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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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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
> ;
> 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
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> 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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_y[1]) < min_size then
min_size := omniabs(array_y[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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> 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 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[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, " ")
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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> 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 2;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_y_higher[1, 1]) then
tmp := omniabs(array_y_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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 2
> 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 2;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_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 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) 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
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #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_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> 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 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #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_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_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 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> 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 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_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 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_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;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_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 - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_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_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_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;
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_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 4
> 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_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> 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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_y[iii]) then
array_norms[iii] := omniabs(array_y[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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre exp 1 $eq_no = 1
> array_tmp3[1] := exp(array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre exp ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := array_tmp3[1] * array_tmp2[2] / 1;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre exp ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := array_tmp3[2] * array_tmp2[2] / 2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre exp ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := array_tmp3[3] * array_tmp2[2] / 3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre exp ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := array_tmp3[4] * array_tmp2[2] / 4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_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 exp LINEAR $eq_no = 1
> array_tmp3[kkk] := array_tmp3[kkk - 1] * array_tmp2[2] / (kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_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_y_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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := exp(array_tmp2[1]);
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp3[1]*array_tmp2[2];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 1/2*array_tmp3[2]*array_tmp2[2];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 1/3*array_tmp3[3]*array_tmp2[2];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 1/4*array_tmp3[4]*array_tmp2[2];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := array_tmp3[kkk - 1]*array_tmp2[2]/(kkk - 1);
array_tmp4[kkk] := array_tmp3[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_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_y_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_y := proc(x)
> return(10.0 * exp(0.1 * x + 0.2));
> end;
exact_soln_y := proc(x) return 10.0*exp(0.1*x + 0.2) 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_0D1,
> array_const_0D2,
> #END CONST
> array_y_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_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_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 := 1;
> 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/lin_exppostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 1.0;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 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_y := proc(x)");
> omniout_str(ALWAYS,"return(10.0 * exp(0.1 * x + 0.2));");
> omniout_str(ALWAYS,"end;");
> 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
> max_terms:=30;
> Digits:=32;
> #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_y_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..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= 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_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 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_y_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 <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) 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_y[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_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_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_y_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_y_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_y_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 <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_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 <= 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 <=2) 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 <=2) 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 <=2) 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 <=2) 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_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[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_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_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_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_0D1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D1[1] := 0.1;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D2[1] := 0.2;
> 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 := 1.0;
> x_end := 10.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 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_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := 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 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> 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_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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
> ;
> atomall();
> 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 4
> 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 5
> 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 5;
> 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 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> 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_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_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_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_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 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T02:34:50-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"lin_exp")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;")
> ;
> 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 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"lin_exp diffeq.mxt")
> ;
> logitem_str(html_log_file,"lin_exp maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #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_0D1,
array_const_0D2, array_y_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_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_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 := 1;
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/lin_exppostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 1.0;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 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_y := proc(x)");
omniout_str(ALWAYS, "return(10.0 * exp(0.1 * x + 0.2));");
omniout_str(ALWAYS, "end;");
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;
max_terms := 30;
Digits := 32;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_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 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := 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_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_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 <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_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_y_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_y_higher_work2[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_y_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 <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 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 <= 2 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 <= 2 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 <= 2 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_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[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_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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_0D1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D1[term] := 0.; term := term + 1
end do;
array_const_0D1[1] := 0.1;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
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 := 1.0;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 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_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
atomall();
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_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
atomall();
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_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_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 ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;");
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, "2013-05-26T02:34:50-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"lin_exp");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;");
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,
"lin_exp diffeq.mxt");
logitem_str(html_log_file, "lin_exp maple results");
logitem_str(html_log_file, "All Tests - All Languages");
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/lin_exppostode.ode#################
diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;
!
#BEGIN FIRST INPUT BLOCK
max_terms:=30;
Digits:=32;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 1.0;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 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_y := proc(x)
return(10.0 * exp(0.1 * x + 0.2));
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
estimated_steps = 9000000
step_error = 1.1111111111111111111111111111111e-17
est_needed_step_err = 1.1111111111111111111111111111111e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3471048613448805519312798502671e-208
estimated_step_error = 3.3471048613448805519312798502671e-208
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 = 2.2462040534969616035412032436192e-200
estimated_step_error = 2.2462040534969616035412032436192e-200
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5074020290067337029176062157728e-192
estimated_step_error = 1.5074020290067337029176062157728e-192
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0116003850727057068159858011451e-184
estimated_step_error = 1.0116003850727057068159858011451e-184
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 = 6.7887353669930423582015021996076e-177
estimated_step_error = 6.7887353669930423582015021996076e-177
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5558433197432154713507560148724e-169
estimated_step_error = 4.5558433197432154713507560148724e-169
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.0573748786773397943043782129225e-161
estimated_step_error = 3.0573748786773397943043782129225e-161
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0517697924744828390447773562202e-153
estimated_step_error = 2.0517697924744828390447773562202e-153
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 = 1.3769197260058240886618407275073e-145
estimated_step_error = 1.3769197260058240886618407275073e-145
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.2403562437593957945269852956286e-138
estimated_step_error = 9.2403562437593957945269852956286e-138
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.2011039843102379887432738311894e-130
estimated_step_error = 6.2011039843102379887432738311894e-130
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.1614983307765716425246007749769e-122
estimated_step_error = 4.1614983307765716425246007749769e-122
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.7927448469424044837649603197435e-114
estimated_step_error = 2.7927448469424044837649603197435e-114
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 = 1.8741935574030659356776654765293e-106
estimated_step_error = 1.8741935574030659356776654765293e-106
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.2577690866156942755732006444692e-98
estimated_step_error = 1.2577690866156942755732006444692e-98
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 8.4410015708865133801823139070925e-91
estimated_step_error = 8.4410015708865133801823139070925e-91
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.6650040438998599244147166829723e-83
estimated_step_error = 5.6650040438998599244147166829723e-83
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 = 3.8021813533736531197741433141026e-75
estimated_step_error = 3.8021813533736531197741433141026e-75
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 13.49858807576003103983744313328
y[1] (numeric) = 13.49858807576003103983744313328
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 13.512093415380156183862947018688
y[1] (numeric) = 13.512093415380156183862947018688
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 13.52561226709482271586678337355
y[1] (numeric) = 13.525612267094822715866783373549
absolute error = 1e-30
relative error = 7.3933806488953184752294233964677e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 13.539144644422883477086497976278
y[1] (numeric) = 13.539144644422883477086497976277
absolute error = 1e-30
relative error = 7.3859909637048254921900108568643e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 13.552690560896716923281000308256
y[1] (numeric) = 13.552690560896716923281000308255
absolute error = 1e-30
relative error = 7.3786086645059117132435825513280e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 13.566250030062240657110147010985
y[1] (numeric) = 13.566250030062240657110147010985
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 13.579823065478924974053473372451
y[1] (numeric) = 13.579823065478924974053473372451
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 13.593409680719806421881618762549
y[1] (numeric) = 13.593409680719806421881618762549
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 13.607009889371501373694005490144
y[1] (numeric) = 13.607009889371501373694005490144
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 13.620623705034219614536344120559
y[1] (numeric) = 13.62062370503421961453634412056
absolute error = 1e-30
relative error = 7.3418077002626339107499078783661e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 13.634251141321777941611551872143
y[1] (numeric) = 13.634251141321777941611551872144
absolute error = 1e-30
relative error = 7.3344695622428926389283166331545e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=4001064, alloc=3079628, time=0.35
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 13.647892211861613778097684303954
y[1] (numeric) = 13.647892211861613778097684303955
absolute error = 1e-30
relative error = 7.3271387586933248158165914175717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 13.661546930294798800586494113641
y[1] (numeric) = 13.661546930294798800586494113642
absolute error = 1e-30
relative error = 7.3198152822831262809465929592301e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 13.675215310276052580156244485206
y[1] (numeric) = 13.675215310276052580156244485207
absolute error = 1e-30
relative error = 7.3124991256888200138300651952634e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 13.688897365473756237092418060604
y[1] (numeric) = 13.688897365473756237092418060605
absolute error = 1e-30
relative error = 7.3051902815942488104810044942971e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 13.702593109569966109269976257023
y[1] (numeric) = 13.702593109569966109269976257024
absolute error = 1e-30
relative error = 7.2978887426905679672578459906585e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 13.716302556260427434210837313244
y[1] (numeric) = 13.716302556260427434210837313246
absolute error = 2e-30
relative error = 1.4581189003352475944036301744799e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 13.730025719254588044830255123704
y[1] (numeric) = 13.730025719254588044830255123706
absolute error = 2e-30
relative error = 1.4566615102514034405156971554421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 13.743762612275612078885794607768
y[1] (numeric) = 13.74376261227561207888579460777
absolute error = 2e-30
relative error = 1.4552055768291909264944385511001e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 13.757513249060393702142613064349
y[1] (numeric) = 13.757513249060393702142613064351
absolute error = 2e-30
relative error = 1.4537510986126765087995511115594e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 13.771277643359570845268770678281
y[1] (numeric) = 13.771277643359570845268770678283
absolute error = 2e-30
relative error = 1.4522980741473818497100950588472e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 13.785055808937538954474307074914
y[1] (numeric) = 13.785055808937538954474307074916
absolute error = 2e-30
relative error = 1.4508465019802823628460351594399e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 13.798847759572464755907834563142
y[1] (numeric) = 13.798847759572464755907834563144
absolute error = 2e-30
relative error = 1.4493963806598057601435332588421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 13.812653509056300033824412464617
y[1] (numeric) = 13.812653509056300033824412464619
absolute error = 2e-30
relative error = 1.4479477087358306002825392533870e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 13.826473071194795422538480698163
y[1] (numeric) = 13.826473071194795422538480698164
absolute error = 1e-30
relative error = 7.2325024237984241928261446336412e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 13.840306459807514212175644573469
y[1] (numeric) = 13.84030645980751421217564457347
absolute error = 1e-30
relative error = 7.2252735364207218912191926467110e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 13.854153688727846168237116547012
y[1] (numeric) = 13.854153688727846168237116547013
absolute error = 1e-30
relative error = 7.2180518743171581164822371437574e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 13.868014771803021364990634505786
y[1] (numeric) = 13.868014771803021364990634505787
absolute error = 1e-30
relative error = 7.2108374302660701632463080306706e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 13.881889722894124032701689970918
y[1] (numeric) = 13.881889722894124032701689970919
absolute error = 1e-30
relative error = 7.2036301970530133792197611074026e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 13.89577855587610641871891345355
y[1] (numeric) = 13.895778555876106418718913453551
absolute error = 1e-30
relative error = 7.1964301674707539507430245725823e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 13.909681284637802662427478049531
y[1] (numeric) = 13.909681284637802662427478049532
absolute error = 1e-30
relative error = 7.1892373343192616955541847611043e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 13.92359792308194268408439622747
y[1] (numeric) = 13.923597923081942684084396227471
absolute error = 1e-30
relative error = 7.1820516904057028627582038796822e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 13.937528485125166087549598646617
y[1] (numeric) = 13.937528485125166087549598646618
absolute error = 1e-30
relative error = 7.1748732285444329399925697089767e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 13.951472984698036076926697736798
y[1] (numeric) = 13.951472984698036076926697736799
absolute error = 1e-30
relative error = 7.1677019415569894677821844373542e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 13.965431435745053387127352682333
y[1] (numeric) = 13.965431435745053387127352682333
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 13.979403852224670228373166375461
y[1] (numeric) = 13.979403852224670228373166375461
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 13.993390248109304244649058842335
y[1] (numeric) = 13.993390248109304244649058842335
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 14.007390637385352486122075596116
y[1] (numeric) = 14.007390637385352486122075596116
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 14.021405034053205395539603337146
y[1] (numeric) = 14.021405034053205395539603337145
absolute error = 1e-30
relative error = 7.1319528789828226016357089532599e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 14.035433452127260808620979399574
y[1] (numeric) = 14.035433452127260808620979399573
absolute error = 1e-30
relative error = 7.1248244908919175625618246631899e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 14.049475905635937968456495337223
y[1] (numeric) = 14.049475905635937968456495337222
absolute error = 1e-30
relative error = 7.1177032276260971507995351075697e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 14.063532408621691553927809048855
y[1] (numeric) = 14.063532408621691553927809048854
absolute error = 1e-30
relative error = 7.1105890820640975070898032577880e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=8003716, alloc=4193536, time=0.73
x[1] = 1.42
y[1] (analytic) = 14.077602975141025722163793864425
y[1] (numeric) = 14.077602975141025722163793864424
absolute error = 1e-30
relative error = 7.1034820470917724765875021426269e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 14.091687619264508165045867049339
y[1] (numeric) = 14.091687619264508165045867049338
absolute error = 1e-30
relative error = 7.0963821156020864947146671576021e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 14.10578635507678417977685423322
y[1] (numeric) = 14.105786355076784179776854233219
absolute error = 1e-30
relative error = 7.0892892804951074801243392340142e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 14.119899196676590753527460333212
y[1] (numeric) = 14.119899196676590753527460333211
absolute error = 1e-30
relative error = 7.0822035346779997347678918309640e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 14.134026158176770662174431619473
y[1] (numeric) = 14.134026158176770662174431619473
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 14.148167253704286583144507662196
y[1] (numeric) = 14.148167253704286583144507662195
absolute error = 1e-30
relative error = 7.0680532825774946261253514049706e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 14.16232249740023522237827600527
y[1] (numeric) = 14.162322497400235222378276005269
absolute error = 1e-30
relative error = 7.0609887621438439831464353911381e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 14.176491903419861455428056531639
y[1] (numeric) = 14.176491903419861455428056531638
absolute error = 1e-30
relative error = 7.0539313026995438997612950354292e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 14.190675485932572482703956619399
y[1] (numeric) = 14.190675485932572482703956619398
absolute error = 1e-30
relative error = 7.0468808971871343435482069903086e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 14.204873259121951998882252335876
y[1] (numeric) = 14.204873259121951998882252335875
absolute error = 1e-30
relative error = 7.0398375385562092145638027574322e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 14.219085237185774376490265079252
y[1] (numeric) = 14.219085237185774376490265079251
absolute error = 1e-30
relative error = 7.0328012197634092949363812104160e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 14.233311434336018863681917253788
y[1] (numeric) = 14.233311434336018863681917253788
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 14.247551864798883796218164755393
y[1] (numeric) = 14.247551864798883796218164755393
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 14.261806542814800823666518249144
y[1] (numeric) = 14.261806542814800823666518249144
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 14.276075482638449149833879439474
y[1] (numeric) = 14.276075482638449149833879439474
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 14.290358698538769787446932767051
y[1] (numeric) = 14.290358698538769787446932767051
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 14.304656204798979827094347213914
y[1] (numeric) = 14.304656204798979827094347213914
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 14.318968015716586720445057160277
y[1] (numeric) = 14.318968015716586720445057160277
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 14.333294145603402577756905512456
y[1] (numeric) = 14.333294145603402577756905512456
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 14.34763460878555847968994661176
y[1] (numeric) = 14.34763460878555847968994661176
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 14.361989419603518803438720738841
y[1] (numeric) = 14.361989419603518803438720738842
absolute error = 1e-30
relative error = 6.9628236784177096729447570814679e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 14.376358592412095563197826346978
y[1] (numeric) = 14.376358592412095563197826346978
