392814224
y2[1] (numeric) = 1.8545989080882806628332392814219
absolute error = 5e-31
relative error = 2.6960007245739170191702287097197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4278
Order of pole (three term test) = -7.41
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2473052436, alloc=4848776, time=136.19
x[1] = 8.41
y1[1] (analytic) = 0.47219146345120736116182234815788
y1[1] (numeric) = 0.47219146345120736116182234815773
absolute error = 1.5e-31
relative error = 3.1766775050032188441013299633662e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8493633785054673671707439719806
y2[1] (numeric) = 1.84936337850546736717074397198
absolute error = 6e-31
relative error = 3.2443596914138104278099173408483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4321
Order of pole (three term test) = -7.626
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.42
y1[1] (analytic) = 0.46372436143291591974054514062359
y1[1] (numeric) = 0.46372436143291591974054514062345
absolute error = 1.4e-31
relative error = 3.0190348328346971588465332524598e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8440429132926039808542494306898
y2[1] (numeric) = 1.8440429132926039808542494306892
absolute error = 6e-31
relative error = 3.2537203753500439637469512970960e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4363
Order of pole (three term test) = -7.843
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2477053424, alloc=4848776, time=136.41
x[1] = 8.43
y1[1] (analytic) = 0.45531088653158631090661529246805
y1[1] (numeric) = 0.45531088653158631090661529246791
absolute error = 1.4e-31
relative error = 3.0748221521008540864774479466473e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8386380444917780839907114629715
y2[1] (numeric) = 1.838638044491778083990711462971
absolute error = 5e-31
relative error = 2.7194041888663632037861743809853e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4403
Order of pole (three term test) = -8.063
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2481055128, alloc=4848776, time=136.63
x[1] = 8.44
y1[1] (analytic) = 0.44695188008769746190719673732551
y1[1] (numeric) = 0.44695188008769746190719673732538
absolute error = 1.3e-31
relative error = 2.9085905170483319008022077247604e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8331493125853657168492924788064
y2[1] (numeric) = 1.8331493125853657168492924788058
absolute error = 6e-31
relative error = 3.2730558055513512595397874588535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4441
Order of pole (three term test) = -8.285
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.45
y1[1] (analytic) = 0.43864817799492794614336959040814
y1[1] (numeric) = 0.43864817799492794614336959040801
absolute error = 1.3e-31
relative error = 2.9636507461226290473651001271589e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8275772664419835926578132727978
y2[1] (numeric) = 1.8275772664419835926578132727972
absolute error = 6e-31
relative error = 3.2830349283568689497715301809706e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4478
Order of pole (three term test) = -8.508
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2485056320, alloc=4848776, time=136.85
TOP MAIN SOLVE Loop
x[1] = 8.46
y1[1] (analytic) = 0.43040061061656731188853359559002
y1[1] (numeric) = 0.4304006106165673118885335955899
absolute error = 1.2e-31
relative error = 2.7881001336892821673629555215937e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.821922463261602693320419537459
y2[1] (numeric) = 1.8219224632616026933204195374584
absolute error = 6e-31
relative error = 3.2932246684410540455730550070665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4512
Order of pole (three term test) = -8.734
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2489058108, alloc=4848776, time=137.07
x[1] = 8.47
y1[1] (analytic) = 0.42221000270248044530068218175304
y1[1] (numeric) = 0.42221000270248044530068218175293
absolute error = 1.1e-31
relative error = 2.6053385589141031504388264586972e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8161854685198287366511528252971
y2[1] (numeric) = 1.8161854685198287366511528252965
absolute error = 6e-31
relative error = 3.3036273574471082401657467997806e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4545
Order of pole (three term test) = -8.961
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2493059576, alloc=4848776, time=137.29
x[1] = 8.48
y1[1] (analytic) = 0.41407717330663327122304976748636
y1[1] (numeric) = 0.41407717330663327122304976748625
absolute error = 1.1e-31
relative error = 2.6565096337378292547689500455515e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.810366855911355087030269813403
y2[1] (numeric) = 1.8103668559113550870302698134024
absolute error = 6e-31
relative error = 3.3142453864576224841374723742034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4576
Order of pole (three term test) = -9.189
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.49
y1[1] (analytic) = 0.40600293570518803913432389583803
y1[1] (numeric) = 0.40600293570518803913432389583792
absolute error = 1.1e-31
relative error = 2.7093400152129585647547461112296e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.8044672072925937641451218212426
y2[1] (numeric) = 1.804467207292593764145121821242
absolute error = 6e-31
relative error = 3.3250812072125963403520364712250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4606
Order of pole (three term test) = -9.419
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2497062160, alloc=4848776, time=137.51
x[1] = 8.5
y1[1] (analytic) = 0.397988097315176384651573477043
y1[1] (numeric) = 0.3979880973151763846515734770429
absolute error = 1.0e-31
relative error = 2.5126379576323757556375218865004e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7984871126234902866669131603391
y2[1] (numeric) = 1.7984871126234902866669131603385
absolute error = 6e-31
relative error = 3.3361373333655286030538623823181e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4633
Order of pole (three term test) = -9.651
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2501063600, alloc=4848776, time=137.74
x[1] = 8.51
y1[1] (analytic) = 0.39003345961375829921197062356349
y1[1] (numeric) = 0.3900334596137582992119706235634
absolute error = 9e-32
relative error = 2.3074943387966010351408016711366e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7924271699085281693304831713681
y2[1] (numeric) = 1.7924271699085281693304831713675
absolute error = 6e-31
relative error = 3.3474163417787258272789722774330e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4659
Order of pole (three term test) = -9.884
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2505065508, alloc=4848776, time=137.96
x[1] = 8.52
y1[1] (analytic) = 0.38213981805807508196905393760653
y1[1] (numeric) = 0.38213981805807508196905393760645
absolute error = 8e-32
relative error = 2.0934745927953032400912509737068e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7862879851369289729182412152366
y2[1] (numeric) = 1.786287985136928972918241215236
absolute error = 6e-31
relative error = 3.3589208738590191069492320722636e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.93
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4682
Order of pole (three term test) = -10.12
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.53
y1[1] (analytic) = 0.37430796200570428854155464066714
y1[1] (numeric) = 0.37430796200570428854155464066707
absolute error = 7e-32
relative error = 1.8701178469437214594818640122769e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7800701722220538870934230990784
y2[1] (numeric) = 1.7800701722220538870934230990778
absolute error = 6e-31
relative error = 3.3706536369351248574671200377188e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.24
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4704
Order of pole (three term test) = -10.35
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2509067328, alloc=4848776, time=138.18
x[1] = 8.54
y1[1] (analytic) = 0.36653867463572463105362334073292
y1[1] (numeric) = 0.36653867463572463105362334073286
absolute error = 6e-32
relative error = 1.6369350399280379229041459878911e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7737743529400129058738870988791
y2[1] (numeric) = 1.7737743529400129058738870988785
absolute error = 6e-31
relative error = 3.3826174056779325801352535227587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.55
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4724
Order of pole (three term test) = -10.59
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2513070132, alloc=4848776, time=138.40
x[1] = 8.55
y1[1] (analytic) = 0.35883273287039872291067438377066
y1[1] (numeric) = 0.35883273287039872291067438377061
absolute error = 5e-32
relative error = 1.3934068834812439243223286061415e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7674011568674877347777433492199
y2[1] (numeric) = 1.7674011568674877347777433492192
absolute error = 7e-31
relative error = 3.9606175274925603096948818643148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4742
Order of pole (three term test) = -10.83
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.56
y1[1] (analytic) = 0.35119090729748149997110604325389
y1[1] (numeric) = 0.35119090729748149997110604325384
absolute error = 5e-32
relative error = 1.4237270658504479357187544740998e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.7609512213187746472982879658692
y2[1] (numeric) = 1.7609512213187746472982879658685
absolute error = 7e-31
relative error = 3.9751243051228340365639330479231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4758
Order of pole (three term test) = -11.06
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2517072544, alloc=4848776, time=138.62
TOP MAIN SOLVE Loop
x[1] = 8.57
y1[1] (analytic) = 0.34361396209316208720703660916504
y1[1] (numeric) = 0.343613962093162087207036609165
absolute error = 4e-32
relative error = 1.1640970511307404004878701879704e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.754425191282053586370130296421
y2[1] (numeric) = 1.7544251912820535863701302964203
absolute error = 7e-31
relative error = 3.9899107894618866952506024430893e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4772
Order of pole (three term test) = -11.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2521075316, alloc=4848776, time=138.84
x[1] = 8.58
y1[1] (analytic) = 0.33610265494564681660317540579733
y1[1] (numeric) = 0.3361026549456468166031754057973
absolute error = 3e-32
relative error = 8.9258443985964587443334324350158e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7478237193548898838632577811713
y2[1] (numeric) = 1.7478237193548898838632577811706
absolute error = 7e-31
relative error = 4.0049805495165459062565031444997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.87
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4785
Order of pole (three term test) = -11.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2525078012, alloc=4848776, time=139.06
x[1] = 8.59
y1[1] (analytic) = 0.32865773697939103792835824510594
y1[1] (numeric) = 0.32865773697939103792835824510591
absolute error = 3e-32
relative error = 9.1280370502524313594881018769790e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7411474656789750478793406298218
y2[1] (numeric) = 1.7411474656789750478793406298211
absolute error = 7e-31
relative error = 4.0203372419522727379408724369968e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.21
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4795
Order of pole (three term test) = -11.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.6
y1[1] (analytic) = 0.32127995267998729913553021483952
y1[1] (numeric) = 0.3212799526799872991355302148395
absolute error = 2e-32
