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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> 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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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 - 2 - 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 - 2 - 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 - 2 - 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_2, array_const_0D0, array_const_1,
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_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 - 12;
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 - 3;
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 - 3;
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_2,
> array_const_0D0,
> array_const_1,
> #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_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_2, array_const_0D0, array_const_1,
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_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_2,
> array_const_0D0,
> array_const_1,
> #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_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 diff $eq_no = 1 i = 1 order_d = 1
> array_tmp1[1] := array_y_higher[2,1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * expt(glob_h , (2)) * factorial_3(0,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[3,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2 order_d = 1
> array_tmp1[2] := array_y_higher[2,2];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * expt(glob_h , (2)) * factorial_3(1,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[3,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3 order_d = 1
> array_tmp1[3] := array_y_higher[2,3];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * expt(glob_h , (2)) * factorial_3(2,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp1[4] := array_y_higher[2,4];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * expt(glob_h , (2)) * factorial_3(3,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[3,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp1[5] := array_y_higher[2,5];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,7]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * expt(glob_h , (2)) * factorial_3(4,6);
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> temporary := temporary / glob_h * (6.0);
> array_y_higher[2,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[3,5] := 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 diff $eq_no = 1
> array_tmp1[kkk] := array_y_higher[2,kkk];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> 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_tmp2[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_2, array_const_0D0, array_const_1,
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_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_y_higher[2, 1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*expt(glob_h, 2)*factorial_3(0, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_y_higher[2, 2];
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 2)*factorial_3(1, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_y_higher[2, 3];
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 2)*factorial_3(2, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_y_higher[2, 4];
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 2)*factorial_3(3, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_y_higher[2, 5];
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 2)*factorial_3(4, 6);
array_y[7] := temporary;
array_y_higher[1, 7] := temporary;
temporary := temporary*6.0/glob_h;
array_y_higher[2, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[3, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_y_higher[2, kkk];
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 2;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[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(1.0 + exp(x));
> end;
exact_soln_y := proc(x) return 1.0 + exp(x) end proc
> exact_soln_yp := proc(x)
> return(exp(x));
> end;
exact_soln_yp := proc(x) return exp(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_1,
> #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_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/diffpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -5.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + exp(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"return(exp(x));");
> 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
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_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_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(3+ 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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_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 <=3) 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 <=3) 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_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_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2[1] := 2;
> 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_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_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 := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> glob_look_poles := true;
> glob_max_iter := 10000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := true;
> 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 := 2;
> #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 := 2;
> #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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> 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 := 2;
> calc_term := 2;
> #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 := 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 := 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 := 3;
> #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 := 3;
> #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 , 2 ) = diff ( y , x , 1 ) ;");
> 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,"2013-05-26T00:22:26-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"diff")
> ;
> logitem_str(html_log_file,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;")
> ;
> 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,"diff diffeq.mxt")
> ;
> logitem_str(html_log_file,"diff 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_2, array_const_0D0, array_const_1,
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_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/diffpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 2 ) = diff ( y , x , 1 ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -5.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0 + exp(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "return(exp(x));");
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;
Digits := 32;
max_terms := 30;
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_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 4, 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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 3 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_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_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
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_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_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 := -5.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
glob_look_poles := true;
glob_max_iter := 10000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := true;
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 := 2;
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 := 2;
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 := 3;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
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 := 2;
calc_term := 2;
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 := 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 := 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 := 3;
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 := 3;
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 , 2 ) = diff ( y , x , 1 ) ;");
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, "2013-05-26T00:22:26-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "diff");
logitem_str(html_log_file,
"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;");
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,
"diff diffeq.mxt");
logitem_str(html_log_file,
"diff 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/diffpostode.ode#################
diff ( y , x , 2 ) = diff ( y , x , 1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
glob_look_poles := true;
glob_max_iter := 10000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0 + exp(x));
end;
exact_soln_yp := proc(x)
return(exp(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 10
estimated_steps = 10000000
step_error = 1.0000000000000000000000000000000e-17
est_needed_step_err = 1.0000000000000000000000000000000e-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 = 1.6707388510135145318336278216148e-185
estimated_step_error = 1.6707388510135145318336278216148e-185
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1212138840850425077445713955376e-177
estimated_step_error = 1.1212138840850425077445713955376e-177
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 = 7.5243392848767301974381056101704e-170
estimated_step_error = 7.5243392848767301974381056101704e-170
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 = 5.0494989916234845162087581339859e-162
estimated_step_error = 5.0494989916234845162087581339859e-162
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 = 3.3886619129940291314972567327097e-154
estimated_step_error = 3.3886619129940291314972567327097e-154
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 = 2.2740931884165287534899973804413e-146
estimated_step_error = 2.2740931884165287534899973804413e-146
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 = 1.5261190094150109279521457218486e-138
estimated_step_error = 1.5261190094150109279521457218486e-138
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 = 1.0241623443297890615626508578016e-130
estimated_step_error = 1.0241623443297890615626508578016e-130
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 = 6.8730534396716051320554906013074e-123
estimated_step_error = 6.8730534396716051320554906013074e-123
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 = 4.6124499519984951434514169271136e-115
estimated_step_error = 4.6124499519984951434514169271136e-115
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 = 3.0953921145061884358451603243403e-107
estimated_step_error = 3.0953921145061884358451603243403e-107
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 = 2.0773218772353800142339251534024e-99
estimated_step_error = 2.0773218772353800142339251534024e-99
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 = 1.3941199885175437103096968951314e-91
estimated_step_error = 1.3941199885175437103096968951314e-91
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 = 9.3564906260931470770328224636127e-84
estimated_step_error = 9.3564906260931470770328224636127e-84
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 = 6.2799873957036472828680343021075e-76
estimated_step_error = 6.2799873957036472828680343021075e-76
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 = 4.2157076233574059713240087837619e-68
estimated_step_error = 4.2157076233574059713240087837619e-68
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 = 2.8308322136530815525163584828263e-60
estimated_step_error = 2.8308322136530815525163584828263e-60
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 = 1.9020502070240742375686819415174e-52
estimated_step_error = 1.9020502070240742375686819415174e-52
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (analytic) = 1.0067379469990854670966360484231
y[1] (numeric) = 1.0067379469990854670966360484231
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0068056644922305447989653325038
y[1] (numeric) = 1.0068056644922305447989653325038
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (analytic) = 1.0068740625574962515372906482734
y[1] (numeric) = 1.0068740625574962515372906482734
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0069431480347461124600022155601
y[1] (numeric) = 1.00694314803474611246000221556
absolute error = 1e-31
relative error = 9.9310472686735385727626713945250e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.96
y[1] (analytic) = 1.0070129278325854239761383024475
y[1] (numeric) = 1.0070129278325854239761383024474
absolute error = 1e-31
relative error = 9.9303591082223791072002433493796e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.95
y[1] (analytic) = 1.0070834089290521200422164000473
y[1] (numeric) = 1.0070834089290521200422164000473
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0071545983723145817706798693521
y[1] (numeric) = 1.007154598372314581770679869352
absolute error = 1e-31
relative error = 9.9289622627561122127996230791568e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=4000168, alloc=3079628, time=0.15
x[1] = -4.93
y[1] (analytic) = 1.0072265032813764601415024147785
y[1] (numeric) = 1.0072265032813764601415024147784
absolute error = 1e-31
relative error = 9.9282534439092526446011658340670e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (analytic) = 1.0072991308467885822998088990669
y[1] (numeric) = 1.0072991308467885822998088990668
absolute error = 1e-31
relative error = 9.9275376040416857170774081411481e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.91
y[1] (analytic) = 1.0073724883313680126307355188432
y[1] (numeric) = 1.007372488331368012630735518843
absolute error = 2e-31
relative error = 1.9853629349287075526147880025351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (analytic) = 1.0074465830709243405182360464201
y[1] (numeric) = 1.00744658307092434051823604642
absolute error = 1e-31
relative error = 9.9260845865571802696463205777188e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.89
y[1] (analytic) = 1.0075214224749932674172152602805
y[1] (numeric) = 1.0075214224749932674172152602804
absolute error = 1e-31
relative error = 9.9253472699715231166426641926472e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (analytic) = 1.0075970140275775665983081021806
y[1] (numeric) = 1.0075970140275775665983081021805
absolute error = 1e-31
relative error = 9.9246026544162660741430998839844e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.87
y[1] (analytic) = 1.0076733652878954896618965073037
y[1] (numeric) = 1.0076733652878954896618965073036
absolute error = 1e-31
relative error = 9.9238506687561084363750361143262e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (analytic) = 1.00775048389113669466263898332
y[1] (numeric) = 1.0077504838911366946626389833199
absolute error = 1e-31
relative error = 9.9230912411849166739567711237250e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.85
y[1] (analytic) = 1.0078283775492257714379553335143
y[1] (numeric) = 1.0078283775492257714379553335142
absolute error = 1e-31
relative error = 9.9223242992198499906928184684916e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.84
y[1] (analytic) = 1.0079070540515934404936356456817
y[1] (numeric) = 1.0079070540515934404936356456816
absolute error = 1e-31
relative error = 9.9215497696954436756552094551766e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.83
y[1] (analytic) = 1.0079865212659555025671047755709
y[1] (numeric) = 1.0079865212659555025671047755708
absolute error = 1e-31
relative error = 9.9207675787576501459388760495678e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.82
y[1] (analytic) = 1.0080667871390996167639477781226
y[1] (numeric) = 1.0080667871390996167639477781225
absolute error = 1e-31
relative error = 9.9199776518578375802789425893765e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.81
y[1] (analytic) = 1.0081478596976799859461655896795