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 14.390742141580462764975130491041
y[1] (numeric) = 14.390742141580462764975130491041
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 14.405140081492170775766972266571
y[1] (numeric) = 14.405140081492170775766972266572
absolute error = 1e-30
relative error = 6.9419665087797883079833072465646e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 14.419552426545160707109728435358
y[1] (numeric) = 14.419552426545160707109728435358
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 14.433979191151778813022124790276
y[1] (numeric) = 14.433979191151778813022124790276
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 14.448420389738790902352691202912
y[1] (numeric) = 14.448420389738790902352691202912
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 14.462876036747396765546772702613
y[1] (numeric) = 14.462876036747396765546772702613
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 14.477346146633244615847523355192
y[1] (numeric) = 14.477346146633244615847523355192
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 14.491830733866445544945324143472
y[1] (numeric) = 14.491830733866445544945324143472
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 14.506329812931587993090080500295
y[1] (numeric) = 14.506329812931587993090080500295
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 14.520843398327752233680869607509
y[1] (numeric) = 14.520843398327752233680869607509
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 14.535371504568524872347422051772
y[1] (numeric) = 14.535371504568524872347422051772
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 = 190
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
bytes used=12005164, alloc=4259060, time=1.12
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 14.549914146182013360537936919875
y[1] (numeric) = 14.549914146182013360537936919875
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 14.564471337710860523627743922601
y[1] (numeric) = 14.5644713377108605236277439226
absolute error = 1e-30
relative error = 6.8660233304230104002775444232737e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 14.579043093712259103563340656996
y[1] (numeric) = 14.579043093712259103563340656996
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 14.593629428757966316056347652308
y[1] (numeric) = 14.593629428757966316056347652308
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 14.608230357434318422341938394742
y[1] (numeric) = 14.608230357434318422341938394742
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 14.6228458943422453155163160907
y[1] (numeric) = 14.6228458943422453155163160907
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 14.637476054097285121467823507183
y[1] (numeric) = 14.637476054097285121467823507183
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 14.652120851329598814416286821681
y[1] (numeric) = 14.652120851329598814416286821681
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 14.666780300683984847075209022125
y[1] (numeric) = 14.666780300683984847075209022125
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 14.681454416819893795451443020301
y[1] (numeric) = 14.681454416819893795451443020301
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 14.696143214411443018296989279622
y[1] (numeric) = 14.696143214411443018296989279622
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 14.710846708147431331227577410286
y[1] (numeric) = 14.710846708147431331227577410286
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 14.725564912731353695522705851613
y[1] (numeric) = 14.725564912731353695522705851613
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 14.740297842881415921621828442831
y[1] (numeric) = 14.740297842881415921621828442831
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 14.755045513330549387331391379721
y[1] (numeric) = 14.755045513330549387331391379721
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 14.769807938826425770757438765387
y[1] (numeric) = 14.769807938826425770757438765387
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 14.78458513413147179797851968898
y[1] (numeric) = 14.78458513413147179797851968898
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 14.799377114022884005473644506515
y[1] (numeric) = 14.799377114022884005473644506515
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 14.814183893292643517320052752968
y[1] (numeric) = 14.814183893292643517320052752968
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 14.829005486747530837175569884649
y[1] (numeric) = 14.82900548674753083717556988465
absolute error = 1e-30
relative error = 6.7435405624044419803823379686906e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 14.843841909209140655060344835447
y[1] (numeric) = 14.843841909209140655060344835448
absolute error = 1e-30
relative error = 6.7368003924886762382254990142613e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 14.858693175513896668952775169906
y[1] (numeric) = 14.858693175513896668952775169907
absolute error = 1e-30
relative error = 6.7300669593738643847963190097754e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 14.87355930051306642121444143031
y[1] (numeric) = 14.87355930051306642121444143031
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 14.888440299072776149858887103929
y[1] (numeric) = 14.888440299072776149858887103929
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 14.903336186074025654679095480461
y[1] (numeric) = 14.903336186074025654679095480462
absolute error = 1e-30
relative error = 6.7099070135344590112628394876196e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 14.918246976412703178248529528372
y[1] (numeric) = 14.918246976412703178248529528373
absolute error = 1e-30
relative error = 6.7032004603563930074443292514784e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 14.933172684999600301810615792419
y[1] (numeric) = 14.933172684999600301810615792419
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 14.948113326760426856071568203083
y[1] (numeric) = 14.948113326760426856071568203083
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 14.96306891663582584691146259198
y[1] (numeric) = 14.96306891663582584691146259198
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 14.97803946958138839602848762556
y[1] (numeric) = 14.97803946958138839602848762556
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 14.993025000567668696531312802597
y[1] (numeric) = 14.993025000567668696531312802597
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 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 15.008025524580198983494529109084
y[1] (numeric) = 15.008025524580198983494529109083
absolute error = 1e-30
relative error = 6.6631016742488633831084171096931e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 15.023041056619504519492132887216
y[1] (numeric) = 15.023041056619504519492132887215
absolute error = 1e-30
relative error = 6.6564419030152122721686890861766e-30 %
Correct digits = 32
h = 0.01
bytes used=16006128, alloc=4259060, time=1.50
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 15.038071611701118595124038453205
y[1] (numeric) = 15.038071611701118595124038453204
absolute error = 1e-30
relative error = 6.6497887882240188799516412824325e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 15.053117204855597544550619991671
y[1] (numeric) = 15.05311720485559754455061999167
absolute error = 1e-30
relative error = 6.6431423232221678608376304010892e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 15.068177851128535776050298262424
y[1] (numeric) = 15.068177851128535776050298262423
absolute error = 1e-30
relative error = 6.6365025013631936591035353781475e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 15.083253565580580817615202678457
y[1] (numeric) = 15.083253565580580817615202678456
absolute error = 1e-30
relative error = 6.6298693160072738624566477877125e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 15.098344363287448377599954352081
y[1] (numeric) = 15.098344363287448377599954352079
absolute error = 2e-30
relative error = 1.3246485521042445124423412461462e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 15.113450259339937420438630759226
y[1] (numeric) = 15.113450259339937420438630759224
absolute error = 2e-30
relative error = 1.3233245656556967440208869768444e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 15.128571268843945257444987740145
y[1] (numeric) = 15.128571268843945257444987740144
absolute error = 1e-30
relative error = 6.6100095126591245417349530239762e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 15.143707406920482652711029637988
y[1] (numeric) = 15.143707406920482652711029637987
absolute error = 1e-30
relative error = 6.6034028070498288566344289635910e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 15.158858688705688944119033475074
y[1] (numeric) = 15.158858688705688944119033475073
absolute error = 1e-30
relative error = 6.5968027048438905049483584759423e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 15.17402512935084717948214818016
y[1] (numeric) = 15.174025129350847179482148180158
absolute error = 2e-30
relative error = 1.3180418398882413461459708759625e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 15.189206744022399267828705008548
y[1] (numeric) = 15.189206744022399267828705008546
absolute error = 2e-30
relative error = 1.3167244568496543163672681168847e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 15.204403547901961145845390440623
y[1] (numeric) = 15.204403547901961145845390440621
absolute error = 2e-30
relative error = 1.3154083905356338632846100976023e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 15.219615556186337959494448003237
y[1] (numeric) = 15.219615556186337959494448003236
absolute error = 1e-30
relative error = 6.5704681981505678160267362233997e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 15.23484278408753926082009063243
y[1] (numeric) = 15.234842784087539260820090632428
absolute error = 2e-30
relative error = 1.3127802028183424010466003667436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 15.25008524683279421995932038514
y[1] (numeric) = 15.250085246832794219959320385139
absolute error = 1e-30
relative error = 6.5573403939344172779206800450701e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 15.265342959664566852372367512021
y[1] (numeric) = 15.265342959664566852372367512019
absolute error = 2e-30
relative error = 1.3101572662236125860153357759923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 15.28061593784057126130797612304
y[1] (numeric) = 15.280615937840571261307976123039
absolute error = 1e-30
relative error = 6.5442388190885855991747309257986e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 15.295904196633786895518778912449
y[1] (numeric) = 15.295904196633786895518778912447
absolute error = 2e-30
relative error = 1.3075395702596945420222969273310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 15.311207751332473822242018659738
y[1] (numeric) = 15.311207751332473822242018659736
absolute error = 2e-30
relative error = 1.3062326842413511855386767207711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 15.3265266172401880154608894886
y[1] (numeric) = 15.326526617240188015460889488598
absolute error = 2e-30
relative error = 1.3049271044558009231335572563410e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 15.341860809675796659461786146494
y[1] (numeric) = 15.341860809675796659461786146492
absolute error = 2e-30
relative error = 1.3036228295974638604583570397890e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 15.35721034397349346770276486335
y[1] (numeric) = 15.357210343973493467702764863348
absolute error = 2e-30
relative error = 1.3023198583620650304864382448403e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 15.372575235482814017008534659144
y[1] (numeric) = 15.372575235482814017008534659142
absolute error = 2e-30
relative error = 1.3010181894466330892380309969758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 15.387955499568651097107313296613
y[1] (numeric) = 15.387955499568651097107313296611
absolute error = 2e-30
relative error = 1.2997178215494990128087808127127e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 15.403351151611270075524897417249
y[1] (numeric) = 15.403351151611270075524897417247
absolute error = 2e-30
relative error = 1.2984187533702947957006162228281e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 15.418762207006324277851311755918
y[1] (numeric) = 15.418762207006324277851311755916
absolute error = 2e-30
relative error = 1.2971209836099521504536349102831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 15.43418868116487038339541770204
y[1] (numeric) = 15.434188681164870383395417702038
absolute error = 2e-30
relative error = 1.2958245109707012085777079946265e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 15.449630589513383836242876863213
y[1] (numeric) = 15.449630589513383836242876863211
absolute error = 2e-30
relative error = 1.2945293341560692227825033943735e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 15.465087947493774271732880690543
y[1] (numeric) = 15.46508794749377427173288069054
absolute error = 3e-30
relative error = 1.9398531778063189057569457459105e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 15.480560770563400958369072643675
y[1] (numeric) = 15.480560770563400958369072643672
absolute error = 3e-30
relative error = 1.9379142942318734380959144982611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 15.496049074195088255180104807756
y[1] (numeric) = 15.496049074195088255180104807754
absolute error = 2e-30
relative error = 1.2906515657145891301143713986693e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=20007828, alloc=4259060, time=1.90
x[1] = 2.39
y[1] (analytic) = 15.511552873877141084545286324161
y[1] (numeric) = 15.511552873877141084545286324159
absolute error = 2e-30
relative error = 1.2893615592596025703879912719321e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.774e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 15.527072185113360420500796461917
y[1] (numeric) = 15.527072185113360420500796461915
absolute error = 2e-30
relative error = 1.2880728421662827170643680600179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 15.542607023423058792541950637344
y[1] (numeric) = 15.542607023423058792541950637342
absolute error = 2e-30
relative error = 1.2867854131459123694305537495459e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 15.558157404341075804937023185458
y[1] (numeric) = 15.558157404341075804937023185455
absolute error = 3e-30
relative error = 1.9282489063665935997456681494714e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 15.573723343417793671568146198251
y[1] (numeric) = 15.573723343417793671568146198248
absolute error = 3e-30
relative error = 1.9263216212633856993533255501500e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 15.589304856219152766314819272056
y[1] (numeric) = 15.589304856219152766314819272053
absolute error = 3e-30
relative error = 1.9243962624819595891538051464503e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.477e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 15.604901958326667188995580548785
y[1] (numeric) = 15.604901958326667188995580548782
absolute error = 3e-30
relative error = 1.9224728280969563272744262717905e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.477e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 15.620514665337440346883404994018
y[1] (numeric) = 15.620514665337440346883404994015
absolute error = 3e-30
relative error = 1.9205513161849413684257229536466e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 15.636142992864180551810411428642
y[1] (numeric) = 15.636142992864180551810411428639
absolute error = 3e-30
relative error = 1.9186317248244026404667383378687e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 15.651786956535216632877475420034
y[1] (numeric) = 15.651786956535216632877475420031
absolute error = 3e-30
relative error = 1.9167140520957486228927924217134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 15.667446571994513564784360743721
y[1] (numeric) = 15.667446571994513564784360743718
absolute error = 3e-30
relative error = 1.9147982960813064272438015831977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 15.683121854901688111795997746932
y[1] (numeric) = 15.683121854901688111795997746929
absolute error = 3e-30
relative error = 1.9128844548653198794312303149367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 15.698812820932024487360552581636
y[1] (numeric) = 15.698812820932024487360552581633
absolute error = 3e-30
relative error = 1.9109725265339476039817574892543e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 15.714519485776490029394946926437
y[1] (numeric) = 15.714519485776490029394946926434
absolute error = 3e-30
relative error = 1.9090625091752611101957413980760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 15.730241865141750891253503484149
y[1] (numeric) = 15.730241865141750891253503484146
absolute error = 3e-30
relative error = 1.9071544008792428802185697259074e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 15.745979974750187748395408225012
y[1] (numeric) = 15.745979974750187748395408225008
absolute error = 4e-30
relative error = 2.5403309329837126120306433694533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 15.761733830339911520766696044306
y[1] (numeric) = 15.761733830339911520766696044302
absolute error = 4e-30
relative error = 2.5377918717929127284006109193310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 15.777503447664779110912482217678
y[1] (numeric) = 15.777503447664779110912482217674
absolute error = 4e-30
relative error = 2.5352553483941961203463390345389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 15.793288842494409157835177767706
y[1] (numeric) = 15.793288842494409157835177767702
absolute error = 4e-30
relative error = 2.5327213602510391777742627218561e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 15.809090030614197806614442601243
y[1] (numeric) = 15.809090030614197806614442601239
absolute error = 4e-30
relative error = 2.5301899048294535463617537739383e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 15.824907027825334493804646038798
y[1] (numeric) = 15.824907027825334493804646038794
absolute error = 4e-30
relative error = 2.5276609795979835935685552809865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 15.840739849944817748625620134736
y[1] (numeric) = 15.840739849944817748625620134732
absolute error = 4e-30
relative error = 2.5251345820277038771809381358471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 15.856588512805471009962506980365
y[1] (numeric) = 15.85658851280547100996250698036
absolute error = 5e-30
relative error = 3.1532633869902707704825600956106e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 15.872453032255958459190516991073
y[1] (numeric) = 15.872453032255958459190516991068
absolute error = 5e-30
relative error = 3.1501116997095614567173929249905e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 15.888333424160800868840431003602
y[1] (numeric) = 15.888333424160800868840431003597
absolute error = 5e-30
relative error = 3.1469631625408143618307419123179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 15.904229704400391467120694850268
y[1] (numeric) = 15.904229704400391467120694850263
absolute error = 5e-30
relative error = 3.1438177723354920546974060294138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 15.920141888871011818311970933552
y[1] (numeric) = 15.920141888871011818311970933547
absolute error = 5e-30
relative error = 3.1406755259482040678792189622216e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 15.936069993484847719050027196939
y[1] (numeric) = 15.936069993484847719050027196934
absolute error = 5e-30
relative error = 3.1375364202367037522343195567597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 15.952014034170005110512859776214
y[1] (numeric) = 15.952014034170005110512859776209
absolute error = 5e-30
relative error = 3.1344004520618851346702408233641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 15.96797402687052600652796151966
y[1] (numeric) = 15.967974026870526006527961519656
absolute error = 4e-30
relative error = 2.5050140946302238232301402016388e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.774e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 15.983949987546404437615664485769
y[1] (numeric) = 15.983949987546404437615664485765
absolute error = 4e-30
relative error = 2.5025103326252429201294218659877e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=24008796, alloc=4259060, time=2.29
x[1] = 2.7
y[1] (analytic) = 15.999941932173602410984500463115
y[1] (numeric) = 15.999941932173602410984500463111
absolute error = 4e-30
relative error = 2.5000090731308031848062938477165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.477e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 16.0159498767440658864945395091
y[1] (numeric) = 16.015949876744065886494539509097
absolute error = 3e-30
relative error = 1.8731327352342336857870420043323e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 16.031973837265740768604682472234
y[1] (numeric) = 16.031973837265740768604682472231
absolute error = 3e-30
relative error = 1.8712605387532563116028554093059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 16.04801382976258891431989944657
y[1] (numeric) = 16.048013829762588914319899446566
absolute error = 4e-30
relative error = 2.4925202847106315054112104015929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 16.06406987027460415715442210687
y[1] (numeric) = 16.064069870274604157154422106867
absolute error = 3e-30
relative error = 1.8675217577030602620105764166463e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 16.080141974857828347126913889043
y[1] (numeric) = 16.080141974857828347126913889039
absolute error = 4e-30
relative error = 2.4875402258600802997884486998579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.774e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 16.09623015958436740680365801233
y[1] (numeric) = 16.096230159584367406803658012326
absolute error = 4e-30
relative error = 2.4850539289898467386688268067453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 16.112334440542407403405819387801
y[1] (numeric) = 16.112334440542407403405819387797
absolute error = 4e-30
relative error = 2.4825701171737492552302623307249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 16.128454833836230636996852521731
y[1] (numeric) = 16.128454833836230636996852521727
absolute error = 4e-30
relative error = 2.4800887879279758263909469256311e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 16.144591355586231744766143602628
y[1] (numeric) = 16.144591355586231744766143602624
absolute error = 4e-30
relative error = 2.4776099387711969996000077117814e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 16.16074402192893382142499105688
y[1] (numeric) = 16.160744021928933821424991056876
absolute error = 4e-30
relative error = 2.4751335672245634115078479476423e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 16.176912849017004555731044970359
y[1] (numeric) = 16.176912849017004555731044970356
absolute error = 3e-30
relative error = 1.8544947531087774818374328320837e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 16.193097853019272383157341901757
y[1] (numeric) = 16.193097853019272383157341901754
absolute error = 3e-30
relative error = 1.8526411852940400550560386467316e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.774e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 16.209299050120742654722087758036
y[1] (numeric) = 16.209299050120742654722087758032
absolute error = 4e-30
relative error = 2.4677192934941897454470492173722e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 16.225516456522613821995357563122
y[1] (numeric) = 16.225516456522613821995357563118
absolute error = 4e-30
relative error = 2.4652528076491585549571049779013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 16.241750088442293638298897127901
y[1] (numeric) = 16.241750088442293638298897127897
absolute error = 4e-30
relative error = 2.4627887870571404513665343833365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 16.257999962113415376115227822654
y[1] (numeric) = 16.25799996211341537611522782265
absolute error = 4e-30
relative error = 2.4603272292541146373221776637631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 16.274266093785854060722271862396
y[1] (numeric) = 16.274266093785854060722271862391
absolute error = 5e-30
relative error = 3.0723351647231538808354962729324e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.774e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 16.290548499725742720069731741093
y[1] (numeric) = 16.290548499725742720069731741088
absolute error = 5e-30
relative error = 3.0692643652140852161110791623129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 16.3068471962154886509134736925
y[1] (numeric) = 16.306847196215488650913473692495
absolute error = 5e-30
relative error = 3.0661966349696375375108384043740e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 16.323162199553789701224181313345
y[1] (numeric) = 16.32316219955378970122418131334
absolute error = 5e-30
relative error = 3.0631319709220803449428998400952e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 16.339493526055650568886561758877
y[1] (numeric) = 16.339493526055650568886561758872
absolute error = 5e-30
relative error = 3.0600703700067493354613917588162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 16.355841192052399116705403211345
y[1] (numeric) = 16.35584119205239911670540321134
absolute error = 5e-30
relative error = 3.0570118291620433386018865636644e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 16.372205213891702703734798628821
y[1] (numeric) = 16.372205213891702703734798628816
absolute error = 5e-30
relative error = 3.0539563453294212547799751736877e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 16.38858560793758453294686710495
y[1] (numeric) = 16.388585607937584532946867104944
absolute error = 6e-30
relative error = 3.6610846985440787960998950732149e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 16.404982390570440015256320509714
y[1] (numeric) = 16.404982390570440015256320509708
absolute error = 6e-30
relative error = 3.6574254437778557209443310576993e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 16.421395578187053149917239437142
y[1] (numeric) = 16.421395578187053149917239437137
absolute error = 5e-30
relative error = 3.0448082053644843409235797137178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 16.437825187200612921308438858105
y[1] (numeric) = 16.437825187200612921308438858099
absolute error = 6e-30
relative error = 3.6501179028670576154841551728186e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.477e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 16.454271234040729712123820264918
y[1] (numeric) = 16.454271234040729712123820264912
absolute error = 6e-30
relative error = 3.6464696094149410654196749780438e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 16.470733735153451732984123499494