relative error = 6.2251005184631337083960497724645e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7343970978741131437171641875634
y2[1] (numeric) = 1.7343970978741131437171641875628
absolute error = 6e-31
relative error = 3.4594153826446813664454265955244e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4803
Order of pole (three term test) = -12.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2529080336, alloc=4848776, time=139.29
x[1] = 8.61
y1[1] (analytic) = 0.31397003981971740750954282881698
y1[1] (numeric) = 0.31397003981971740750954282881696
absolute error = 2e-32
relative error = 6.3700345458070022928680017646996e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7275732909714593698140812814806
y2[1] (numeric) = 1.72757329097145936981408128148
absolute error = 6e-31
relative error = 3.4730798579468915208135301896437e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.481
Order of pole (three term test) = -12.26
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2533081480, alloc=4848776, time=139.50
x[1] = 8.62
y1[1] (analytic) = 0.30672872938377581629461101739017
y1[1] (numeric) = 0.30672872938377581629461101739016
absolute error = 1e-32
relative error = 3.2602097690979912565436708883561e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7206767273460175047502560674387
y2[1] (numeric) = 1.720676727346017504750256067438
absolute error = 7e-31
relative error = 4.0681668373563949889061290211901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.28
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -12.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2537082888, alloc=4848776, time=139.73
x[1] = 8.63
y1[1] (analytic) = 0.29955674549717171440128690618464
y1[1] (numeric) = 0.29955674549717171440128690618464
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7137080966484029755147470130818
y2[1] (numeric) = 1.7137080966484029755147470130811
absolute error = 7e-31
relative error = 4.0847096501967287833240414532531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.65
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -12.75
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.64
y1[1] (analytic) = 0.29245480535231712892306496354556
y1[1] (numeric) = 0.29245480535231712892306496354556
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.7066680957358783706697384884108
y2[1] (numeric) = 1.7066680957358783706697384884101
absolute error = 7e-31
relative error = 4.1015590655790348020866967662852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.02
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2541084628, alloc=4848776, time=139.95
x[1] = 8.65
y1[1] (analytic) = 0.28542361913730828159202380941506
y1[1] (numeric) = 0.28542361913730828159202380941507
absolute error = 1e-32
relative error = 3.5035642916395493102755358663023e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.6995574286026682948041343266528
y2[1] (numeric) = 1.699557428602668294804134326652
absolute error = 8e-31
relative error = 4.7071077830993866121364294907324e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -13.23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2545085708, alloc=4848776, time=140.17
x[1] = 8.66
y1[1] (analytic) = 0.27846388996490737097809378439138
y1[1] (numeric) = 0.2784638899649073709780937843914
absolute error = 2e-32
relative error = 7.1822597904957959840567580452026e-30 %
Correct digits = 32
h = 0.01
y2[1] (analytic) = 1.6923768063095605327329972350144
y2[1] (numeric) = 1.6923768063095605327329972350137
absolute error = 7e-31
relative error = 4.1361947137909412833866674906700e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4814
Order of pole (three term test) = -13.47
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 18.23
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.67
y1[1] (analytic) = 0.27157631380223188219454870131795
y1[1] (numeric) = 0.27157631380223188219454870131798
absolute error = 3e-32
relative error = 1.1046618749618455305444825324981e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6851269469128005632677486104297
y2[1] (numeric) = 1.6851269469128005632677486104289
absolute error = 8e-31
relative error = 4.7474168131108593992690373275251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.81
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = -13.71
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.87
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2549087496, alloc=4848776, time=140.39
TOP MAIN SOLVE Loop
x[1] = 8.68
y1[1] (analytic) = 0.26476157940115845512015918362236
y1[1] (numeric) = 0.2647615794011584551201591836224
absolute error = 4e-32
relative error = 1.5107932234908318191379743977615e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6778085753922865330464973659756
y2[1] (numeric) = 1.6778085753922865330464973659748
absolute error = 8e-31
relative error = 4.7681243959130015839815719227340e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4802
Order of pole (three term test) = -13.95
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2553089216, alloc=4848776, time=140.61
x[1] = 8.69
y1[1] (analytic) = 0.2580203682294482706931887919121
y1[1] (numeric) = 0.25802036822944827069318879191215
absolute error = 5e-32
relative error = 1.9378315108649403636896996672470e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6704224235790718708672774127254
y2[1] (numeric) = 1.6704224235790718708672774127247
absolute error = 7e-31
relative error = 4.1905567724610018898168657414456e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4793
Order of pole (three term test) = -14.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 17.17
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2557093248, alloc=4848776, time=140.83
x[1] = 8.7
y1[1] (analytic) = 0.25135335440260084268120821911072
y1[1] (numeric) = 0.25135335440260084268120821911077
absolute error = 5e-32
relative error = 1.9892314593865882456575055248446e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6629692300821827922023461866156
y2[1] (numeric) = 1.6629692300821827922023461866149
absolute error = 7e-31
relative error = 4.2093382567602076610493206272281e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4782
Order of pole (three term test) = -14.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.71
y1[1] (analytic) = 0.24476120461644302949076225515113
y1[1] (numeric) = 0.24476120461644302949076225515119
absolute error = 6e-32
relative error = 2.4513688798853544668953973603941e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6554497402147580120821075808528
y2[1] (numeric) = 1.6554497402147580120821075808521
absolute error = 7e-31
relative error = 4.2284581826639476995047697768623e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.477
Order of pole (three term test) = -14.67
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2561095956, alloc=4848776, time=141.05
x[1] = 8.72
y1[1] (analytic) = 0.23824457808046000705953291829004
y1[1] (numeric) = 0.23824457808046000705953291829011
absolute error = 7e-32
relative error = 2.9381571057772230120894832246935e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.647864705919518052315820857473
y2[1] (numeric) = 1.6478647059195180523158208574723
absolute error = 7e-31
relative error = 4.2479215525730672455828923112137e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.01
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4755
Order of pole (three term test) = -14.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 16.16
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2565096924, alloc=4848776, time=141.28
x[1] = 8.73
y1[1] (analytic) = 0.23180412645187486967815219933192
y1[1] (numeric) = 0.231804126451874869678152199332
absolute error = 8e-32
relative error = 3.4511896412080867389069121125954e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6402148856935715960562647635402
y2[1] (numeric) = 1.6402148856935715960562647635396
absolute error = 6e-31
relative error = 3.6580572779418931899722430681450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4739
Order of pole (three term test) = -15.15
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.83
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2569097640, alloc=4848776, time=141.50
x[1] = 8.74
y1[1] (analytic) = 0.22544049377048345072664875461818
y1[1] (numeric) = 0.22544049377048345072664875461827
absolute error = 9e-32
relative error = 3.9921843008216277453145858307541e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6325010445125664090102392232487
y2[1] (numeric) = 1.6325010445125664090102392232481
absolute error = 6e-31
relative error = 3.6753422119809333736151555899366e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.33
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.472
Order of pole (three term test) = -15.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.75
y1[1] (analytic) = 0.21915431639425087978915076807331
y1[1] (numeric) = 0.2191543163942508797891507680734
absolute error = 9e-32
relative error = 4.1066952949305902191205251731634e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6247239537541924121395762007922
y2[1] (numeric) = 1.6247239537541924121395762007915
absolute error = 7e-31
relative error = 4.3084241995850104638633699505964e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.47
Order of pole (three term test) = -15.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 15.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2573099600, alloc=4848776, time=141.72
x[1] = 8.76
y1[1] (analytic) = 0.2129462229356763164374641551822
y1[1] (numeric) = 0.2129462229356763164374641551823
absolute error = 1.0e-31
relative error = 4.6960213062903932722429619031353e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6168843911210445554816424059899
y2[1] (numeric) = 1.6168843911210445554816424059892
absolute error = 7e-31
relative error = 4.3293138572181071470387640967513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.68
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4678
Order of pole (three term test) = -15.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.89
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2577100312, alloc=4848776, time=141.94
x[1] = 8.77
y1[1] (analytic) = 0.20681683419893222415711853932893
y1[1] (numeric) = 0.20681683419893222415711853932904
absolute error = 1.1e-31
relative error = 5.3187159752282834065037461559275e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6089831405628532067376710681854
y2[1] (numeric) = 1.6089831405628532067376710681847
absolute error = 7e-31
relative error = 4.3505738646529668105353640208564e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4654
Order of pole (three term test) = -16.09
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.59
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.78
y1[1] (analytic) = 0.20076676311778447043610463211708
y1[1] (numeric) = 0.2007667631177844704361046321172
absolute error = 1.2e-31
relative error = 5.9770849585097520021793768405203e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.6010209921980898315252561517566
y2[1] (numeric) = 1.6010209921980898315252561517558
absolute error = 8e-31
relative error = 4.9968114340690558945911604453206e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.04
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4628
Order of pole (three term test) = -16.32
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 14.29
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2581102184, alloc=4848776, time=142.16
TOP MAIN SOLVE Loop
x[1] = 8.79
y1[1] (analytic) = 0.19479661469429946095456106645153
y1[1] (numeric) = 0.19479661469429946095456106645165
absolute error = 1.2e-31
relative error = 6.1602713264971173404441854000660e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5929987422349558046616553817875
y2[1] (numeric) = 1.5929987422349558046616553817868
absolute error = 7e-31