y[1] (numeric) = 1.0081478596976799859461655896794
absolute error = 1e-31
relative error = 9.9191799137467460486663417203571e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.8
y[1] (analytic) = 1.0082297470490200288413620267661
y[1] (numeric) = 1.008229747049020028841362026766
absolute error = 1e-31
relative error = 9.9183742884684010481986457496691e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -4.79
y[1] (analytic) = 1.0083124573819231191407419157932
y[1] (numeric) = 1.0083124573819231191407419157931
absolute error = 1e-31
relative error = 9.9175606993539843606584427182949e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.78
y[1] (analytic) = 1.0083959989674914726605057716668
y[1] (numeric) = 1.0083959989674914726605057716666
absolute error = 2e-31
relative error = 1.9833478138031324305450216674911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.77
y[1] (analytic) = 1.0084803801599532644560395730107
y[1] (numeric) = 1.0084803801599532644560395730106
absolute error = 1e-31
relative error = 9.9159093193403702453006000972383e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -4.76
y[1] (analytic) = 1.0085656093974980586013003195423
y[1] (numeric) = 1.0085656093974980586013003195422
absolute error = 1e-31
relative error = 9.9150713714835564841691465355643e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.75
y[1] (analytic) = 1.0086516952031206341770715039573
y[1] (numeric) = 1.0086516952031206341770715039571
absolute error = 2e-31
relative error = 1.9828450291725760300235380162015e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.74
y[1] (analytic) = 1.008738646185473291851390514541
y[1] (numeric) = 1.0087386461854732918513905145409
absolute error = 1e-31
relative error = 9.9133705621518683527219827276012e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.73
y[1] (analytic) = 1.0088264710397267262835162690968
y[1] (numeric) = 1.0088264710397267262835162690966
absolute error = 2e-31
relative error = 1.9825015078547058716511393177356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.72
y[1] (analytic) = 1.0089151785484395504393948730148
y[1] (numeric) = 1.0089151785484395504393948730146
absolute error = 2e-31
relative error = 1.9823271990787845617220425764169e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=8001600, alloc=4193536, time=0.30
TOP MAIN SOLVE Loop
x[1] = -4.71
y[1] (analytic) = 1.009004777582436558771779454061
y[1] (numeric) = 1.0090047775824365587717794540609
absolute error = 1e-31
relative error = 9.9107558479156867947243605284125e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (analytic) = 1.0090952771016958170920540742914
y[1] (numeric) = 1.0090952771016958170920540742913
absolute error = 1e-31
relative error = 9.9098670134715217548198077183492e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.69
y[1] (analytic) = 1.0091866861562446678434881455062
y[1] (numeric) = 1.0091866861562446678434881455061
absolute error = 1e-31
relative error = 9.9089694079176311747226363268872e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.68
y[1] (analytic) = 1.0092790138870647403771953472374
y[1] (numeric) = 1.0092790138870647403771953472373
absolute error = 1e-31
relative error = 9.9080629463271190747284714613768e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.67
y[1] (analytic) = 1.0093722695270060567325788209032
y[1] (numeric) = 1.0093722695270060567325788209031
absolute error = 1e-31
relative error = 9.9071475429833442748410703508965e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.66
y[1] (analytic) = 1.0094664624017103243336024420067
y[1] (numeric) = 1.0094664624017103243336024420066
absolute error = 1e-31
relative error = 9.9062231113732314377862222560719e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.65
y[1] (analytic) = 1.0095616019305435079309272106497
y[1] (numeric) = 1.0095616019305435079309272106497
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0096576976275377740478841198775
y[1] (numeric) = 1.0096576976275377740478841198775
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0097547591023429021255130554615
y[1] (numeric) = 1.0097547591023429021255130554615
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0098527960611872575085750762749
y[1] (numeric) = 1.0098527960611872575085750762749
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0099518183078484223706374899795
y[1] (numeric) = 1.0099518183078484223706374899794
absolute error = 1e-31
relative error = 9.9014624447676873306209070173920e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.6
y[1] (analytic) = 1.0100518357446335816421330943316
y[1] (numeric) = 1.0100518357446335816421330943315
absolute error = 1e-31
relative error = 9.9004819813309567842705096155051e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -4.59
y[1] (analytic) = 1.0101528583733697619808033810288
y[1] (numeric) = 1.0101528583733697619808033810287
absolute error = 1e-31
relative error = 9.8994918611652624558191624573620e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.58
y[1] (analytic) = 1.0102548962964040228092479483096
y[1] (numeric) = 1.0102548962964040228092479483095
absolute error = 1e-31
relative error = 9.8984919911400727862257840773689e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.57
y[1] (analytic) = 1.0103579597176136994395173725574
y[1] (numeric) = 1.0103579597176136994395173725573
absolute error = 1e-31
relative error = 9.8974822772662803637833128948875e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.56
y[1] (analytic) = 1.0104620589434267993099038702723
y[1] (numeric) = 1.0104620589434267993099038702722
absolute error = 1e-31
relative error = 9.8964626246890825281234740145476e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.55
y[1] (analytic) = 1.0105672043838526533744037625093
y[1] (numeric) = 1.0105672043838526533744037625092
absolute error = 1e-31
relative error = 9.8954329376808193060881743383969e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.54
y[1] (analytic) = 1.0106734065535229257108495670498
y[1] (numeric) = 1.0106734065535229257108495670496
absolute error = 2e-31
relative error = 1.9788786239267537573432532382456e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.53
y[1] (analytic) = 1.0107806760727430854495400424133
y[1] (numeric) = 1.0107806760727430854495400424132
absolute error = 1e-31
relative error = 9.8933430730529000531222045416999e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.52
y[1] (analytic) = 1.0108890236685544461704372762439
y[1] (numeric) = 1.0108890236685544461704372762438
absolute error = 1e-31
relative error = 9.8922826995485837998281423503751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.51
y[1] (analytic) = 1.0109984601758068789737555735586
y[1] (numeric) = 1.0109984601758068789737555735584
absolute error = 2e-31
relative error = 1.9782423799658521550315608222319e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.5
y[1] (analytic) = 1.0111089965382423064961431342869
y[1] (numeric) = 1.0111089965382423064961431342867
absolute error = 2e-31
relative error = 1.9780261147388136399227292430062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=12003516, alloc=4259060, time=0.45
TOP MAIN SOLVE Loop
x[1] = -4.49
y[1] (analytic) = 1.0112206438095890862227610529593
y[1] (numeric) = 1.0112206438095890862227610529591
absolute error = 2e-31
relative error = 1.9778077240050848645486013421971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.48
y[1] (analytic) = 1.0113334131546673925345028375762
y[1] (numeric) = 1.011333413154667392534502837576
absolute error = 2e-31
relative error = 1.9775871873563142585717748215029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.47
y[1] (analytic) = 1.0114473158505057080294803243879
y[1] (numeric) = 1.0114473158505057080294803243878
absolute error = 1e-31
relative error = 9.8868224209890765261213281057043e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.46
y[1] (analytic) = 1.0115623632874685357688385497119
y[1] (numeric) = 1.0115623632874685357688385497118
absolute error = 1e-31
relative error = 9.8856979687352927739114428620900e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.45
y[1] (analytic) = 1.0116785669703954452190639236115
y[1] (numeric) = 1.0116785669703954452190639236114
absolute error = 1e-31
relative error = 9.8845624751607771001453689198422e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.44
y[1] (analytic) = 1.0117959385197515657963291443707
y[1] (numeric) = 1.0117959385197515657963291443706
absolute error = 1e-31
relative error = 9.8834158344516689931873516268457e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.43
y[1] (analytic) = 1.0119144896727896430631880360715
y[1] (numeric) = 1.0119144896727896430631880360714
absolute error = 1e-31
relative error = 9.8822579398320278503315847189528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.42
y[1] (analytic) = 1.01203423228472377378420836215
y[1] (numeric) = 1.0120342322847237737842083621499
absolute error = 1e-31
relative error = 9.8810886835561300864390753253886e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.41
y[1] (analytic) = 1.0121551783299149372150262940186
y[1] (numeric) = 1.0121551783299149372150262940186
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.4
y[1] (analytic) = 1.0122773399030684411789393862365
y[1] (numeric) = 1.0122773399030684411789393862365
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0124007292204434026766435925812
y[1] (numeric) = 1.0124007292204434026766435925812
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0125253586210743839781832005917
y[1] (numeric) = 1.0125253586210743839781832005916
absolute error = 1e-31
relative error = 9.8762958525983757508630990224003e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.37
y[1] (analytic) = 1.0126512405680053063617409130458
y[1] (numeric) = 1.0126512405680053063617409130457
absolute error = 1e-31
relative error = 9.8750681373687044488197366255369e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.36
y[1] (analytic) = 1.0127783876495357648916702202577
y[1] (numeric) = 1.0127783876495357648916702202576
absolute error = 1e-31
relative error = 9.8738283932066130497011202952860e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.35
y[1] (analytic) = 1.0129068125804798688682864655417
y[1] (numeric) = 1.0129068125804798688682864655416
absolute error = 1e-31
relative error = 9.8725765053588839767593044649357e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.34
y[1] (analytic) = 1.0130365282034377338345106201543
y[1] (numeric) = 1.0130365282034377338345106201542
absolute error = 1e-31
relative error = 9.8713123580394749436990192078239e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.33
y[1] (analytic) = 1.0131675474900797522896260122973
y[1] (numeric) = 1.0131675474900797522896260122972
absolute error = 1e-31
relative error = 9.8700358344214664064609992488146e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.32
y[1] (analytic) = 1.013299883542443771538289615015
y[1] (numeric) = 1.0132998835424437715382896150148
absolute error = 2e-31
relative error = 1.9737493633257943949513494633564e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.31
y[1] (analytic) = 1.0134335495942453083936637792599
y[1] (numeric) = 1.0134335495942453083936637792597
absolute error = 2e-31
relative error = 1.9734890371458024412706491471097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.3
y[1] (analytic) = 1.0135685590122009317572305745258
y[1] (numeric) = 1.0135685590122009317572305745256
absolute error = 2e-31
relative error = 1.9732261643446704449592628233718e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.29
y[1] (analytic) = 1.0137049252973649454146495409732
y[1] (numeric) = 1.013704925297364945414649540973
absolute error = 2e-31
relative error = 1.9729607207080607238653791729298e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.28
y[1] (analytic) = 1.0138426620864795047170523448676
y[1] (numeric) = 1.0138426620864795047170523448674
absolute error = 2e-31
relative error = 1.9726926818052982208382587002422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16007952, alloc=4259060, time=0.60
TOP MAIN SOLVE Loop
x[1] = -4.27
y[1] (analytic) = 1.0139817831533383021605675677785
y[1] (numeric) = 1.0139817831533383021605675677783
absolute error = 2e-31
relative error = 1.9724220229877168866760119287828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.455e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.26
y[1] (analytic) = 1.0141223024101639582337699904576
y[1] (numeric) = 1.0141223024101639582337699904574
absolute error = 2e-31
relative error = 1.9721487193869992172113456587938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.25
y[1] (analytic) = 1.014264233908999255273286945856
y[1] (numeric) = 1.0142642339089992552732869458558
absolute error = 2e-31
relative error = 1.9718727459135090515125449537487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.24
y[1] (analytic) = 1.0144075918431123534521066673262
y[1] (numeric) = 1.014407591843112353452106667326
absolute error = 2e-31
relative error = 1.9715940772546177421829098158680e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.23
y[1] (analytic) = 1.0145523905484161294233584800719
y[1] (numeric) = 1.0145523905484161294233584800717
absolute error = 2e-31
relative error = 1.9713126878730238128299309351177e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.22
y[1] (analytic) = 1.0146986445049017795546120000092
y[1] (numeric) = 1.014698644504901779554612000009
absolute error = 2e-31
relative error = 1.9710285520050662219468699321761e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.21
y[1] (analytic) = 1.0148463683380868311142134433043
y[1] (numeric) = 1.0148463683380868311142134433041
absolute error = 2e-31
relative error = 1.9707416436590313567053152769389e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -4.2
y[1] (analytic) = 1.0149955768204777062119843602287
y[1] (numeric) = 1.0149955768204777062119843602285
absolute error = 2e-31
relative error = 1.9704519366134538844989319982663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.19
y[1] (analytic) = 1.0151462848730469847518956705525
y[1] (numeric) = 1.0151462848730469847518956705523
absolute error = 2e-31
relative error = 1.9701594044154115945072348782972e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.18
y[1] (analytic) = 1.015298507566725514124243324443
y[1] (numeric) = 1.0152985075667255141242433244428
absolute error = 2e-31
relative error = 1.9698640203788143660650212096576e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.17
y[1] (analytic) = 1.0154522601239095148495382353233
y[1] (numeric) = 1.0154522601239095148495382353231
absolute error = 2e-31
relative error = 1.9695657575826874052293368973881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.16
y[1] (analytic) = 1.0156075579199828328859307992401
y[1] (numeric) = 1.0156075579199828328859307992399
absolute error = 2e-31
relative error = 1.9692645888694488956327612040250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.15
y[1] (analytic) = 1.0157644164848544908266692910111
y[1] (numeric) = 1.0157644164848544908266692910109
absolute error = 2e-31
relative error = 1.9689604868431822145006288620803e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.14
y[1] (analytic) = 1.0159228515045116917439931799265
y[1] (numeric) = 1.0159228515045116917439931799263
absolute error = 2e-31
relative error = 1.9686534238679028695918169101620e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.13
y[1] (analytic) = 1.0160828788225884309811399285206
y[1] (numeric) = 1.0160828788225884309811399285204
absolute error = 2e-31
relative error = 1.9683433720658203177991655251048e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.12
y[1] (analytic) = 1.0162445144419498727549516559441
y[1] (numeric) = 1.0162445144419498727549516559439
absolute error = 2e-31
relative error = 1.9680303033155948312177397420157e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 8.165e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.11
y[1] (analytic) = 1.0164077745262926500080622448391
y[1] (numeric) = 1.0164077745262926500080622448388
absolute error = 3e-31
relative error = 2.9515712838758843724873578664299e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.1