y[1] (numeric) = 16.470733735153451732984123499488
absolute error = 6e-30
relative error = 3.6428249624327378027738405304619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 16.487212707001281468486507878142
y[1] (numeric) = 16.487212707001281468486507878135
absolute error = 7e-30
relative error = 4.2457146179884339652265967449382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.01
bytes used=28010220, alloc=4259060, time=2.70
y[1] (analytic) = 16.503708166063192139708408663979
y[1] (numeric) = 16.503708166063192139708408663972
absolute error = 7e-30
relative error = 4.2414710255203122918809707856921e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 16.520220128834644183182131392183
y[1] (numeric) = 16.520220128834644183182131392176
absolute error = 7e-30
relative error = 4.2372316745235695947782119309445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 16.536748611827601746356663024044
y[1] (numeric) = 16.536748611827601746356663024037
absolute error = 7e-30
relative error = 4.2329965607588545238963615734036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.774e+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 16.553293631570549199563195393012
y[1] (numeric) = 16.553293631570549199563195393005
absolute error = 7e-30
relative error = 4.2287656799910529615941900074241e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 16.569855204608507664500872909628
y[1] (numeric) = 16.569855204608507664500872909621
absolute error = 7e-30
relative error = 4.2245390279892837874967258615914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 16.586433347503051559259293012479
y[1] (numeric) = 16.586433347503051559259293012472
absolute error = 7e-30
relative error = 4.2203166005268946476137831503097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 16.603028076832325159894304389042
y[1] (numeric) = 16.603028076832325159894304389034
absolute error = 8e-30
relative error = 4.8183981638645231173568629286579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 16.619639409191059178573664543598
y[1] (numeric) = 16.61963940919105917857366454359
absolute error = 8e-30
relative error = 4.8135821740968748923005118112869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 16.636267361190587358309134859266
y[1] (numeric) = 16.636267361190587358309134859259
absolute error = 7e-30
relative error = 4.2076746231728266589827322796896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 16.652911949458863084291607887622
y[1] (numeric) = 16.652911949458863084291607887615
absolute error = 7e-30
relative error = 4.2034690516858615995927947613967e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 16.669573190640476011845878202418
y[1] (numeric) = 16.669573190640476011845878202411
absolute error = 7e-30
relative error = 4.1992676836682985151637736274949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 16.686251101396668711021684773561
y[1] (numeric) = 16.686251101396668711021684773553
absolute error = 8e-30
relative error = 4.7943663027643074720212243598923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 16.702945698405353327837669453779
y[1] (numeric) = 16.702945698405353327837669453771
absolute error = 8e-30
relative error = 4.7895743328458332215584417815261e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 16.719656998361128262194912823323
y[1] (numeric) = 16.719656998361128262194912823315
absolute error = 8e-30
relative error = 4.7847871525020909481365889544213e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 16.736385017975294862476725307627
y[1] (numeric) = 16.736385017975294862476725307619
absolute error = 8e-30
relative error = 4.7800047569458999090816838471453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 16.753129773975874136851388169108
y[1] (numeric) = 16.7531297739758741368513881691
absolute error = 8e-30
relative error = 4.7752271413948641496697111044408e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 16.769891283107623481294555677248
y[1] (numeric) = 16.76989128310762348129455567724
absolute error = 8e-30
relative error = 4.7704543010713677207302687902006e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 16.78666956213205342434804648074
y[1] (numeric) = 16.786669562132053424348046480732
absolute error = 8e-30
relative error = 4.7656862312025699010302210823901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 16.803464627827444388631768941903
y[1] (numeric) = 16.803464627827444388631768941895
absolute error = 8e-30
relative error = 4.7609229270204004244325793031709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 16.820276496988863469125541946667
y[1] (numeric) = 16.820276496988863469125541946659
absolute error = 8e-30
relative error = 4.7561643837615547118258384427110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 16.837105186428181228237589473365
y[1] (numeric) = 16.837105186428181228237589473358
absolute error = 7e-30
relative error = 4.1574842720840529693416259674154e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 16.85395071297408850767650399022
y[1] (numeric) = 16.853950712974088507676503990213
absolute error = 7e-30
relative error = 4.1533288658613641069228348777939e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 16.870813093472113257143490554882
y[1] (numeric) = 16.870813093472113257143490554875
absolute error = 7e-30
relative error = 4.1491776129678872166185095161830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 16.88769234478463737986172030968
y[1] (numeric) = 16.887692344784637379861720309673
absolute error = 7e-30
relative error = 4.1450305092523690590140069239248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 16.904588483790913594959638903331
y[1] (numeric) = 16.904588483790913594959638903324
absolute error = 7e-30
relative error = 4.1408875505677055729991816836043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 16.921501527387082316725092223825
y[1] (numeric) = 16.921501527387082316725092223818
absolute error = 7e-30
relative error = 4.1367487327709377286639792168868e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 16.93843149248618855074714869802
y[1] (numeric) = 16.938431492486188550747148698013
absolute error = 7e-30
relative error = 4.1326140517232473843390606278666e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 16.955378396018198806962514301173
y[1] (numeric) = 16.955378396018198806962514301166
absolute error = 7e-30
relative error = 4.1284835032899531477773161322044e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 16.972342254930018029623453324238
y[1] (numeric) = 16.972342254930018029623453324231
absolute error = 7e-30
relative error = 4.1243570833405062414721282532234e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 16.989323086185506544204144868253
y[1] (numeric) = 16.989323086185506544204144868246
absolute error = 7e-30
relative error = 4.1202347877484863721082501028825e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 17.006320906765497021262421973596
y[1] (numeric) = 17.006320906765497021262421973589
absolute error = 7e-30
relative error = 4.1161166123915976041411681981596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 17.023335733667811457273857247253
y[1] (numeric) = 17.023335733667811457273857247246
absolute error = 7e-30
relative error = 4.1120025531516642375008233918661e-29 %
Correct digits = 31
h = 0.01
bytes used=32011416, alloc=4259060, time=3.09
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 17.040367583907278172455175823604
y[1] (numeric) = 17.040367583907278172455175823597
absolute error = 7e-30
relative error = 4.1078926059146266894155676212675e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 17.057416474515748825593993483557
y[1] (numeric) = 17.05741647451574882559399348355
absolute error = 7e-30
relative error = 4.1037867665705373803522382981252e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 17.074482422542115445901894763181
y[1] (numeric) = 17.074482422542115445901894763174
absolute error = 7e-30
relative error = 4.0996850310135566240682362798914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 17.091565445052327481907882906341
y[1] (numeric) = 17.091565445052327481907882906334
absolute error = 7e-30
relative error = 4.0955873951419485217714974737909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 17.108665559129408867409250556203
y[1] (numeric) = 17.108665559129408867409250556195
absolute error = 8e-30
relative error = 4.6759929769806592690105739810525e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 17.1257827818734751044969371379
y[1] (numeric) = 17.125782781873475104496937137892
absolute error = 8e-30
relative error = 4.6713193212210297313216809271839e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 17.142917130401750363672455959148
y[1] (numeric) = 17.14291713040175036367245595914
absolute error = 8e-30
relative error = 4.6666503367811106912855968347089e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 17.16006862184858460107349114715
y[1] (numeric) = 17.160068621848584601073491147142
absolute error = 8e-30
relative error = 4.6619860189919173199012320382220e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 17.177237273365470692825281648827
y[1] (numeric) = 17.17723727336547069282528164882
absolute error = 7e-30
relative error = 4.0751605677904900093717964602884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 17.194423102121061586534926647178
y[1] (numeric) = 17.194423102121061586534926647171
absolute error = 7e-30
relative error = 4.0710874441239597510453266904310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 17.211626125301187469945763889502
y[1] (numeric) = 17.211626125301187469945763889495
absolute error = 7e-30
relative error = 4.0670183915452128739769268723153e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 17.228846360108872956768989583302
y[1] (numeric) = 17.228846360108872956768989583296
absolute error = 6e-30
relative error = 3.4825314908444541088559946334667e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 17.246083823764354289709705692916
y[1] (numeric) = 17.24608382376435428970970569291
absolute error = 6e-30
relative error = 3.4790507000390782382959763023060e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 17.263338533505096560704597664348
y[1] (numeric) = 17.263338533505096560704597664342
absolute error = 6e-30
relative error = 3.4755733882846923277155302202030e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 17.28061050658581094838846281743
y[1] (numeric) = 17.280610506585810948388462817423
absolute error = 7e-30
relative error = 4.0507828107879817217782160512450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 17.297899760278471972806826873261
y[1] (numeric) = 17.297899760278471972806826873255
absolute error = 6e-30
relative error = 3.4686291880231177838133026831044e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 17.315206311872334767391903330999
y[1] (numeric) = 17.315206311872334767391903330992
absolute error = 7e-30
relative error = 4.0426893413336830286058700560941e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 17.332530178673952368219167671373
y[1] (numeric) = 17.332530178673952368219167671366
absolute error = 7e-30
relative error = 4.0386486726634068672355897541711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 17.349871378007193020561835644969
y[1] (numeric) = 17.349871378007193020561835644962
absolute error = 7e-30
relative error = 4.0346120426421399233394504404787e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 17.367229927213257502760552201173
y[1] (numeric) = 17.367229927213257502760552201167
absolute error = 6e-30
relative error = 3.4547823833427872907982816289470e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 17.384605843650696467425614928937
y[1] (numeric) = 17.384605843650696467425614928931
absolute error = 6e-30
relative error = 3.4513293277749830314915812430850e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 17.401999144695427799989073213005
y[1] (numeric) = 17.401999144695427799989073212999
absolute error = 6e-30
relative error = 3.4478797235367941579548139568052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 17.419409847740753994624061659172
y[1] (numeric) = 17.419409847740753994624061659166
absolute error = 6e-30
relative error = 3.4444335671786161445320768020336e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 17.436837970197379547548743709341
y[1] (numeric) = 17.436837970197379547548743709335
absolute error = 6e-30
relative error = 3.4409908552542923458656502685416e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 17.454283529493428367732258751777
y[1] (numeric) = 17.45428352949342836773225875177
absolute error = 7e-30
relative error = 4.0104768483746289758622433942466e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 17.471746543074461205020083433949
y[1] (numeric) = 17.471746543074461205020083433942
absolute error = 7e-30
relative error = 4.0064683760964327959253754368530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 17.489227028403493095696235304792
y[1] (numeric) = 17.489227028403493095696235304785
absolute error = 7e-30
relative error = 4.0024639102869465847971071865889e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 17.506725002961010825499764350019
y[1] (numeric) = 17.506725002961010825499764350012
absolute error = 7e-30
relative error = 3.9984634469417041992857322678189e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 17.524240484244990410112995438455
y[1] (numeric) = 17.524240484244990410112995438449
absolute error = 6e-30
relative error = 3.4238288417659216806659216742038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 17.54177348977091459313900216908
y[1] (numeric) = 17.541773489770914593139002169074
absolute error = 6e-30
relative error = 3.4204067242680811326596970093230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 17.559324037071790361585810097709
y[1] (numeric) = 17.559324037071790361585810097703
absolute error = 6e-30
relative error = 3.4169880271772498866377951408597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=36016244, alloc=4259060, time=3.48
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 17.576892143698166478874844828986
y[1] (numeric) = 17.57689214369816647887484482898
absolute error = 6e-30
relative error = 3.4135727470747305668775363145936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 17.594477827218151035391157983586
y[1] (numeric) = 17.594477827218151035391157983579
absolute error = 7e-30
relative error = 3.9785210273027832506284020856722e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 17.612081105217429016592981592322
y[1] (numeric) = 17.612081105217429016592981592315
absolute error = 7e-30
relative error = 3.9745444948730730194462557788205e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 17.62970199529927988869817902818
y[1] (numeric) = 17.629701995299279888698179028173
absolute error = 7e-30
relative error = 3.9705719369881888733894087425477e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 17.64734051508459520196517816418
y[1] (numeric) = 17.647340515084595201965178164173
absolute error = 7e-30
relative error = 3.9666033496755725965272134781118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 17.664996682211896211585990039486
y[1] (numeric) = 17.66499668221189621158599003948
absolute error = 6e-30
relative error = 3.3965474819714027533095194698063e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 17.682670514337351516208933928238
y[1] (numeric) = 17.682670514337351516208933928232
absolute error = 6e-30
relative error = 3.3931526321972225837742560247887e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 17.700362029134794714108707335301
y[1] (numeric) = 17.700362029134794714108707335295
absolute error = 6e-30
relative error = 3.3897611755759573741903515467224e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 17.718071244295742077021457090478
y[1] (numeric) = 17.718071244295742077021457090472
absolute error = 6e-30
relative error = 3.3863731087161502206712019255559e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 17.735798177529410241662525377732
y[1] (numeric) = 17.735798177529410241662525377726
absolute error = 6e-30
relative error = 3.3829884282297339810707392469129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 17.753542846562733918944562218627
y[1] (numeric) = 17.753542846562733918944562218621
absolute error = 6e-30
relative error = 3.3796071307320278869160073070870e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 17.771305269140383620913713629587
y[1] (numeric) = 17.771305269140383620913713629581
absolute error = 6e-30
relative error = 3.3762292128417341587261110833455e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 17.789085463024783405421612390635
y[1] (numeric) = 17.78908546302478340542161239063
absolute error = 5e-30
relative error = 2.8107122259841121872617962318411e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 17.806883445996128638550916099082
y[1] (numeric) = 17.806883445996128638550916099077
absolute error = 5e-30
relative error = 2.8079029186459061190573266994732e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 17.824699235852403774812154935176
y[1] (numeric) = 17.824699235852403774812154935171
absolute error = 5e-30
relative error = 2.8050964192108526886766631137441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 17.842532850409400155129669338057
y[1] (numeric) = 17.842532850409400155129669338052
absolute error = 5e-30
relative error = 2.8022927248724522271914143770391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 17.860384307500733822634435579423
y[1] (numeric) = 17.860384307500733822634435579418
absolute error = 5e-30
relative error = 2.7994918328270101625599163493643e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 17.878253624977863356281595029227
y[1] (numeric) = 17.878253624977863356281595029222
absolute error = 5e-30
relative error = 2.7966937402736342159324261654607e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 17.896140820710107722310520732418
y[1] (numeric) = 17.896140820710107722310520732413
absolute error = 5e-30
relative error = 2.7938984444142316007586099773629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 17.914045912584664143565272758274
y[1] (numeric) = 17.914045912584664143565272758269
absolute error = 5e-30
relative error = 2.7911059424535062246945232296594e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 17.931968918506625986693311644282
y[1] (numeric) = 17.931968918506625986693311644278
absolute error = 4e-30
relative error = 2.2306529852791647154450282993589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 17.949909856399000667240357134765
y[1] (numeric) = 17.94990985639900066724035713476
absolute error = 5e-30
relative error = 2.7855293090608695225676537276849e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 17.967868744202727572659297310596
y[1] (numeric) = 17.967868744202727572659297310591
absolute error = 5e-30
relative error = 2.7827451720523243391487039695040e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 17.985845599876696003251071120425
y[1] (numeric) = 17.98584559987669600325107112042
absolute error = 5e-30
relative error = 2.7799638177891831034928275682269e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 18.003840441397763131055465255772
y[1] (numeric) = 18.003840441397763131055465255768
absolute error = 4e-30
relative error = 2.2217481947920730565434073708454e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 18.021853286760771976709784262299
y[1] (numeric) = 18.021853286760771976709784262294
absolute error = 5e-30
relative error = 2.7744094463764744600683501160142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 18.039884153978569404293370747409
y[1] (numeric) = 18.039884153978569404293370747404
absolute error = 5e-30
relative error = 2.7716364236725351767268058194045e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 18.057933061082024134175970530218
y[1] (numeric) = 18.057933061082024134175970530213
absolute error = 5e-30
relative error = 2.7688661726052505356301099510686e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 18.076000026120044773887955583742
y[1] (numeric) = 18.076000026120044773887955583736
absolute error = 6e-30
relative error = 3.3193184284852430863672297345380e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 18.094085067159597867030435641032
y[1] (numeric) = 18.094085067159597867030435641026
absolute error = 6e-30
relative error = 3.3160007691628906250996746610801e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 18.112188202285725960243307376886
y[1] (numeric) = 18.11218820228572596024330737688
absolute error = 6e-30
relative error = 3.3126864258415836601293860415945e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=40017628, alloc=4324584, time=3.87
x[1] = 3.95
y[1] (analytic) = 18.130309449601565688249308134672
y[1] (numeric) = 18.130309449601565688249308134666
absolute error = 6e-30
relative error = 3.3093753952069785939541129237026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 18.148448827228365876992159243832
y[1] (numeric) = 18.148448827228365876992159243826
absolute error = 6e-30
relative error = 3.3060676739480445160495603844019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 18.166606353305505664886902067728
y[1] (numeric) = 18.166606353305505664886902067722
absolute error = 6e-30
relative error = 3.3027632587570598918382030865184e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 18.184782045990512642200548033659
y[1] (numeric) = 18.184782045990512642200548033653
absolute error = 6e-30
relative error = 3.2994621463296092549674750577114e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 18.202975923459081008581182027221
y[1] (numeric) = 18.202975923459081008581182027215
absolute error = 6e-30
relative error = 3.2961643333645799028940279699432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 18.221188003905089748753676681629
y[1] (numeric) = 18.221188003905089748753676681622
absolute error = 7e-30
relative error = 3.8416814526581850283992124206279e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 18.239418305540620826400193259218
y[1] (numeric) = 18.239418305540620826400193259211
absolute error = 7e-30
relative error = 3.8378416914061329684054801285127e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 18.257666846595977396243663007155
y[1] (numeric) = 18.257666846595977396243663007149
absolute error = 6e-30
relative error = 3.2862906582823646868825663638691e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 18.275933645319702034352461072352
y[1] (numeric) = 18.275933645319702034352461072346
absolute error = 6e-30
relative error = 3.2830060102218332550605363777708e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 18.294218719978594986684503281767
y[1] (numeric) = 18.294218719978594986684503281761
absolute error = 6e-30
relative error = 3.2797246451675856289150660662826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 18.312522088857732435889014333731
y[1] (numeric) = 18.312522088857732435889014333725
absolute error = 6e-30
relative error = 3.2764465598382564807514323150620e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 18.330843770260484786384234203567
y[1] (numeric) = 18.330843770260484786384234203561
absolute error = 6e-30
relative error = 3.2731717509557602080667004105872e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 18.349183782508534967729347842752
y[1] (numeric) = 18.349183782508534967729347842746
absolute error = 6e-30
relative error = 3.2699002152452876554638483634116e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 18.36754214394189675630894154506
y[1] (numeric) = 18.367542143941896756308941545054
absolute error = 6e-30
relative error = 3.2666319494353028398423386103715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 18.385918872918933115348307665684
y[1] (numeric) = 18.385918872918933115348307665678
absolute error = 6e-30
relative error = 3.2633669502575396788618622860392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 18.404313987816374553277937710156
y[1] (numeric) = 18.40431398781637455327793771015
absolute error = 6e-30
relative error = 3.2601052144469987226759845268995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 18.422727507029337500465562159103
y[1] (numeric) = 18.422727507029337500465562159096
absolute error = 7e-30
relative error = 3.7996545285322678704211596318870e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 18.441159448971342704334113762392
y[1] (numeric) = 18.441159448971342704334113762385
absolute error = 7e-30
relative error = 3.7958567731978824012094733553079e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 18.459609832074333642884009422182
y[1] (numeric) = 18.459609832074333642884009422175
absolute error = 7e-30
relative error = 3.7920628137205864512884988251828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 18.478078674788694956638164188678
y[1] (numeric) = 18.478078674788694956638164188672
absolute error = 6e-30
relative error = 3.2470908396912173375991306917985e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 18.496565995583270899028169315154
y[1] (numeric) = 18.496565995583270899028169315148
absolute error = 6e-30
relative error = 3.2438453718558994276520701452394e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 18.515071812945383805240084759946
y[1] (numeric) = 18.51507181294538380524008475994
absolute error = 6e-30
relative error = 3.2406031478662236940611025907854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 18.533596145380852579538314982761
y[1] (numeric) = 18.533596145380852579538314982755
absolute error = 6e-30
relative error = 3.2373641644799658769651529583134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 18.552139011414011201086055360707
y[1] (numeric) = 18.552139011414011201086055360701
absolute error = 6e-30
relative error = 3.2341284184581423201911129665460e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 18.570700429587727248280815046038
y[1] (numeric) = 18.570700429587727248280815046032
absolute error = 6e-30
relative error = 3.2308959065650067322699150346299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 18.589280418463420441623540602681
y[1] (numeric) = 18.589280418463420441623540602674
absolute error = 7e-30
relative error = 3.7656110631627214424716330287908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 18.607878996621081205139883292207
y[1] (numeric) = 18.607878996621081205139883292201
absolute error = 6e-30
relative error = 3.2244405722379817093847410684440e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 18.626496182659289246372171432076
y[1] (numeric) = 18.626496182659289246372171432069
absolute error = 7e-30
relative error = 3.7580873672402169776930631263352e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 18.645131995195232154960667819651
y[1] (numeric) = 18.645131995195232154960667819644
absolute error = 7e-30
relative error = 3.7543311582904690419452818490593e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 18.663786452864724019832710804818
y[1] (numeric) = 18.663786452864724019832710804811
absolute error = 7e-30