relative error = 4.3942282027034711724630264761138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.46
Order of pole (three term test) = -16.55
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
Radius of convergence (ratio test) for eq 2 = 13.99
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2585104240, alloc=4848776, time=142.38
x[1] = 8.8
y1[1] (analytic) = 0.18890698593834443711091449578068
y1[1] (numeric) = 0.18890698593834443711091449578081
absolute error = 1.3e-31
relative error = 6.8816936205011216144342349373697e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5849171928917622535309313118124
y2[1] (numeric) = 1.5849171928917622535309313118116
absolute error = 8e-31
relative error = 5.0475823190507461012388477727445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4571
Order of pole (three term test) = -16.78
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2589104960, alloc=4848776, time=142.60
x[1] = 8.81
y1[1] (analytic) = 0.18309846580788698680430409481551
y1[1] (numeric) = 0.18309846580788698680430409481565
absolute error = 1.4e-31
relative error = 7.6461590970889218892496583710037e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.576777152316708895484243810161
y2[1] (numeric) = 1.5767771523167088954842438101602
absolute error = 8e-31
relative error = 5.0736402339708262118543681751182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4539
Order of pole (three term test) = -17.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.82
y1[1] (analytic) = 0.17737163515009973847246197742839
y1[1] (numeric) = 0.17737163515009973847246197742854
absolute error = 1.5e-31
relative error = 8.4568200475269539154754408557965e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5685794345070698913227031896634
y2[1] (numeric) = 1.5685794345070698913227031896626
absolute error = 8e-31
relative error = 5.1001561183377496656287650451851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4506
Order of pole (three term test) = -17.24
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2593106088, alloc=4848776, time=142.82
x[1] = 8.83
y1[1] (analytic) = 0.17172706664327612786656648565256
y1[1] (numeric) = 0.17172706664327612786656648565272
absolute error = 1.6e-31
relative error = 9.3171101753204439160084318492010e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5603248592277947962100907977845
y2[1] (numeric) = 1.5603248592277947962100907977837
absolute error = 8e-31
relative error = 5.1271374372380391411447952043830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4471
Order of pole (three term test) = -17.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2597107008, alloc=4848776, time=143.04
x[1] = 8.84
y1[1] (analytic) = 0.1661653247395630459379874981106
y1[1] (numeric) = 0.16616532473956304593798749811076
absolute error = 1.6e-31
relative error = 9.6289644214744451930647556540534e-29 %
Correct digits = 31
h = 0.01
y2[1] (analytic) = 1.5520142519295327478525234803321
y2[1] (numeric) = 1.5520142519295327478525234803313
absolute error = 8e-31
relative error = 5.1545918409280367374951149247919e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4434
Order of pole (three term test) = -17.69
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2601109612, alloc=4848776, time=143.26
x[1] = 8.85
y1[1] (analytic) = 0.16068696560851609452441244898895
y1[1] (numeric) = 0.16068696560851609452441244898912
absolute error = 1.7e-31
relative error = 1.0579576218656924646622934311402e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.5436484436660880894579310034853
y2[1] (numeric) = 1.5436484436660880894579310034845
absolute error = 8e-31
relative error = 5.1825271698524819999246045851665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4396
Order of pole (three term test) = -17.91
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.86
y1[1] (analytic) = 0.15529253708148309426274731481916
y1[1] (numeric) = 0.15529253708148309426274731481934
absolute error = 1.8e-31
relative error = 1.1591027063042490246778913814880e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.535228271011315681844263734824
y2[1] (numeric) = 1.5352282710113156818442637348232
absolute error = 8e-31
relative error = 5.2109514598308452666415576316201e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4355
Order of pole (three term test) = -18.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2605111524, alloc=4848776, time=143.48
x[1] = 8.87
y1[1] (analytic) = 0.14998257859682140633165435671775
y1[1] (numeric) = 0.14998257859682140633165435671794
absolute error = 1.9e-31
relative error = 1.2668137978261608999749730458394e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.5267545759754642150959660868594
y2[1] (numeric) = 1.5267545759754642150959660868587
absolute error = 7e-31
relative error = 4.5848888289904780649676718553655e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4313
Order of pole (three term test) = -18.34
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2609113980, alloc=4848776, time=143.70
x[1] = 8.88
y1[1] (analytic) = 0.14475762114595454624590028460325
y1[1] (numeric) = 0.14475762114595454624590028460344
absolute error = 1.9e-31
relative error = 1.3125388390323780557219057054403e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.5182282059209758853678364011496
y2[1] (numeric) = 1.5182282059209758853678364011488
absolute error = 8e-31
relative error = 5.2693000754436001916783802403107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.427
Order of pole (three term test) = -18.56
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.89
y1[1] (analytic) = 0.13961818722027348399618273657824
y1[1] (numeric) = 0.13961818722027348399618273657844
absolute error = 2.0e-31
relative error = 1.4324781318386769422206538920444e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.5096500134777508567984261849018
y2[1] (numeric) = 1.5096500134777508567984261849011
absolute error = 7e-31
relative error = 4.6368363114005732661125887309208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4224
Order of pole (three term test) = -18.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2613116076, alloc=4848776, time=143.92
TOP MAIN SOLVE Loop
x[1] = 8.9
y1[1] (analytic) = 0.13456479075888794036017232177465
y1[1] (numeric) = 0.13456479075888794036017232177485
absolute error = 2.0e-31
relative error = 1.4862728866301907820912633921806e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.5010208564578849820161746471113
y2[1] (numeric) = 1.5010208564578849820161746471106
absolute error = 7e-31
relative error = 4.6634928288195994726027832510196e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4177
Order of pole (three term test) = -18.98
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2617118324, alloc=4848776, time=144.14
x[1] = 8.91
y1[1] (analytic) = 0.12959793709723290421159868118538
y1[1] (numeric) = 0.12959793709723290421159868118559
absolute error = 2.1e-31
relative error = 1.6203961629608670013164173440806e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.492341597769889307395176258041
y2[1] (numeric) = 1.4923415977698893073951762580403
absolute error = 7e-31
relative error = 4.6906150779825415577119039506386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4128
Order of pole (three term test) = -19.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2621119180, alloc=4848776, time=144.35
x[1] = 8.92
y1[1] (analytic) = 0.12471812291653551013282189839333
y1[1] (numeric) = 0.12471812291653551013282189839355
absolute error = 2.2e-31
relative error = 1.7639777993389902697529875425402e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4836131053323999410385722479477
y2[1] (numeric) = 1.4836131053323999410385722479469
absolute error = 8e-31
relative error = 5.3922413945026586148964811685205e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4078
Order of pole (three term test) = -19.4
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.93
y1[1] (analytic) = 0.11992583619414732960101720810331
y1[1] (numeric) = 0.11992583619414732960101720810353
absolute error = 2.2e-31
relative error = 1.8344670921772278728400786279780e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.474836251987386912430859502249
y2[1] (numeric) = 1.4748362519873869124308595022483
absolute error = 7e-31
relative error = 4.7462896240632043852532125915764e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4025
Order of pole (three term test) = -19.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2625119896, alloc=4848776, time=144.57
x[1] = 8.94
y1[1] (analytic) = 0.1152215561547470424774647646268
y1[1] (numeric) = 0.11522155615474704247746476462703
absolute error = 2.3e-31
relative error = 1.9961542585929062800883486396873e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4660119154128707028008259130412
y2[1] (numeric) = 1.4660119154128707028008259130404
absolute error = 8e-31
relative error = 5.4569815674021804830252755356895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3972
Order of pole (three term test) = -19.8
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2629122072, alloc=4848776, time=144.80
x[1] = 8.95
y1[1] (analytic) = 0.11060575322241836849213123646506
y1[1] (numeric) = 0.11060575322241836849213123646529
absolute error = 2.3e-31
relative error = 2.0794578337845625558143994356650e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4571409780351551744693399111853
y2[1] (numeric) = 1.4571409780351551744693399111845
absolute error = 8e-31
relative error = 5.4902031585079689867115461130640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3916
Order of pole (three term test) = -20
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2633123188, alloc=4848776, time=145.02
x[1] = 8.96
y1[1] (analytic) = 0.10607888897360805089045984485144
y1[1] (numeric) = 0.10607888897360805089045984485168
absolute error = 2.4e-31
relative error = 2.2624671348104986043351736535989e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4482243269405856758159204182652
y2[1] (numeric) = 1.4482243269405856758159204182644
absolute error = 8e-31
relative error = 5.5240060888220427528808541805363e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3859
Order of pole (three term test) = -20.19
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 8.97
y1[1] (analytic) = 0.10164141609096859640480261762689
y1[1] (numeric) = 0.10164141609096859640480261762713
absolute error = 2.4e-31
relative error = 2.3612421907345438018797113371788e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4392628537868411459800558940076
y2[1] (numeric) = 1.4392628537868411459800558940068
absolute error = 8e-31
relative error = 5.5584009404197562752100700460981e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3801
Order of pole (three term test) = -20.38
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2637124736, alloc=4848776, time=145.24
x[1] = 8.98
y1[1] (analytic) = 0.09729377831809038723803346008035
y1[1] (numeric) = 0.097293778318090387238033460080598
absolute error = 2.48e-31
relative error = 2.5489810786173152988282350991868e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4302574547137690900128793475898
y2[1] (numeric) = 1.430257454713769090012879347589
absolute error = 8e-31
relative error = 5.5933985686521057582782887016899e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3741
Order of pole (three term test) = -20.57
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2641126740, alloc=4848776, time=145.46
x[1] = 8.99
y1[1] (analytic) = 0.09303641041512769181042056717737
y1[1] (numeric) = 0.093036410415127691810420567177627
absolute error = 2.57e-31
relative error = 2.7623593693401124468898797728105e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4212090302537723409073802056387
y2[1] (numeric) = 1.4212090302537723409073802056379
absolute error = 8e-31