y[1] (analytic) = 1.0165726754017612475419836980835
y[1] (numeric) = 1.0165726754017612475419836980832
absolute error = 3e-31
relative error = 2.9510925018856771797752841008200e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.09
y[1] (analytic) = 1.0167392335585806300707520444753
y[1] (numeric) = 1.016739233558580630070752044475
absolute error = 3e-31
relative error = 2.9506090657090311464196015358218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.08
y[1] (analytic) = 1.0169074656527052784592986858592
y[1] (numeric) = 1.016907465652705278459298685859
absolute error = 2e-31
relative error = 1.9667472877842367534077639022472e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.07
y[1] (analytic) = 1.0170773885074847990515452242772
y[1] (numeric) = 1.017077388507484799051545224277
absolute error = 2e-31
relative error = 1.9664187038263723539171567955079e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.06
y[1] (analytic) = 1.0172490191153462726505425910253
y[1] (numeric) = 1.0172490191153462726505425910251
absolute error = 2e-31
relative error = 1.9660869289795984566442243666688e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
bytes used=20008956, alloc=4259060, time=0.75
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.05
y[1] (analytic) = 1.0174223746394935113869544536867
y[1] (numeric) = 1.0174223746394935113869544536865
absolute error = 2e-31
relative error = 1.9657519333685445309604081259138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -4.04
y[1] (analytic) = 1.017597472415623393402987801592
y[1] (numeric) = 1.0175974724156233934029878015917
absolute error = 3e-31
relative error = 2.9481205302902837213806840053325e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.03
y[1] (analytic) = 1.017774329953659446986669386436
y[1] (numeric) = 1.0177743299536594469866693864357
absolute error = 3e-31
relative error = 2.9476082385931209287259726743155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.02
y[1] (analytic) = 1.0179529649395028575163261039565
y[1] (numeric) = 1.0179529649395028575163261039562
absolute error = 3e-31
relative error = 2.9470909789808319708246572893625e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.01
y[1] (analytic) = 1.01813339523680107231742294203
y[1] (numeric) = 1.0181333952368010723174229420297
absolute error = 3e-31
relative error = 2.9465687050784238061265723352286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4
y[1] (analytic) = 1.0183156388887341802937180212732
y[1] (numeric) = 1.018315638888734180293718021273
absolute error = 2e-31
relative error = 1.9640275800758168839464137241010e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.99
y[1] (analytic) = 1.0184997141198192449721864983093
y[1] (numeric) = 1.0184997141198192449721864983091
absolute error = 2e-31
relative error = 1.9636726179431349644399573462294e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.98
y[1] (analytic) = 1.0186856393377327713965214399713
y[1] (numeric) = 1.0186856393377327713965214399711
absolute error = 2e-31
relative error = 1.9633142186045134261763179194024e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.97
y[1] (analytic) = 1.0188734331351514891174197460049
y[1] (numeric) = 1.0188734331351514891174197460046
absolute error = 3e-31
relative error = 2.9444285251101017767253548619969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.96
y[1] (analytic) = 1.0190631142916116353594861398
y[1] (numeric) = 1.0190631142916116353594861397998
absolute error = 2e-31
relative error = 1.9625869800912907943799282923468e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.95
y[1] (analytic) = 1.0192547017753869242946213253559
y[1] (numeric) = 1.0192547017753869242946213253557
absolute error = 2e-31
relative error = 1.9622180761259218966873445832043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (analytic) = 1.0194482147453853902203866289042
y[1] (numeric) = 1.019448214745385390220386628904
absolute error = 2e-31
relative error = 1.9618456053694836802073369207277e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (analytic) = 1.0196436725530652943292436695736
y[1] (numeric) = 1.0196436725530652943292436695735
absolute error = 1e-31
relative error = 9.8073476736840832100654563954738e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.92
y[1] (analytic) = 1.0198410947443702866609425773594
y[1] (numeric) = 1.0198410947443702866609425773592
absolute error = 2e-31
relative error = 1.9610898308636139351648760888659e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.91
y[1] (analytic) = 1.0200405010616840167558666375535
y[1] (numeric) = 1.0200405010616840167558666375534
absolute error = 1e-31
relative error = 9.8035323005231130026550313349086e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.9
y[1] (analytic) = 1.0202419114458043884720275437437
y[1] (numeric) = 1.0202419114458043884720275437435
absolute error = 2e-31
relative error = 1.9603193885318449868951736106286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.89
y[1] (analytic) = 1.0204453460379376563928381767342
y[1] (numeric) = 1.0204453460379376563928381767341
absolute error = 1e-31
relative error = 9.7996429096637033557705749908180e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.88
y[1] (analytic) = 1.0206508251817125632369654392163
y[1] (numeric) = 1.0206508251817125632369654392162
absolute error = 1e-31
relative error = 9.7976700290421459907924515078549e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.87
y[1] (analytic) = 1.0208583694252147196856825849039
y[1] (numeric) = 1.0208583694252147196856825849038
absolute error = 1e-31
relative error = 9.7956781268594698381282294031717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.86
y[1] (analytic) = 1.0210679995230414300673990995446
y[1] (numeric) = 1.0210679995230414300673990995445
absolute error = 1e-31
relative error = 9.7936670277309380177839421104296e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.85
y[1] (analytic) = 1.0212797364383771693836489472373
y[1] (numeric) = 1.0212797364383771693836489472373
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0214936013450899192259693508355
y[1] (numeric) = 1.0214936013450899192259693508355
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
bytes used=24010964, alloc=4324584, time=0.90
TOP MAIN SOLVE Loop
x[1] = -3.83
y[1] (analytic) = 1.0217096156298485722190087467336
y[1] (numeric) = 1.0217096156298485722190087467336
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0219278008942616167320727344178
y[1] (numeric) = 1.0219278008942616167320727344178
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0221481789570373157293614185755
y[1] (numeric) = 1.0221481789570373157293614185756
absolute error = 1e-31
relative error = 9.7833173368303946994183403370637e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.8
y[1] (analytic) = 1.0223707718561655957785833225408
y[1] (numeric) = 1.0223707718561655957785833225409
absolute error = 1e-31
relative error = 9.7811872906386952604774870301435e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.79
y[1] (analytic) = 1.0225956018511218644086649813674
y[1] (numeric) = 1.0225956018511218644086649813674
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.78
y[1] (analytic) = 1.0228226914250929762001285060763
y[1] (numeric) = 1.0228226914250929762001285060763
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0230520632872255702066011347591
y[1] (numeric) = 1.0230520632872255702066011347592
absolute error = 1e-31
relative error = 9.7746736054355268917485844818480e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.76
y[1] (analytic) = 1.0232837403748970035430725422555
y[1] (numeric) = 1.0232837403748970035430725422556
absolute error = 1e-31
relative error = 9.7724605653719600946646641496976e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.75
y[1] (analytic) = 1.0235177458560091082361511851004
y[1] (numeric) = 1.0235177458560091082361511851005
absolute error = 1e-31
relative error = 9.7702263008997438504609611330987e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.74
y[1] (analytic) = 1.0237541031313050007139161777898
y[1] (numeric) = 1.0237541031313050007139161777899
absolute error = 1e-31
relative error = 9.7679706185435591958341833488479e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.73
y[1] (analytic) = 1.0239928358367091756182443665626
y[1] (numeric) = 1.0239928358367091756182443665627
absolute error = 1e-31
relative error = 9.7656933232632968473375828888476e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.72
y[1] (analytic) = 1.024233967845691117950943918083
y[1] (numeric) = 1.0242339678456911179509439180831
absolute error = 1e-31
relative error = 9.7633942184453879065769525937927e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.71
y[1] (analytic) = 1.0244775232716526699168787197371
y[1] (numeric) = 1.0244775232716526699168787197372
absolute error = 1e-31
relative error = 9.7610731058941723893048341933284e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.7
y[1] (analytic) = 1.0247235264703393912027573829834
y[1] (numeric) = 1.0247235264703393912027573829835
absolute error = 1e-31
relative error = 9.7587297858233079871961975186281e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.69
y[1] (analytic) = 1.024972002042276153829624202256
y[1] (numeric) = 1.0249720020422761538296242022561
absolute error = 1e-31
relative error = 9.7563640568472215227542482840406e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.68
y[1] (analytic) = 1.0252229748352272151405669876582
y[1] (numeric) = 1.0252229748352272151405669876583
absolute error = 1e-31
relative error = 9.7539757159726056101816175413068e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (analytic) = 1.0254764699466810149329906098868
y[1] (numeric) = 1.0254764699466810149329906098868
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (analytic) = 1.0257325127263599452172401559202
y[1] (numeric) = 1.0257325127263599452172401559202
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0259911287787553435806410395574
y[1] (numeric) = 1.0259911287787553435806410395574
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (analytic) = 1.0262523439656879636584049723293
y[1] (numeric) = 1.0262523439656879636584049723293
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (analytic) = 1.0265161844088941787605826178852
y[1] (numeric) = 1.0265161844088941787605826178852
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (analytic) = 1.0267826764926381772775808019925
y[1] (numeric) = 1.0267826764926381772775808019925
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
bytes used=28013408, alloc=4324584, time=1.05
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (analytic) = 1.0270518468663504110859616666317
y[1] (numeric) = 1.0270518468663504110859616666317
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (analytic) = 1.0273237224472925608015630624356
y[1] (numeric) = 1.0273237224472925608015630624356
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.59
y[1] (analytic) = 1.0275983304232492843786863032922
y[1] (numeric) = 1.0275983304232492843786863032923
absolute error = 1e-31
relative error = 9.7314288121519034769885014814130e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.58
y[1] (analytic) = 1.0278756982552470182324543331974
y[1] (numeric) = 1.0278756982552470182324543331975
absolute error = 1e-31
relative error = 9.7288028279823696028136184499231e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = -3.57
y[1] (analytic) = 1.0281558536803001027667182163266
y[1] (numeric) = 1.0281558536803001027667182163267
absolute error = 1e-31
relative error = 9.7261518904987431602638499671080e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.56
y[1] (analytic) = 1.0284388247141845069223531865445
y[1] (numeric) = 1.0284388247141845069223531865446
absolute error = 1e-31
relative error = 9.7234757767717686305421014316514e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.55
y[1] (analytic) = 1.0287246396542394291207105307843
y[1] (numeric) = 1.0287246396542394291207105307845
absolute error = 2e-31
relative error = 1.9441548524318539620617803033737e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.54
y[1] (analytic) = 1.0290133270821970547646543267218
y[1] (numeric) = 1.0290133270821970547646543267219
absolute error = 1e-31
relative error = 9.7180471202985742755568090094584e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.53
y[1] (analytic) = 1.029304915867040753275291277527
y[1] (numeric) = 1.0293049158670407532752912775272
absolute error = 2e-31
relative error = 1.9430588246198055053914143116204e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.52
y[1] (analytic) = 1.0295994351678920004864791554834
y[1] (numeric) = 1.0295994351678920004864791554835
absolute error = 1e-31
relative error = 9.7125150407346002671961940007315e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.51
y[1] (analytic) = 1.0298969144369263150917590819967
y[1] (numeric) = 1.0298969144369263150917590819968
absolute error = 1e-31
relative error = 9.7097096416365923256556132401645e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.5
y[1] (analytic) = 1.0301973834223185007397862923636
y[1] (numeric) = 1.0301973834223185007397862923638
absolute error = 2e-31
relative error = 1.9413755384972873622694208837717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -3.49
y[1] (analytic) = 1.030500872171217488304923304969
y[1] (numeric) = 1.0305008721712174883049233049692
absolute error = 2e-31
relative error = 1.9408037916417216282592652870365e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.48
y[1] (analytic) = 1.0308074110327510758197015977179
y[1] (numeric) = 1.030807411032751075819701597718
absolute error = 1e-31
relative error = 9.7011332019636376585630352733735e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.47
y[1] (analytic) = 1.0311170306610608665456489961601
y[1] (numeric) = 1.0311170306610608665456489961602
absolute error = 1e-31
relative error = 9.6982201851412406217944310682952e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.46
y[1] (analytic) = 1.0314297620183677086788189795365
y[1] (numeric) = 1.0314297620183677086788189795367
absolute error = 2e-31
relative error = 1.9390559334707116833245641511998e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.45
y[1] (analytic) = 1.0317456363780679432365469992797
y[1] (numeric) = 1.0317456363780679432365469992799
absolute error = 2e-31
relative error = 1.9384622812857039816669397228148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.44
y[1] (analytic) = 1.0320646853278607697528027007736
y[1] (numeric) = 1.0320646853278607697528027007738
absolute error = 2e-31
relative error = 1.9378630316806651850098690529583e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.43
y[1] (analytic) = 1.0323869407729070425213137303623
y[1] (numeric) = 1.0323869407729070425213137303625
absolute error = 2e-31
relative error = 1.9372581355036121862288849368170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.42
y[1] (analytic) = 1.0327124349390198132687177789643
y[1] (numeric) = 1.0327124349390198132687177789645
absolute error = 2e-31
relative error = 1.9366475432418872043693065838785e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -3.41
y[1] (analytic) = 1.0330412003758869393146689719212
y[1] (numeric) = 1.0330412003758869393146689719214
absolute error = 2e-31
relative error = 1.9360312050209334883516658689408e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (analytic) = 1.0333732699603260794824001314709
y[1] (numeric) = 1.0333732699603260794824001314711
absolute error = 2e-31
relative error = 1.9354090706030989805224487577461e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=32014600, alloc=4324584, time=1.20
TOP MAIN SOLVE Loop
x[1] = -3.39
y[1] (analytic) = 1.0337086768995724032620444737059
y[1] (numeric) = 1.033708676899572403262044473706
absolute error = 1e-31
relative error = 9.6739054469323440487146388468089e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -3.38
y[1] (analytic) = 1.0340474547345993420003728389543
y[1] (numeric) = 1.0340474547345993420003728389544
absolute error = 1e-31
relative error = 9.6707360520186374923638905833581e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.37