relative error = 3.7505787036721922576068287540002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 18.682459574322224065018356201881
y[1] (numeric) = 18.682459574322224065018356201874
absolute error = 7e-30
relative error = 3.7468299996329316936963575561543e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 18.701151378240855304111155857939
y[1] (numeric) = 18.701151378240855304111155857932
absolute error = 7e-30
relative error = 3.7430850424239829985612906602697e-29 %
Correct digits = 31
bytes used=44018788, alloc=4324584, time=4.27
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 18.719861883312423213392727340073
y[1] (numeric) = 18.719861883312423213392727340066
absolute error = 7e-30
relative error = 3.7393438283003886511731551162292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 18.738591108247434423639787867474
y[1] (numeric) = 18.738591108247434423639787867467
absolute error = 7e-30
relative error = 3.7356063535209342161697495107731e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 18.757339071775115430632344297095
y[1] (numeric) = 18.757339071775115430632344297088
absolute error = 7e-30
relative error = 3.7318726143481446026403968374185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 18.776105792643431324381749672586
y[1] (numeric) = 18.77610579264343132438174967258
absolute error = 6e-30
relative error = 3.1955508060413831371290361110119e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 18.794891289619104537097355566127
y[1] (numeric) = 18.79489128961910453709735556612
absolute error = 7e-30
relative error = 3.7244163278913337775019573807162e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 18.81369558148763360991050818136
y[1] (numeric) = 18.813695581487633609910508181353
absolute error = 7e-30
relative error = 3.7206937731510254877248200127864e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 18.832518687053311978374654943006
y[1] (numeric) = 18.832518687053311978374654942999
absolute error = 7e-30
relative error = 3.7169749391048004067979348824662e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 18.851360625139246776760347074814
y[1] (numeric) = 18.851360625139246776760347074808
absolute error = 6e-30
relative error = 3.1827941331718492959371773263019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 18.870221414587377661163942462428
y[1] (numeric) = 18.870221414587377661163942462422
absolute error = 6e-30
relative error = 3.1796129299054109336072642015093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 18.889101074258495651448831911433
y[1] (numeric) = 18.889101074258495651448831911427
absolute error = 6e-30
relative error = 3.1764349062521674444412757265218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 18.907999623032261992038030743384
y[1] (numeric) = 18.907999623032261992038030743378
absolute error = 6e-30
relative error = 3.1732600590340949103604094705497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 18.926917079807227031576996523978
y[1] (numeric) = 18.926917079807227031576996523972
absolute error = 6e-30
relative error = 3.1700883850763458487215210276621e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 18.94585346350084912148555258776
y[1] (numeric) = 18.945853463500849121485552587754
absolute error = 6e-30
relative error = 3.1669198812072460374693768030097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 18.964808793049513533417815912859
y[1] (numeric) = 18.964808793049513533417815912853
absolute error = 6e-30
relative error = 3.1637545442582913434621676513979e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 18.983783087408551395649046807268
y[1] (numeric) = 18.983783087408551395649046807262
absolute error = 6e-30
relative error = 3.1605923710641445539671116934565e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 19.00277636555225864840835679508
y[1] (numeric) = 19.002776365552258648408356795074
absolute error = 6e-30
relative error = 3.1574333584626322113229778047495e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 19.021788646473915018176230036983
y[1] (numeric) = 19.021788646473915018176230036977
absolute error = 6e-30
relative error = 3.1542775032947414507663644400791e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 19.040819949185803010965832584107
y[1] (numeric) = 19.040819949185803010965832584101
absolute error = 6e-30
relative error = 3.1511248024046168414185716190041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 19.059870292719226924607102748117
y[1] (numeric) = 19.059870292719226924607102748112
absolute error = 5e-30
relative error = 2.6233127105329643586915892159819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 19.078939696124531880052634873233
y[1] (numeric) = 19.078939696124531880052634873228
absolute error = 5e-30
relative error = 2.6206907090416771585652255012944e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 19.098028178471122871724387817631
y[1] (numeric) = 19.098028178471122871724387817626
absolute error = 5e-30
relative error = 2.6180713282413173910157201881397e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 19.117135758847483836920268492545
y[1] (numeric) = 19.117135758847483836920268492539
absolute error = 6e-30
relative error = 3.1385454786150048448818781051684e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 19.136262456361196744299659867213
y[1] (numeric) = 19.136262456361196744299659867208
absolute error = 5e-30
relative error = 2.6128404182384741508458385824100e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 19.155408290138960701466981926821
y[1] (numeric) = 19.155408290138960701466981926815
absolute error = 6e-30
relative error = 3.1322746605660962873676488232530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 19.174573279326611081672393168558
y[1] (numeric) = 19.174573279326611081672393168552
absolute error = 6e-30
relative error = 3.1291439515209451827136599863884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 19.193757443089138669648759338116
y[1] (numeric) = 19.193757443089138669648759338111
absolute error = 5e-30
relative error = 2.6050136430166719675079216738636e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 19.212960800610708826604035245173
y[1] (numeric) = 19.212960800610708826604035245168
absolute error = 5e-30
relative error = 2.6024099314464163839039150721266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 19.232183371094680674388224651844
y[1] (numeric) = 19.232183371094680674388224651839
absolute error = 5e-30
relative error = 2.5998088222863091142178084922753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 19.25142517376362629885410240267
y[1] (numeric) = 19.251425173763626298854102402665
absolute error = 5e-30
relative error = 2.5972103129352407815832283472940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 19.270686227859349972430902158449
y[1] (numeric) = 19.270686227859349972430902158444
absolute error = 5e-30
relative error = 2.5946144007947018183893888621600e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 19.289966552642907395930192309217
y[1] (numeric) = 19.289966552642907395930192309212
absolute error = 5e-30
relative error = 2.5920210832687798677713079205861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
bytes used=48020236, alloc=4324584, time=4.67
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 19.309266167394624959603181873842
y[1] (numeric) = 19.309266167394624959603181873836
absolute error = 6e-30
relative error = 3.1073164293169886252366806488026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 19.32858509141411902346871744515
y[1] (numeric) = 19.328585091414119023468717445145
absolute error = 5e-30
relative error = 2.5868422216901080576506873999846e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 19.347923344020315216931251510197
y[1] (numeric) = 19.347923344020315216931251510192
absolute error = 5e-30
relative error = 2.5842566724584961879045250919588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 19.367280944551467757708081765234
y[1] (numeric) = 19.367280944551467757708081765229
absolute error = 5e-30
relative error = 2.5816737074837721313844340540255e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 19.38665791236517879008518035425
y[1] (numeric) = 19.386657912365178790085180354245
absolute error = 5e-30
relative error = 2.5790933241829706981192693641861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 19.406054266838417742520951288509
y[1] (numeric) = 19.406054266838417742520951288504
absolute error = 5e-30
relative error = 2.5765155199757083722756488560914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 19.425470027367540704617273652457
y[1] (numeric) = 19.425470027367540704617273652452
absolute error = 5e-30
relative error = 2.5739402922841807317742222536933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 19.444905213368309823477207568665
y[1] (numeric) = 19.444905213368309823477207568661
absolute error = 4e-30
relative error = 2.0570941108265278963880274198812e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 19.464359844275912719468759281124
y[1] (numeric) = 19.46435984427591271946875928112
absolute error = 4e-30
relative error = 2.0550380449199934583995231192362e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 19.483833939544981921414121122268
y[1] (numeric) = 19.483833939544981921414121122264
absolute error = 4e-30
relative error = 2.0529840340516751935805956566850e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 19.503327518649614321223821554603
y[1] (numeric) = 19.503327518649614321223821554599
absolute error = 4e-30
relative error = 2.0509320761675620624454021478586e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 19.522840601083390647995239922694
y[1] (numeric) = 19.52284060108339064799523992269
absolute error = 4e-30
relative error = 2.0488821692156960098843154149195e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 19.542373206359394961594960015662
y[1] (numeric) = 19.542373206359394961594960015658
absolute error = 4e-30
relative error = 2.0468343111461699132056978804239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 19.561925354010234165744456024157
y[1] (numeric) = 19.561925354010234165744456024153
absolute error = 4e-30
relative error = 2.0447884999111255322286080500848e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 19.581497063588057540628623979132
y[1] (numeric) = 19.581497063588057540628623979127
absolute error = 5e-30
relative error = 2.5534309168309393267804870962142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 19.601088354664576295046691282562
y[1] (numeric) = 19.601088354664576295046691282557
absolute error = 5e-30
relative error = 2.5508787622041013551313696857047e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 19.620699246831083138125056482665
y[1] (numeric) = 19.62069924683108313812505648266
absolute error = 5e-30
relative error = 2.5483291584562381608208768561438e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 19.640329759698471870611631008079
y[1] (numeric) = 19.640329759698471870611631008074
absolute error = 5e-30
relative error = 2.5457821030377457835188282262064e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 19.659979912897256995771274156975
y[1] (numeric) = 19.65997991289725699577127415697
absolute error = 5e-30
relative error = 2.5432375934015685924782212109917e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 19.679649726077593349901932238183
y[1] (numeric) = 19.679649726077593349901932238179
absolute error = 4e-30
relative error = 2.0325565016025573915835104163021e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 19.699339218909295752491112382096
y[1] (numeric) = 19.699339218909295752491112382092
absolute error = 4e-30
relative error = 2.0305249610405308914559483174870e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 19.719048411081858676032341179464
y[1] (numeric) = 19.71904841108185867603234117946
absolute error = 4e-30
relative error = 2.0284954510036346422783380660758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 19.738777322304475935521277966183
y[1] (numeric) = 19.738777322304475935521277966179
absolute error = 4e-30
relative error = 2.0264679694623584380285884389096e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 19.758525972306060397651172251827
y[1] (numeric) = 19.758525972306060397651172251823
absolute error = 4e-30
relative error = 2.0244425143892205684736944479951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 19.778294380835263709727374489023
y[1] (numeric) = 19.77829438083526370972737448902
absolute error = 3e-30
relative error = 1.5168143128190743437658936130139e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 19.798082567660496048320629099831
y[1] (numeric) = 19.798082567660496048320629099828
absolute error = 3e-30
relative error = 1.5152982566606724814478084519533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 19.817890552569945887678898414053
y[1] (numeric) = 19.81789055256994588767889841405
absolute error = 3e-30
relative error = 1.5137837158006535546611356233073e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 19.83771835537159978791748593296
y[1] (numeric) = 19.837718355371599787917485932957
absolute error = 3e-30
relative error = 1.5122706887244765771752057984343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 19.857565995893262203007247110196
y[1] (numeric) = 19.857565995893262203007247110192
absolute error = 4e-30
relative error = 2.0143455652254857956365968095155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 19.877433493982575308580695639724
y[1] (numeric) = 19.87743349398257530858069563972
absolute error = 4e-30
relative error = 2.0123322264974025759947457193129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 19.897320869507038849575833058582
y[1] (numeric) = 19.897320869507038849575833058578
absolute error = 4e-30
relative error = 2.0103209001017135481132685525774e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=52021468, alloc=4324584, time=5.05
x[1] = 4.89
y[1] (analytic) = 19.917228142354030007737549309913
y[1] (numeric) = 19.917228142354030007737549309909
absolute error = 4e-30
relative error = 2.0083115840270921486925988667284e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 19.937155332430823288996461769344
y[1] (numeric) = 19.93715533243082328899646176934
absolute error = 4e-30
relative error = 2.0063042762642221356683254412125e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 19.957102459664610430745080115201
y[1] (numeric) = 19.957102459664610430745080115197
absolute error = 4e-30
relative error = 2.0042989748057955788947827700669e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 19.977069544002520329031204320385
y[1] (numeric) = 19.977069544002520329031204320381
absolute error = 4e-30
relative error = 2.0022956776465108528369536405874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 19.997056605411638985688482960969
y[1] (numeric) = 19.997056605411638985688482960965
absolute error = 4e-30
relative error = 2.0002943827830706312686764898365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 20.017063663879029475424078973737
y[1] (numeric) = 20.017063663879029475424078973733
absolute error = 4e-30
relative error = 1.9982950882141798839751522370327e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 20.037090739411751932883409951988
y[1] (numeric) = 20.037090739411751932883409951984
absolute error = 4e-30
relative error = 1.9962977919405438754577472941601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 20.057137852036883559711950046024
y[1] (numeric) = 20.057137852036883559711950046021
absolute error = 3e-30
relative error = 1.4957268689736496242293185945758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 20.07720502180153865163410053178
y[1] (numeric) = 20.077205021801538651634100531777
absolute error = 3e-30
relative error = 1.4942318897188849594248535489179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 20.097292268772888645569156128137
y[1] (numeric) = 20.097292268772888645569156128133
absolute error = 4e-30
relative error = 1.9903178729281793771115224169854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 20.117399613038182186804414180557
y[1] (numeric) = 20.117399613038182186804414180554
absolute error = 3e-30
relative error = 1.4912464124119131972481674170558e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5
y[1] (analytic) = 20.137527074704765216245493885831
y[1] (numeric) = 20.137527074704765216245493885827
absolute error = 4e-30
relative error = 1.9863412151656380588192003735901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.01
y[1] (analytic) = 20.157674673900101077763952809906
y[1] (numeric) = 20.157674673900101077763952809902
absolute error = 4e-30
relative error = 1.9843558667901058820523510947295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.02
y[1] (analytic) = 20.177842430771790645662308048117
y[1] (numeric) = 20.177842430771790645662308048114
absolute error = 3e-30
relative error = 1.4867793770779543937893463575790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.03
y[1] (analytic) = 20.1980303654875924722765894945
y[1] (numeric) = 20.198030365487592472276589494496
absolute error = 4e-30
relative error = 1.9803911211237738030391683854815e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.04
y[1] (analytic) = 20.218238498235442955736572824417
y[1] (numeric) = 20.218238498235442955736572824413
absolute error = 4e-30
relative error = 1.9784117198682279040652727343889e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.05
y[1] (analytic) = 20.238466849223476527903859952429
y[1] (numeric) = 20.238466849223476527903859952425
absolute error = 4e-30
relative error = 1.9764342970245667409680990891031e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.06
y[1] (analytic) = 20.258715438680045862507994905152
y[1] (numeric) = 20.258715438680045862507994905148
absolute error = 4e-30
relative error = 1.9744588506153673053012418878458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.07
y[1] (analytic) = 20.278984286853742103500823246915
y[1] (numeric) = 20.278984286853742103500823246911
absolute error = 4e-30
relative error = 1.9724853786651830232447258764556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.08
y[1] (analytic) = 20.299273414013415113649323414258
y[1] (numeric) = 20.299273414013415113649323414253
absolute error = 5e-30
relative error = 2.4631423490006772251978345848242e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.09
y[1] (analytic) = 20.319582840448193743387158553785
y[1] (numeric) = 20.31958284044819374338715855378
absolute error = 5e-30
relative error = 2.4606804378124299338862458072183e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.1
y[1] (analytic) = 20.339912586467506119945217716624
y[1] (numeric) = 20.33991258646750611994521771662
absolute error = 4e-30
relative error = 1.9665767898438604093716617401974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.11
y[1] (analytic) = 20.360262672401099956781435541719
y[1] (numeric) = 20.360262672401099956781435541714
absolute error = 5e-30
relative error = 2.4557639950184132461241907183980e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.12
y[1] (analytic) = 20.380633118599062883330199859456
y[1] (numeric) = 20.380633118599062883330199859451
absolute error = 5e-30
relative error = 2.4533094584962006459534568202854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.13
y[1] (analytic) = 20.401023945431842795091676966752
y[1] (numeric) = 20.401023945431842795091676966747
absolute error = 5e-30
relative error = 2.4508573752836509844450583076341e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.14
y[1] (analytic) = 20.421435173290268224081404664595
y[1] (numeric) = 20.421435173290268224081404664591
absolute error = 4e-30
relative error = 1.9587261943429446757672473185855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.15
y[1] (analytic) = 20.441866822585568729660523509357
y[1] (numeric) = 20.441866822585568729660523509352
absolute error = 5e-30
relative error = 2.4459605589816576676392832206996e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.16
y[1] (analytic) = 20.462318913749395309767037109779
y[1] (numeric) = 20.462318913749395309767037109774
absolute error = 5e-30
relative error = 2.4435158209953973022805510722637e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.17
y[1] (analytic) = 20.482791467233840832568512702623
y[1] (numeric) = 20.482791467233840832568512702618
absolute error = 5e-30
relative error = 2.4410735265251615586443250315558e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.18
y[1] (analytic) = 20.503284503511460488556653661363
y[1] (numeric) = 20.503284503511460488556653661358
absolute error = 5e-30
relative error = 2.4386336731286557629703154918865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.19
y[1] (analytic) = 20.523798043075292263104196034213
y[1] (numeric) = 20.523798043075292263104196034208
absolute error = 5e-30
relative error = 2.4361962583660263154316036263926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.2
y[1] (analytic) = 20.544332106438877429504601670086
bytes used=56022652, alloc=4324584, time=5.45
y[1] (numeric) = 20.54433210643887742950460167008
absolute error = 6e-30
relative error = 2.9205135357598299003370058879737e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.21
y[1] (analytic) = 20.564886714136281062515040973882
y[1] (numeric) = 20.564886714136281062515040973877
absolute error = 5e-30
relative error = 2.4313287349951727984350669040431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.22
y[1] (analytic) = 20.585461886722112572423178835812
y[1] (numeric) = 20.585461886722112572423178835807
absolute error = 5e-30
relative error = 2.4288986215194249524967639586259e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.23
y[1] (analytic) = 20.606057644771546259658297803231
y[1] (numeric) = 20.606057644771546259658297803226
absolute error = 5e-30
relative error = 2.4264709369425010342086204027878e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.24
y[1] (analytic) = 20.626674008880341889967313107838
y[1] (numeric) = 20.626674008880341889967313107833
absolute error = 5e-30
relative error = 2.4240456788367162643396631278237e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.25
y[1] (analytic) = 20.647310999664865290176254725963
y[1] (numeric) = 20.647310999664865290176254725958
absolute error = 5e-30
relative error = 2.4216228447768123350002733792174e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.26
y[1] (analytic) = 20.66796863776210896455781223514
y[1] (numeric) = 20.667968637762108964557812235135
absolute error = 5e-30
relative error = 2.4192024323399549843836767621569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.27
y[1] (analytic) = 20.688646943829712731825558836229
y[1] (numeric) = 20.688646943829712731825558836224
absolute error = 5e-30
relative error = 2.4167844391057315739314795318984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.28
y[1] (analytic) = 20.709345938545984382775491537031
y[1] (numeric) = 20.709345938545984382775491537025
absolute error = 6e-30
relative error = 2.8972426351873784015049940011747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.29
y[1] (analytic) = 20.730065642609920358595545140656
y[1] (numeric) = 20.730065642609920358595545140651
absolute error = 5e-30
relative error = 2.4119557005756296154707729835707e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.3
y[1] (analytic) = 20.750806076741226449863758349892
y[1] (numeric) = 20.750806076741226449863758349887
absolute error = 5e-30
relative error = 2.4095449504510121349654142831358e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.31
y[1] (analytic) = 20.771567261680338516255790987445
y[1] (numeric) = 20.771567261680338516255790987439
absolute error = 6e-30
relative error = 2.8885639318458550810697055755965e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.32
y[1] (analytic) = 20.79234921818844322698251204131
y[1] (numeric) = 20.792349218188443226982512041305
absolute error = 5e-30
relative error = 2.4047306764288901330875050204739e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.33
y[1] (analytic) = 20.813151967047498821978398974595
y[1] (numeric) = 20.813151967047498821978398974589
absolute error = 6e-30
relative error = 2.8827925772605334260841248366247e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.34
y[1] (analytic) = 20.833975529060255893861509489898
y[1] (numeric) = 20.833975529060255893861509489893
absolute error = 5e-30
relative error = 2.3999260213326801547662076676888e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.35
y[1] (analytic) = 20.854819925050278190685807709983
y[1] (numeric) = 20.854819925050278190685807709978
absolute error = 5e-30
relative error = 2.3975272948744704476509102557002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.36
y[1] (analytic) = 20.875685175861963439506647528774
y[1] (numeric) = 20.875685175861963439506647528768
absolute error = 6e-30
relative error = 2.8741571591325064907447517983833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.37
y[1] (analytic) = 20.896571302360564190780236699911
y[1] (numeric) = 20.896571302360564190780236699906
absolute error = 5e-30
relative error = 2.3927370321442059082662334835402e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.38
y[1] (analytic) = 20.917478325432208683617926064067
y[1] (numeric) = 20.917478325432208683617926064061
absolute error = 6e-30
relative error = 2.8684145892982655358524886924336e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.39
y[1] (analytic) = 20.938406265983921731916189171036
y[1] (numeric) = 20.93840626598392173191618917103
absolute error = 6e-30
relative error = 2.8655476084383123146081090643483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.4
y[1] (analytic) = 20.959355144943645631383178428338
y[1] (numeric) = 20.959355144943645631383178428332
absolute error = 6e-30
relative error = 2.8626834931262063273180404250082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.41
y[1] (analytic) = 20.980324983260261087482764804619
y[1] (numeric) = 20.980324983260261087482764804613
absolute error = 6e-30
relative error = 2.8598222404978320232000115196366e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.42
y[1] (analytic) = 21.001315801903608164316989033638
y[1] (numeric) = 21.001315801903608164316989033632
absolute error = 6e-30
relative error = 2.8569638476919365354419912510884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.43
y[1] (analytic) = 21.022327621864507254467873203041
y[1] (numeric) = 21.022327621864507254467873203035
absolute error = 6e-30
relative error = 2.8541083118501268199490834300723e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.44
y[1] (analytic) = 21.043360464154780069819562571469
y[1] (numeric) = 21.043360464154780069819562571463
absolute error = 6e-30
relative error = 2.8512556301168667969502444808271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.45
y[1] (analytic) = 21.06441434980727065338178843791
y[1] (numeric) = 21.064414349807270653381788437904
absolute error = 6e-30
relative error = 2.8484057996394744954619657087288e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.46
y[1] (analytic) = 21.085489299875866412135663888488
y[1] (numeric) = 21.085489299875866412135663888482
absolute error = 6e-30