relative error = 5.6290101101957626369319586339875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.368
Order of pole (three term test) = -20.76
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9
y1[1] (analytic) = 0.08886973811532301163170528881883
y1[1] (numeric) = 0.088869738115323011631705288819103
absolute error = 2.73e-31
relative error = 3.0719118317389196769861014563608e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4121184852417565697562725663524
y2[1] (numeric) = 1.4121184852417565697562725663516
absolute error = 8e-31
relative error = 5.6652469913885372873225038182902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3617
Order of pole (three term test) = -20.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2645127680, alloc=4848776, time=145.68
x[1] = 9.01
y1[1] (analytic) = 0.08479417808243411182747065006893
y1[1] (numeric) = 0.084794178082434111827470650069205
absolute error = 2.75e-31
relative error = 3.2431471855609478546100431256321e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.4029867287246475492114605615293
y2[1] (numeric) = 1.4029867287246475492114605615284
absolute error = 9e-31
relative error = 6.4148860539694774236811177140371e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3552
Order of pole (three term test) = -21.12
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2649128904, alloc=4848776, time=145.91
x[1] = 9.02
y1[1] (analytic) = 0.08081013786906799258126953319692
y1[1] (numeric) = 0.080810137869067992581269533197205
absolute error = 2.85e-31
relative error = 3.5267852216979145464597563424312e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3938146738704872184433528508576
y2[1] (numeric) = 1.3938146738704872184433528508567
absolute error = 9e-31
relative error = 6.4570994757917700857106633787968e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3487
Order of pole (three term test) = -21.3
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2653131088, alloc=4848776, time=146.13
x[1] = 9.03
y1[1] (analytic) = 0.07691801587592596806064673398849
y1[1] (numeric) = 0.076918015875925968060646733988789
absolute error = 2.99e-31
relative error = 3.8872557566007357093156761584358e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3846032378771176399177772903272
y2[1] (numeric) = 1.3846032378771176399177772903262
absolute error = 1.0e-30
relative error = 7.2222855807646836496508112470583e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3419
Order of pole (three term test) = -21.47
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.04
y1[1] (analytic) = 0.07311820131196392828519996910056
y1[1] (numeric) = 0.073118201311963928285199969100865
absolute error = 3.05e-31
relative error = 4.1713279939518223764937355842133e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3753533418804619795187216342643
y2[1] (numeric) = 1.3753533418804619795187216342634
absolute error = 9e-31
relative error = 6.5437729534249604239747056508989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3351
Order of pole (three term test) = -21.64
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2657132564, alloc=4848776, time=146.35
x[1] = 9.05
y1[1] (analytic) = 0.06941107415547176787729335724793
y1[1] (numeric) = 0.069411074155471767877293357248241
absolute error = 3.11e-31
relative error = 4.4805530498404403924553629108926e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3660659108624116818424557351316
y2[1] (numeric) = 1.3660659108624116818424557351307
absolute error = 9e-31
relative error = 6.5882619048140993213502352792873e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3281
Order of pole (three term test) = -21.81
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2661133260, alloc=4848776, time=146.57
x[1] = 9.06
y1[1] (analytic) = 0.06579700511607587372011460161184
y1[1] (numeric) = 0.065797005116075873720114601612162
absolute error = 3.22e-31
relative error = 4.8938397641646952399785280821963e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3567418735583290518687453974845
y2[1] (numeric) = 1.3567418735583290518687453974836
absolute error = 9e-31
relative error = 6.6335389033108308241769926390634e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.321
Order of pole (three term test) = -21.97
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2665135300, alloc=4848776, time=146.79
x[1] = 9.07
y1[1] (analytic) = 0.0622763555976684712426455796823
y1[1] (numeric) = 0.062276355597668471242645579682631
absolute error = 3.31e-31
relative error = 5.3150187872007095923936414254885e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3473821623641744926739098396967
y2[1] (numeric) = 1.3473821623641744926739098396958
absolute error = 9e-31
relative error = 6.6796193770356988013273154046317e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3137
Order of pole (three term test) = -22.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.08
y1[1] (analytic) = 0.05884947766226753636602573501985
y1[1] (numeric) = 0.058849477662267536366025735020194
absolute error = 3.44e-31
relative error = 5.8454214661715196989347179237430e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3379877132432676863845577471149
y2[1] (numeric) = 1.337987713243267686384557747114
absolute error = 9e-31
relative error = 6.7265191682396677169792188396712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3064
Order of pole (three term test) = -22.28
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2669137000, alloc=4848776, time=147.01
x[1] = 9.09
y1[1] (analytic) = 0.05551671399481088708999699494192
y1[1] (numeric) = 0.055516713994810887089996994942272
absolute error = 3.52e-31
relative error = 6.3404329015744920029771216132940e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3285594656326920421762077861611
y2[1] (numeric) = 1.3285594656326920421762077861602
absolute error = 9e-31
relative error = 6.7742545462306296217790169784895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2989
Order of pole (three term test) = -22.43
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2673137968, alloc=4848776, time=147.23
x[1] = 9.1
y1[1] (analytic) = 0.05227839786888797528093341042463
y1[1] (numeric) = 0.052278397868887975280933410424988
absolute error = 3.58e-31
relative error = 6.8479527796136552255428011674929e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3190983623493517707939976839854
y2[1] (numeric) = 1.3190983623493517707939976839845
absolute error = 9e-31
relative error = 6.8228422207808245222596730429352e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2913
Order of pole (three term test) = -22.58
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.11
y1[1] (analytic) = 0.04913485311341280545371997026879
y1[1] (numeric) = 0.049134853113412805453719970269156
absolute error = 3.66e-31
relative error = 7.4488876389881690569587194519303e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3096053494956909798097442924788
y2[1] (numeric) = 1.3096053494956909798097442924779
absolute error = 9e-31
relative error = 6.8722993560355893129914544926357e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2835
Order of pole (three term test) = -22.73
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2677139352, alloc=4848776, time=147.46
x[1] = 9.12
y1[1] (analytic) = 0.04608639408024131322782992654193
y1[1] (numeric) = 0.046086394080241313227829926542305
absolute error = 3.75e-31
relative error = 8.1368917548004541210603298134811e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.3000813763650842176272617719129
y2[1] (numeric) = 1.300081376365084217627261771912
absolute error = 9e-31
relative error = 6.9226435849448335477717302325254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2757
Order of pole (three term test) = -22.87
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2681142112, alloc=4848776, time=147.68
x[1] = 9.13
y1[1] (analytic) = 0.04313332561273644169276959556212
y1[1] (numeric) = 0.0431333256127364416927695955625
absolute error = 3.80e-31
relative error = 8.8098933852620282675141939432813e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.290527395346907927102696411862
y2[1] (numeric) = 1.2905273953469079271026964118611
absolute error = 9e-31
relative error = 6.9738930242396762349435126682342e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2677
Order of pole (three term test) = -23
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2685143120, alloc=4848776, time=147.90
x[1] = 9.14
y1[1] (analytic) = 0.04027594301528405914905840756707
y1[1] (numeric) = 0.04027594301528405914905840756746
absolute error = 3.90e-31
relative error = 9.6831997168136175675905353017152e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 1.280944361831302301555409197633
y2[1] (numeric) = 1.2809443618313023015554091976321
absolute error = 9e-31
relative error = 7.0260662899777697075639064096877e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2597
Order of pole (three term test) = -23.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.15
y1[1] (analytic) = 0.03751453202376276660756678985896
y1[1] (numeric) = 0.037514532023762766607566789859358
absolute error = 3.98e-31
relative error = 1.0609222040885263682740066382200e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2713332341136330669044401785046
y2[1] (numeric) = 1.2713332341136330669044401785036
absolute error = 1.0e-30
relative error = 7.8657583485355419846805498278082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2515
Order of pole (three term test) = -23.26
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2689143920, alloc=4848776, time=148.12
x[1] = 9.16
y1[1] (analytic) = 0.03484936877697054804185353791419
y1[1] (numeric) = 0.034849368776970548041853537914597
absolute error = 4.07e-31
relative error = 1.1678834202269888778827241330095e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.26169497329866274367272607517
y2[1] (numeric) = 1.2616949732986627436727260751691
absolute error = 9e-31
relative error = 7.1332613590983694845529372222107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2432
Order of pole (three term test) = -23.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2693145104, alloc=4848776, time=148.34
x[1] = 9.17
y1[1] (analytic) = 0.03228071978901112070466639530159
y1[1] (numeric) = 0.032280719789011120704666395302008
absolute error = 4.18e-31
relative error = 1.2948905809166435097385098447149e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2520305432044409716530136891507
y2[1] (numeric) = 1.2520305432044409716530136891497
absolute error = 1.0e-30
relative error = 7.9870255995561002267092909478415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2349
Order of pole (three term test) = -23.51
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2697145888, alloc=4848776, time=148.57
x[1] = 9.18
y1[1] (analytic) = 0.02980884192264274685056289431924
y1[1] (numeric) = 0.029808841922642746850562894319672
absolute error = 4.32e-31
relative error = 1.4492344289022966604833181226608e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2423409102659235081229113936966
y2[1] (numeric) = 1.2423409102659235081229113936956
absolute error = 1.0e-30
relative error = 8.0493203736319819720325876313377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2264
Order of pole (three term test) = -23.62
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.19
y1[1] (analytic) = 0.02743398236359217196126994573233
y1[1] (numeric) = 0.027433982363592171961269945732767
absolute error = 4.37e-31
relative error = 1.5929149264889290270863209954186e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2326270434383295376289399672643
y2[1] (numeric) = 1.2326270434383295376289399672633
absolute error = 1.0e-30
relative error = 8.1127540185275168282686370366038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2179
Order of pole (three term test) = -23.73
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2701147572, alloc=4848776, time=148.78