y[1] (analytic) = 1.0343896373434727141948327311903
y[1] (numeric) = 1.0343896373434727141948327311904
absolute error = 1e-31
relative error = 9.6675369116052589159806238498543e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -3.36
y[1] (analytic) = 1.0347352589447385603072136841051
y[1] (numeric) = 1.0347352589447385603072136841053
absolute error = 2e-31
relative error = 1.9328615534370349625534177169317e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = -3.35
y[1] (analytic) = 1.0350843541008450258832435254655
y[1] (numeric) = 1.0350843541008450258832435254657
absolute error = 2e-31
relative error = 1.9322096716816437026806910525550e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.34
y[1] (analytic) = 1.0354369577215986351692790781561
y[1] (numeric) = 1.0354369577215986351692790781562
absolute error = 1e-31
relative error = 9.6577584230760412225789616177189e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.33
y[1] (analytic) = 1.0357931050676553008563332045916
y[1] (numeric) = 1.0357931050676553008563332045917
absolute error = 1e-31
relative error = 9.6544376971372348660319144161987e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -3.32
y[1] (analytic) = 1.0361528317540464190553217816872
y[1] (numeric) = 1.0361528317540464190553217816873
absolute error = 1e-31
relative error = 9.6510859146826316262203088385288e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.31
y[1] (analytic) = 1.0365161737537404021159665533578
y[1] (numeric) = 1.036516173753740402115966553358
absolute error = 2e-31
relative error = 1.9295405615881570245498471323758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.3
y[1] (analytic) = 1.0368831674012400054456037047415
y[1] (numeric) = 1.0368831674012400054456037047417
absolute error = 2e-31
relative error = 1.9288576214547276544452870519188e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.29
y[1] (analytic) = 1.0372538493962158080635778213451
y[1] (numeric) = 1.0372538493962158080635778213453
absolute error = 2e-31
relative error = 1.9281683082344765882573216316909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (analytic) = 1.0376282568071762102423045830638
y[1] (numeric) = 1.037628256807176210242304583064
absolute error = 2e-31
relative error = 1.9274725672507033172201622657018e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (analytic) = 1.0380064270751743152378246409055
y[1] (numeric) = 1.0380064270751743152378246409057
absolute error = 2e-31
relative error = 1.9267703434510202303501935379574e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.26
y[1] (analytic) = 1.0383883980175520658011108102137
y[1] (numeric) = 1.0383883980175520658011108102138
absolute error = 1e-31
relative error = 9.6303079070332295853817841165312e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (analytic) = 1.0387742078317220098868998352676
y[1] (numeric) = 1.0387742078317220098868998352677
absolute error = 1e-31
relative error = 9.6267311265587053980228583396150e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.24
y[1] (analytic) = 1.0391638950989870737397710903658
y[1] (numeric) = 1.0391638950989870737397710903659
absolute error = 1e-31
relative error = 9.6231210949139407913811391888854e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (analytic) = 1.0395574987883987243379639801109
y[1] (numeric) = 1.0395574987883987243379639801111
absolute error = 2e-31
relative error = 1.9238955058580157895431758444929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (analytic) = 1.0399550582606539070143935667244
y[1] (numeric) = 1.0399550582606539070143935667246
absolute error = 2e-31
relative error = 1.9231600289968692326202923391622e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (analytic) = 1.040356613272031147951873984794
y[1] (numeric) = 1.0403566132720311479518739847942
absolute error = 2e-31
relative error = 1.9224177310795279173867269360006e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.2
y[1] (analytic) = 1.0407622039783662151660792621444
y[1] (numeric) = 1.0407622039783662151660792621446
absolute error = 2e-31
relative error = 1.9216685544064712826832642230889e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.19
y[1] (analytic) = 1.0411718709390677355456529047735
y[1] (numeric) = 1.0411718709390677355456529047737
absolute error = 2e-31
relative error = 1.9209124408980940907905569549750e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.18
y[1] (analytic) = 1.041585655121173169514516615502
y[1] (numeric) = 1.0415856551211731695145166155022
absolute error = 2e-31
relative error = 1.9201493320943724205657793464199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=36015596, alloc=4324584, time=1.36
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (analytic) = 1.04200359790344554891722436736
y[1] (numeric) = 1.0420035979034455489172243673602
absolute error = 2e-31
relative error = 1.9193791691545815584577612768612e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (analytic) = 1.042425741080511387804564326735
y[1] (numeric) = 1.0424257410805113878045643267352
absolute error = 2e-31
relative error = 1.9186018928570670234069109590364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -3.15
y[1] (analytic) = 1.0428521268670401799139354569562
y[1] (numeric) = 1.0428521268670401799139354569564
absolute error = 2e-31
relative error = 1.9178174435990699784599936654569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.14
y[1] (analytic) = 1.0432827979019659007977297661522
y[1] (numeric) = 1.0432827979019659007977297661524
absolute error = 2e-31
relative error = 1.9170257613966082987846433611735e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.13
y[1] (analytic) = 1.0437177972527509367534509677739
y[1] (numeric) = 1.0437177972527509367534509677741
absolute error = 2e-31
relative error = 1.9162267858844145826476308520059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.12
y[1] (analytic) = 1.0441571684196928669520158516001
y[1] (numeric) = 1.0441571684196928669520158516003
absolute error = 2e-31
relative error = 1.9154204563159324088174318686373e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.11
y[1] (analytic) = 1.0446009553402745294460401924352
y[1] (numeric) = 1.0446009553402745294460401924354
absolute error = 2e-31
relative error = 1.9146067115633721607583090313016e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.1
y[1] (analytic) = 1.0450492023935578060683350921783
y[1] (numeric) = 1.0450492023935578060683350921785
absolute error = 2e-31
relative error = 1.9137854901178277548924575126578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.09
y[1] (analytic) = 1.0455019544046215656027651045195
y[1] (numeric) = 1.0455019544046215656027651045196
absolute error = 1e-31
relative error = 9.5647836504472781355550594734069e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.08
y[1] (analytic) = 1.0459592566490442090254835263785
y[1] (numeric) = 1.0459592566490442090254835263786
absolute error = 1e-31
relative error = 9.5606018460385867430292216225245e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.07
y[1] (analytic) = 1.0464211548574312650748044464352
y[1] (numeric) = 1.0464211548574312650748044464353
absolute error = 1e-31
relative error = 9.5563817241084362948189812930388e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.06
y[1] (analytic) = 1.0468876952199884889130415468398
y[1] (numeric) = 1.04688769521998848891304154684
absolute error = 2e-31
relative error = 1.9104245939004265213046888670207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.05
y[1] (analytic) = 1.0473589243911409211939907702397
y[1] (numeric) = 1.0473589243911409211939907702399
absolute error = 2e-31
relative error = 1.9095650530334250210452728218919e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.04
y[1] (analytic) = 1.0478348894941983694458128291081
y[1] (numeric) = 1.0478348894941983694458128291083
absolute error = 2e-31
relative error = 1.9086976584311125466240351323001e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.03
y[1] (analytic) = 1.0483156381260677783213417597388
y[1] (numeric) = 1.0483156381260677783213417597389
absolute error = 1e-31
relative error = 9.5391117296272035360850419101623e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.02
y[1] (analytic) = 1.04880121836201295995677154006
y[1] (numeric) = 1.0488012183620129599567715400601
absolute error = 1e-31
relative error = 9.5346952548526852955132582846479e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -3.01
y[1] (analytic) = 1.0492916787604621604157230951175
y[1] (numeric) = 1.0492916787604621604157230951176
absolute error = 1e-31
relative error = 9.5302385432171646444220454029302e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3
y[1] (analytic) = 1.0497870683678639429793424156501
y[1] (numeric) = 1.0497870683678639429793424156502
absolute error = 1e-31
relative error = 9.5257412682243321912115184822821e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.99
y[1] (analytic) = 1.050287436723591873874805382468
y[1] (numeric) = 1.0502874367235918738748053824681
absolute error = 1e-31
relative error = 9.5212031015008112562458751066214e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.98
y[1] (analytic) = 1.050792833864898500914889398847
y[1] (numeric) = 1.0507928338648985009148893988472
absolute error = 2e-31
relative error = 1.9033247425601895815418777620053e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.97
y[1] (analytic) = 1.0513033103319191204506041173959
y[1] (numeric) = 1.0513033103319191204506041173961
absolute error = 2e-31
relative error = 1.9024005540024000127715581788696e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.96
y[1] (analytic) = 1.0518189171727258330177463441629
y[1] (numeric) = 1.051818917172725833017746344163
absolute error = 1e-31
relative error = 9.5073399391597335087915567342871e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=40016572, alloc=4324584, time=1.51
TOP MAIN SOLVE Loop
x[1] = -2.95
y[1] (analytic) = 1.0523397059484323930871555025493
y[1] (numeric) = 1.0523397059484323930871555025494
absolute error = 1e-31
relative error = 9.5026348844144327481602855857569e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.94
y[1] (analytic) = 1.0528657287383503634078987382166
y[1] (numeric) = 1.0528657287383503634078987382167
absolute error = 1e-31
relative error = 9.4978872680973347097048621620406e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.93
y[1] (analytic) = 1.053397038145197089563116793104
y[1] (numeric) = 1.0533970381451970895631167931041
absolute error = 1e-31
relative error = 9.4930967506874933711927667437801e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.92
y[1] (analytic) = 1.053933687300356015540326226409
y[1] (numeric) = 1.0539336873003560155403262264091
absolute error = 1e-31
relative error = 9.4882629908290834750363545446905e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.91
y[1] (analytic) = 1.0544757298691898663521186236729
y[1] (numeric) = 1.0544757298691898663521186236729
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.9
y[1] (analytic) = 1.0550232200564072290299465308342
y[1] (numeric) = 1.0550232200564072290299465308342
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0555762126114830686535676575805
y[1] (numeric) = 1.0555762126114830686535676575805
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.88
y[1] (analytic) = 1.0561347628341337214722674061654
y[1] (numeric) = 1.0561347628341337214722674061654
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (analytic) = 1.0566989265798469126217343574206
y[1] (numeric) = 1.0566989265798469126217343574206
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0572687602654673514429687649702
y[1] (numeric) = 1.0572687602654673514429687649702
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0578443208748384629674106267774
y[1] (numeric) = 1.0578443208748384629674106267774
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.84
y[1] (analytic) = 1.0584256659645008197461373054073
y[1] (numeric) = 1.0584256659645008197461373054073
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.83
y[1] (analytic) = 1.059012853669447843871062325787
y[1] (numeric) = 1.059012853669447843871062325787
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -2.82
y[1] (analytic) = 1.0596059427089393547631339046828
y[1] (numeric) = 1.0596059427089393547631339046829
absolute error = 1e-31
relative error = 9.4374706642683263064200597200057e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.81
y[1] (analytic) = 1.0602049923923735440871566710524
y[1] (numeric) = 1.0602049923923735440871566710525
absolute error = 1e-31
relative error = 9.4321381919121151518966036670019e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.8
y[1] (analytic) = 1.0608100626252179649956213881839
y[1] (numeric) = 1.060810062625217964995621388184
absolute error = 1e-31
relative error = 9.4267582410113125379170882601282e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.79
y[1] (analytic) = 1.0614212139150001288054095681066
y[1] (numeric) = 1.0614212139150001288054095681067
absolute error = 1e-31
relative error = 9.4213304472363898640683906716129e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.78
y[1] (analytic) = 1.0620385073773583081720328292716
y[1] (numeric) = 1.0620385073773583081720328292716
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
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) = 1.0626620047421531518467667742247
y[1] (numeric) = 1.0626620047421531518467667742247
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.76
y[1] (analytic) = 1.0632917683596407221832481299345
y[1] (numeric) = 1.0632917683596407221832481299346
absolute error = 1e-31
relative error = 9.4047563402349849075859753729787e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (analytic) = 1.063927861206707572702430025558
y[1] (numeric) = 1.063927861206707572702430025558
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.74
y[1] (analytic) = 1.0645703468931684892288478184621
y[1] (numeric) = 1.0645703468931684892288478184622
absolute error = 1e-31
relative error = 9.3934609668434787113770102795863e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=44017732, alloc=4324584, time=1.66
x[1] = -2.73
y[1] (analytic) = 1.065219289668127524377557230193
y[1] (numeric) = 1.0652192896681275243775572301931
absolute error = 1e-31
relative error = 9.3877383718009199532477217780467e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.72
y[1] (analytic) = 1.0658747544264029615004943659454
y[1] (numeric) = 1.0658747544264029615004943659455
absolute error = 1e-31
relative error = 9.3819653373641141663187915148742e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.71
y[1] (analytic) = 1.0665368067150168505940064080062
y[1] (numeric) = 1.0665368067150168505940064080063
absolute error = 1e-31
relative error = 9.3761414862000560380224040169638e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.7
y[1] (analytic) = 1.067205512739749765126551700856
y[1] (numeric) = 1.0672055127397497651265517008561
absolute error = 1e-31
relative error = 9.3702664394300351048584367149103e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.69
y[1] (analytic) = 1.0678809393717614352677143135015
y[1] (numeric) = 1.0678809393717614352677143135017
absolute error = 2e-31
relative error = 1.8728679633298894549194302612849e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.68
y[1] (analytic) = 1.068563154154277919587373193244
y[1] (numeric) = 1.0685631541542779195873731932442
absolute error = 2e-31
relative error = 1.8716722471896521144263194095820e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.67
y[1] (analytic) = 1.0692522253093459839477684894559
y[1] (numeric) = 1.0692522253093459839477684894561
absolute error = 2e-31
relative error = 1.8704660627864289320196865880350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.66
y[1] (analytic) = 1.0699482217446553630319829218383
y[1] (numeric) = 1.0699482217446553630319829218385
absolute error = 2e-31
relative error = 1.8692493331488547418471268095666e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.65
y[1] (analytic) = 1.0706512130604295867406762781867
y[1] (numeric) = 1.0706512130604295867406762781869
absolute error = 2e-31