relative error = 2.8455588175681192006060645932779e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.47
y[1] (analytic) = 21.106585335435519170922845268254
y[1] (numeric) = 21.106585335435519170922845268248
absolute error = 6e-30
relative error = 2.8427146810558186037787324240150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.48
y[1] (analytic) = 21.127702477582266247399113268886
y[1] (numeric) = 21.12770247758226624739911326888
absolute error = 6e-30
relative error = 2.8398733872584359556679884481787e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.49
y[1] (analytic) = 21.148840747433251548073448587638
y[1] (numeric) = 21.148840747433251548073448587632
absolute error = 6e-30
relative error = 2.8370349333346772221166935473215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.5
y[1] (analytic) = 21.170000166126746685453698198371
y[1] (numeric) = 21.170000166126746685453698198365
absolute error = 6e-30
relative error = 2.8341993164460882428282793056596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.51
y[1] (analytic) = 21.191180754822172116319949382093
y[1] (numeric) = 21.191180754822172116319949382087
absolute error = 6e-30
relative error = 2.8313665337570518929123511756502e-29 %
Correct digits = 31
h = 0.01
bytes used=60023432, alloc=4324584, time=5.85
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.52
y[1] (analytic) = 21.212382534700118301146749792143
y[1] (numeric) = 21.212382534700118301146749792138
absolute error = 5e-30
relative error = 2.3571138186956543727227727384682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.53
y[1] (analytic) = 21.233605526962366884695332978007
y[1] (numeric) = 21.233605526962366884695332978001
absolute error = 6e-30
relative error = 2.8257094596493367477972772756405e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.54
y[1] (analytic) = 21.254849752831911897797029961738
y[1] (numeric) = 21.254849752831911897797029961732
absolute error = 6e-30
relative error = 2.8228851625735833734601283668759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.55
y[1] (analytic) = 21.276115233552980980349068652192
y[1] (numeric) = 21.276115233552980980349068652186
absolute error = 6e-30
relative error = 2.8200636883832278131444087313345e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.56
y[1] (analytic) = 21.297401990391056625543984094612
y[1] (numeric) = 21.297401990391056625543984094605
absolute error = 7e-30
relative error = 3.2867858732995949149336511895002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.57
y[1] (analytic) = 21.318710044632897445353883786764
y[1] (numeric) = 21.318710044632897445353883786757
absolute error = 7e-30
relative error = 3.2835007302715712462923120532600e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.58
y[1] (analytic) = 21.340039417586559457290833547657
y[1] (numeric) = 21.34003941758655945729083354765
absolute error = 7e-30
relative error = 3.2802188707445514742921960091270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.59
y[1] (analytic) = 21.361390130581417392464650701002
y[1] (numeric) = 21.361390130581417392464650700995
absolute error = 7e-30
relative error = 3.2769402914366757984252280223943e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.6
y[1] (analytic) = 21.38276220496818602495941263298
y[1] (numeric) = 21.382762204968186024959412632973
absolute error = 7e-30
relative error = 3.2736649890693646376007807959560e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.61
y[1] (analytic) = 21.404155662118941522550010102614
y[1] (numeric) = 21.404155662118941522550010102607
absolute error = 7e-30
relative error = 3.2703929603673153515658204647059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.62
y[1] (analytic) = 21.425570523427142818780096023063
y[1] (numeric) = 21.425570523427142818780096023057
absolute error = 6e-30
relative error = 2.8003921731929991133731372005210e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.63
y[1] (analytic) = 21.447006810307653006422801793583
y[1] (numeric) = 21.447006810307653006422801793577
absolute error = 6e-30
relative error = 2.7975931807492773415683247073582e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.64
y[1] (analytic) = 21.468464544196760752345614644636
y[1] (numeric) = 21.46846454419676075234561464463
absolute error = 6e-30
relative error = 2.7947969858989694518136873146062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.65
y[1] (analytic) = 21.489943746552201733800830862832
y[1] (numeric) = 21.489943746552201733800830862826
absolute error = 6e-30
relative error = 2.7920035858458803607850899747619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.66
y[1] (analytic) = 21.511444438853180096163021187921
y[1] (numeric) = 21.511444438853180096163021187915
absolute error = 6e-30
relative error = 2.7892129777966097826100961423590e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.67
y[1] (analytic) = 21.532966642600389932134966121103
y[1] (numeric) = 21.532966642600389932134966121097
absolute error = 6e-30
relative error = 2.7864251589605494354674491181664e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.68
y[1] (analytic) = 21.554510379316036782443540352376
y[1] (numeric) = 21.55451037931603678244354035237
absolute error = 6e-30
relative error = 2.7836401265498802509785576772334e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.69
y[1] (analytic) = 21.5760756705438591580470470046
y[1] (numeric) = 21.576075670543859158047047004594
absolute error = 6e-30
relative error = 2.7808578777795695863881953720353e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.7
y[1] (analytic) = 21.5976625378491500838755239034
y[1] (numeric) = 21.597662537849150083875523903394
absolute error = 6e-30
relative error = 2.7780784098673684395316256911854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.71
y[1] (analytic) = 21.619271002818778664125565615019
y[1] (numeric) = 21.619271002818778664125565615013
absolute error = 6e-30
relative error = 2.7753017200338086665853680406075e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.72
y[1] (analytic) = 21.640901087061211669131226548728
y[1] (numeric) = 21.640901087061211669131226548722
absolute error = 6e-30
relative error = 2.7725278055022002025988222977020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.73
y[1] (analytic) = 21.662552812206535143832591996506
y[1] (numeric) = 21.662552812206535143832591996501
absolute error = 5e-30
relative error = 2.3081305529155235706699770582497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.74
y[1] (analytic) = 21.684226199906476037863625580358
y[1] (numeric) = 21.684226199906476037863625580353
absolute error = 5e-30
relative error = 2.3058235760432922322503273058950e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.75
y[1] (analytic) = 21.705921271834423857280923196915
y[1] (numeric) = 21.705921271834423857280923196909
absolute error = 6e-30
relative error = 2.7642226859937949069127821725882e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.76
y[1] (analytic) = 21.727638049685452337955025189881
y[1] (numeric) = 21.727638049685452337955025189875
absolute error = 6e-30
relative error = 2.7614598449585554808182563702808e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.77
y[1] (analytic) = 21.749376555176341140645960143449
y[1] (numeric) = 21.749376555176341140645960143443
absolute error = 6e-30
relative error = 2.7586997653833911349406286544483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.78
y[1] (analytic) = 21.771136810045597567784715374027
y[1] (numeric) = 21.771136810045597567784715374021
absolute error = 6e-30
relative error = 2.7559424445082220641089142168797e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.79
y[1] (analytic) = 21.792918836053478301982350903559
y[1] (numeric) = 21.792918836053478301982350903553
absolute error = 6e-30
relative error = 2.7531878795757271633772949692132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.8
y[1] (analytic) = 21.81472265498201116628849542537
y[1] (numeric) = 21.814722654982011166288495425364
absolute error = 6e-30
relative error = 2.7504360678313412707037848203518e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.81
y[1] (analytic) = 21.836548288635016906220984522842
y[1] (numeric) = 21.836548288635016906220984522836
absolute error = 6e-30
relative error = 2.7476870065232524123848380873727e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.82
y[1] (analytic) = 21.85839575883813099358842317237
y[1] (numeric) = 21.858395758838130993588423172364
absolute error = 6e-30
relative error = 2.7449406929023990512431464743093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
bytes used=64026460, alloc=4324584, time=6.25
TOP MAIN SOLVE Loop
x[1] = 5.83
y[1] (analytic) = 21.880265087438825452127476354985
y[1] (numeric) = 21.880265087438825452127476354979
absolute error = 6e-30
relative error = 2.7421971242224673375658728063742e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.84
y[1] (analytic) = 21.902156296306430704976713415748
y[1] (numeric) = 21.902156296306430704976713415742
absolute error = 6e-30
relative error = 2.7394562977398883627905724576266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.85
y[1] (analytic) = 21.924069407332157444008853646581
y[1] (numeric) = 21.924069407332157444008853646575
absolute error = 6e-30
relative error = 2.7367182107138354159360561577781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.86
y[1] (analytic) = 21.946004442429118521043282426608
y[1] (numeric) = 21.946004442429118521043282426601
absolute error = 7e-30
relative error = 3.1896466704739247832380257102306e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.87
y[1] (analytic) = 21.967961423532350860960729134333
y[1] (numeric) = 21.967961423532350860960729134326
absolute error = 7e-30
relative error = 3.1864586180953111923735020979430e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.88
y[1] (analytic) = 21.989940372598837396742019948181
y[1] (numeric) = 21.989940372598837396742019948174
absolute error = 7e-30
relative error = 3.1832737521755812350471967425207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.89
y[1] (analytic) = 22.011941311607529026452840575957
y[1] (numeric) = 22.011941311607529026452840575951
absolute error = 6e-30
relative error = 2.7257932024541731938202715656961e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.9
y[1] (analytic) = 22.03396426255936659219646589984
y[1] (numeric) = 22.033964262559366592196465899833
absolute error = 7e-30
relative error = 3.1769135669764907547501241127204e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.91
y[1] (analytic) = 22.056009247477302881056435491449
y[1] (numeric) = 22.056009247477302881056435491442
absolute error = 7e-30
relative error = 3.1737382413369445026734256165483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.92
y[1] (analytic) = 22.078076288406324648051175941515
y[1] (numeric) = 22.078076288406324648051175941508
absolute error = 7e-30
relative error = 3.1705660894359040657368238122271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 5.93
y[1] (analytic) = 22.100165407413474661122592960596
y[1] (numeric) = 22.100165407413474661122592960589
absolute error = 7e-30
relative error = 3.1673971081012172785538811982520e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.94
y[1] (analytic) = 22.122276626587873768180678241275
y[1] (numeric) = 22.122276626587873768180678241268
absolute error = 7e-30
relative error = 3.1642312941639025423560238983888e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 5.95
y[1] (analytic) = 22.144409968040742986226198128284
y[1] (numeric) = 22.144409968040742986226198128277
absolute error = 7e-30
relative error = 3.1610686444581456560106788112909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.96
y[1] (analytic) = 22.166565453905425612573553221084
y[1] (numeric) = 22.166565453905425612573553221076
absolute error = 8e-30
relative error = 3.6090390352243390288077813257918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.97
y[1] (analytic) = 22.188743106337409358195920133598
y[1] (numeric) = 22.18874310633740935819592013359
absolute error = 8e-30
relative error = 3.6054318001072761426339190023713e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.98
y[1] (analytic) = 22.210942947514348503214808758097
y[1] (numeric) = 22.210942947514348503214808758089
absolute error = 8e-30
relative error = 3.6018281704223138163962233410609e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 5.99
y[1] (analytic) = 22.233164999636086074556190524624
y[1] (numeric) = 22.233164999636086074556190524617
absolute error = 7e-30
relative error = 3.1484496247450943067261488038191e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6
y[1] (analytic) = 22.255409284924676045795375313951
y[1] (numeric) = 22.255409284924676045795375313943
absolute error = 8e-30
relative error = 3.5946317129377727314408190801245e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.01
y[1] (analytic) = 22.277675825624405559212836870774
y[1] (numeric) = 22.277675825624405559212836870766
absolute error = 8e-30
relative error = 3.5910388779417358884772151565104e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.02
y[1] (analytic) = 22.299964644001817170083208774851
y[1] (numeric) = 22.299964644001817170083208774843
absolute error = 8e-30
relative error = 3.5874496339848762404993032962747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.03
y[1] (analytic) = 22.322275762345731113219695260907
y[1] (numeric) = 22.322275762345731113219695260899
absolute error = 8e-30
relative error = 3.5838639774779495315437624797458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.04
y[1] (analytic) = 22.344609202967267591796163433588
y[1] (numeric) = 22.344609202967267591796163433579
absolute error = 9e-30
relative error = 4.0278171429397113253640604907498e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.05
y[1] (analytic) = 22.366964988199869088469205701403
y[1] (numeric) = 22.366964988199869088469205701394
absolute error = 9e-30
relative error = 4.0237913390342080188924802462757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.06
y[1] (analytic) = 22.389343140399322698822483553591
y[1] (numeric) = 22.389343140399322698822483553582
absolute error = 9e-30
relative error = 4.0197695589203790625850156099804e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.07
y[1] (analytic) = 22.4117436819437824871556861261
y[1] (numeric) = 22.41174368194378248715568612609
absolute error = 1.0e-29
relative error = 4.4619464428627155638492847596753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.08
y[1] (analytic) = 22.434166635233791864640459347508
y[1] (numeric) = 22.434166635233791864640459347498
absolute error = 1.0e-29
relative error = 4.4574867266496024164245266575167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.09
y[1] (analytic) = 22.456612022692305989865683822685
y[1] (numeric) = 22.456612022692305989865683822676
absolute error = 9e-30
relative error = 4.0077283211312286382576089190933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.1
y[1] (analytic) = 22.479079866764714191794502001334
y[1] (numeric) = 22.479079866764714191794502001325
absolute error = 9e-30
relative error = 4.0037225960064702103330089519522e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.11
y[1] (analytic) = 22.501570189918862415155517590301
y[1] (numeric) = 22.501570189918862415155517590292
absolute error = 9e-30
relative error = 3.9997208746046414324394079755251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.12
y[1] (analytic) = 22.524083014645075688290612602742
y[1] (numeric) = 22.524083014645075688290612602733
absolute error = 9e-30
relative error = 3.9957231529240205692712334945865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.13
y[1] (analytic) = 22.546618363456180613481849893817
y[1] (numeric) = 22.546618363456180613481849893807
absolute error = 1.0e-29
relative error = 4.4352549188520951189601531678970e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
bytes used=68027552, alloc=4324584, time=6.64
x[1] = 6.14
y[1] (analytic) = 22.569176258887527879779951511698
y[1] (numeric) = 22.569176258887527879779951511688
absolute error = 1.0e-29
relative error = 4.4308218808216780620807236848834e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.15
y[1] (analytic) = 22.591756723497014798356865694248
y[1] (numeric) = 22.591756723497014798356865694238
absolute error = 1.0e-29
relative error = 4.4263932736135110620483992612097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.16
y[1] (analytic) = 22.614359779865107860404957865805
y[1] (numeric) = 22.614359779865107860404957865795
absolute error = 1.0e-29
relative error = 4.4219690927989865416455668822811e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.17
y[1] (analytic) = 22.636985450594865317605383535152
y[1] (numeric) = 22.636985450594865317605383535142
absolute error = 1.0e-29
relative error = 4.4175493339539233176659593121639e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.18
y[1] (analytic) = 22.659633758311959785188223564922
y[1] (numeric) = 22.659633758311959785188223564912
absolute error = 1.0e-29
relative error = 4.4131339926585621767331032055404e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.19
y[1] (analytic) = 22.682304725664700867606984874462
y[1] (numeric) = 22.682304725664700867606984874452
absolute error = 1.0e-29
relative error = 4.4087230644975614555407374179554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.2
y[1] (analytic) = 22.704998375324057806850092252533
y[1] (numeric) = 22.704998375324057806850092252523
absolute error = 1.0e-29
relative error = 4.4043165450599926255107817544049e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.21
y[1] (analytic) = 22.727714729983682153412019593238
y[1] (numeric) = 22.727714729983682153412019593228
absolute error = 1.0e-29
relative error = 4.3999144299393358818644408138652e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.22
y[1] (analytic) = 22.750453812359930459946731528186
y[1] (numeric) = 22.750453812359930459946731528176
absolute error = 1.0e-29
relative error = 4.3955167147334757371020320005023e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.23
y[1] (analytic) = 22.773215645191886997626129110234
y[1] (numeric) = 22.773215645191886997626129110223
absolute error = 1.1e-29
relative error = 4.8302357345491662807758442991214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.24
y[1] (analytic) = 22.796000251241386495226215909137
y[1] (numeric) = 22.796000251241386495226215909127
absolute error = 1.0e-29
relative error = 4.3867344664796784723306338719236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.25
y[1] (analytic) = 22.818807653293036900963723607183
y[1] (numeric) = 22.818807653293036900963723607172
absolute error = 1.1e-29
relative error = 4.8205849171144416033373676644433e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.26
y[1] (analytic) = 22.841637874154242167105958933306
y[1] (numeric) = 22.841637874154242167105958933296
absolute error = 1.0e-29
relative error = 4.3779697651695961063416285980333e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.27
y[1] (analytic) = 22.864490936655225057376656547464
y[1] (numeric) = 22.864490936655225057376656547454
absolute error = 1.0e-29
relative error = 4.3735939836598298464349544576436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.28
y[1] (analytic) = 22.887366863649049977180645282991
y[1] (numeric) = 22.887366863649049977180645282981
absolute error = 1.0e-29
relative error = 4.3692225757444117125355806104227e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.29
y[1] (analytic) = 22.91026567801164582667015797353
y[1] (numeric) = 22.910265678011645826670157973519
absolute error = 1.1e-29
relative error = 4.8013410907571267674355048689540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.3
y[1] (analytic) = 22.933187402641828876675637932731
y[1] (numeric) = 22.933187402641828876675637932721
absolute error = 1.0e-29
relative error = 4.3604928632153559272541260496991e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.31
y[1] (analytic) = 22.956132060461325667523918019455
y[1] (numeric) = 22.956132060461325667523918019445
absolute error = 1.0e-29
relative error = 4.3561345498720050193401917175579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.32
y[1] (analytic) = 22.979099674414795930766671108543
y[1] (numeric) = 22.979099674414795930766671108533
absolute error = 1.0e-29
relative error = 4.3517805926635669946558664333257e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.33
y[1] (analytic) = 23.002090267469855533842053697532
y[1] (numeric) = 23.002090267469855533842053697522
absolute error = 1.0e-29
relative error = 4.3474309872360842819333460485160e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.34
y[1] (analytic) = 23.025103862617099447692487312864
y[1] (numeric) = 23.025103862617099447692487312854
absolute error = 1.0e-29
relative error = 4.3430857292399510912227868014783e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.35
y[1] (analytic) = 23.048140482870124737361545335286
y[1] (numeric) = 23.048140482870124737361545335276
absolute error = 1.0e-29
relative error = 4.3387448143299090642861529003929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.36
y[1] (analytic) = 23.071200151265553575592935843244
y[1] (numeric) = 23.071200151265553575592935843234
absolute error = 1.0e-29
relative error = 4.3344082381650429293384961803596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.37
y[1] (analytic) = 23.094282890863056279454594075168
y[1] (numeric) = 23.094282890863056279454594075157
absolute error = 1.1e-29
relative error = 4.7630835960496537761455548330484e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.38
y[1] (analytic) = 23.117388724745374370010921136662
y[1] (numeric) = 23.117388724745374370010921136651
absolute error = 1.1e-29
relative error = 4.7583228932017533033187749390741e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.39
y[1] (analytic) = 23.140517676018343655066228626768
y[1] (numeric) = 23.140517676018343655066228626757
absolute error = 1.1e-29
relative error = 4.7535669486771425591662827404781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.4
y[1] (analytic) = 23.163669767810917335002471928655
y[1] (numeric) = 23.163669767810917335002471928644
absolute error = 1.1e-29
relative error = 4.7488157577198766227486104895826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.41
y[1] (analytic) = 23.186845023275189131734378004407
y[1] (numeric) = 23.186845023275189131734378004396
absolute error = 1.1e-29
relative error = 4.7440693155787641408672287988008e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.42
y[1] (analytic) = 23.210043465586416440805096650958
y[1] (numeric) = 23.210043465586416440805096650946
absolute error = 1.2e-29
relative error = 5.1701755827353046293157791012537e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.43
y[1] (analytic) = 23.233265117943043506645527314753
y[1] (numeric) = 23.233265117943043506645527314741
absolute error = 1.2e-29
relative error = 5.1650079913788801427878910971082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.44
y[1] (analytic) = 23.256510003566724621020496726403
y[1] (numeric) = 23.256510003566724621020496726391
absolute error = 1.2e-29
relative error = 5.1598455650308774524871080322091e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.45
y[1] (analytic) = 23.279778145702347344684985803432
y[1] (numeric) = 23.27977814570234734468498580342
bytes used=72029108, alloc=4324584, time=7.04
absolute error = 1.2e-29
relative error = 5.1546882985288697802085295988090e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.46
y[1] (analytic) = 23.303069567618055752273627479285
y[1] (numeric) = 23.303069567618055752273627479273
absolute error = 1.2e-29
relative error = 5.1495361867155901941722606919495e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.47
y[1] (analytic) = 23.326384292605273700446720350032
y[1] (numeric) = 23.326384292605273700446720350021
absolute error = 1.1e-29
relative error = 4.7156901224023492474430457025322e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.48
y[1] (analytic) = 23.349722343978728119316026286723
y[1] (numeric) = 23.349722343978728119316026286712
absolute error = 1.1e-29
relative error = 4.7109767893392561934340658823897e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.49
y[1] (analytic) = 23.37308374507647232717364344112
y[1] (numeric) = 23.373083745076472327173643441108
absolute error = 1.2e-29
relative error = 5.1341107279127400655565205249452e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.5
y[1] (analytic) = 23.396468519259909368547269375638
y[1] (numeric) = 23.396468519259909368547269375626
absolute error = 1.2e-29
relative error = 5.1289791833847200390454100941166e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.51
y[1] (analytic) = 23.419876689913815375605192374698
y[1] (numeric) = 23.419876689913815375605192374686
absolute error = 1.2e-29
relative error = 5.1238527678363108122005346000207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.52
y[1] (analytic) = 23.443308280446362952934372344421
y[1] (numeric) = 23.443308280446362952934372344409
absolute error = 1.2e-29
relative error = 5.1187314761410964094113572569697e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.53
y[1] (analytic) = 23.466763314289144585714996080705
y[1] (numeric) = 23.466763314289144585714996080692
absolute error = 1.3e-29
relative error = 5.5397499117759334344132492083954e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.54
y[1] (analytic) = 23.490241814897196071314915082181
y[1] (numeric) = 23.490241814897196071314915082168
absolute error = 1.3e-29
relative error = 5.5342129308160525137389986572502e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.55
y[1] (analytic) = 23.513743805749019974327397504452
y[1] (numeric) = 23.513743805749019974327397504439
absolute error = 1.3e-29
relative error = 5.5286814840695635935435359967842e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.56
y[1] (analytic) = 23.5372693103466091050756492953
y[1] (numeric) = 23.537269310346609105075649295287
absolute error = 1.3e-29
relative error = 5.5231555660050194663840301256615e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.57
y[1] (analytic) = 23.560818352215470021607583017364
y[1] (numeric) = 23.560818352215470021607583017351
absolute error = 1.3e-29
relative error = 5.5176351710965016072231664892595e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.58
y[1] (analytic) = 23.584390954904646555204336354993
y[1] (numeric) = 23.58439095490464655520433635498
absolute error = 1.3e-29
relative error = 5.5121202938236146475101615491291e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.59
y[1] (analytic) = 23.607987141986743359426065815772
y[1] (numeric) = 23.607987141986743359426065815759
absolute error = 1.3e-29
relative error = 5.5066109286714808547849341992482e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.6
y[1] (analytic) = 23.631606937057949482718564674462
y[1] (numeric) = 23.631606937057949482718564674449
absolute error = 1.3e-29
relative error = 5.5011070701307346177999137327810e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.61