x[1] = 9.2
y1[1] (analytic) = 0.0251563785958362580585546615242
y1[1] (numeric) = 0.025156378595836258058554661524646
absolute error = 4.46e-31
relative error = 1.7729101917468335654557285162244e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2228899141002469575280690577583
y2[1] (numeric) = 1.2228899141002469575280690577573
absolute error = 1.0e-30
relative error = 8.1773509493351217930560893122612e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2092
Order of pole (three term test) = -23.84
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2705148844, alloc=4848776, time=149.01
x[1] = 9.21
y1[1] (analytic) = 0.02297625837785378392067655333447
y1[1] (numeric) = 0.022976258377853783920676553334932
absolute error = 4.62e-31
relative error = 2.0107712596290688827663404989556e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2131304959564953286774397976603
y2[1] (numeric) = 1.2131304959564953286774397976593
absolute error = 1.0e-30
relative error = 8.2431362770379279414303072759031e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2005
Order of pole (three term test) = -23.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.22
y1[1] (analytic) = 0.02089383971984978700260936084514
y1[1] (numeric) = 0.020893839719849787002609360845607
absolute error = 4.67e-31
relative error = 2.2351085595642609991374826904003e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.2033497649407562048962573265169
y2[1] (numeric) = 1.2033497649407562048962573265159
absolute error = 1.0e-30
relative error = 8.3101358319476831281154392365556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1917
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2709149696, alloc=4848776, time=149.23
x[1] = 9.23
y1[1] (analytic) = 0.01890933086195472460686083613089
y1[1] (numeric) = 0.018909330861954724606860836131371
absolute error = 4.81e-31
relative error = 2.5437177206929326730524807694293e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1935486991179805780857659098894
y2[1] (numeric) = 1.1935486991179805780857659098884
absolute error = 1.0e-30
relative error = 8.3783761880766914010189844654291e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1829
Order of pole (three term test) = -24.13
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2713150680, alloc=4848776, time=149.45
x[1] = 9.24
y1[1] (analytic) = 0.01702293025340063437060609686214
y1[1] (numeric) = 0.017022930253400634370606096862632
absolute error = 4.92e-31
relative error = 2.8902192083041297324034464763198e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1837282785865831981814677992768
y2[1] (numeric) = 1.1837282785865831981814677992758
absolute error = 1.0e-30
relative error = 8.4478846884864338617746316970058e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1739
Order of pole (three term test) = -24.22
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2717153304, alloc=4848776, time=149.67
x[1] = 9.25
y1[1] (analytic) = 0.01523482653267637643573269327515
y1[1] (numeric) = 0.015234826532676376435732693275654
absolute error = 5.04e-31
relative error = 3.3082096400572527999035269356260e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1738894853804335484240861494355
y2[1] (numeric) = 1.1738894853804335484240861494345
absolute error = 1.0e-30
relative error = 8.5186894716577214560997191048084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1649
Order of pole (three term test) = -24.31
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.26
y1[1] (analytic) = 0.01354519850866394176104314133525
y1[1] (numeric) = 0.013545198508663941761043141335756
absolute error = 5.06e-31
relative error = 3.7356410810542660732203812086452e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1640333033706532767700709817761
y2[1] (numeric) = 1.1640333033706532767700709817751
absolute error = 1.0e-30
relative error = 8.5908194989295633602516766150214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1558
Order of pole (three term test) = -24.39
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2721154184, alloc=4848776, time=149.89
x[1] = 9.27
y1[1] (analytic) = 0.01195421514275771293006401116561
y1[1] (numeric) = 0.011954215142757712930064011166132
absolute error = 5.22e-31
relative error = 4.3666605775975689579197585626506e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1541607181672299036166719422002
y2[1] (numeric) = 1.1541607181672299036166719421993
absolute error = 9e-31
relative error = 7.7978741247507630576827427713105e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1467
Order of pole (three term test) = -24.46
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2725155512, alloc=4848776, time=150.11
x[1] = 9.28
y1[1] (analytic) = 0.01046203553196846551348022350807
y1[1] (numeric) = 0.010462035531968465513480223508596
absolute error = 5.26e-31
relative error = 5.0277022897955252337488435125308e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1442727170204566443888170425023
y2[1] (numeric) = 1.1442727170204566443888170425013
absolute error = 1.0e-30
relative error = 8.7391754179359899884983379343362e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1375
Order of pole (three term test) = -24.54
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2729157208, alloc=4848776, time=150.34
x[1] = 9.29
y1[1] (analytic) = 0.00906880889301379957197835885467
y1[1] (numeric) = 0.0090688088930137995719783588552064
absolute error = 5.364e-31
relative error = 5.9147789563987649223534137355356e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.13437028872220820292340549006
y2[1] (numeric) = 1.134370288722208202923405490059
absolute error = 1.0e-30
relative error = 8.8154636095629118492928051135126e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1282
Order of pole (three term test) = -24.6
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.3
y1[1] (analytic) = 0.00777467454739659224309076536484
y1[1] (numeric) = 0.0077746745473965922430907653653929
absolute error = 5.529e-31
relative error = 7.1115517007093588067024367644009e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1244544235070624079894062785863
y2[1] (numeric) = 1.1244544235070624079894062785854
absolute error = 9e-31
relative error = 8.0038815374391857893595881131803e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1189
Order of pole (three term test) = -24.66
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2733158928, alloc=4848776, time=150.55
x[1] = 9.31
y1[1] (analytic) = 0.00657976190747296355434719976161
y1[1] (numeric) = 0.0065797619074729635543471997621711
absolute error = 5.611e-31
relative error = 8.5276641904432858430797635423021e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 1.1145261129532775806977121685111
y2[1] (numeric) = 1.1145261129532775806977121685102
absolute error = 9e-31
relative error = 8.0751809180600975194875828558422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1096
Order of pole (three term test) = -24.72
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2737161092, alloc=4848776, time=150.78
x[1] = 9.32
y1[1] (analytic) = 0.00548419046351114865454269625377
y1[1] (numeric) = 0.0054841904635111486545426962543381
absolute error = 5.681e-31
relative error = 1.0358867070351250679092856399175e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.1045863498836355349814894861648
y2[1] (numeric) = 1.1045863498836355349814894861639
absolute error = 9e-31
relative error = 8.1478464775054660021897599140796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1002
Order of pole (three term test) = -24.77
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.33
y1[1] (analytic) = 0.00448806977174257056511429950408
y1[1] (numeric) = 0.0044880697717425705651142995046585
absolute error = 5.785e-31
relative error = 1.2889728311317838281372593077523e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.0946361282661601267643451492879
y2[1] (numeric) = 1.094636128266160126764345149287
absolute error = 9e-31
relative error = 8.2219102472485316384032799349034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09072
Order of pole (three term test) = -24.82
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2741161952, alloc=4848776, time=151.00
x[1] = 9.34
y1[1] (analytic) = 0.00359149944340630833439411778771
y1[1] (numeric) = 0.003591499443406308334394117788297
absolute error = 5.870e-31
relative error = 1.6344148432980624653574646849894e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.0846764431147212798786598355838
y2[1] (numeric) = 1.0846764431147212798786598355829
absolute error = 9e-31
relative error = 8.2974052374142977967227194425153e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08125
Order of pole (three term test) = -24.86
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2745163932, alloc=4848776, time=151.22
x[1] = 9.35
y1[1] (analytic) = 0.00279456913478805613879369159611
y1[1] (numeric) = 0.0027945691347880561387936915967079
absolute error = 5.979e-31
relative error = 2.1395069191778844138447746887068e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.0747082903895344282486657586974
y2[1] (numeric) = 1.0747082903895344282486657586965
absolute error = 9e-31
relative error = 8.3743654724556896585785201579515e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07174
Order of pole (three term test) = -24.9
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2749168916, alloc=4848776, time=151.44
x[1] = 9.36
y1[1] (analytic) = 0.00209735853825456942670871950334
y1[1] (numeric) = 0.0020973585382545694267087195039448
absolute error = 6.048e-31
relative error = 2.8836271384639704804346245351995e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.0647326668975653243111338887167
y2[1] (numeric) = 1.0647326668975653243111338887158
absolute error = 9e-31
relative error = 8.4528260283629134606703686474847e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0622
Order of pole (three term test) = -24.94
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.37
y1[1] (analytic) = 0.00149993737428449465305848084639
y1[1] (numeric) = 0.0014999373742844946530584808470003
absolute error = 6.103e-31
relative error = 4.0688365425331669610629742996133e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.054750570192850173109832832146
y2[1] (numeric) = 1.0547505701928501731098328321451
absolute error = 9e-31
relative error = 8.5328230714816713429689677162608e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05264
Order of pole (three term test) = -24.96
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2753170700, alloc=4848776, time=151.67
x[1] = 9.38
y1[1] (analytic) = 0.00100236538449637951484554819261
y1[1] (numeric) = 0.001002365384496379514845548193235
absolute error = 6.250e-31
relative error = 6.2352512334014808893520877396852e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 1.0447629984767410599672836474296
y2[1] (numeric) = 1.0447629984767410599672836474287
absolute error = 9e-31
relative error = 8.6143938990201151071062806825178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04306
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2757171976, alloc=4848776, time=151.89
x[1] = 9.39
y1[1] (analytic) = 0.00060469232567456088090226151925
y1[1] (numeric) = 0.00060469232567456088090226151988095
absolute error = 6.3095e-31
relative error = 1.0434231975677011093118753916175e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 1.0347709504980866471079148873655
y2[1] (numeric) = 1.0347709504980866471079148873646
absolute error = 9e-31
relative error = 8.6975769813289144263345442476369e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03346
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2761173468, alloc=4848776, time=152.11
x[1] = 9.4
y1[1] (analytic) = 0.00030695796479352782205257932708
y1[1] (numeric) = 0.00030695796479352782205257932772423
absolute error = 6.4423e-31