relative error = 1.8680219810175624427790278647755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.64
y[1] (analytic) = 1.0713612695563860605454550895863
y[1] (numeric) = 1.0713612695563860605454550895865
absolute error = 2e-31
relative error = 1.8667839288498186730116732096086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (analytic) = 1.0720784622387660958127129062998
y[1] (numeric) = 1.0720784622387660958127129063
absolute error = 2e-31
relative error = 1.8655350988242999212982401699560e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.62
y[1] (analytic) = 1.0728028628274355931068319365058
y[1] (numeric) = 1.0728028628274355931068319365059
absolute error = 1e-31
relative error = 9.3213770642300550091992433390508e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.61
y[1] (analytic) = 1.0735345437630570885469936238617
y[1] (numeric) = 1.0735345437630570885469936238618
absolute error = 1e-31
relative error = 9.3150239627567391049785376980016e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (analytic) = 1.07427357821433388042821057017
y[1] (numeric) = 1.0742735782143338804282105701701
absolute error = 1e-31
relative error = 9.3086157965665318214747685796835e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.59
y[1] (analytic) = 1.0750200400853269605252786986446
y[1] (numeric) = 1.0750200400853269605252786986448
absolute error = 2e-31
relative error = 1.8604304342468398317272232340262e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.58
y[1] (analytic) = 1.0757740040228454817788775160744
y[1] (numeric) = 1.0757740040228454817788775160746
absolute error = 2e-31
relative error = 1.8591265382143658479282197554773e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.57
y[1] (analytic) = 1.0765355454239115014167458275085
y[1] (numeric) = 1.0765355454239115014167458275087
absolute error = 2e-31
relative error = 1.8578113918314256716340992333181e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.56
y[1] (analytic) = 1.0773047404432997459904656610398
y[1] (numeric) = 1.07730474044329974599046566104
absolute error = 2e-31
relative error = 1.8564849154724973256275757424238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.55
y[1] (analytic) = 1.0780816660011531523106412395528
y[1] (numeric) = 1.078081666001153152310641239553
absolute error = 2e-31
relative error = 1.8551470292769645643121529877046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.54
y[1] (analytic) = 1.0788663997906749458409128226
y[1] (numeric) = 1.0788663997906749458409128226003
absolute error = 3e-31
relative error = 2.7806964797328653865020405740424e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -6.667e+29
TOP MAIN SOLVE Loop
x[1] = -2.53
y[1] (analytic) = 1.0796590202858980257650549064864
y[1] (numeric) = 1.0796590202858980257650549064867
absolute error = 3e-31
relative error = 2.7786550601926041464543635894306e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.52
y[1] (analytic) = 1.0804596067495324336721400015193
y[1] (numeric) = 1.0804596067495324336721400015196
absolute error = 3e-31
relative error = 2.7765961645019157888778578505918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
bytes used=48018984, alloc=4324584, time=1.81
x[1] = -2.51
y[1] (analytic) = 1.0812682392408916906131760818382
y[1] (numeric) = 1.0812682392408916906131760818385
absolute error = 3e-31
relative error = 2.7745196715536201611115060345220e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.5
y[1] (analytic) = 1.0820849986238987951695286744672
y[1] (numeric) = 1.0820849986238987951695286744675
absolute error = 3e-31
relative error = 2.7724254599362693464200814700612e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.49
y[1] (analytic) = 1.0829099665751726831396061170947
y[1] (numeric) = 1.082909966575172683139606117095
absolute error = 3e-31
relative error = 2.7703134079445635132467690216117e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.48
y[1] (analytic) = 1.0837432255921959574965153919751
y[1] (numeric) = 1.0837432255921959574965153919754
absolute error = 3e-31
relative error = 2.7681833935900203525673755136366e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.47
y[1] (analytic) = 1.084584859001564705396490765854
y[1] (numeric) = 1.0845848590015647053964907658543
absolute error = 3e-31
relative error = 2.7660352946119008744595030653128e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.46
y[1] (analytic) = 1.0854349509673212272266709492054
y[1] (numeric) = 1.0854349509673212272266709492057
absolute error = 3e-31
relative error = 2.7638689884883943143360813372525e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.45
y[1] (analytic) = 1.0862935864993705109720735165162
y[1] (numeric) = 1.0862935864993705109720735165165
absolute error = 3e-31
relative error = 2.7616843524480648767951299253734e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.44
y[1] (analytic) = 1.0871608514619812935562170370773
y[1] (numeric) = 1.0871608514619812935562170370776
absolute error = 3e-31
relative error = 2.7594812634815630206616438783167e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.43
y[1] (analytic) = 1.088036832582372559268609219894
y[1] (numeric) = 1.0880368325823725592686092198944
absolute error = 4e-31
relative error = 3.6763461311381386166638816184592e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.42
y[1] (analytic) = 1.0889216174593863339360992607368
y[1] (numeric) = 1.0889216174593863339360992607371
absolute error = 3e-31
relative error = 2.7550192336152160475900113377876e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.41
y[1] (analytic) = 1.0898152945722476421247388791339
y[1] (numeric) = 1.0898152945722476421247388791342
absolute error = 3e-31
relative error = 2.7527600456162616071351496888123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.4
y[1] (analytic) = 1.0907179532894125033751722200797
y[1] (numeric) = 1.09071795328941250337517222008
absolute error = 3e-31
relative error = 2.7504819105182328880111426827184e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.39
y[1] (analytic) = 1.0916296838775048522785515142203
y[1] (numeric) = 1.0916296838775048522785515142206
absolute error = 3e-31
relative error = 2.7481847043073256070599405548770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.38
y[1] (analytic) = 1.092550577510343276092433546306
y[1] (numeric) = 1.0925505775103432760924335463063
absolute error = 3e-31
relative error = 2.7458683028077926452156372420223e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.37
y[1] (analytic) = 1.093480726278058472577940827977
y[1] (numeric) = 1.0934807262780584725779408279773
absolute error = 3e-31
relative error = 2.7435325816955803580079858349987e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.36
y[1] (analytic) = 1.0944202231963023398115690978577
y[1] (numeric) = 1.094420223196302339811569097858
absolute error = 3e-31
relative error = 2.7411774165122499379290190912757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.35
y[1] (analytic) = 1.0953691622155496188882965967998
y[1] (numeric) = 1.0953691622155496188882965968001
absolute error = 3e-31
relative error = 2.7388026826791862208169934687480e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (analytic) = 1.0963276382304930196880168239591
y[1] (numeric) = 1.0963276382304930196880168239594
absolute error = 3e-31
relative error = 2.7364082555120962827426217086384e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.33
y[1] (analytic) = 1.0972957470895327692257007145515
y[1] (numeric) = 1.0972957470895327692257007145518
absolute error = 3e-31
relative error = 2.7339940102358001258316278429119e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.32
y[1] (analytic) = 1.0982735856043615315480312388239
y[1] (numeric) = 1.0982735856043615315480312388241
absolute error = 2e-31
relative error = 1.8210398813328771339862620046121e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.31
y[1] (analytic) = 1.0992612515596456576764875455719
y[1] (numeric) = 1.0992612515596456576764875455721
absolute error = 2e-31
relative error = 1.8194037105941603083082652417712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.3
y[1] (analytic) = 1.100258843722803733729940693798
y[1] (numeric) = 1.1002588437228037337299406937982
absolute error = 2e-31
relative error = 1.8177540779702877293213905060472e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=52020548, alloc=4324584, time=1.96
TOP MAIN SOLVE Loop
x[1] = -2.29
y[1] (analytic) = 1.1012664618538834050897220493467
y[1] (numeric) = 1.1012664618538834050897220493469
absolute error = 2e-31
relative error = 1.8160909001379913250964914295214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.28
y[1] (analytic) = 1.1022842067155374642978115675971
y[1] (numeric) = 1.1022842067155374642978115675973
absolute error = 2e-31
relative error = 1.8144140937656859978275778047023e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.27
y[1] (analytic) = 1.1033121800831002003052492153345
y[1] (numeric) = 1.1033121800831002003052492153347
absolute error = 2e-31
relative error = 1.8127235755245286132668852783666e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.26
y[1] (analytic) = 1.1043504847547650167140913586396
y[1] (numeric) = 1.1043504847547650167140913586398
absolute error = 2e-31
relative error = 1.8110192620996814054656515775236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.25
y[1] (analytic) = 1.1053992245618643367832176892407
y[1] (numeric) = 1.1053992245618643367832176892409
absolute error = 2e-31
relative error = 1.8093010702017810120607704735433e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.24
y[1] (analytic) = 1.1064585043792528231970558860814
y[1] (numeric) = 1.1064585043792528231970558860816
absolute error = 2e-31
relative error = 1.8075689165786143076761213341228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.23
y[1] (analytic) = 1.107528430135794950927853596553
y[1] (numeric) = 1.1075284301357949509278535965533
absolute error = 3e-31
relative error = 2.7087340770405032301804478828549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.22
y[1] (analytic) = 1.1086091088249579819575236377746
y[1] (numeric) = 1.1086091088249579819575236377748
absolute error = 2e-31
relative error = 1.8040623914048921292654182773754e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.21
y[1] (analytic) = 1.1097006485155114011653621107986
y[1] (numeric) = 1.1097006485155114011653621107988
absolute error = 2e-31
relative error = 1.8022878536436612617575430166251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.164e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = -2.2
y[1] (analytic) = 1.1108031583623338833341444258499
y[1] (numeric) = 1.1108031583623338833341444258502
absolute error = 3e-31
relative error = 2.7007485326409445590171919959011e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.19
y[1] (analytic) = 1.1119167486173288719803056840571
y[1] (numeric) = 1.1119167486173288719803056840574
absolute error = 3e-31
relative error = 2.6980437193076794218826190096989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.18
y[1] (analytic) = 1.1130415306404498615751847797268
y[1] (numeric) = 1.113041530640449861575184779727
absolute error = 2e-31
relative error = 1.7968781442047267016861517007293e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.17
y[1] (analytic) = 1.1141776169108364856947421133822
y[1] (numeric) = 1.1141776169108364856947421133825
absolute error = 3e-31
relative error = 2.6925688996677079230926734391883e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.16
y[1] (analytic) = 1.1153251210380625247158459917298
y[1] (numeric) = 1.1153251210380625247158459917301
absolute error = 3e-31
relative error = 2.6897986456252512513525998130982e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.15
y[1] (analytic) = 1.1164841577734969578692707141828
y[1] (numeric) = 1.1164841577734969578692707141831
absolute error = 3e-31
relative error = 2.6870063306429961078902893425762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.000e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -2.14
y[1] (analytic) = 1.1176548430217791957640792206891
y[1] (numeric) = 1.1176548430217791957640792206893
absolute error = 2e-31
relative error = 1.7894612209549804400181830193304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.13
y[1] (analytic) = 1.1188372938524096409162054647724
y[1] (numeric) = 1.1188372938524096409162054647727
absolute error = 3e-31
relative error = 2.6813550249744733222730054809633e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.12
y[1] (analytic) = 1.1200316285114567353469482026623
y[1] (numeric) = 1.1200316285114567353469482026626
absolute error = 3e-31
relative error = 2.6784957885404154750820745446828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.11
y[1] (analytic) = 1.1212379664333816659658919534078
y[1] (numeric) = 1.1212379664333816659658919534081
absolute error = 3e-31
relative error = 2.6756139997139893025369493771899e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.1
y[1] (analytic) = 1.1224564282529819102186473760726
y[1] (numeric) = 1.1224564282529819102186473760729
absolute error = 3e-31
relative error = 2.6727095364131611851026817827747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.09
y[1] (analytic) = 1.12368713581745481636392882593
y[1] (numeric) = 1.1236871358174548163639288259303
absolute error = 3e-31
relative error = 2.6697822769124909658192606431407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.08
y[1] (analytic) = 1.1249302121985824247480498144888
y[1] (numeric) = 1.1249302121985824247480498144891
absolute error = 3e-31
relative error = 2.6668320998657772871804785469574e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=56023096, alloc=4324584, time=2.11
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (analytic) = 1.1261857817050387485691178744718
y[1] (numeric) = 1.126185781705038748569117874472
absolute error = 2e-31
relative error = 1.7759059228860193809816504376858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.06
y[1] (analytic) = 1.1274539698948207448692613507224
y[1] (numeric) = 1.1274539698948207448692613507227
absolute error = 3e-31
relative error = 2.6608625097837630894894662380687e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.05
y[1] (analytic) = 1.1287349035878042188623465167449
y[1] (numeric) = 1.1287349035878042188623465167452
absolute error = 3e-31
relative error = 2.6578428561606274312894481134833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.04
y[1] (analytic) = 1.1300287108784259171980810770711
y[1] (numeric) = 1.1300287108784259171980810770714
absolute error = 3e-31
relative error = 2.6547998038633505579818857335535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.03
y[1] (analytic) = 1.1313355211484930783823989120881
y[1] (numeric) = 1.1313355211484930783823989120884
absolute error = 3e-31
relative error = 2.6517332337930154754375131242788e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.02
y[1] (analytic) = 1.1326554650801217213198427647316
y[1] (numeric) = 1.1326554650801217213198427647319
absolute error = 3e-31
relative error = 2.6486430273726584292648101862469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2.01
y[1] (analytic) = 1.1339886746688049658175810503738
y[1] (numeric) = 1.133988674668804965817581050374
absolute error = 2e-31
relative error = 1.7636860443814609169319730755154e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -2
y[1] (analytic) = 1.1353352832366126918939994949725
y[1] (numeric) = 1.1353352832366126918939994949727
absolute error = 2e-31
relative error = 1.7615941559557648881194582826048e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (analytic) = 1.1366954254455238578687982134042
y[1] (numeric) = 1.1366954254455238578687982134044
absolute error = 2e-31
relative error = 1.7594862750644983785925444595802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (analytic) = 1.1380692373108928104775135397954
y[1] (numeric) = 1.1380692373108928104775135397956
absolute error = 2e-31
relative error = 1.7573623242165262815174651731321e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (analytic) = 1.1394568562150509336526980245391
y[1] (numeric) = 1.1394568562150509336526980245394
absolute error = 3e-31