y[1] (analytic) = 23.655250363738061964604277767948
y[1] (numeric) = 23.655250363738061964604277767935
absolute error = 1.3e-29
relative error = 5.4956087126975169371539694806914e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.62
y[1] (analytic) = 23.678917445670509455481309334171
y[1] (numeric) = 23.678917445670509455481309334158
absolute error = 1.3e-29
relative error = 5.4901158508734699214329527556793e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.63
y[1] (analytic) = 23.702608206522375860054043696015
y[1] (numeric) = 23.702608206522375860054043696002
absolute error = 1.3e-29
relative error = 5.4846284791657312888513472415270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.64
y[1] (analytic) = 23.726322669984424004419022222751
y[1] (numeric) = 23.726322669984424004419022222738
absolute error = 1.3e-29
relative error = 5.4791465920869288743895294690437e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.65
y[1] (analytic) = 23.750060859771119326829743656881
y[1] (numeric) = 23.750060859771119326829743656868
absolute error = 1.3e-29
relative error = 5.4736701841551751424211465154125e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.66
y[1] (analytic) = 23.773822799620653592164078573154
y[1] (numeric) = 23.773822799620653592164078573141
absolute error = 1.3e-29
relative error = 5.4681992498940617048251235538616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.67
y[1] (analytic) = 23.79760851329496863011801243915
y[1] (numeric) = 23.797608513294968630118012439137
absolute error = 1.3e-29
relative error = 5.4627337838326538445768193652083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.68
y[1] (analytic) = 23.82141802457978009714945547315
y[1] (numeric) = 23.821418024579780097149455473137
absolute error = 1.3e-29
relative error = 5.4572737805054850448128534019765e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.69
y[1] (analytic) = 23.845251357284601262195881245086
y[1] (numeric) = 23.845251357284601262195881245073
absolute error = 1.3e-29
relative error = 5.4518192344525515233641334694571e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.7
y[1] (analytic) = 23.869108535242766816189579740184
y[1] (numeric) = 23.869108535242766816189579740171
absolute error = 1.3e-29
relative error = 5.4463701402193067727516185562865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.71
y[1] (analytic) = 23.892989582311456705394334402544
y[1] (numeric) = 23.892989582311456705394334402532
absolute error = 1.2e-29
relative error = 5.0223936852522979436670985937055e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.72
y[1] (analytic) = 23.916894522371719988587356497323
y[1] (numeric) = 23.916894522371719988587356497311
absolute error = 1.2e-29
relative error = 5.0173738019270318822209330237646e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.73
y[1] (analytic) = 23.940823379328498718110333975428
y[1] (numeric) = 23.940823379328498718110333975416
absolute error = 1.2e-29
relative error = 5.0123589359759858623040807437790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.74
y[1] (analytic) = 23.964776177110651844813475893779
y[1] (numeric) = 23.964776177110651844813475893767
absolute error = 1.2e-29
relative error = 5.0073490823842935149650119862113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.75
y[1] (analytic) = 23.988752939670979146916457337163
y[1] (numeric) = 23.988752939670979146916457337151
absolute error = 1.2e-29
relative error = 5.0023442361421008310235661880367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.76
y[1] (analytic) = 24.012753690986245182810193704622
y[1] (numeric) = 24.01275369098624518281019370461
absolute error = 1.2e-29
relative error = 4.9973443922445611512165253227350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=76032612, alloc=4324584, time=7.44
TOP MAIN SOLVE Loop
x[1] = 6.77
y[1] (analytic) = 24.03677845505720326782339716415
y[1] (numeric) = 24.036778455057203267823397164138
absolute error = 1.2e-29
relative error = 4.9923495456918301613505375665032e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.78
y[1] (analytic) = 24.060827255908619474977892044249
y[1] (numeric) = 24.060827255908619474977892044237
absolute error = 1.2e-29
relative error = 4.9873596914890608924573864511969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.79
y[1] (analytic) = 24.084900117589296659756689919656
y[1] (numeric) = 24.084900117589296659756689919644
absolute error = 1.2e-29
relative error = 4.9823748246463987259466056588529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.8
y[1] (analytic) = 24.108997064172098508908849161329
y[1] (numeric) = 24.108997064172098508908849161317
absolute error = 1.2e-29
relative error = 4.9773949401789764037504446099908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 6.81
y[1] (analytic) = 24.133118119753973613315167757546
y[1] (numeric) = 24.133118119753973613315167757534
absolute error = 1.2e-29
relative error = 4.9724200331069090434561949902431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.82
y[1] (analytic) = 24.157263308455979564938782273816
y[1] (numeric) = 24.157263308455979564938782273805
absolute error = 1.1e-29
relative error = 4.5534959235840150618858189016250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.83
y[1] (analytic) = 24.181432654423307077884769904222
y[1] (numeric) = 24.18143265442330707788476990421
absolute error = 1.2e-29
relative error = 4.9624851312541816828634198719431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.84
y[1] (analytic) = 24.205626181825304133592874675782
y[1] (numeric) = 24.20562618182530413359287467577
absolute error = 1.2e-29
relative error = 4.9575251265386190019290184563855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.85
y[1] (analytic) = 24.2298439148555001501875030006
y[1] (numeric) = 24.229843914855500150187503000588
absolute error = 1.2e-29
relative error = 4.9525700793485959867212680914718e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.86
y[1] (analytic) = 24.254085877731630176009157927788
y[1] (numeric) = 24.254085877731630176009157927776
absolute error = 1.2e-29
relative error = 4.9476199847290650342965406368467e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.87
y[1] (analytic) = 24.278352094695659107351505628623
y[1] (numeric) = 24.278352094695659107351505628611
absolute error = 1.2e-29
relative error = 4.9426748377299311126159849566069e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.88
y[1] (analytic) = 24.302642590013805930428291854023
y[1] (numeric) = 24.302642590013805930428291854011
absolute error = 1.2e-29
relative error = 4.9377346334060468104500823725171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.89
y[1] (analytic) = 24.326957387976567987594350333277
y[1] (numeric) = 24.326957387976567987594350333264
absolute error = 1.3e-29
relative error = 5.3438659807186413415833919504307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.9
y[1] (analytic) = 24.351296512898745267844969337052
y[1] (numeric) = 24.35129651289874526784496933704
absolute error = 1.2e-29
relative error = 4.9278690330281458578465601906822e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.91
y[1] (analytic) = 24.375659989119464721617906906091
y[1] (numeric) = 24.375659989119464721617906906079
absolute error = 1.2e-29
relative error = 4.9229436271085280073745957598897e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.92
y[1] (analytic) = 24.400047841002204599922369549609
y[1] (numeric) = 24.400047841002204599922369549597
absolute error = 1.2e-29
relative error = 4.9180231441329475107465725913463e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.93
y[1] (analytic) = 24.424460092934818817819293544427
y[1] (numeric) = 24.424460092934818817819293544414
absolute error = 1.3e-29
relative error = 5.3225332107793310642035434593106e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.94
y[1] (analytic) = 24.448896769329561342277292317131
y[1] (numeric) = 24.448896769329561342277292317118
absolute error = 1.3e-29
relative error = 5.3172133379482899822117139072001e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.95
y[1] (analytic) = 24.473357894623110604428657767256
y[1] (numeric) = 24.473357894623110604428657767243
absolute error = 1.3e-29
relative error = 5.3118987823310299496361322949489e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.96
y[1] (analytic) = 24.49784349327659393624982778951
y[1] (numeric) = 24.497843493276593936249827789497
absolute error = 1.3e-29
relative error = 5.3065895386129949063371165126514e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.97
y[1] (analytic) = 24.522353589775612031690756677561
y[1] (numeric) = 24.522353589775612031690756677548
absolute error = 1.3e-29
relative error = 5.3012856014849406918426320104719e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 6.98
y[1] (analytic) = 24.546888208630263432277649540782
y[1] (numeric) = 24.546888208630263432277649540769
absolute error = 1.3e-29
relative error = 5.2959869656429297361036888895824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 6.99
y[1] (analytic) = 24.571447374375169037213546338735
y[1] (numeric) = 24.571447374375169037213546338722
absolute error = 1.3e-29
relative error = 5.2906936257883257555563298583605e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7
y[1] (analytic) = 24.596031111569496638001265636025
y[1] (numeric) = 24.596031111569496638001265636011
absolute error = 1.4e-29
relative error = 5.6919752363683875663683593550387e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.01
y[1] (analytic) = 24.620639444796985477613242702496
y[1] (numeric) = 24.620639444796985477613242702482
absolute error = 1.4e-29
relative error = 5.6862861061712119418106690238233e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.02
y[1] (analytic) = 24.645272398665970834232821130679
y[1] (numeric) = 24.645272398665970834232821130665
absolute error = 1.4e-29
relative error = 5.6806026622606163456562300104046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.03
y[1] (analytic) = 24.669929997809408629591581713805
y[1] (numeric) = 24.669929997809408629591581713791
absolute error = 1.4e-29
relative error = 5.6749248989531563936891044900327e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.04
y[1] (analytic) = 24.694612266884900061927316923782
y[1] (numeric) = 24.694612266884900061927316923768
absolute error = 1.4e-29
relative error = 5.6692528105710683053023824356879e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.05
y[1] (analytic) = 24.719319230574716263587283949159
y[1] (numeric) = 24.719319230574716263587283949145
absolute error = 1.4e-29
relative error = 5.6635863914422632257339278641726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.06
y[1] (analytic) = 24.744050913585822983301393898375
y[1] (numeric) = 24.744050913585822983301393898361
absolute error = 1.4e-29
relative error = 5.6579256359003215539770513998890e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.07
y[1] (analytic) = 24.768807340649905293150019443555
y[1] (numeric) = 24.76880734064990529315001944354
absolute error = 1.5e-29
relative error = 6.0560041481619506532433254283926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
bytes used=80033660, alloc=4324584, time=7.84
TOP MAIN SOLVE Loop
x[1] = 7.08
y[1] (analytic) = 24.793588536523392320251127874703
y[1] (numeric) = 24.793588536523392320251127874688
absolute error = 1.5e-29
relative error = 6.0499511710067810419196323777818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.09
y[1] (analytic) = 24.818394525987482003191471253503
y[1] (numeric) = 24.818394525987482003191471253489
absolute error = 1.4e-29
relative error = 5.6409772942164008266586125277471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.1
y[1] (analytic) = 24.843225333848165873226590099968
y[1] (numeric) = 24.843225333848165873226590099953
absolute error = 1.5e-29
relative error = 6.0378633605045396200534809748910e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.11
y[1] (analytic) = 24.868080984936253860274411814005
y[1] (numeric) = 24.86808098493625386027441181399
absolute error = 1.5e-29
relative error = 6.0318285150696562999520253257556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.12
y[1] (analytic) = 24.892961504107399123727249827578
y[1] (numeric) = 24.892961504107399123727249827563
absolute error = 1.5e-29
relative error = 6.0257997014637907018998805128450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.13
y[1] (analytic) = 24.917866916242122908107034301518
y[1] (numeric) = 24.917866916242122908107034301504
absolute error = 1.4e-29
relative error = 5.6184584527475868031216113874981e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 7.14
y[1] (analytic) = 24.942797246245839423588630024294
y[1] (numeric) = 24.94279724624583942358863002428
absolute error = 1.4e-29
relative error = 5.6128428025878899036101398794998e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.15
y[1] (analytic) = 24.967752519048880751416122038129
y[1] (numeric) = 24.967752519048880751416122038115
absolute error = 1.4e-29
relative error = 5.6072327652714633289043788694190e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.16
y[1] (analytic) = 24.992732759606521774236974410829
y[1] (numeric) = 24.992732759606521774236974410815
absolute error = 1.4e-29
relative error = 5.6016283351882692950746283658427e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.17
y[1] (analytic) = 25.017737992899005131378992489557
y[1] (numeric) = 25.017737992899005131378992489542
absolute error = 1.5e-29
relative error = 5.9957459000720113413117843267743e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.18
y[1] (analytic) = 25.042768243931566199095043915592
y[1] (numeric) = 25.042768243931566199095043915577
absolute error = 1.5e-29
relative error = 5.9897531510458481554204213767047e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.19
y[1] (analytic) = 25.067823537734458095800518646885
y[1] (numeric) = 25.06782353773445809580051864687
absolute error = 1.5e-29
relative error = 5.9837663917733351614897725378973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 7.2
y[1] (analytic) = 25.092903899362976712328533227943
y[1] (numeric) = 25.092903899362976712328533227927
absolute error = 1.6e-29
relative error = 6.3763046573522267606509026208706e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.21
y[1] (analytic) = 25.118009353897485767227909564335
y[1] (numeric) = 25.11800935389748576722790956432
absolute error = 1.5e-29
relative error = 5.9718108185482044312612185895140e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.22
y[1] (analytic) = 25.143139926443441887128983501903
y[1] (numeric) = 25.143139926443441887128983501887
absolute error = 1.6e-29
relative error = 6.3635647921493466384371000326014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.23
y[1] (analytic) = 25.168295642131419712202323578543
y[1] (numeric) = 25.168295642131419712202323578527
absolute error = 1.6e-29
relative error = 6.3572044080792643299592276882240e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.24
y[1] (analytic) = 25.193476526117137026735465409403
y[1] (numeric) = 25.193476526117137026735465409388
absolute error = 1.5e-29
relative error = 5.9539222323882373760600163842663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.25
y[1] (analytic) = 25.218682603581479914852792284304
y[1] (numeric) = 25.218682603581479914852792284288
absolute error = 1.6e-29
relative error = 6.3445027051998858573047508235910e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.26
y[1] (analytic) = 25.243913899730527941403717699362
y[1] (numeric) = 25.243913899730527941403717699346
absolute error = 1.6e-29
relative error = 6.3381613736888857552743984181438e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.27
y[1] (analytic) = 25.269170439795579358044350713106
y[1] (numeric) = 25.26917043979557935804435071309
absolute error = 1.6e-29
relative error = 6.3318263803397875222618813650383e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.28
y[1] (analytic) = 25.294452249033176334537850210844
y[1] (numeric) = 25.294452249033176334537850210829
absolute error = 1.5e-29
relative error = 5.9301541113914974511745343403443e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.29
y[1] (analytic) = 25.319759352725130215298699379741
y[1] (numeric) = 25.319759352725130215298699379725
absolute error = 1.6e-29
relative error = 6.3191753827936529826685454409499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.3
y[1] (analytic) = 25.345091776178546801206156940979
y[1] (numeric) = 25.345091776178546801206156940963
absolute error = 1.6e-29
relative error = 6.3128593659456180757033563237590e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.31
y[1] (analytic) = 25.370449544725851656712166954577
y[1] (numeric) = 25.370449544725851656712166954561
absolute error = 1.6e-29
relative error = 6.3065496619574751859876074322046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.32
y[1] (analytic) = 25.395832683724815442269034306862
y[1] (numeric) = 25.395832683724815442269034306846
absolute error = 1.6e-29
relative error = 6.3002462645195197995697258450083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.33
y[1] (analytic) = 25.421241218558579272102198310405
y[1] (numeric) = 25.421241218558579272102198310389
absolute error = 1.6e-29
relative error = 6.2939491673283539532111878052351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.34
y[1] (analytic) = 25.446675174635680097353462191288
y[1] (numeric) = 25.446675174635680097353462191271
absolute error = 1.7e-29
relative error = 6.6806370118423099266747820860010e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 7.35
y[1] (analytic) = 25.472134577390076114620061609054
y[1] (numeric) = 25.472134577390076114620061609038
absolute error = 1.6e-29
relative error = 6.2813738485042939671926098712913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 7.36
y[1] (analytic) = 25.497619452281172199914980750537
y[1] (numeric) = 25.497619452281172199914980750521
absolute error = 1.6e-29
relative error = 6.2750956142960799555293136887689e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.37
y[1] (analytic) = 25.523129824793845368073949959983
y[1] (numeric) = 25.523129824793845368073949959967
absolute error = 1.6e-29
relative error = 6.2688236551840031645979285303519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.38
y[1] (analytic) = 25.548665720438470257634584314605
y[1] (numeric) = 25.548665720438470257634584314589
absolute error = 1.6e-29
relative error = 6.2625579648961039596583867028138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=84034376, alloc=4324584, time=8.25
x[1] = 7.39
y[1] (analytic) = 25.574227164750944641213148026824
y[1] (numeric) = 25.574227164750944641213148026808
absolute error = 1.6e-29
relative error = 6.2562985371666915306706085369831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.4
y[1] (analytic) = 25.599814183292714961404455052082
y[1] (numeric) = 25.599814183292714961404455052066
absolute error = 1.6e-29
relative error = 6.2500453657363376266031702067465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.41
y[1] (analytic) = 25.625426801650801892230441804265
y[1] (numeric) = 25.625426801650801892230441804249
absolute error = 1.6e-29
relative error = 6.2437984443518702960045310785861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.42
y[1] (analytic) = 25.651065045437825926162973429434
y[1] (numeric) = 25.651065045437825926162973429418
absolute error = 1.6e-29
relative error = 6.2375577667663676338305611623589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.000e+17
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 7.43
y[1] (analytic) = 25.676728940292032986746470662803
y[1] (numeric) = 25.676728940292032986746470662787
absolute error = 1.6e-29
relative error = 6.2313233267391515345221154903237e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.44
y[1] (analytic) = 25.702418511877320066845969893721
y[1] (numeric) = 25.702418511877320066845969893705
absolute error = 1.6e-29
relative error = 6.2250951180357814513264085014709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.45
y[1] (analytic) = 25.728133785883260892546254688867
y[1] (numeric) = 25.728133785883260892546254688851
absolute error = 1.6e-29
relative error = 6.2188731344280481618559477520064e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.46
y[1] (analytic) = 25.753874788025131612727722674912
y[1] (numeric) = 25.753874788025131612727722674896
absolute error = 1.6e-29
relative error = 6.2126573696939675398787925104073e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.47
y[1] (analytic) = 25.77964154404393651434467735867
y[1] (numeric) = 25.779641544043936514344677358654
absolute error = 1.6e-29
relative error = 6.2064478176177743333339090267862e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.48
y[1] (analytic) = 25.80543407970643376343176016516
y[1] (numeric) = 25.805434079706433763431760165144
absolute error = 1.6e-29
relative error = 6.2002444719899159485654004914033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.49
y[1] (analytic) = 25.83125242080516117186426370217
y[1] (numeric) = 25.831252420805161171864263702154
absolute error = 1.6e-29
relative error = 6.1940473266070462407693959160352e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.5
y[1] (analytic) = 25.857096593158461989898093013769
y[1] (numeric) = 25.857096593158461989898093013753
absolute error = 1.6e-29
relative error = 6.1878563752720193106473883845753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.51
y[1] (analytic) = 25.88296662261051072451516736489
y[1] (numeric) = 25.882966622610510724515167364875
absolute error = 1.5e-29
relative error = 5.7953171360567656005560806178295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.000e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.52
y[1] (analytic) = 25.908862535031338983600080904531
y[1] (numeric) = 25.908862535031338983600080904515
absolute error = 1.6e-29
relative error = 6.1754930299878742370737116605616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.53
y[1] (analytic) = 25.934784356316861345973866386383
y[1] (numeric) = 25.934784356316861345973866386367
absolute error = 1.6e-29
relative error = 6.1693206236754097791981608729487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.54
y[1] (analytic) = 25.960732112388901257310731982824
y[1] (numeric) = 25.960732112388901257310731982808
absolute error = 1.6e-29
relative error = 6.1631543866840831068014992363497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.55
y[1] (analytic) = 25.986705829195216951963667111146
y[1] (numeric) = 25.98670582919521695196366711113
absolute error = 1.6e-29
relative error = 6.1569943128476567147039546151110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.732e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.56
y[1] (analytic) = 26.012705532709527400724839099806
y[1] (numeric) = 26.01270553270952740072483909979
absolute error = 1.6e-29
relative error = 6.1508403960060562531396314315055e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.57
y[1] (analytic) = 26.038731248931538284546728457248
y[1] (numeric) = 26.038731248931538284546728457232
absolute error = 1.6e-29
relative error = 6.1446926300053643676816475602909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.58
y[1] (analytic) = 26.064783003886967994249976466592
y[1] (numeric) = 26.064783003886967994249976466576
absolute error = 1.6e-29
relative error = 6.1385510086978145453242670753648e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.59
y[1] (analytic) = 26.090860823627573656243944816215
y[1] (numeric) = 26.090860823627573656243944816199
absolute error = 1.6e-29
relative error = 6.1324155259417849667158749301356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.6
y[1] (analytic) = 26.116964734231177184286012988948
y[1] (numeric) = 26.116964734231177184286012988932
absolute error = 1.6e-29
relative error = 6.1262861756017923645366458040713e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.61
y[1] (analytic) = 26.14309476180169135730566517135
y[1] (numeric) = 26.143094761801691357305665171334
absolute error = 1.6e-29
relative error = 6.1201629515484858880147654925859e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.62
y[1] (analytic) = 26.169250932469145923319444509332
y[1] (numeric) = 26.169250932469145923319444509316
absolute error = 1.6e-29
relative error = 6.1140458476586409735750693559702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.63
y[1] (analytic) = 26.195433272389713729462878627251
y[1] (numeric) = 26.195433272389713729462878627235
absolute error = 1.6e-29
relative error = 6.1079348578151532216139684754963e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.64
y[1] (analytic) = 26.221641807745736878165506444582
y[1] (numeric) = 26.221641807745736878165506444566
absolute error = 1.6e-29
relative error = 6.1018299759070322793945402911118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.65
y[1] (analytic) = 26.247876564745752909495162467371
y[1] (numeric) = 26.247876564745752909495162467355
absolute error = 1.6e-29
relative error = 6.0957311958293957300556666153042e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.66
y[1] (analytic) = 26.274137569624521009697700900936
y[1] (numeric) = 26.274137569624521009697700900919
absolute error = 1.7e-29
relative error = 6.4702409184511794244621772837502e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.67
y[1] (analytic) = 26.300424848643048245958368125726
y[1] (numeric) = 26.30042484864304824595836812571
absolute error = 1.6e-29
relative error = 6.0835519167765491987584097954167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.68
y[1] (analytic) = 26.326738428088615827411058299901
y[1] (numeric) = 26.326738428088615827411058299884
absolute error = 1.7e-29
relative error = 6.4573133684734378458268867304669e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.69
y[1] (analytic) = 26.353078334274805392421713100058
y[1] (numeric) = 26.353078334274805392421713100042
absolute error = 1.6e-29
relative error = 6.0713969719394811772951704927785e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.7
y[1] (analytic) = 26.379444593541525322172152885726
y[1] (numeric) = 26.379444593541525322172152885709
absolute error = 1.7e-29
relative error = 6.4444116477577799132489109715846e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=88035908, alloc=4390108, time=8.64
TOP MAIN SOLVE Loop
x[1] = 7.71
y[1] (analytic) = 26.405837232255037080570652873613
y[1] (numeric) = 26.405837232255037080570652873596
absolute error = 1.7e-29
relative error = 6.4379704572420458677234975022817e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.72
y[1] (analytic) = 26.432256276807981580515604234421
y[1] (numeric) = 26.432256276807981580515604234404
absolute error = 1.7e-29
relative error = 6.4315357046973055617999385118879e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.73
y[1] (analytic) = 26.458701753619405576538626378044
y[1] (numeric) = 26.458701753619405576538626378028
absolute error = 1.6e-29
relative error = 6.0471598905306408607139119756920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.74
y[1] (analytic) = 26.485173689134788083853523072498
y[1] (numeric) = 26.485173689134788083853523072482