relative error = 2.0987564223438046623174023617324e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 1.0247754254533581210797730773676
y2[1] (numeric) = 1.0247754254533581210797730773667
absolute error = 9e-31
relative error = 8.7824120060435896912649300709381e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02385
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.41
y1[1] (analytic) = 0.00010919207504125730123994018286
y1[1] (numeric) = 0.0001091920750412573012399401835042
absolute error = 6.4420e-31
relative error = 5.8996955571784351856446775833241e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 1.0147774228867303782968183588059
y2[1] (numeric) = 1.014777422886730378296818358805
absolute error = 9e-31
relative error = 8.8689399241833363788982236528260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01423
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2765175924, alloc=4848776, time=152.33
x[1] = 9.42
y1[1] (analytic) = 1.141443284192018673824602560e-05
y1[1] (numeric) = 1.1414432841920186738246026259148e-05
absolute error = 6.59148e-31
relative error = 5.7746890198454677426266054144378e-24 %
Correct digits = 26
h = 0.01
y2[1] (analytic) = 1.0047779425901284404999856666986
y2[1] (numeric) = 1.0047779425901284404999856666977
absolute error = 9e-31
relative error = 8.9572029983059677511988051738421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004601
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2769177748, alloc=4848776, time=152.56
x[1] = 9.43
y1[1] (analytic) = 1.363481587825531536357608654e-05
y1[1] (numeric) = 1.3634815878255315363576087205127e-05
absolute error = 6.65127e-31
relative error = 4.8781516812466730788312305398255e-24 %
Correct digits = 26
h = 0.01
y2[1] (analytic) = 0.99477798450324909541217095950362
y2[1] (numeric) = 0.99477798450324909541217095950269
absolute error = 9.3e-31
relative error = 9.3488196812518268922993350756603e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.005035
Order of pole (three term test) = -0.8935
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.44
y1[1] (analytic) = 0.00011585300211380936663229413049
y1[1] (numeric) = 0.00011585300211380936663229413116289
absolute error = 6.7289e-31
relative error = 5.8081360665904860449550772762831e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 0.98477854861356776033976198064944
y2[1] (numeric) = 0.98477854861356776033976198064852
absolute error = 9.2e-31
relative error = 9.3422018716312716846277891047025e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.01468
Order of pole (three term test) = -0.8985
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2773178744, alloc=4848776, time=152.78
x[1] = 9.45
y1[1] (analytic) = 0.00031805876981514032306333581925
y1[1] (numeric) = 0.00031805876981514032306333581993684
absolute error = 6.8684e-31
relative error = 2.1594751196428253588792314242970e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 0.97478063485634056795102606282269
y2[1] (numeric) = 0.97478063485634056795102606282178
absolute error = 9.1e-31
relative error = 9.3354337115459039714422818325439e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.02431
Order of pole (three term test) = -0.9082
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2777180608, alloc=4848776, time=153.00
x[1] = 9.46
y1[1] (analytic) = 0.00062023189857398229629714879012
y1[1] (numeric) = 0.000620231898573982296297148790817
absolute error = 6.9700e-31
relative error = 1.1237732235354558701491840210100e-25 %
Correct digits = 27
h = 0.01
y2[1] (analytic) = 0.9647852430146116739394458188179
y2[1] (numeric) = 0.96478524301461167393944581881699
absolute error = 9.1e-31
relative error = 9.4321509018584568944058718447499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.03394
Order of pole (three term test) = -0.9228
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2781181836, alloc=4848776, time=153.23
x[1] = 9.47
y1[1] (analytic) = 0.00102234217132926950340047473792
y1[1] (numeric) = 0.0010223421713292695034004747386213
absolute error = 7.013e-31
relative error = 6.8597385461284050811782520984134e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.95479337261923578575790941952403
y2[1] (numeric) = 0.95479337261923578575790941952314
absolute error = 8.9e-31
relative error = 9.3213885383233081807742120550066e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.04355
Order of pole (three term test) = -0.9423
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.48
y1[1] (analytic) = 0.00152434937738881719264435738589
y1[1] (numeric) = 0.0015243493773888171926443573866006
absolute error = 7.106e-31
relative error = 4.6616609718255331880356909767768e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.94480602284892591008756775834644
y2[1] (numeric) = 0.94480602284892591008756775834555
absolute error = 8.9e-31
relative error = 9.4199230156930385028260980602038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.05314
Order of pole (three term test) = -0.9665
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2785184324, alloc=4848776, time=153.45
x[1] = 9.49
y1[1] (analytic) = 0.00212620331645035735318085758929
y1[1] (numeric) = 0.0021262033164503573531808575900148
absolute error = 7.248e-31
relative error = 3.4088931871766396431237956092568e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.93482419243033631418331835021631
y2[1] (numeric) = 0.93482419243033631418331835021543
absolute error = 8.8e-31
relative error = 9.4135347279812525024212055061657e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06271
Order of pole (three term test) = -0.9956
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2789185728, alloc=4848776, time=153.67
x[1] = 9.5
y1[1] (analytic) = 0.00282784380362152710839835982201
y1[1] (numeric) = 0.0028278438036215271083983598227421
absolute error = 7.321e-31
relative error = 2.5888982943910249377906324854759e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.92484887953819069271651749546599
y2[1] (numeric) = 0.92484887953819069271651749546512
absolute error = 8.7e-31
relative error = 9.4069422502238565550640049860489e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07226
Order of pole (three term test) = -1.029
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2793187988, alloc=4848776, time=153.89
x[1] = 9.51
y1[1] (analytic) = 0.00362920067543830779829944423228
y1[1] (numeric) = 0.0036292006754383077982994442330168
absolute error = 7.368e-31
relative error = 2.0301991151564381034747552982666e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.91488108169546552721501018714384
y2[1] (numeric) = 0.91488108169546552721501018714297
absolute error = 8.7e-31
relative error = 9.5094326181464861122263598168153e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08178
Order of pole (three term test) = -1.068
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.52
y1[1] (analytic) = 0.00453019379688131291200843566447
y1[1] (numeric) = 0.0045301937968813129120084356652134
absolute error = 7.434e-31
relative error = 1.6409893998613773328811459770168e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.90492179567363861968135350224591
y2[1] (numeric) = 0.90492179567363861968135350224505
absolute error = 8.6e-31
relative error = 9.5035836700098697639482753295778e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09127
Order of pole (three term test) = -1.111
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2797189436, alloc=4848776, time=154.11
x[1] = 9.53
y1[1] (analytic) = 0.00553073306938922324746226601279
y1[1] (numeric) = 0.0055307330693892232474622660135449
absolute error = 7.549e-31
relative error = 1.3649185207981227887412192472724e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.89497201739301277545274570962751
y2[1] (numeric) = 0.89497201739301277545274570962665
absolute error = 8.6e-31
relative error = 9.6092389849809642892152081435235e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1007
Order of pole (three term test) = -1.16
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2801191788, alloc=4848776, time=154.33
x[1] = 9.54
y1[1] (analytic) = 0.00663071843986856796144652119425
y1[1] (numeric) = 0.0066307184398685679614465211950124
absolute error = 7.624e-31
relative error = 1.1497999906253176023406381153074e-26 %
Correct digits = 28
h = 0.01
y2[1] (analytic) = 0.88503274182312460285131178094508
y2[1] (numeric) = 0.88503274182312460285131178094422
absolute error = 8.6e-31
relative error = 9.7171546244542505110568642474834e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1101
Order of pole (three term test) = -1.212
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.55
y1[1] (analytic) = 0.00783003991069895053937979498404
y1[1] (numeric) = 0.007830039910698950539379794984815
absolute error = 7.750e-31
relative error = 9.8977784128666008855202882588655e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.87510496288324838866178788576117
y2[1] (numeric) = 0.87510496288324838866178788576032
absolute error = 8.5e-31
relative error = 9.7131205518417594388044048485758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1195
Order of pole (three term test) = -1.27
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2805192760, alloc=4848776, time=154.55
x[1] = 9.56
y1[1] (analytic) = 0.00912857755073271917058703179396
y1[1] (numeric) = 0.0091285775507327191705870317947443
absolute error = 7.843e-31
relative error = 8.5917000281938445800254201181101e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.86518967334300499896614394163858
y2[1] (numeric) = 0.86518967334300499896614394163774
absolute error = 8.4e-31
relative error = 9.7088537448017073492067069950956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1288
Order of pole (three term test) = -1.332
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2809196308, alloc=4848776, time=154.77
x[1] = 9.57
y1[1] (analytic) = 0.01052620150728798157119069248431
y1[1] (numeric) = 0.010526201507287981571190692485096
absolute error = 7.86e-31
relative error = 7.4670810686628078306308837692039e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.85528786472308574436223511708336
y2[1] (numeric) = 0.85528786472308574436223511708253
absolute error = 8.3e-31
relative error = 9.7043350459406655041295766152820e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1381
Order of pole (three term test) = -1.399
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2813197688, alloc=4848776, time=154.99
x[1] = 9.58
y1[1] (analytic) = 0.01202277201913376496313159979792
y1[1] (numeric) = 0.012022772019133764963131599798719
absolute error = 7.99e-31
relative error = 6.6457219577017943990796018304260e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.84540052719610113709723058563525
y2[1] (numeric) = 0.84540052719610113709723058563442
absolute error = 8.3e-31
relative error = 9.8178315875058734874209389983230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1473
Order of pole (three term test) = -1.471
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.59
y1[1] (analytic) = 0.01361813943046602270414249191122
y1[1] (numeric) = 0.013618139430466022704142491912028
absolute error = 8.08e-31
relative error = 5.9332627935382333523785397760845e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.83552864948756445515748042792753
y2[1] (numeric) = 0.83552864948756445515748042792671
absolute error = 8.2e-31
relative error = 9.8141458165786620945702111625543e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1564
Order of pole (three term test) = -1.547
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2817200096, alloc=4848776, time=155.21
x[1] = 9.6
y1[1] (analytic) = 0.01531214420587308997965792011627
y1[1] (numeric) = 0.015312144205873089979657920117082
absolute error = 8.12e-31
relative error = 5.3029803604419503300370980081368e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.82567321877702001487589827347958