relative error = 2.6328333395308534017736772246951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (analytic) = 1.140858420921044996147971461096
y[1] (numeric) = 1.1408584209210449961479714610962
absolute error = 2e-31
relative error = 1.7530659048695520171576446431400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (analytic) = 1.1422740715865135718511540088638
y[1] (numeric) = 1.1422740715865135718511540088641
absolute error = 3e-31
relative error = 2.6263399254377507352490813230460e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (analytic) = 1.1437039497777029204400764475696
y[1] (numeric) = 1.1437039497777029204400764475699
absolute error = 3e-31
relative error = 2.6230564304539630067823003454233e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (analytic) = 1.1451481984836237299808130836871
y[1] (numeric) = 1.1451481984836237299808130836874
absolute error = 3e-31
relative error = 2.6197482596335776402848303123988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (analytic) = 1.146606962130350137154394456995
y[1] (numeric) = 1.1466069621303501371543944569953
absolute error = 3e-31
relative error = 2.6164153010427560151655703019250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (analytic) = 1.1480803865954624550259384084542
y[1] (numeric) = 1.1480803865954624550259384084545
absolute error = 3e-31
relative error = 2.6130574435612929280835131511287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (analytic) = 1.1495686192226350526410120691037
y[1] (numeric) = 1.149568619222635052641012069104
absolute error = 3e-31
relative error = 2.6096745769110064435340220267777e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (analytic) = 1.1510718088363708452493410130273
y[1] (numeric) = 1.1510718088363708452493410130276
absolute error = 3e-31
relative error = 2.6062665916844300019271900661084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (analytic) = 1.1525901057568838686171667280872
y[1] (numeric) = 1.1525901057568838686171667280875
absolute error = 3e-31
relative error = 2.6028333793738038402244150543297e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (analytic) = 1.154123661815131425698085826774
y[1] (numeric) = 1.1541236618151314256980858267743
absolute error = 3e-31
relative error = 2.5993748324003625872650483202893e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (analytic) = 1.1556726303679973088895649117416
y[1] (numeric) = 1.1556726303679973088895649117419
absolute error = 3e-31
relative error = 2.5958908441439156997115853200274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=60027552, alloc=4324584, time=2.27
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (analytic) = 1.1572371663136276162100094749031
y[1] (numeric) = 1.1572371663136276162100094749034
absolute error = 3e-31
relative error = 2.5923813089727172051087604426918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (analytic) = 1.158817426106920694990784426392
y[1] (numeric) = 1.1588174261069206949907844263922
absolute error = 2e-31
relative error = 1.7258974148490806772882772549363e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (analytic) = 1.160413567775172762090463784878
y[1] (numeric) = 1.1604135677751727620904637848783
absolute error = 3e-31
relative error = 2.5852851804825178727454704478253e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (analytic) = 1.1620257509338807652063690145142
y[1] (numeric) = 1.1620257509338807652063690145145
absolute error = 3e-31
relative error = 2.5816983811150497657321562978113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (analytic) = 1.1636541368027040655826962573359
y[1] (numeric) = 1.1636541368027040655826962573362
absolute error = 3e-31
relative error = 2.5780856227975974720035464158685e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (analytic) = 1.1652988882215865382968047204322
y[1] (numeric) = 1.1652988882215865382968047204325
absolute error = 3e-31
relative error = 2.5744468052985366312171656745872e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (analytic) = 1.1669601696670407023471299750829
y[1] (numeric) = 1.1669601696670407023471299750832
absolute error = 3e-31
relative error = 2.5707818295597575642954267198506e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (analytic) = 1.1686381472685955089693011128318
y[1] (numeric) = 1.1686381472685955089693011128321
absolute error = 3e-31
relative error = 2.5670905977284438194304650001746e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (analytic) = 1.1703329888254094329729999061631
y[1] (numeric) = 1.1703329888254094329729999061633
absolute error = 2e-31
relative error = 1.7089153421260694707999300265688e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (analytic) = 1.172044863823050528422539948626
y[1] (numeric) = 1.1720448638230505284225399486262
absolute error = 2e-31
relative error = 1.7064193203972352350446025870951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (analytic) = 1.1737739434504451266807172586664
y[1] (numeric) = 1.1737739434504451266807172586666
absolute error = 2e-31
relative error = 1.7039056039366210605876302696313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (analytic) = 1.1755204006169968716998606943422
y[1] (numeric) = 1.1755204006169968716998606943424
absolute error = 2e-31
relative error = 1.7013741309383124985495717588231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (analytic) = 1.1772844099698778044778771942594
y[1] (numeric) = 1.1772844099698778044778771942596
absolute error = 2e-31
relative error = 1.6988248405083121197567123724846e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (analytic) = 1.1790661479114932258021467343306
y[1] (numeric) = 1.1790661479114932258021467343308
absolute error = 2e-31
relative error = 1.6962576726866814386887615120147e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (analytic) = 1.1808657926171220837820954906518
y[1] (numeric) = 1.180865792617122083782095490652
absolute error = 2e-31
relative error = 1.6936725684698276493907668043585e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (analytic) = 1.1826835240527346502239008377589
y[1] (numeric) = 1.1826835240527346502239008377591
absolute error = 2e-31
relative error = 1.6910694698329305913320924692172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (analytic) = 1.1845195239929892676298137659024
y[1] (numeric) = 1.1845195239929892676298137659026
absolute error = 2e-31
relative error = 1.6884483197525052016708467907492e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (analytic) = 1.1863739760394099665117959887401
y[1] (numeric) = 1.1863739760394099665117959887402
absolute error = 1e-31
relative error = 8.4290453111454727379837147735861e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (analytic) = 1.1882470656387467707963511700788
y[1] (numeric) = 1.1882470656387467707963511700789
absolute error = 1e-31
relative error = 8.4157582115504418423026188432352e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (analytic) = 1.1901389801015205273663910582943
y[1] (numeric) = 1.1901389801015205273663910582944
absolute error = 1e-31
relative error = 8.4023800305633094616936080902046e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (analytic) = 1.1920499086207541142385447911733
y[1] (numeric) = 1.1920499086207541142385447911734
absolute error = 1e-31
relative error = 8.3889105042341476280854740321649e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (analytic) = 1.1939800422908919005123384942873
y[1] (numeric) = 1.1939800422908919005123384942874
absolute error = 1e-31
relative error = 8.3753493741930392359826077916689e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=64031128, alloc=4324584, time=2.41
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (analytic) = 1.1959295741269093500530063600373
y[1] (numeric) = 1.1959295741269093500530063600374
absolute error = 1e-31
relative error = 8.3616963877664108556345423708252e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (analytic) = 1.1978986990836146798842262112941
y[1] (numeric) = 1.1978986990836146798842262112942
absolute error = 1e-31
relative error = 8.3479512980938538647839133756685e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (analytic) = 1.1998876140751445034727035921351
y[1] (numeric) = 1.1998876140751445034727035921352
absolute error = 1e-31
relative error = 8.3341138642454035297561660810929e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (analytic) = 1.2018965179946554084851792676434
y[1] (numeric) = 1.2018965179946554084851792676435
absolute error = 1e-31
relative error = 8.3201838513392448184242232820009e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (analytic) = 1.2039256117342134381920455363505
y[1] (numeric) = 1.2039256117342134381920455363507
absolute error = 2e-31
relative error = 1.6612322061319625754688715943832e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (analytic) = 1.2059750982048834654822863400384
y[1] (numeric) = 1.2059750982048834654822863400386
absolute error = 2e-31
relative error = 1.6584090359552510507363316680547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (analytic) = 1.2080451823570204684438838657276
y[1] (numeric) = 1.2080451823570204684438838657277
absolute error = 1e-31
relative error = 8.2778360826612220900083900369731e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (analytic) = 1.2101360712007647366541591331939
y[1] (numeric) = 1.2101360712007647366541591331941
absolute error = 2e-31
relative error = 1.6527067059619899334535068815247e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (analytic) = 1.2122479738267430577177549975797
y[1] (numeric) = 1.2122479738267430577177549975799
absolute error = 2e-31
relative error = 1.6498274636719203637531247958749e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (analytic) = 1.2143811014269779541881664116833
y[1] (numeric) = 1.2143811014269779541881664116835
absolute error = 2e-31
relative error = 1.6469294504417665773259866514364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (analytic) = 1.2165356673160070618139345231369
y[1] (numeric) = 1.2165356673160070618139345231371
absolute error = 2e-31
relative error = 1.6440126284275070084777217008171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (analytic) = 1.2187118869522147610649287664188
y[1] (numeric) = 1.218711886952214761064928766419
absolute error = 2e-31
relative error = 1.6410769611853463891758055838315e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (analytic) = 1.2209099779593781951196459967695
y[1] (numeric) = 1.2209099779593781951196459967697
absolute error = 2e-31
relative error = 1.6381224136957159744494134313909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (analytic) = 1.223130160148429828933280470764
y[1] (numeric) = 1.2231301601484298289332804707642
absolute error = 2e-31
relative error = 1.6351489523872873192144343573125e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (analytic) = 1.2253726555394387256606070068809
y[1] (numeric) = 1.2253726555394387256606070068811
absolute error = 2e-31
relative error = 1.6321565451609914970721586544819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (analytic) = 1.2276376883838127385796374057948
y[1] (numeric) = 1.227637688383812738579637405795
absolute error = 2e-31
relative error = 1.6291451614140354854061091790886e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (analytic) = 1.2299254851867238387537443843114
y[1] (numeric) = 1.2299254851867238387537443843117
absolute error = 3e-31
relative error = 2.4391721580958609140935767841844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (analytic) = 1.2322362747297588209837070706824
y[1] (numeric) = 1.2322362747297588209837070706827
absolute error = 3e-31
relative error = 2.4345980243585416607974714513758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (analytic) = 1.234570288093797653139148917061
y[1] (numeric) = 1.2345702880937976531391489170612
absolute error = 2e-31
relative error = 1.6199968679693740496788150699775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (analytic) = 1.2369277586821217567233665275514
y[1] (numeric) = 1.2369277586821217567233665275516
absolute error = 2e-31
relative error = 1.6169093028770650208491339298285e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (analytic) = 1.2393089222437545295188628493952
y[1] (numeric) = 1.2393089222437545295188628493954
absolute error = 2e-31
relative error = 1.6138026315335671397790780710560e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (analytic) = 1.2417140168970364443852997809855
y[1] (numeric) = 1.2417140168970364443852997809857
absolute error = 2e-31
relative error = 1.6106768328168441813225068415122e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=68032864, alloc=4324584, time=2.57
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (analytic) = 1.2441432831534370817393959731224
y[1] (numeric) = 1.2441432831534370817393959731226
absolute error = 2e-31
relative error = 1.6075318872684417317346129442166e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (analytic) = 1.2465969639416064769398612398338
y[1] (numeric) = 1.246596963941606476939861239834
absolute error = 2e-31
relative error = 1.6043677771171634963086871831038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (analytic) = 1.2490753046316681877321489284998
y[1] (numeric) = 1.2490753046316681877321489285001
absolute error = 3e-31
relative error = 2.4017767294539945895596279267559e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (analytic) = 1.2515785530597565110800150148691
y[1] (numeric) = 1.2515785530597565110800150148694
absolute error = 3e-31
relative error = 2.3969730007484118788046064313120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (analytic) = 1.2541069595528003031260148277283
y[1] (numeric) = 1.2541069595528003031260148277286
absolute error = 3e-31
relative error = 2.3921404607066087001925183866022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.36
y[1] (analytic) = 1.2566607769535558806835867050428
y[1] (numeric) = 1.256660776953555880683586705043
absolute error = 2e-31
relative error = 1.5915193954318164548680118753423e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (analytic) = 1.2592402606458915075717326107116
y[1] (numeric) = 1.2592402606458915075717326107118
absolute error = 2e-31
relative error = 1.5882592563981053420816363809006e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (analytic) = 1.2618456685803259942619996555144
y[1] (numeric) = 1.2618456685803259942619996555146
absolute error = 2e-31
relative error = 1.5849798828807287814708995800400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (analytic) = 1.2644772612998239647190094577137
y[1] (numeric) = 1.264477261299823964719009457714
absolute error = 3e-31
relative error = 2.3725219043608100725283405076077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (analytic) = 1.2671353019658503699827155236038
y[1] (numeric) = 1.2671353019658503699827155236041
absolute error = 3e-31
relative error = 2.3675451195667586174490720208987e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (analytic) = 1.2698200563846868539654590407689
y[1] (numeric) = 1.2698200563846868539654590407692
absolute error = 3e-31
relative error = 2.3625394676323824931201656257588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.3
y[1] (analytic) = 1.2725317930340126031223331675634
y[1] (numeric) = 1.2725317930340126031223331675637
absolute error = 3e-31
relative error = 2.3575049491276758378062654167752e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (analytic) = 1.2752707830897523381019736371362
y[1] (numeric) = 1.2752707830897523381019736371365
absolute error = 3e-31
relative error = 2.3524415675324562572258743084837e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (analytic) = 1.2780373004531941321993141560141
y[1] (numeric) = 1.2780373004531941321993141560144
absolute error = 3e-31
relative error = 2.3473493292693374894090653315350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (analytic) = 1.2808316217783797684147501301548
y[1] (numeric) = 1.2808316217783797684147501301551
absolute error = 3e-31
relative error = 2.3422282437363848640226425417408e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.26
y[1] (analytic) = 1.2836540264997703741782420084759
y[1] (numeric) = 1.2836540264997703741782420084763
absolute error = 4e-31