absolute error = 1.6e-29
relative error = 6.0411157532124474180293589329984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.75
y[1] (analytic) = 26.51167210982606682383750144771
y[1] (numeric) = 26.511672109826066823837501447694
absolute error = 1.6e-29
relative error = 6.0350776570105106141217725010072e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.76
y[1] (analytic) = 26.538197042191664695971099367612
y[1] (numeric) = 26.538197042191664695971099367596
absolute error = 1.6e-29
relative error = 6.0290455958867337438796485049085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.77
y[1] (analytic) = 26.564748512756516276263293112661
y[1] (numeric) = 26.564748512756516276263293112645
absolute error = 1.6e-29
relative error = 6.0230195638090551808543396321134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.78
y[1] (analytic) = 26.591326548072094342188283800101
y[1] (numeric) = 26.591326548072094342188283800085
absolute error = 1.6e-29
relative error = 6.0169995547514423451979263117881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.79
y[1] (analytic) = 26.617931174716436424160487480972
y[1] (numeric) = 26.617931174716436424160487480957
absolute error = 1.5e-29
relative error = 5.6352989650255178227782512789391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.8
y[1] (analytic) = 26.644562419294171383574280391061
y[1] (numeric) = 26.644562419294171383574280391046
absolute error = 1.5e-29
relative error = 5.6296664827709930807140084871624e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.81
y[1] (analytic) = 26.671220308436546017435077397755
y[1] (numeric) = 26.671220308436546017435077397739
absolute error = 1.6e-29
relative error = 5.9989756055289815984341851963187e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.82
y[1] (analytic) = 26.697904868801451689608348276095
y[1] (numeric) = 26.69790486880145168960834827608
absolute error = 1.5e-29
relative error = 5.6184184016359462697551415722565e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.83
y[1] (analytic) = 26.724616127073450988713203065274
y[1] (numeric) = 26.724616127073450988713203065259
absolute error = 1.5e-29
relative error = 5.6128027915073421284735806583557e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.84
y[1] (analytic) = 26.751354109963804412687204401361
y[1] (numeric) = 26.751354109963804412687204401346
absolute error = 1.5e-29
relative error = 5.6071927941819972281156982823568e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.85
y[1] (analytic) = 26.778118844210497080049091393319
y[1] (numeric) = 26.778118844210497080049091393304
absolute error = 1.5e-29
relative error = 5.6015884040499137758368013909760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 7.86
y[1] (analytic) = 26.804910356578265467886126307243
y[1] (numeric) = 26.804910356578265467886126307228
absolute error = 1.5e-29
relative error = 5.5959896155067011725209111306115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.87
y[1] (analytic) = 26.831728673858624176592802048403
y[1] (numeric) = 26.831728673858624176592802048388
absolute error = 1.5e-29
relative error = 5.5903964229535704083896966987986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.88
y[1] (analytic) = 26.858573822869892721387675182026
y[1] (numeric) = 26.858573822869892721387675182011
absolute error = 1.5e-29
relative error = 5.5848088207973284642129990001132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.89
y[1] (analytic) = 26.885445830457222350635116011892
y[1] (numeric) = 26.885445830457222350635116011877
absolute error = 1.5e-29
relative error = 5.5792268034503727181153453165779e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.9
y[1] (analytic) = 26.91234472349262289099879404071
y[1] (numeric) = 26.912344723492622890998794040695
absolute error = 1.5e-29
relative error = 5.5736503653306853579728617986230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.91
y[1] (analytic) = 26.939270528874989619453743968019
y[1] (numeric) = 26.939270528874989619453743968004
absolute error = 1.5e-29
relative error = 5.5680795008618277993949961730455e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.92
y[1] (analytic) = 26.966223273530130162183884239901
y[1] (numeric) = 26.966223273530130162183884239886
absolute error = 1.5e-29
relative error = 5.5625142044729351092854686492260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.93
y[1] (analytic) = 26.993202984410791420391887050278
y[1] (numeric) = 26.993202984410791420391887050263
absolute error = 1.5e-29
relative error = 5.5569544705987104349768745840894e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.94
y[1] (analytic) = 27.0202096884966865230483256059
y[1] (numeric) = 27.020209688496686523048325605886
absolute error = 1.4e-29
relative error = 5.1813069407674581430044768372834e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.95
y[1] (analytic) = 27.047243412794521806607051406423
y[1] (numeric) = 27.047243412794521806607051406408
absolute error = 1.5e-29
relative error = 5.5458516681608847390158609374380e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.96
y[1] (analytic) = 27.074304184338023821713781257191
y[1] (numeric) = 27.074304184338023821713781257176
absolute error = 1.5e-29
relative error = 5.5403085884944803543041780683167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.97
y[1] (analytic) = 27.10139203018796636693490072558
y[1] (numeric) = 27.101392030187966366934900725566
absolute error = 1.4e-29
relative error = 5.1657863125279844127059062037732e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.98
y[1] (analytic) = 27.128506977432197549533517771941
y[1] (numeric) = 27.128506977432197549533517771926
absolute error = 1.5e-29
relative error = 5.5292390445512823266993417732904e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 7.99
y[1] (analytic) = 27.155649053185666873319827333453
y[1] (numeric) = 27.155649053185666873319827333438
absolute error = 1.5e-29
relative error = 5.5237125692049438181461347273132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8
y[1] (analytic) = 27.182818284590452353602874713527
y[1] (numeric) = 27.182818284590452353602874713512
absolute error = 1.5e-29
relative error = 5.5181916175716348239328565524218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.01
y[1] (analytic) = 27.210014698815787659270832730755
y[1] (numeric) = 27.21001469881578765927083273074
absolute error = 1.5e-29
relative error = 5.5126761841304032506711949236115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.225e+17
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 8.02
y[1] (analytic) = 27.237238323058089282026934709967
y[1] (numeric) = 27.237238323058089282026934709952
absolute error = 1.5e-29
relative error = 5.5071662633658151975101078226075e-29 %
Correct digits = 31
bytes used=92037132, alloc=4390108, time=9.04
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.03
y[1] (analytic) = 27.26448918454098373280823255358
y[1] (numeric) = 27.264489184540983732808232553565
absolute error = 1.5e-29
relative error = 5.5016618497679494407014630673159e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.04
y[1] (analytic) = 27.291767310515334765414376314268
y[1] (numeric) = 27.291767310515334765414376314253
absolute error = 1.5e-29
relative error = 5.4961629378323919236783554035742e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.05
y[1] (analytic) = 27.319072728259270627373638900002
y[1] (numeric) = 27.319072728259270627373638899987
absolute error = 1.5e-29
relative error = 5.4906695220602302526405912370591e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.06
y[1] (analytic) = 27.346405465078211338073436779749
y[1] (numeric) = 27.346405465078211338073436779734
absolute error = 1.5e-29
relative error = 5.4851815969580481976418365903789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.07
y[1] (analytic) = 27.373765548304895994182624822638
y[1] (numeric) = 27.373765548304895994182624822622
absolute error = 1.6e-29
relative error = 5.8450124341737815457844579968400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.08
y[1] (analytic) = 27.401153005299410102392870695142
y[1] (numeric) = 27.401153005299410102392870695127
absolute error = 1.5e-29
relative error = 5.4742221968174058802358625401281e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.09
y[1] (analytic) = 27.428567863449212939506441559956
y[1] (numeric) = 27.42856786344921293950644155994
absolute error = 1.6e-29
relative error = 5.8333340915408475348298135832300e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.1
y[1] (analytic) = 27.456010150169164939897763166604
y[1] (numeric) = 27.456010150169164939897763166588
absolute error = 1.6e-29
relative error = 5.8275036731443731161127407301975e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.11
y[1] (analytic) = 27.48347989290155511037613879765
y[1] (numeric) = 27.483479892901555110376138797634
absolute error = 1.6e-29
relative error = 5.8216790822520574670910668648244e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 8.12
y[1] (analytic) = 27.510977119116128472477042935493
y[1] (numeric) = 27.510977119116128472477042935477
absolute error = 1.6e-29
relative error = 5.8158603130393092100665524263798e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.13
y[1] (analytic) = 27.538501856310113532209431943337
y[1] (numeric) = 27.53850185631011353220943194332
absolute error = 1.7e-29
relative error = 6.1731753196678185628555829458764e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.14
y[1] (analytic) = 27.566054132008249777286541509929
y[1] (numeric) = 27.566054132008249777286541509912
absolute error = 1.7e-29
relative error = 6.1670052299072051891278034887151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.15
y[1] (analytic) = 27.593633973762815201867668091167
y[1] (numeric) = 27.59363397376281520186766809115
absolute error = 1.7e-29
relative error = 6.1608413071523356397248359968453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.16
y[1] (analytic) = 27.621241409153653858838459092636
y[1] (numeric) = 27.621241409153653858838459092619
absolute error = 1.7e-29
relative error = 6.1546835452392866461168843728291e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.17
y[1] (analytic) = 27.648876465788203439657264075669
y[1] (numeric) = 27.648876465788203439657264075653
absolute error = 1.6e-29
relative error = 5.7868535887155725008076346507337e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.18
y[1] (analytic) = 27.676539171301522881795126835586
y[1] (numeric) = 27.67653917130152288179512683557
absolute error = 1.6e-29
relative error = 5.7810696275894167586576013945993e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.19
y[1] (analytic) = 27.704229553356320003797025794385
y[1] (numeric) = 27.704229553356320003797025794369
absolute error = 1.6e-29
relative error = 5.7752914475333703617426844411597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.2
y[1] (analytic) = 27.731947639642979167991997771454
y[1] (numeric) = 27.731947639642979167991997771439
absolute error = 1.5e-29
relative error = 5.4089241025961744742201245198103e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.21
y[1] (analytic) = 27.759693457879588970879807844716
y[1] (numeric) = 27.759693457879588970879807844701
absolute error = 1.5e-29
relative error = 5.4035178820543675741711977334728e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.22
y[1] (analytic) = 27.787467035811969961221855691182
y[1] (numeric) = 27.787467035811969961221855691167
absolute error = 1.5e-29
relative error = 5.3981170650308930216616927544602e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.23
y[1] (analytic) = 27.815268401213702385864036500145
y[1] (numeric) = 27.81526840121370238586403650013
absolute error = 1.5e-29
relative error = 5.3927216461249333431489567814517e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.24
y[1] (analytic) = 27.84309758188615396331930228417
y[1] (numeric) = 27.843097581886153963319302284156
absolute error = 1.4e-29
relative error = 5.0281761786116645708513838743879e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.25
y[1] (analytic) = 27.87095460565850768513769717277
y[1] (numeric) = 27.870954605658507685137697172756
absolute error = 1.4e-29
relative error = 5.0231505156833223144571637324867e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.26
y[1] (analytic) = 27.898839500387789645091668061106
y[1] (numeric) = 27.898839500387789645091668061092
absolute error = 1.4e-29
relative error = 5.0181298759059143372755181874015e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.27
y[1] (analytic) = 27.926752293958896896204479801354
y[1] (numeric) = 27.92675229395889689620447980134
absolute error = 1.4e-29
relative error = 5.0131142542588004435118079939335e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.28
y[1] (analytic) = 27.95469301428462533564959196747
y[1] (numeric) = 27.954693014284625335649591967456
absolute error = 1.4e-29
relative error = 5.0081036457263585680836548632652e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.29
y[1] (analytic) = 27.982661689305697617548882095049
y[1] (numeric) = 27.982661689305697617548882095035
absolute error = 1.4e-29
relative error = 5.0030980452979797609984584120635e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.3
y[1] (analytic) = 28.010658346990791093697628196836
y[1] (numeric) = 28.010658346990791093697628196822
absolute error = 1.4e-29
relative error = 4.9980974479680631767440286191188e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.31
y[1] (analytic) = 28.038683015336565782244191281195
y[1] (numeric) = 28.038683015336565782244191281182
absolute error = 1.3e-29
relative error = 4.6364517166834388494953715240421e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.32
y[1] (analytic) = 28.066735722367692364352366555551
y[1] (numeric) = 28.066735722367692364352366555537
absolute error = 1.4e-29
relative error = 4.9881112426062237884762841562071e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.33
y[1] (analytic) = 28.094816496136880208874399979479
y[1] (numeric) = 28.094816496136880208874399979466
absolute error = 1.3e-29
relative error = 4.6271880799746594482655038024854e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=96039776, alloc=4390108, time=9.43
x[1] = 8.34
y[1] (analytic) = 28.122925364724905425062694842819
y[1] (numeric) = 28.122925364724905425062694842806
absolute error = 1.3e-29
relative error = 4.6225632047177195237677098665450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.35
y[1] (analytic) = 28.151062356240638943348261082825
y[1] (numeric) = 28.151062356240638943348261082812
absolute error = 1.3e-29
relative error = 4.6179429520243695306026732951839e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.36
y[1] (analytic) = 28.179227498821074624213988121168
y[1] (numeric) = 28.179227498821074624213988121155
absolute error = 1.3e-29
relative error = 4.6133273172743563903993303101639e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.37
y[1] (analytic) = 28.20742082063135739519085009639
y[1] (numeric) = 28.207420820631357395190850096377
absolute error = 1.3e-29
relative error = 4.6087162958520449685082987191724e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.38
y[1] (analytic) = 28.235642349864811416005180490368
y[1] (numeric) = 28.235642349864811416005180490355
absolute error = 1.3e-29
relative error = 4.6041098831464134583663586301663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.39
y[1] (analytic) = 28.263892114742968271905181298406
y[1] (numeric) = 28.263892114742968271905181298393
absolute error = 1.3e-29
relative error = 4.5995080745510487704742616363220e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.4
y[1] (analytic) = 28.292170143515595195194860071813
y[1] (numeric) = 28.2921701435155951951948600718
absolute error = 1.3e-29
relative error = 4.5949108654641419259832574490165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.41
y[1] (analytic) = 28.32047646446072331500361636926
y[1] (numeric) = 28.320476464460723315003616369247
absolute error = 1.3e-29
relative error = 4.5903182512884834548857315649831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.42
y[1] (analytic) = 28.34881110588467593531972738885
y[1] (numeric) = 28.348811105884675935319727388837
absolute error = 1.3e-29
relative error = 4.5857302274314587988053521578949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.43
y[1] (analytic) = 28.377174096122096841316010816751
y[1] (numeric) = 28.377174096122096841316010816738
absolute error = 1.3e-29
relative error = 4.5811467893050437183821289841402e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 8.44
y[1] (analytic) = 28.405565463535978633995971220407
y[1] (numeric) = 28.405565463535978633995971220394
absolute error = 1.3e-29
relative error = 4.5765679323257997052477916874664e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.45
y[1] (analytic) = 28.43398523651769109318876463484
y[1] (numeric) = 28.433985236517691093188764634827
absolute error = 1.3e-29
relative error = 4.5719936519148693985868994774876e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.46
y[1] (analytic) = 28.462433443487009568921344339362
y[1] (numeric) = 28.462433443487009568921344339349
absolute error = 1.3e-29
relative error = 4.5674239434979720062790987427848e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.47
y[1] (analytic) = 28.490910112892143401196179199226
y[1] (numeric) = 28.490910112892143401196179199212
absolute error = 1.4e-29
relative error = 4.9138479411596601714347151051247e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.48
y[1] (analytic) = 28.519415273209764368202964352279
y[1] (numeric) = 28.519415273209764368202964352265
absolute error = 1.4e-29
relative error = 4.9089365493237011369557287022739e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.49
y[1] (analytic) = 28.547948952945035162992772454722
y[1] (numeric) = 28.547948952945035162992772454709
absolute error = 1.3e-29
relative error = 4.5537422045372218967917712963958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.5
y[1] (analytic) = 28.576511180631637898643122162488
y[1] (numeric) = 28.576511180631637898643122162474
absolute error = 1.4e-29
relative error = 4.8991284875561749654051842300753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.51
y[1] (analytic) = 28.605101984831802641942469015675
y[1] (numeric) = 28.605101984831802641942469015661
absolute error = 1.4e-29
relative error = 4.8942318078165452434689467383857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.52
y[1] (analytic) = 28.633721394136335975622652412928
y[1] (numeric) = 28.633721394136335975622652412914
absolute error = 1.4e-29
relative error = 4.8893400223091311907421991830110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 8.53
y[1] (analytic) = 28.662369437164649589167860910568
y[1] (numeric) = 28.662369437164649589167860910555
absolute error = 1.3e-29
relative error = 4.5355636171319935427219341812341e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.54
y[1] (analytic) = 28.691046142564788898228706657838
y[1] (numeric) = 28.691046142564788898228706657825
absolute error = 1.3e-29
relative error = 4.5310303205409317896813002019757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.55
y[1] (analytic) = 28.719751539013461692670028384709
y[1] (numeric) = 28.719751539013461692670028384696
absolute error = 1.3e-29
relative error = 4.5265015549805681634450871772262e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.56
y[1] (analytic) = 28.748485655216066813281070992449
y[1] (numeric) = 28.748485655216066813281070992436
absolute error = 1.3e-29
relative error = 4.5219773159221367262525262605659e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.57
y[1] (analytic) = 28.777248519906722857176718459518
y[1] (numeric) = 28.777248519906722857176718459505
absolute error = 1.3e-29
relative error = 4.5174575988413980426522461561499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.58
y[1] (analytic) = 28.806040161848296911918485466416
y[1] (numeric) = 28.806040161848296911918485466402
absolute error = 1.4e-29
relative error = 4.8600918145431450133595730048610e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.59
y[1] (analytic) = 28.834860609832433318384001862864
y[1] (numeric) = 28.83486060983243331838400186285
absolute error = 1.4e-29
relative error = 4.8552341519646963008264526159356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.6
y[1] (analytic) = 28.863709892679582462413752849215
y[1] (numeric) = 28.863709892679582462413752849201
absolute error = 1.4e-29
relative error = 4.8503813446208041558491168732618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.61
y[1] (analytic) = 28.892588039239029595263866521213
y[1] (numeric) = 28.892588039239029595263866521199
absolute error = 1.4e-29
relative error = 4.8455333876586608301347953284715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.62
y[1] (analytic) = 28.921495078388923682893769233309
y[1] (numeric) = 28.921495078388923682893769233294
absolute error = 1.5e-29
relative error = 5.1864538673896167402254306665195e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 8.63
y[1] (analytic) = 28.950431039036306284117558070577
y[1] (numeric) = 28.950431039036306284117558070562
absolute error = 1.5e-29
relative error = 5.1812700058849678994265339435343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.64
y[1] (analytic) = 28.979395950117140457647968583027
y[1] (numeric) = 28.979395950117140457647968583012
absolute error = 1.5e-29
relative error = 5.1760913256507567161104194780146e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.65
y[1] (analytic) = 29.008389840596339698061844828672
y[1] (numeric) = 29.008389840596339698061844828657
absolute error = 1.5e-29
relative error = 5.1709178215083025245092033843576e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=100041280, alloc=4390108, time=9.82
TOP MAIN SOLVE Loop
x[1] = 8.66
y[1] (analytic) = 29.037412739467796900716047693244
y[1] (numeric) = 29.037412739467796900716047693229
absolute error = 1.5e-29
relative error = 5.1657494882841007510433344859861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.67
y[1] (analytic) = 29.066464675754413355642766404877
y[1] (numeric) = 29.066464675754413355642766404862
absolute error = 1.5e-29
relative error = 5.1605863208098177408165896104022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.68
y[1] (analytic) = 29.095545678508127770453227141486
y[1] (numeric) = 29.095545678508127770453227141471
absolute error = 1.5e-29
relative error = 5.1554283139222855892819879984778e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 8.69
y[1] (analytic) = 29.124655776809945322278821636965
y[1] (numeric) = 29.12465577680994532227882163695
absolute error = 1.5e-29
relative error = 5.1502754624634969790734564934682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.7
y[1] (analytic) = 29.153794999769966738778707729755
y[1] (numeric) = 29.153794999769966738778707729741
absolute error = 1.4e-29
relative error = 4.8021192438618933538648768515826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.71
y[1] (analytic) = 29.182963376527417408242962863816
y[1] (numeric) = 29.182963376527417408242962863802
absolute error = 1.4e-29
relative error = 4.7973195248775002324382092189445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.72
y[1] (analytic) = 29.212160936250676518820400647562
y[1] (numeric) = 29.212160936250676518820400647548
absolute error = 1.4e-29
relative error = 4.7925246032130317651521730373420e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.73
y[1] (analytic) = 29.241387708137306226900189701024
y[1] (numeric) = 29.24138770813730622690018970101
absolute error = 1.4e-29
relative error = 4.7877344740735658879614823291396e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.74
y[1] (analytic) = 29.270643721414080854676443175278
y[1] (numeric) = 29.270643721414080854676443175264
absolute error = 1.4e-29
relative error = 4.7829491326689730622228183089092e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.75
y[1] (analytic) = 29.299929005337016116924976511169
y[1] (numeric) = 29.299929005337016116924976511155
absolute error = 1.4e-29
relative error = 4.7781685742139114845648915626357e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.76
y[1] (analytic) = 29.329243589191398377021460216515
y[1] (numeric) = 29.329243589191398377021460216501
absolute error = 1.4e-29
relative error = 4.7733927939278223015462398979318e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.77
y[1] (analytic) = 29.358587502291813932230223682388
y[1] (numeric) = 29.358587502291813932230223682374
absolute error = 1.4e-29
relative error = 4.7686217870349248290959765226572e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.78
y[1] (analytic) = 29.38796077398217832829299532972
y[1] (numeric) = 29.387960773982178328292995329706
absolute error = 1.4e-29
relative error = 4.7638555487642117767327079922954e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.79
y[1] (analytic) = 29.417363433635765703346893677405
y[1] (numeric) = 29.41736343363576570334689367739
absolute error = 1.5e-29
relative error = 5.0990293653744047963109065835063e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.8
y[1] (analytic) = 29.446795510655238161201013252344
y[1] (numeric) = 29.446795510655238161201013252329
absolute error = 1.5e-29
relative error = 5.0939328846740872682266532287147e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.81
y[1] (analytic) = 29.476257034472675174000978620467
y[1] (numeric) = 29.476257034472675174000978620452
absolute error = 1.5e-29
relative error = 5.0888414979070789086508740883365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.82
y[1] (analytic) = 29.505748034549603014310869205724
y[1] (numeric) = 29.505748034549603014310869205709
absolute error = 1.5e-29
relative error = 5.0837551999819925262929648598215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.83
y[1] (analytic) = 29.535268540377024216641946981439
y[1] (numeric) = 29.535268540377024216641946981424
absolute error = 1.5e-29
relative error = 5.0786739858125297722083686327895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.84
y[1] (analytic) = 29.564818581475447068457648565196
y[1] (numeric) = 29.564818581475447068457648565181
absolute error = 1.5e-29
relative error = 5.0735978503174760534998030862642e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 8.85
y[1] (analytic) = 29.594398187394915130684332724717
y[1] (numeric) = 29.594398187394915130684332724702
absolute error = 1.5e-29
relative error = 5.0685267884206954521022441568266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.86
y[1] (analytic) = 29.624007387715036787757303807931
y[1] (numeric) = 29.624007387715036787757303807916
absolute error = 1.5e-29
relative error = 5.0634607950511256486465849622513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.87
y[1] (analytic) = 29.653646212045014827231661145728
y[1] (numeric) = 29.653646212045014827231661145713
absolute error = 1.5e-29
relative error = 5.0583998651427728513968938438580e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.88
y[1] (analytic) = 29.683314690023676048987554040703
y[1] (numeric) = 29.683314690023676048987554040689