y2[1] (numeric) = 0.82567321877702001487589827347877
absolute error = 8.1e-31
relative error = 9.8101764908854007628924187485578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1655
Order of pole (three term test) = -1.628
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2821202896, alloc=4848776, time=155.44
x[1] = 9.61
y1[1] (analytic) = 0.01710461694628909202356247115011
y1[1] (numeric) = 0.017104616946289092023562471150931
absolute error = 8.21e-31
relative error = 4.7998736398368681022092615977935e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.81583522059932603914720611244047
y2[1] (numeric) = 0.81583522059932603914720611243967
absolute error = 8.0e-31
relative error = 9.8059017286886287609381497257644e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1745
Order of pole (three term test) = -1.713
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.62
y1[1] (analytic) = 0.01899537840593370954024970188484
y1[1] (numeric) = 0.018995378405933709540249701885673
absolute error = 8.33e-31
relative error = 4.3852772090067465456901391399943e-27 %
Correct digits = 29
h = 0.01
bytes used=2825203692, alloc=4848776, time=155.66
y2[1] (analytic) = 0.80601563874610199288195575052908
y2[1] (numeric) = 0.80601563874610199288195575052829
absolute error = 7.9e-31
relative error = 9.8012986600233078069948905419518e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1835
Order of pole (three term test) = -1.803
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.63
y1[1] (analytic) = 0.02098423951023660736556600461514
y1[1] (numeric) = 0.020984239510236607365566004615975
absolute error = 8.35e-31
relative error = 3.9791768464740754119058626307309e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.79621545516735024088365455832705
y2[1] (numeric) = 0.79621545516735024088365455832626
absolute error = 7.9e-31
relative error = 9.9219375217221340745103099396790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1924
Order of pole (three term test) = -1.897
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2829205448, alloc=4848776, time=155.88
x[1] = 9.64
y1[1] (analytic) = 0.02307100137474473393871028265082
y1[1] (numeric) = 0.023071001374744733938710282651667
absolute error = 8.47e-31
relative error = 3.6712754086486699805623648834068e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.78643564987326186590122612385328
y2[1] (numeric) = 0.7864356498732618659012261238525
absolute error = 7.8e-31
relative error = 9.9181668598785036785925165116270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2012
Order of pole (three term test) = -1.996
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2833206084, alloc=4848776, time=156.10
x[1] = 9.65
y1[1] (analytic) = 0.02525545532501060087089827662006
y1[1] (numeric) = 0.025255455325010600870898276620914
absolute error = 8.54e-31
relative error = 3.3814476476861600082847683860984e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.77667720083621646619317235015962
y2[1] (numeric) = 0.77667720083621646619317235015885
absolute error = 7.7e-31
relative error = 9.9140286231007244953923586166161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2099
Order of pole (three term test) = -2.099
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.66
y1[1] (analytic) = 0.02753738291745955379940818611257
y1[1] (numeric) = 0.027537382917459553799408186113432
absolute error = 8.62e-31
relative error = 3.1302902043515010197052721030480e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.76694108389298573254201401859704
y2[1] (numeric) = 0.76694108389298573254201401859628
absolute error = 7.6e-31
relative error = 9.9094965175453522981467752524784e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2185
Order of pole (three term test) = -2.206
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2837206952, alloc=4848776, time=156.33
x[1] = 9.67
y1[1] (analytic) = 0.02991655596123394781731151651455
y1[1] (numeric) = 0.029916555961233947817311516515419
absolute error = 8.69e-31
relative error = 2.9047461249418395572323737306924e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.75722827264715058427981162619756
y2[1] (numeric) = 0.75722827264715058427981162619681
absolute error = 7.5e-31
relative error = 9.9045430168384801137330612933586e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2271
Order of pole (three term test) = -2.318
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2841209364, alloc=4848776, time=156.55
x[1] = 9.68
y1[1] (analytic) = 0.03239273654101204307954959679726
y1[1] (numeric) = 0.032392736541012043079549596798138
absolute error = 8.78e-31
relative error = 2.7104841818114843730201571951605e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.7475397383717416225298451628392
y2[1] (numeric) = 0.74753973837174162252984516283846
absolute error = 7.4e-31
relative error = 9.8991392967527806477308246004528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2355
Order of pole (three term test) = -2.434
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2845210120, alloc=4848776, time=156.77
x[1] = 9.69
y1[1] (analytic) = 0.03496567704079933871481084356017
y1[1] (numeric) = 0.034965677040799338714810843561056
absolute error = 8.86e-31
relative error = 2.5339134688173778563389039031530e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.73787644991211263653799597502699
y2[1] (numeric) = 0.73787644991211263653799597502627
absolute error = 7.2e-31
relative error = 9.7577311226799300367202118962251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2439
Order of pole (three term test) = -2.554
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.7
y1[1] (analytic) = 0.03763512016868996592964362910856
y1[1] (numeric) = 0.037635120168689965929643629109454
absolute error = 8.94e-31
relative error = 2.3754408010200836933172183451094e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.72823937358905687566225910317516
y2[1] (numeric) = 0.72823937358905687566225910317445
absolute error = 7.1e-31
relative error = 9.7495415072221940142423222815566e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2522
Order of pole (three term test) = -2.678
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2849212520, alloc=4848776, time=156.98
x[1] = 9.71
y1[1] (analytic) = 0.04040079898259566418612876775069
y1[1] (numeric) = 0.040400798982595664186128767751594
absolute error = 9.04e-31
relative error = 2.2375795102206663092509134190271e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.71862947310217577531245097026894
y2[1] (numeric) = 0.71862947310217577531245097026823
absolute error = 7.1e-31
relative error = 9.8799176289705442629915379749642e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2603
Order of pole (three term test) = -2.807
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2853214148, alloc=4848776, time=157.20
x[1] = 9.72
y1[1] (analytic) = 0.04326243691693976757693459507806
y1[1] (numeric) = 0.043262436916939767576934595078967
absolute error = 9.07e-31
relative error = 2.0965069576209115352555531052806e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.70904770943350979988699265784006
y2[1] (numeric) = 0.70904770943350979988699265783936
absolute error = 7.0e-31
relative error = 9.8723963237856247629038060053292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2684
Order of pole (three term test) = -2.939
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.73
y1[1] (analytic) = 0.04621974781031353202136204921682
y1[1] (numeric) = 0.04621974781031353202136204921773
absolute error = 9.10e-31
relative error = 1.9688553986375093721459143220071e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.69949504075144103954216772773388
y2[1] (numeric) = 0.6994950407514410395421677277332
absolute error = 6.8e-31
relative error = 9.7212983707432971170018237210452e-29 %
Correct digits = 31
h = 0.01
bytes used=2857215276, alloc=4848776, time=157.42
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2763
Order of pole (three term test) = -3.076
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.74
y1[1] (analytic) = 0.04927243593409203767270701204934
y1[1] (numeric) = 0.049272435934092037672707012050263
absolute error = 9.23e-31
relative error = 1.8732583086304610154550711818705e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.68997242231487717045409676146381
y2[1] (numeric) = 0.68997242231487717045409676146313
absolute error = 6.8e-31
relative error = 9.8554663636929225526275402919379e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2842
Order of pole (three term test) = -3.216
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2861216564, alloc=4848776, time=157.64
x[1] = 9.75
y1[1] (analytic) = 0.05242019602200680497054568002278
y1[1] (numeric) = 0.052420196022006804970545680023709
absolute error = 9.29e-31
relative error = 1.7722177147334426293735141454974e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.68048080637772636009755598607246
y2[1] (numeric) = 0.68048080637772636009755598607179
absolute error = 6.7e-31
relative error = 9.8459793975157530609038917178101e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2919
Order of pole (three term test) = -3.361
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2865218040, alloc=4848776, time=157.86
x[1] = 9.76
y1[1] (analytic) = 0.05566271330067216710098150057171
y1[1] (numeric) = 0.055662713300672167100981500572647
absolute error = 9.37e-31
relative error = 1.6833530822305154398355360246641e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.67102114209367266997150812438323
y2[1] (numeric) = 0.67102114209367266997150812438257
absolute error = 6.6e-31
relative error = 9.8357556654729941513940509373133e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2995
Order of pole (three term test) = -3.509
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.77
y1[1] (analytic) = 0.05899966352106234625304620838286
y1[1] (numeric) = 0.058999663521062346253046208383804
absolute error = 9.44e-31
relative error = 1.6000091249045861728215813740384e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.66159437542126147815171935000727
y2[1] (numeric) = 0.66159437542126147815171935000662
absolute error = 6.5e-31
relative error = 9.8247509977109628119672274324758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.307
Order of pole (three term test) = -3.661
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2869220412, alloc=4848776, time=158.08
x[1] = 9.78
y1[1] (analytic) = 0.06243071299093608598986013084239
y1[1] (numeric) = 0.062430712990936085989860130843339
absolute error = 9.49e-31
relative error = 1.5200851544620020778576366359326e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.65220144902930441304911186785548
y2[1] (numeric) = 0.65220144902930441304911186785484
absolute error = 6.4e-31
relative error = 9.8129190137883888203420130357950e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3144
Order of pole (three term test) = -3.817
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2873221984, alloc=4848776, time=158.30
x[1] = 9.79
y1[1] (analytic) = 0.06595551860820559729833508354291
y1[1] (numeric) = 0.065955518608205597298335083543868
absolute error = 9.58e-31
relative error = 1.4524940751217354318753453309726e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.64284330220261325780164732579296
y2[1] (numeric) = 0.64284330220261325780164732579232
absolute error = 6.4e-31
relative error = 9.9557699023561250797010516339930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3216
Order of pole (three term test) = -3.976
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2877223912, alloc=4848776, time=158.52
x[1] = 9.8
y1[1] (analytic) = 0.06957372789524648145062224791078
y1[1] (numeric) = 0.069573727895246481450622247911739
absolute error = 9.59e-31
relative error = 1.3783938693696506785343208352356e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.63352087074807225183074705127114