relative error = 3.1161044311192487332104975687437e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 8.165e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (analytic) = 1.2865047968601901003248854266478
y[1] (numeric) = 1.2865047968601901003248854266482
absolute error = 4e-31
relative error = 3.1091994446987645879980781906463e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.24
y[1] (analytic) = 1.2893842179390506387131321849311
y[1] (numeric) = 1.2893842179390506387131321849314
absolute error = 3e-31
relative error = 2.3266920428072203951237890767539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (analytic) = 1.2922925776808594009609443919072
y[1] (numeric) = 1.2922925776808594009609443919075
absolute error = 3e-31
relative error = 2.3214557228083614127355177678531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (analytic) = 1.2952301669240142091415122843203
y[1] (numeric) = 1.2952301669240142091415122843206
absolute error = 3e-31
relative error = 2.3161906482803512236204855533798e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (analytic) = 1.298197279429887377931600950376
y[1] (numeric) = 1.2981972794298873779316009503763
absolute error = 3e-31
relative error = 2.3108968471398056394421585460387e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (analytic) = 1.3011942119122020966449776070832
y[1] (numeric) = 1.3011942119122020966449776070836
absolute error = 4e-31
relative error = 3.0740991339960705717236506098538e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
bytes used=72033932, alloc=4324584, time=2.72
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (analytic) = 1.3042212640667040488136031743295
y[1] (numeric) = 1.3042212640667040488136031743299
absolute error = 4e-31
relative error = 3.0669642569141711727966589411696e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (analytic) = 1.3072787386011312365032726969182
y[1] (numeric) = 1.3072787386011312365032726969186
absolute error = 4e-31
relative error = 3.0597912150550588419744506649077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (analytic) = 1.3103669412654850063711111154575
y[1] (numeric) = 1.3103669412654850063711111154579
absolute error = 4e-31
relative error = 3.0525800629074217178001107520587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (analytic) = 1.313486180882605304592756074811
y[1] (numeric) = 1.3134861808826053045927560748114
absolute error = 4e-31
relative error = 3.0453308593716416790000581355376e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (analytic) = 1.3166367693790532182101999524295
y[1] (numeric) = 1.3166367693790532182101999524299
absolute error = 4e-31
relative error = 3.0380436677964442983428774237018e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (analytic) = 1.3198190218163038911801614276738
y[1] (numeric) = 1.3198190218163038911801614276742
absolute error = 4e-31
relative error = 3.0307185560148194361059923371987e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (analytic) = 1.3230332564222529344405856126403
y[1] (numeric) = 1.3230332564222529344405856126407
absolute error = 4e-31
relative error = 3.0233555963791882398242006182313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (analytic) = 1.3262797946230394806625348237426
y[1] (numeric) = 1.3262797946230394806625348237429
absolute error = 3e-31
relative error = 2.2619661493468442187808136766506e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (analytic) = 1.3295589610751890660194644838161
y[1] (numeric) = 1.3295589610751890660194644838165
absolute error = 4e-31
relative error = 3.0085164457582806350919220329429e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (analytic) = 1.3328710836980795532888469064313
y[1] (numeric) = 1.3328710836980795532888469064317
absolute error = 4e-31
relative error = 3.0010404223804704168399073696483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (analytic) = 1.336216493706733342905508150893
y[1] (numeric) = 1.3362164937067333429055081508934
absolute error = 4e-31
relative error = 2.9935268864282569040831623377999e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (analytic) = 1.3395955256449391512151102152476
y[1] (numeric) = 1.339595525644939151215110215248
absolute error = 4e-31
relative error = 2.9859759333506486713562932623629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (analytic) = 1.3430085174187066681332054893988
y[1] (numeric) = 1.3430085174187066681332054893991
absolute error = 3e-31
relative error = 2.2337907474824278562746077164423e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (analytic) = 1.3464558103300574397035083480901
y[1] (numeric) = 1.3464558103300574397035083480905
absolute error = 4e-31
relative error = 2.9707621812107430696159068365441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (analytic) = 1.3499377491111553546717988735768
y[1] (numeric) = 1.3499377491111553546717988735772
absolute error = 4e-31
relative error = 2.9630995967286159751635825082572e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (analytic) = 1.353454681958780148152558265309
y[1] (numeric) = 1.3534546819587801481525582653093
absolute error = 3e-31
relative error = 2.2165500182527469828981111784822e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (analytic) = 1.3570069605691473697674306156514
y[1] (numeric) = 1.3570069605691473697674306156517
absolute error = 3e-31
relative error = 2.2107476875002606975868399217983e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (analytic) = 1.360594940173078298281341634654
y[1] (numeric) = 1.3605949401730782982813416346544
absolute error = 4e-31
relative error = 2.9398903978660752426461936532144e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -1.01
y[1] (analytic) = 1.3642189795715233197570462956374
y[1] (numeric) = 1.3642189795715233197570462956377
absolute error = 3e-31
relative error = 2.1990604477165726870998236132422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = 1.3678794411714423215955237701615
y[1] (numeric) = 1.3678794411714423215955237701618
absolute error = 3e-31
relative error = 2.1931757358900146377534777254654e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = 1.3715766910220456905315241199082
y[1] (numeric) = 1.3715766910220456905315241199085
absolute error = 3e-31
relative error = 2.1872637670479194953604281562358e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (analytic) = 1.3753110988513995387142672324775
y[1] (numeric) = 1.3753110988513995387142672324778
absolute error = 3e-31
relative error = 2.1813246490233885977377796717952e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=76034676, alloc=4324584, time=2.87
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (analytic) = 1.3790830381033988184264065277403
y[1] (numeric) = 1.3790830381033988184264065277406
absolute error = 3e-31
relative error = 2.1753584933694692444848625431972e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = 1.3828928859751120227835403627544
y[1] (numeric) = 1.3828928859751120227835403627548
absolute error = 4e-31
relative error = 2.8924872204975593142523721965663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = 1.386741023454501206915461774036
y[1] (numeric) = 1.3867410234545012069154617740363
absolute error = 3e-31
relative error = 2.1633455340685892752958905919581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = 1.3906278353585211016626981379217
y[1] (numeric) = 1.390627835358521101662698137922
absolute error = 3e-31
relative error = 2.1572989722491516185230304293178e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = 1.3945537103716011297314597702349
y[1] (numeric) = 1.3945537103716011297314597702353
absolute error = 4e-31
relative error = 2.8683011419718901004058204815604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (analytic) = 1.3985190410845141725406814138044
y[1] (numeric) = 1.3985190410845141725406814138048
absolute error = 4e-31
relative error = 2.8601684228039589719248860642473e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (analytic) = 1.4025242240336359746702320649927
y[1] (numeric) = 1.4025242240336359746702320649931
absolute error = 4e-31
relative error = 2.8520006510091266547301871460528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = 1.4065696597405991118834542396456
y[1] (numeric) = 1.406569659740599111883454239646
absolute error = 4e-31
relative error = 2.8437980105000158538523929472014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = 1.4106557527523454881538800158902
y[1] (numeric) = 1.4106557527523454881538800158906
absolute error = 4e-31
relative error = 2.8355606902644797129023559514432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (analytic) = 1.4147829116815813669792037174992
y[1] (numeric) = 1.4147829116815813669792037174997
absolute error = 5e-31
relative error = 3.5341111054678379004528746687791e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = 1.4189515492476389825193552735605
y[1] (numeric) = 1.418951549247638982519355273561
absolute error = 5e-31
relative error = 3.5237284899904552428550183710825e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (analytic) = 1.4231620823177488167538395179062
y[1] (numeric) = 1.4231620823177488167538395179067
absolute error = 5e-31
relative error = 3.5133032717236574340605673377709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = 1.4274149319487266699204508411764
y[1] (numeric) = 1.4274149319487266699204508411768
absolute error = 4e-31
relative error = 2.8022685698958918004059510801443e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = 1.4317105234290796929771464081439
y[1] (numeric) = 1.4317105234290796929771464081443
absolute error = 4e-31
relative error = 2.7938608640101551018981074122370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = 1.4360492863215355927254126049699
y[1] (numeric) = 1.4360492863215355927254126049703
absolute error = 4e-31
relative error = 2.7854197192953365108718988476479e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = 1.4404316545059992625510781754405
y[1] (numeric) = 1.4404316545059992625510781754409
absolute error = 4e-31
relative error = 2.7769453604321220335225348133170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (analytic) = 1.4448580662229411344814454391058
y[1] (numeric) = 1.4448580662229411344814454391062
absolute error = 4e-31
relative error = 2.7684380172071526420106333269745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (analytic) = 1.4493289641172215914301023850156
y[1] (numeric) = 1.449328964117221591430102385016
absolute error = 4e-31
relative error = 2.7598979245104497705354962477937e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = 1.4538447952823558221071605875315
y[1] (numeric) = 1.4538447952823558221071605875319
absolute error = 4e-31
relative error = 2.7513253223313615651310838932204e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = 1.4584060113052235451172974700586
y[1] (numeric) = 1.4584060113052235451172974700591
absolute error = 5e-31
relative error = 3.4284005696912692058539990097913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = 1.4630130683112280732552709485309
y[1] (numeric) = 1.4630130683112280732552709485314
absolute error = 5e-31
relative error = 3.4176044686815781375259926599884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = 1.4676664270099092339429686851366
y[1] (numeric) = 1.4676664270099092339429686851371
absolute error = 5e-31
relative error = 3.4067686689451277693291860606138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=80035416, alloc=4324584, time=3.02
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (analytic) = 1.4723665527410147071380465509433
y[1] (numeric) = 1.4723665527410147071380465509438
absolute error = 5e-31
relative error = 3.3958934958769648657984005788828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (analytic) = 1.4771139155210343878863400708347
y[1] (numeric) = 1.4771139155210343878863400708352
absolute error = 5e-31
relative error = 3.3849792811926149867837799399296e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = 1.4819089900902024269930828566272
y[1] (numeric) = 1.4819089900902024269930828566276
absolute error = 4e-31
relative error = 2.6992210903292540972177960473861e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (analytic) = 1.4867522559599716500561676479956
y[1] (numeric) = 1.4867522559599716500561676479961
absolute error = 5e-31
relative error = 3.3630350853388022336852116897145e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = 1.4916441974609651023429154350493
y[1] (numeric) = 1.4916441974609651023429154350498
absolute error = 5e-31
relative error = 3.3520057990443429478172524433917e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (analytic) = 1.4965853037914095147048000933975
y[1] (numeric) = 1.496585303791409514704800093398
absolute error = 5e-31
relative error = 3.3409388608408305326539416481494e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (analytic) = 1.5015760690660555339170813603031
y[1] (numeric) = 1.5015760690660555339170813603036
absolute error = 5e-31
relative error = 3.3298346337591012816090994160151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (analytic) = 1.5066169923655896095071471097274
y[1] (numeric) = 1.5066169923655896095071471097279
absolute error = 5e-31
relative error = 3.3186934870217633547078706720491e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (analytic) = 1.511708577786542478301424470106
y[1] (numeric) = 1.5117085777865424783014244701065
absolute error = 5e-31
relative error = 3.3075157960147621288394927684670e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (analytic) = 1.5168513344916992375809050183918
y[1] (numeric) = 1.5168513344916992375809050183923
absolute error = 5e-31
relative error = 3.2963019422569271038105653567629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (analytic) = 1.5220457767610160478946081372088
y[1] (numeric) = 1.5220457767610160478946081372094
absolute error = 6e-31
relative error = 3.9420627760409927155993999334121e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (analytic) = 1.5272924240430485572436946085663
y[1] (numeric) = 1.5272924240430485572436946085669
absolute error = 6e-31
relative error = 3.9285207636379153865451835321759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (analytic) = 1.532591801006897189521506018502
y[1] (numeric) = 1.5325918010068971895215060185026
absolute error = 6e-31
relative error = 3.9149367731564668204243033351001e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (analytic) = 1.5379444375946744917816618612558
y[1] (numeric) = 1.5379444375946744917816618612565
absolute error = 7e-31
relative error = 4.5515298400167894398118278847267e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (analytic) = 1.5433508690744997871126640878166
y[1] (numeric) = 1.5433508690744997871126640878172
absolute error = 6e-31
relative error = 3.8876448124839014096543048938396e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (analytic) = 1.5488116360940264326284589172326
y[1] (numeric) = 1.5488116360940264326284589172332
absolute error = 6e-31
relative error = 3.8739378373547727174546638184712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (analytic) = 1.5543272847345070353453611638809
y[1] (numeric) = 1.5543272847345070353453611638815
absolute error = 6e-31
relative error = 3.8601908741664105313027572711356e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (analytic) = 1.5598983665654020325119832698729
y[1] (numeric) = 1.5598983665654020325119832698735
absolute error = 6e-31
relative error = 3.8464044380089023779941916036131e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (analytic) = 1.5655254386995370972957093374648
y[1] (numeric) = 1.5655254386995370972957093374654
absolute error = 6e-31
relative error = 3.8325790508930515222850885855157e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (analytic) = 1.5712090638488148856122474668313
y[1] (numeric) = 1.5712090638488148856122474668319
absolute error = 6e-31
relative error = 3.8187152416893980574879535613013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (analytic) = 1.5769498103804866953193699648816
y[1] (numeric) = 1.5769498103804866953193699648822
absolute error = 6e-31
relative error = 3.8048135460648040964293145543671e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (analytic) = 1.5827482523739896649876540047778