absolute error = 1.4e-29
relative error = 4.7164543940590596149057871001225e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.89
y[1] (analytic) = 29.713012851319500904059451549626
y[1] (numeric) = 29.713012851319500904059451549612
absolute error = 1.4e-29
relative error = 4.7117402971063183321133610358388e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.9
y[1] (analytic) = 29.742740725630653163119065891359
y[1] (numeric) = 29.742740725630653163119065891345
absolute error = 1.4e-29
relative error = 4.7070309118942668006771141125028e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.225e+17
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 8.91
y[1] (analytic) = 29.772498342685009614641597965635
y[1] (numeric) = 29.772498342685009614641597965621
absolute error = 1.4e-29
relative error = 4.7023262337135194160967341412807e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.92
y[1] (analytic) = 29.802285732240189792785003151405
y[1] (numeric) = 29.802285732240189792785003151391
absolute error = 1.4e-29
relative error = 4.6976262578593976055683084109601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.93
y[1] (analytic) = 29.832102924083585735012005266506
y[1] (numeric) = 29.832102924083585735012005266493
absolute error = 1.3e-29
relative error = 4.3577216239439304716406903397986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.94
y[1] (analytic) = 29.861949948032391769484616313138
y[1] (numeric) = 29.861949948032391769484616313124
absolute error = 1.4e-29
relative error = 4.6882403943358233505622044627304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.95
y[1] (analytic) = 29.891826833933634332260949406148
y[1] (numeric) = 29.891826833933634332260949406134
absolute error = 1.4e-29
relative error = 4.6835544972805066003549515356858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.96
y[1] (analytic) = 29.921733611664201814324142083434
y[1] (numeric) = 29.92173361166420181432414208342
absolute error = 1.4e-29
relative error = 4.6788732837800774268754155463122e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
bytes used=104042104, alloc=4390108, time=10.22
x[1] = 8.97
y[1] (analytic) = 29.951670311130874438473237029863
y[1] (numeric) = 29.951670311130874438473237029849
absolute error = 1.4e-29
relative error = 4.6741967491533219395932849759378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.98
y[1] (analytic) = 29.981636962270354166105897108083
y[1] (numeric) = 29.981636962270354166105897108069
absolute error = 1.4e-29
relative error = 4.6695248887237051220418406557672e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 8.99
y[1] (analytic) = 30.011633595049294633922861481429
y[1] (numeric) = 30.011633595049294633922861481415
absolute error = 1.4e-29
relative error = 4.6648576978193661552825495888978e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9
y[1] (analytic) = 30.041660239464331120584079535887
y[1] (numeric) = 30.041660239464331120584079535873
absolute error = 1.4e-29
relative error = 4.6601951717731137460438566900384e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.01
y[1] (analytic) = 30.071716925542110543346489259728
y[1] (numeric) = 30.071716925542110543346489259715
absolute error = 1.3e-29
relative error = 4.3229989269279627838488238255245e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.02
y[1] (analytic) = 30.101803683339321484713436721111
y[1] (numeric) = 30.101803683339321484713436721098
absolute error = 1.3e-29
relative error = 4.3186780887801785528280073770647e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.03
y[1] (analytic) = 30.131920542942724249125763295557
y[1] (numeric) = 30.131920542942724249125763295544
absolute error = 1.3e-29
relative error = 4.3143615693108429918384717663969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.04
y[1] (analytic) = 30.162067534469180949724617336901
y[1] (numeric) = 30.162067534469180949724617336888
absolute error = 1.3e-29
relative error = 4.3100493642034362718346882356901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.05
y[1] (analytic) = 30.192244688065685625216077057034
y[1] (numeric) = 30.19224468806568562521607705702
absolute error = 1.4e-29
relative error = 4.6369523513877339203717683537082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.06
y[1] (analytic) = 30.222452033909394386867701481565
y[1] (numeric) = 30.222452033909394386867701481552
absolute error = 1.3e-29
relative error = 4.3014378798298975378382920675755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.07
y[1] (analytic) = 30.252689602207655595667156480479
y[1] (numeric) = 30.252689602207655595667156480466
absolute error = 1.3e-29
relative error = 4.2971385919522804326832237180869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.08
y[1] (analytic) = 30.282957423198040069673093034912
y[1] (numeric) = 30.282957423198040069673093034899
absolute error = 1.3e-29
relative error = 4.2928436012136133747031872381598e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.09
y[1] (analytic) = 30.313255527148371321588485093454
y[1] (numeric) = 30.313255527148371321588485093441
absolute error = 1.3e-29
relative error = 4.2885529033189052673152178283066e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.1
y[1] (analytic) = 30.343583944356755826586664593838
y[1] (numeric) = 30.343583944356755826586664593824
absolute error = 1.4e-29
relative error = 4.6138254550526469242725027734257e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.11
y[1] (analytic) = 30.373942705151613320420321478555
y[1] (numeric) = 30.373942705151613320420321478541
absolute error = 1.4e-29
relative error = 4.6092139357415430987814068299575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.12
y[1] (analytic) = 30.404331839891707127843766815947
y[1] (numeric) = 30.404331839891707127843766815933
absolute error = 1.4e-29
relative error = 4.6046070256447591160075248354265e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.13
y[1] (analytic) = 30.434751378966174521378787451541
y[1] (numeric) = 30.434751378966174521378787451527
absolute error = 1.4e-29
relative error = 4.6000047201553844952576864869798e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.14
y[1] (analytic) = 30.465201352794557110454450958028
y[1] (numeric) = 30.465201352794557110454450958014
absolute error = 1.4e-29
relative error = 4.5954070146711133636318008027116e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.15
y[1] (analytic) = 30.495681791826831260951250026217
y[1] (numeric) = 30.495681791826831260951250026203
absolute error = 1.4e-29
relative error = 4.5908139045942398537165996960709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.16
y[1] (analytic) = 30.52619272654343854518000584364
y[1] (numeric) = 30.526192726543438545180005843626
absolute error = 1.4e-29
relative error = 4.5862253853316535058793874204249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.17
y[1] (analytic) = 30.556734187455316222325980442257
y[1] (numeric) = 30.556734187455316222325980442243
absolute error = 1.4e-29
relative error = 4.5816414522948346751571981771453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.18
y[1] (analytic) = 30.58730620510392774938867846191
y[1] (numeric) = 30.587306205103927749388678461896
absolute error = 1.4e-29
relative error = 4.5770621008998499427367687759926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.19
y[1] (analytic) = 30.617908810061293322647849271863
y[1] (numeric) = 30.617908810061293322647849271849
absolute error = 1.4e-29
relative error = 4.5724873265673475320207378273890e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.2
y[1] (analytic) = 30.648542032930020449686230918988
y[1] (numeric) = 30.648542032930020449686230918975
absolute error = 1.3e-29
relative error = 4.2416373300995132486129527086535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.21
y[1] (analytic) = 30.679205904343334551999607927883
y[1] (numeric) = 30.67920590434333455199960792787
absolute error = 1.3e-29
relative error = 4.2373978128813159296520452380107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.22
y[1] (analytic) = 30.709900454965109598224785565521
y[1] (numeric) = 30.709900454965109598224785565508
absolute error = 1.3e-29
relative error = 4.2331625330612846085032447454311e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.23
y[1] (analytic) = 30.740625715489898768016113800976
y[1] (numeric) = 30.740625715489898768016113800963
absolute error = 1.3e-29
relative error = 4.2289314864041391121952333148376e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.24
y[1] (analytic) = 30.771381716642965146601224839288
y[1] (numeric) = 30.771381716642965146601224839275
absolute error = 1.3e-29
relative error = 4.2247046686788324309952814565199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.25
y[1] (analytic) = 30.80216848918031245004667878777
y[1] (numeric) = 30.802168489180312450046678787758
absolute error = 1.2e-29
relative error = 3.8958296083001967575648176496697e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.26
y[1] (analytic) = 30.832986063888715781264242722967
y[1] (numeric) = 30.832986063888715781264242722955
absolute error = 1.2e-29
relative error = 3.8919357259575580699627746954351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.27
y[1] (analytic) = 30.863834471585752416788559167095
y[1] (numeric) = 30.863834471585752416788559167083
absolute error = 1.2e-29
relative error = 3.8880457355509696679067757665796e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.28
y[1] (analytic) = 30.894713743119832624356990754214
y[1] (numeric) = 30.894713743119832624356990754201
absolute error = 1.3e-29
relative error = 4.2078396026229775556960858513644e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=108042844, alloc=4390108, time=10.62
TOP MAIN SOLVE Loop
x[1] = 9.29
y[1] (analytic) = 30.925623909370230511322458668527
y[1] (numeric) = 30.925623909370230511322458668514
absolute error = 1.3e-29
relative error = 4.2036338662390245807826273433659e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.3
y[1] (analytic) = 30.956565001247114903930123270235
y[1] (numeric) = 30.956565001247114903930123270222
absolute error = 1.3e-29
relative error = 4.1994323334892881477276129643244e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.31
y[1] (analytic) = 30.987537049691580257488786188181
y[1] (numeric) = 30.987537049691580257488786188168
absolute error = 1.3e-29
relative error = 4.1952350001722351566668688435984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.32
y[1] (analytic) = 31.018540085675677597467924053276
y[1] (numeric) = 31.018540085675677597467924053263
absolute error = 1.3e-29
relative error = 4.1910418620905319407696158401019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.33
y[1] (analytic) = 31.049574140202445491551294972316
y[1] (numeric) = 31.049574140202445491551294972303
absolute error = 1.3e-29
relative error = 4.1868529150510400689044529337076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.34
y[1] (analytic) = 31.080639244305941052678089798371
y[1] (numeric) = 31.080639244305941052678089798359
absolute error = 1.2e-29
relative error = 3.8609244506444419869236092298149e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.35
y[1] (analytic) = 31.111735429051270973102631241492
y[1] (numeric) = 31.111735429051270973102631241479
absolute error = 1.3e-29
relative error = 4.1784875773470876566000434886736e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.36
y[1] (analytic) = 31.142862725534622589503654882003
y[1] (numeric) = 31.142862725534622589503654881991
absolute error = 1.2e-29
relative error = 3.8532103184467280447048179192682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.37
y[1] (analytic) = 31.174021164883294979174237198279
y[1] (numeric) = 31.174021164883294979174237198267
absolute error = 1.2e-29
relative error = 3.8493590340913993386082143228205e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.38
y[1] (analytic) = 31.20521077825573008732346680149
y[1] (numeric) = 31.205210778255730087323466801477
absolute error = 1.3e-29
relative error = 4.1659708990200442958279120833208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.39
y[1] (analytic) = 31.236431596841543885520986181606
y[1] (numeric) = 31.236431596841543885520986181593
absolute error = 1.3e-29
relative error = 4.1618070104123188257943782901157e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.4
y[1] (analytic) = 31.267683651861557561315562411795
y[1] (numeric) = 31.267683651861557561315562411782
absolute error = 1.3e-29
relative error = 4.1576472836119505853420985597598e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.41
y[1] (analytic) = 31.298966974567828739058876432372
y[1] (numeric) = 31.298966974567828739058876432359
absolute error = 1.3e-29
relative error = 4.1534917144592124274589208544896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.42
y[1] (analytic) = 31.330281596243682731965751740702
y[1] (numeric) = 31.330281596243682731965751740689
absolute error = 1.3e-29
relative error = 4.1493402987985348531092463530332e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.43
y[1] (analytic) = 31.361627548203743825442074549888
y[1] (numeric) = 31.361627548203743825442074549875
absolute error = 1.3e-29
relative error = 4.1451930324785018556641841175412e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.44
y[1] (analytic) = 31.393004861793966591711688746769
y[1] (numeric) = 31.393004861793966591711688746755
absolute error = 1.4e-29
relative error = 4.4595922122250657517532907066851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.45
y[1] (analytic) = 31.424413568391667235773580278727
y[1] (numeric) = 31.424413568391667235773580278713
absolute error = 1.4e-29
relative error = 4.4551348490658672090153362698724e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.46
y[1] (analytic) = 31.455853699405554972720696929117
y[1] (numeric) = 31.455853699405554972720696929103
absolute error = 1.4e-29
relative error = 4.4506819410418889933943883787985e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.47
y[1] (analytic) = 31.487325286275763436451780802733
y[1] (numeric) = 31.487325286275763436451780802719
absolute error = 1.4e-29
relative error = 4.4462334837002227098365503784749e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.48
y[1] (analytic) = 31.518828360473882119807622235773
y[1] (numeric) = 31.518828360473882119807622235759
absolute error = 1.4e-29
relative error = 4.4417894725924106459707478820473e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.49
y[1] (analytic) = 31.550362953502987846163175269177
y[1] (numeric) = 31.550362953502987846163175269163
absolute error = 1.4e-29
relative error = 4.4373499032744413236506456948988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.225e+17
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 9.5
y[1] (analytic) = 31.581929096897676272507006280068
y[1] (numeric) = 31.581929096897676272507006280054
absolute error = 1.4e-29
relative error = 4.4329147713067450549427993340134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.51
y[1] (analytic) = 31.613526822224093424039578853379
y[1] (numeric) = 31.613526822224093424039578853365
absolute error = 1.4e-29
relative error = 4.4284840722541895025565971303776e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.52
y[1] (analytic) = 31.645156161079967260321909494573
y[1] (numeric) = 31.645156161079967260321909494559
absolute error = 1.4e-29
relative error = 4.4240578016860752447115533439956e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.53
y[1] (analytic) = 31.676817145094639273006160334744
y[1] (numeric) = 31.676817145094639273006160334729
absolute error = 1.5e-29
relative error = 4.7353242376887121547544826697563e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.54
y[1] (analytic) = 31.708509805929096115179766561321
y[1] (numeric) = 31.708509805929096115179766561307
absolute error = 1.4e-29
relative error = 4.4152185283025109233033668547736e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.55
y[1] (analytic) = 31.740234175276001262354727921153
y[1] (numeric) = 31.740234175276001262354727921139
absolute error = 1.4e-29
relative error = 4.4108055166477867395697628931826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.56
y[1] (analytic) = 31.77199028485972670513372528788
y[1] (numeric) = 31.771990284859726705133725287865
absolute error = 1.5e-29
relative error = 4.7211395526417286829587907728726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.57
y[1] (analytic) = 31.803778166436384673584754962368
y[1] (numeric) = 31.803778166436384673584754962354
absolute error = 1.4e-29
relative error = 4.4019927213473898006553072149334e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.58
y[1] (analytic) = 31.835597851793859393356005083486
y[1] (numeric) = 31.835597851793859393356005083472
absolute error = 1.4e-29
relative error = 4.3975929288889210106778837374205e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.59
y[1] (analytic) = 31.867449372751838873562730266726
y[1] (numeric) = 31.867449372751838873562730266712
absolute error = 1.4e-29
relative error = 4.3931975340237475757110938840072e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.6
y[1] (analytic) = 31.899332761161846726477912360218
y[1] (numeric) = 31.899332761161846726477912360204
bytes used=112043836, alloc=4390108, time=11.01
absolute error = 1.4e-29
relative error = 4.3888065323564742642985850473539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.61
y[1] (analytic) = 31.931248048907274019058527011435
y[1] (numeric) = 31.931248048907274019058527011421
absolute error = 1.4e-29
relative error = 4.3844199194960990432502280116152e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.62
y[1] (analytic) = 31.963195267903411156339267573512
y[1] (numeric) = 31.963195267903411156339267573498
absolute error = 1.4e-29
relative error = 4.3800376910560086866397178454631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.63
y[1] (analytic) = 31.99517445009747979672560974756
y[1] (numeric) = 31.995174450097479796725609747546
absolute error = 1.4e-29
relative error = 4.3756598426539743891909824246674e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.64
y[1] (analytic) = 32.027185627468664799218132256705
y[1] (numeric) = 32.027185627468664799218132256691
absolute error = 1.4e-29
relative error = 4.3712863699121473840490119702775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.65
y[1] (analytic) = 32.059228832028146202600040778825
y[1] (numeric) = 32.059228832028146202600040778811
absolute error = 1.4e-29
relative error = 4.3669172684570545649307273728705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.66
y[1] (analytic) = 32.091304095819131236619874328181
y[1] (numeric) = 32.091304095819131236619874328168
absolute error = 1.3e-29
relative error = 4.0509416386396231046049730638408e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.67
y[1] (analytic) = 32.123411450916886365201405271318
y[1] (numeric) = 32.123411450916886365201405271304
absolute error = 1.4e-29
relative error = 4.3581921619350311260230156865817e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.68
y[1] (analytic) = 32.155550929428769361712776189791
y[1] (numeric) = 32.155550929428769361712776189778
absolute error = 1.3e-29
relative error = 4.0428478518470651673237784788923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.69
y[1] (analytic) = 32.187722563494261416326948861554
y[1] (numeric) = 32.18772256349426141632694886154
absolute error = 1.4e-29
relative error = 4.3494844881874663508971779068765e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.7
y[1] (analytic) = 32.219926385284999275505572724101
y[1] (numeric) = 32.219926385284999275505572724087
absolute error = 1.4e-29
relative error = 4.3451371777167900891955556164043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.71
y[1] (analytic) = 32.252162427004807413638412305939
y[1] (numeric) = 32.252162427004807413638412305926
absolute error = 1.3e-29
relative error = 4.0307374829276783791279805025828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.72
y[1] (analytic) = 32.284430720889730236870505268483
y[1] (numeric) = 32.28443072088973023687050526847
absolute error = 1.3e-29
relative error = 4.0267087601418704979113360986054e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.73
y[1] (analytic) = 32.316731299208064319149254888211
y[1] (numeric) = 32.316731299208064319149254888198
absolute error = 1.3e-29
relative error = 4.0226840640651583176397200641503e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.74
y[1] (analytic) = 32.349064194260390670523693028876
y[1] (numeric) = 32.349064194260390670523693028864
absolute error = 1.2e-29
relative error = 3.7095354375441650088088626663460e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.75
y[1] (analytic) = 32.381429438379607037728181905713
y[1] (numeric) = 32.381429438379607037728181905701
absolute error = 1.2e-29
relative error = 3.7058277562562382426941177972753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.76
y[1] (analytic) = 32.413827063930960237082855228031
y[1] (numeric) = 32.413827063930960237082855228019
absolute error = 1.2e-29
relative error = 3.7021237807963765518075976083494e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.77
y[1] (analytic) = 32.446257103312078519743131623343
y[1] (numeric) = 32.446257103312078519743131623331
absolute error = 1.2e-29
relative error = 3.6984235074606041676229792690863e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.78
y[1] (analytic) = 32.478719588953003969330665595226
y[1] (numeric) = 32.478719588953003969330665595214
absolute error = 1.2e-29
relative error = 3.6947269325486474460117570019651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.79
y[1] (analytic) = 32.511214553316224931978133648575
y[1] (numeric) = 32.511214553316224931978133648563
absolute error = 1.2e-29
relative error = 3.6910340523639311669692895977728e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.8
y[1] (analytic) = 32.543742028896708478820285629729
y[1] (numeric) = 32.543742028896708478820285629717
absolute error = 1.2e-29
relative error = 3.6873448632135748380392723630182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.81
y[1] (analytic) = 32.576302048221932900963723775236
y[1] (numeric) = 32.576302048221932900963723775224
absolute error = 1.2e-29
relative error = 3.6836593614083890014329369235754e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.82
y[1] (analytic) = 32.608894643851920236967904441737
y[1] (numeric) = 32.608894643851920236967904441725
absolute error = 1.2e-29
relative error = 3.6799775432628715448392860034506e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.83
y[1] (analytic) = 32.641519848379268832869890000679
y[1] (numeric) = 32.641519848379268832869890000667
absolute error = 1.2e-29
relative error = 3.6762994050952040159226739885989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.84
y[1] (analytic) = 32.674177694429185934785410925333
y[1] (numeric) = 32.674177694429185934785410925322
absolute error = 1.1e-29
relative error = 3.3665728646249772787953771253083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.85
y[1] (analytic) = 32.706868214659520314118830673888
y[1] (numeric) = 32.706868214659520314118830673876
absolute error = 1.2e-29
relative error = 3.6689541539845411444221660683731e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.225e+17
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 9.86
y[1] (analytic) = 32.739591441760794925414638581296
y[1] (numeric) = 32.739591441760794925414638581284
absolute error = 1.2e-29
relative error = 3.6652870336962940790711190371094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.87
y[1] (analytic) = 32.772347408456239596883128614104
y[1] (numeric) = 32.772347408456239596883128614092
absolute error = 1.2e-29
relative error = 3.6616235786953861506104737878579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.88
y[1] (analytic) = 32.805136147501823753632954516656
y[1] (numeric) = 32.805136147501823753632954516644
absolute error = 1.2e-29
relative error = 3.6579637853183620528443749413819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.89
y[1] (analytic) = 32.837957691686289173643284583956
y[1] (numeric) = 32.837957691686289173643284583945
absolute error = 1.1e-29
relative error = 3.3497820124133090951187720512469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.9
y[1] (analytic) = 32.870812073831182776508312036078
y[1] (numeric) = 32.870812073831182776508312036067
absolute error = 1.1e-29
relative error = 3.3464339047337445369496349176243e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.91
y[1] (analytic) = 32.903699326790889444986909741357
y[1] (numeric) = 32.903699326790889444986909741346
absolute error = 1.1e-29
relative error = 3.3430891434883635820263915289161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
bytes used=116047516, alloc=4390108, time=11.40
TOP MAIN SOLVE Loop
x[1] = 9.92
y[1] (analytic) = 32.936619483452664879390250840762
y[1] (numeric) = 32.936619483452664879390250840751
absolute error = 1.1e-29
relative error = 3.3397477253324047062379738891289e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.93
y[1] (analytic) = 32.969572576736668484840249663801
y[1] (numeric) = 32.96957257673666848484024966379
absolute error = 1.1e-29
relative error = 3.3364096469244494751739839315549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.94
y[1] (analytic) = 33.002558639595996291431710197145
y[1] (numeric) = 33.002558639595996291431710197134
absolute error = 1.1e-29
relative error = 3.3330749049264192027059806568282e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.95
y[1] (analytic) = 33.035577705016713907331102270859
y[1] (numeric) = 33.035577705016713907331102270848
absolute error = 1.1e-29
relative error = 3.3297434960035716129085158312502e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.96
y[1] (analytic) = 33.068629806017889504844918563765
y[1] (numeric) = 33.068629806017889504844918563754
absolute error = 1.1e-29
relative error = 3.3264154168244975053165801661432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.414e+17
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 9.97
y[1] (analytic) = 33.101714975651626839490598499039
y[1] (numeric) = 33.101714975651626839490598499028
absolute error = 1.1e-29
relative error = 3.3230906640611174235161252353979e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.98
y[1] (analytic) = 33.134833247003098302103038103722
y[1] (numeric) = 33.134833247003098302103038103711
absolute error = 1.1e-29
relative error = 3.3197692343886783270643297214616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
TOP MAIN SOLVE Loop
x[1] = 9.99
y[1] (analytic) = 33.167984653190578004009737941409
y[1] (numeric) = 33.167984653190578004009737941398
absolute error = 1.1e-29
relative error = 3.3164511244857502667362819097535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 190
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
Finished!
diff ( y , x , 1 ) = exp (0.1 * x + 0.2 ) ;
Iterations = 900
Total Elapsed Time = 11 Seconds
Elapsed Time(since restart) = 11 Seconds
Time to Timeout = 2 Minutes 48 Seconds
Percent Done = 100.1 %
> quit
bytes used=117105568, alloc=4390108, time=11.50