y2[1] (numeric) = 0.63352087074807225183074705127052
absolute error = 6.2e-31
relative error = 9.7865757645504783924490264502129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3287
Order of pole (three term test) = -4.139
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.81
y1[1] (analytic) = 0.0732849790341451987136103932452
y1[1] (numeric) = 0.07328497903414519871361039324617
absolute error = 9.70e-31
relative error = 1.3236000238849139080344166006153e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.62423508690105818225382064978751
y2[1] (numeric) = 0.6242350869010581822538206497869
absolute error = 6.1e-31
relative error = 9.7719595197423682110733254688562e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3357
Order of pole (three term test) = -4.306
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2881226100, alloc=4848776, time=158.74
x[1] = 9.82
y1[1] (analytic) = 0.07708890090288055818897628602886
y1[1] (numeric) = 0.077088900902880558188976286029828
absolute error = 9.68e-31
relative error = 1.2556930876722734931801928844288e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.6149868792322176230657787151004
y2[1] (numeric) = 0.61498687923221762306577871509979
absolute error = 6.1e-31
relative error = 9.9189108028053621449231990252718e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3426
Order of pole (three term test) = -4.476
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2885228596, alloc=4848776, time=158.96
x[1] = 9.83
y1[1] (analytic) = 0.08098511311243561066495442249836
y1[1] (numeric) = 0.080985113112435610664954422499339
absolute error = 9.79e-31
relative error = 1.2088641509221654229227871151745e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.60577717255461064428792612486422
y2[1] (numeric) = 0.60577717255461064428792612486362
absolute error = 6.0e-31
relative error = 9.9046320525706202013980218942959e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3493
Order of pole (three term test) = -4.649
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.84
y1[1] (analytic) = 0.08497322604483623332146738178955
y1[1] (numeric) = 0.084973226044836233321467381790537
absolute error = 9.87e-31
relative error = 1.1615423421481116479523040595674e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.59660688783123027663594104791333
y2[1] (numeric) = 0.59660688783123027663594104791274
absolute error = 5.9e-31
relative error = 9.8892589414237662905085928367531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
bytes used=2889229592, alloc=4848776, time=159.19
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3559
Order of pole (three term test) = -4.826
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.85
y1[1] (analytic) = 0.08905284089211260246184500154721
y1[1] (numeric) = 0.0890528408921126024618450015482
absolute error = 9.90e-31
relative error = 1.1116995146728487582163000245817e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.5874769420829069796834060094069
y2[1] (numeric) = 0.58747694208290697968340600940632
absolute error = 5.8e-31
relative error = 9.8727279056026031198862089482080e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3623
Order of pole (three term test) = -5.006
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2893231400, alloc=4848776, time=159.41
x[1] = 9.86
y1[1] (analytic) = 0.0932235496961796581563269897987
y1[1] (numeric) = 0.093223549696179658156326989799694
absolute error = 9.94e-31
relative error = 1.0662541849559441896984389840621e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.57838824829660732299732864001849
y2[1] (numeric) = 0.57838824829660732299732864001793
absolute error = 5.6e-31
relative error = 9.6820777678183821470650600706100e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3686
Order of pole (three term test) = -5.189
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2897232212, alloc=4848776, time=159.62
x[1] = 9.87
y1[1] (analytic) = 0.09748493538963257278411823258771
y1[1] (numeric) = 0.097484935389632572784118232588712
absolute error = 1.002e-30
relative error = 1.0278511197603580878290050786657e-27 %
Correct digits = 29
h = 0.01
y2[1] (analytic) = 0.56934171533413605030112104610044
y2[1] (numeric) = 0.56934171533413605030112104609988
absolute error = 5.6e-31
relative error = 9.8359207645859293564085233580284e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3747
Order of pole (three term test) = -5.376
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.88
y1[1] (analytic) = 0.10183657183745314396113870230185
y1[1] (numeric) = 0.10183657183745314396113870230286
absolute error = 1.01e-30
relative error = 9.9178515318849851423524808887199e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.56033824784125065638254014329326
y2[1] (numeric) = 0.56033824784125065638254014329271
absolute error = 5.5e-31
relative error = 9.8154998720669236949320035228312e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3807
Order of pole (three term test) = -5.565
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2901233320, alloc=4848776, time=159.85
x[1] = 9.89
y1[1] (analytic) = 0.10627802387962294124893040329212
y1[1] (numeric) = 0.10627802387962294124893040329314
absolute error = 1.02e-30
relative error = 9.5974686277128660658927849222436e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.55137874615719756521316055942936
y2[1] (numeric) = 0.55137874615719756521316055942882
absolute error = 5.4e-31
relative error = 9.7936310342663535435174024488441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3865
Order of pole (three term test) = -5.757
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2905236900, alloc=4848776, time=160.07
x[1] = 9.9
y1[1] (analytic) = 0.11080884737463894536556130131089
y1[1] (numeric) = 0.11080884737463894536556130131192
absolute error = 1.03e-30
relative error = 9.2952866526769618997165856556079e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.54246410622467895558618189249464
y2[1] (numeric) = 0.5424641062246789555861818924941
absolute error = 5.4e-31
relative error = 9.9545756816643944595663978918776e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3922
Order of pole (three term test) = -5.953
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2909239116, alloc=4848776, time=160.28
x[1] = 9.91
y1[1] (analytic) = 0.11542858924392732837086805817458
y1[1] (numeric) = 0.11542858924392732837086805817561
absolute error = 1.03e-30
relative error = 8.9232659495072886717340869731165e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.53359521950025923751497914771223
y2[1] (numeric) = 0.53359521950025923751497914771171
absolute error = 5.2e-31
relative error = 9.7452147432469148549915419862261e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3977
Order of pole (three term test) = -6.151
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.92
y1[1] (analytic) = 0.12013678751715093348503040749387
y1[1] (numeric) = 0.1201367875171509334850304074949
absolute error = 1.03e-30
relative error = 8.5735603663695055640346940245478e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.52477297286522013867009547790727
y2[1] (numeric) = 0.52477297286522013867009547790676
absolute error = 5.1e-31
relative error = 9.7184883058180218175878728264158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4031
Order of pole (three term test) = -6.351
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2913241172, alloc=4848776, time=160.50
x[1] = 9.93
y1[1] (analytic) = 0.12493297137840592383025142136221
y1[1] (numeric) = 0.12493297137840592383025142136325
absolute error = 1.04e-30
relative error = 8.3244638186822082242809741207033e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.51599824853687331527174634753366
y2[1] (numeric) = 0.51599824853687331527174634753315
absolute error = 5.1e-31
relative error = 9.8837544787432610927491641477575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4083
Order of pole (three term test) = -6.555
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2917242376, alloc=4848776, time=160.72
x[1] = 9.94
y1[1] (analytic) = 0.12981666121330298046916657893683
y1[1] (numeric) = 0.12981666121330298046916657893787
absolute error = 1.04e-30
relative error = 8.0112983208770574582047985696184e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.50727192398033935610283995871037
y2[1] (numeric) = 0.50727192398033935610283995870988
absolute error = 4.9e-31
relative error = 9.6595135042204942831140949674716e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4133
Order of pole (three term test) = -6.761
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.95
y1[1] (analytic) = 0.13478736865692834165941199692317
y1[1] (numeric) = 0.13478736865692834165941199692421
absolute error = 1.04e-30
relative error = 7.7158565402897039914419630800701e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.4985948718208020016685953856268
y2[1] (numeric) = 0.49859487182080200166859538562632
absolute error = 4.8e-31
relative error = 9.6270544910962279103259673076896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4182
Order of pole (three term test) = -6.969
NO COMPLEX POLE (six term test) for Equation 2
bytes used=2921243260, alloc=4848776, time=160.94
TOP MAIN SOLVE Loop
x[1] = 9.96
y1[1] (analytic) = 0.13984459664267988726039376462704
y1[1] (numeric) = 0.13984459664267988726039376462809
absolute error = 1.05e-30
relative error = 7.5083344312750166920632352342250e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.48996795975624635300772121520774
y2[1] (numeric) = 0.48996795975624635300772121520727
absolute error = 4.7e-31
relative error = 9.5924639691505503260304544308339e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4229
Order of pole (three term test) = -7.18
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2925244184, alloc=4848776, time=161.16
x[1] = 9.97
y1[1] (analytic) = 0.14498783945197338472451430799106
y1[1] (numeric) = 0.14498783945197338472451430799211
absolute error = 1.05e-30
relative error = 7.2419866657010783819826703787560e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.48139205047068979626155565924353
y2[1] (numeric) = 0.48139205047068979626155565924308
absolute error = 4.5e-31
relative error = 9.3478901357013342795156942954656e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4274
Order of pole (three term test) = -7.393
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
bytes used=2929245072, alloc=4848776, time=161.38
x[1] = 9.98
y1[1] (analytic) = 0.15021658276481392608967839356558
y1[1] (numeric) = 0.15021658276481392608967839356664
absolute error = 1.06e-30
relative error = 7.0564779233434256617726395141523e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.47286800154791431983640390213977
y2[1] (numeric) = 0.47286800154791431983640390213933
absolute error = 4.4e-31
relative error = 9.3049222734394747963032607077462e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4318
Order of pole (three term test) = -7.608
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 9.99
y1[1] (analytic) = 0.15553030371122749887152224549834
y1[1] (numeric) = 0.15553030371122749887152224549941
absolute error = 1.07e-30
relative error = 6.8796882309615030228379529060099e-28 %
Correct digits = 30
h = 0.01
y2[1] (analytic) = 0.46439666538570885085546695448582
y2[1] (numeric) = 0.46439666538570885085546695448538
absolute error = 4.4e-31
relative error = 9.4746589025257969982606467433002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.436
Order of pole (three term test) = -7.826
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
diff ( y2 , x , 1 ) = y1 - 1.0;
Iterations = 990
Total Elapsed Time = 2 Minutes 41 Seconds
Elapsed Time(since restart) = 2 Minutes 38 Seconds
Time to Timeout = 18 Seconds
Percent Done = 100.1 %
> quit
bytes used=2932943456, alloc=4848776, time=161.58