y[1] (numeric) = 1.5827482523739896649876540047784
absolute error = 6e-31
relative error = 3.7908745064166099065355428547100e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=84036500, alloc=4324584, time=3.17
x[1] = -0.53
y[1] (analytic) = 1.5886049696783551960154643004118
y[1] (numeric) = 1.5886049696783551960154643004124
absolute error = 6e-31
relative error = 3.7768986718043692340720610819636e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (analytic) = 1.5945205479701943389782298053389
y[1] (numeric) = 1.5945205479701943389782298053395
absolute error = 6e-31
relative error = 3.7628865978791734720246130921549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (analytic) = 1.6004955788122659427989706801995
y[1] (numeric) = 1.6004955788122659427989706802001
absolute error = 6e-31
relative error = 3.7488388468105757426178916162339e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (analytic) = 1.6065306597126334236037995349912
y[1] (numeric) = 1.6065306597126334236037995349918
absolute error = 6e-31
relative error = 3.7347559872111273878334033944730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (analytic) = 1.612626394184416068988579968019
y[1] (numeric) = 1.6126263941844160689885799680197
absolute error = 7e-31
relative error = 4.3407450264016309196966308971522e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (analytic) = 1.6187833918061408528769619869106
y[1] (numeric) = 1.6187833918061408528769619869112
absolute error = 6e-31
relative error = 3.7064872486154938614782967810314e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (analytic) = 1.6250022682827007962015734619291
y[1] (numeric) = 1.6250022682827007962015734619298
absolute error = 7e-31
relative error = 4.3076862947382751927893824650320e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (analytic) = 1.6312836455069259692952345339618
y[1] (numeric) = 1.6312836455069259692952345339624
absolute error = 6e-31
relative error = 3.6780850568360128243749335188611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (analytic) = 1.6376281516217732931437434383122
y[1] (numeric) = 1.6376281516217732931437434383129
absolute error = 7e-31
relative error = 4.2744746376445539180843846311258e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (analytic) = 1.644036421083141358532184030009
y[1] (numeric) = 1.6440364210831413585321840300096
absolute error = 6e-31
relative error = 3.6495541844790864928567125537860e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (analytic) = 1.6505090947233165446190154984879
y[1] (numeric) = 1.6505090947233165446190154984885
absolute error = 6e-31
relative error = 3.6352420105905634652902743048829e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (analytic) = 1.65704681981505678160267362234
y[1] (numeric) = 1.6570468198150567816026736223406
absolute error = 6e-31
relative error = 3.6208994991883577597844592913272e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (analytic) = 1.6636502501363193659103535378148
y[1] (numeric) = 1.6636502501363193659103535378154
absolute error = 6e-31
relative error = 3.6065272730902186255758654482618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (analytic) = 1.6703200460356393007444329251478
y[1] (numeric) = 1.6703200460356393007444329251485
absolute error = 7e-31
relative error = 4.1908136207871640025835506158386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (analytic) = 1.6770568744981646998750723870924
y[1] (numeric) = 1.6770568744981646998750723870931
absolute error = 7e-31
relative error = 4.1739788950775148585979461263099e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (analytic) = 1.6838614092123558582744019662858
y[1] (numeric) = 1.6838614092123558582744019662865
absolute error = 7e-31
relative error = 4.1571117205389989269849494069695e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (analytic) = 1.6907343306373546595549399642394
y[1] (numeric) = 1.6907343306373546595549399642402
absolute error = 8e-31
relative error = 4.7316718274622405716941366124194e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (analytic) = 1.6976763260710310572091292638382
y[1] (numeric) = 1.6976763260710310572091292638389
absolute error = 7e-31
relative error = 4.1232830384106556991648950986231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (analytic) = 1.7046880897187134343548206990309
y[1] (numeric) = 1.7046880897187134343548206990316
absolute error = 7e-31
relative error = 4.1063230524213104045592410826380e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (analytic) = 1.711770322762609715079953510757
y[1] (numeric) = 1.7117703227626097150799535107577
absolute error = 7e-31
relative error = 4.0893336605478514787936250112632e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (analytic) = 1.7189237334319261695554184761104
y[1] (numeric) = 1.7189237334319261695554184761111
absolute error = 7e-31
relative error = 4.0723156378928536821268667251349e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (analytic) = 1.7261490370736909248550475294236
y[1] (numeric) = 1.7261490370736909248550475294243
absolute error = 7e-31
relative error = 4.0552697650412462156808533297639e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
bytes used=88037288, alloc=4324584, time=3.32
x[1] = -0.31
y[1] (analytic) = 1.7334469562242892638928316633154
y[1] (numeric) = 1.7334469562242892638928316633162
absolute error = 8e-31
relative error = 4.6150820890563706614167401387659e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (analytic) = 1.7408182206817178660668737793178
y[1] (numeric) = 1.7408182206817178660668737793186
absolute error = 8e-31
relative error = 4.5955401344932718972165701218773e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (analytic) = 1.7482635675785652150943529512748
y[1] (numeric) = 1.7482635675785652150943529512756
absolute error = 8e-31
relative error = 4.5759690634521490743498989489082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (analytic) = 1.7557837414557254721391008071943
y[1] (numeric) = 1.7557837414557254721391008071951
absolute error = 8e-31
relative error = 4.5563697915138321271890753563099e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (analytic) = 1.7633794943368531856805312195579
y[1] (numeric) = 1.7633794943368531856805312195587
absolute error = 8e-31
relative error = 4.5367432397236346602794734184191e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (analytic) = 1.7710515858035662836569559954336
y[1] (numeric) = 1.7710515858035662836569559954344
absolute error = 8e-31
relative error = 4.5170903344242333331154565428813e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (analytic) = 1.7788007830714048682451702669783
y[1] (numeric) = 1.7788007830714048682451702669791
absolute error = 8e-31
relative error = 4.4974120070863848322185891032236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (analytic) = 1.7866278610665534092190847475156
y[1] (numeric) = 1.7866278610665534092190847475164
absolute error = 8e-31
relative error = 4.4777091941375435584559631319064e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (analytic) = 1.7945336025033340081706760906637
y[1] (numeric) = 1.7945336025033340081706760906645
absolute error = 8e-31
relative error = 4.4579828367884446169335040626583e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (analytic) = 1.8025187979624784829842553829934
y[1] (numeric) = 1.8025187979624784829842553829942
absolute error = 8e-31
relative error = 4.4382338808577181163358148443138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (analytic) = 1.8105842459701870998377291515507
y[1] (numeric) = 1.8105842459701870998377291515515
absolute error = 8e-31
relative error = 4.4184632765946021627627566353813e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (analytic) = 1.818730753077981858669935508619
y[1] (numeric) = 1.8187307530779818586699355086198
absolute error = 8e-31
relative error = 4.3986719784998232684732203347135e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (analytic) = 1.8269591339433623175091467937083
y[1] (numeric) = 1.8269591339433623175091467937091
absolute error = 8e-31
relative error = 4.3788609451447141870676915211930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (analytic) = 1.8352702114112720213123849740188
y[1] (numeric) = 1.8352702114112720213123849740195
absolute error = 7e-31
relative error = 3.8141522466150603781262212503641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (analytic) = 1.8436648165963836820263226519154
y[1] (numeric) = 1.8436648165963836820263226519161
absolute error = 7e-31
relative error = 3.7967855854204569431358508415381e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (analytic) = 1.8521437889662113384563469814686
y[1] (numeric) = 1.8521437889662113384563469814692
absolute error = 6e-31
relative error = 3.2394893073333940855170672751515e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (analytic) = 1.8607079764250578072290337645433
y[1] (numeric) = 1.8607079764250578072290337645439
absolute error = 6e-31
relative error = 3.2245790720624972966700941621545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (analytic) = 1.8693582353988058196630844161712
y[1] (numeric) = 1.8693582353988058196630844161718
absolute error = 6e-31
relative error = 3.2096576709492869576703488962507e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (analytic) = 1.8780954309205613237330724091574
y[1] (numeric) = 1.878095430920561323733072409158
absolute error = 6e-31
relative error = 3.1947258383239125145564566046392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (analytic) = 1.8869204367171575155275652287698
y[1] (numeric) = 1.8869204367171575155275652287704
absolute error = 6e-31
relative error = 3.1797843105874305046244072327248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (analytic) = 1.8958341352965282506768545828765
y[1] (numeric) = 1.8958341352965282506768545828771
absolute error = 6e-31
relative error = 3.1648338260675622669243947862593e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (analytic) = 1.9048374180359595731642490594464
y[1] (numeric) = 1.904837418035959573164249059447
absolute error = 6e-31
relative error = 3.1498751248736399165951590956249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=92038336, alloc=4324584, time=3.48
x[1] = -0.09
y[1] (analytic) = 1.9139311852712281867473535464995
y[1] (numeric) = 1.9139311852712281867473535465001
absolute error = 6e-31
relative error = 3.1349089487508007401072092507920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (analytic) = 1.9231163463866357829107598495724
y[1] (numeric) = 1.923116346386635782910759849573
absolute error = 6e-31
relative error = 3.1199360409334907115298282267535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (analytic) = 1.932393819905948228857972632485
y[1] (numeric) = 1.9323938199059482288579726324856
absolute error = 6e-31
relative error = 3.1049571459983383298655127000324e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.06
y[1] (analytic) = 1.9417645335842487095371527832712
y[1] (numeric) = 1.9417645335842487095371527832718
absolute error = 6e-31
relative error = 3.0899730097164604337577145009711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (analytic) = 1.9512294245007140090914253197796
y[1] (numeric) = 1.9512294245007140090914253197803
absolute error = 7e-31
relative error = 3.5874817753894724056305093249062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (analytic) = 1.9607894391523232094392106913232
y[1] (numeric) = 1.9607894391523232094392106913239
absolute error = 7e-31
relative error = 3.5699906681597582614059935415526e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (analytic) = 1.9704455335485081769325283519592
y[1] (numeric) = 1.9704455335485081769325283519599
absolute error = 7e-31
relative error = 3.5524960628543427295048098225841e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (analytic) = 1.9801986733067553022208141042253
y[1] (numeric) = 1.980198673306755302220814104226
absolute error = 7e-31
relative error = 3.5349988333799981111876512189810e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (analytic) = 1.99004983374916805357390597718
y[1] (numeric) = 1.9900498337491680535739059771807
absolute error = 7e-31
relative error = 3.5174998541681249852432050524977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 2
y[1] (numeric) = 2.0000000000000000000000000000007
absolute error = 7e-31
relative error = 3.5000000000000000000000000000000e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 2.0100501670841680575421654569029
y[1] (numeric) = 2.0100501670841680575421654569036
absolute error = 7e-31
relative error = 3.4825001458318750147567949475023e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = 2.0202013400267558101601439204832
y[1] (numeric) = 2.0202013400267558101601439204839
absolute error = 7e-31
relative error = 3.4650011666200018888123487810190e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 2.0304545339535168556124399538312
y[1] (numeric) = 2.0304545339535168556124399538319
absolute error = 7e-31
relative error = 3.4475039371456572704951901774159e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 2.0408107741923882267570447579169
y[1] (numeric) = 2.0408107741923882267570447579176
absolute error = 7e-31
relative error = 3.4300093318402417385940064584474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = 2.0512710963760240396975176363356
y[1] (numeric) = 2.0512710963760240396975176363364
absolute error = 8e-31
relative error = 3.9000208281263172507079893429645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 2.0618365465453596222246848771684
y[1] (numeric) = 2.0618365465453596222246848771691
absolute error = 7e-31
relative error = 3.3950314886641294939493330822003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 2.0725081812542164790531039498891
y[1] (numeric) = 2.0725081812542164790531039498898
absolute error = 7e-31
relative error = 3.3775499963352719484902351832955e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 2.0832870676749585544359877586749
y[1] (numeric) = 2.0832870676749585544359877586756
absolute error = 7e-31
relative error = 3.3600746189109275032152004021209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 2.0941742837052103578728976235449
y[1] (numeric) = 2.0941742837052103578728976235456
absolute error = 7e-31
relative error = 3.3426062264573991365415892074093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 2.1051709180756476248117078264902
y[1] (numeric) = 2.105170918075647624811707826491
absolute error = 8e-31
relative error = 3.8001665001684801112064545391669e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 2.116278070458871291500737769053
y[1] (numeric) = 2.1162780704588712915007377690537
absolute error = 7e-31
relative error = 3.3076938695878440219215394160308e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 2.1274968515793756714792655693748
y[1] (numeric) = 2.1274968515793756714792655693756
absolute error = 8e-31
relative error = 3.7602875858834259938341236897004e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=96039144, alloc=4390108, time=3.63
x[1] = 0.13
y[1] (analytic) = 2.138828383324621830615712602619
y[1] (numeric) = 2.1388283833246218306157126026197
absolute error = 7e-31
relative error = 3.2728198552887687330174672945876e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 2.1502737988572272681235642576211
y[1] (numeric) = 2.1502737988572272681235642576219
absolute error = 8e-31
relative error = 3.7204564387342840564395348049991e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 2.1618342427282831226166202143317
y[1] (numeric) = 2.1618342427282831226166202143324
absolute error = 7e-31
relative error = 3.2379910825937531538848901441530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 2.173510870991810235018611086892
y[1] (numeric) = 2.1735108709918102350186110868927
absolute error = 7e-31
relative error = 3.2205958081110402335634215123232e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 2.1853048513203655140288527643693
y[1] (numeric) = 2.18530485132036551402885276437
absolute error = 7e-31
relative error = 3.2032144145795430568641491584619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 2.1972173631218101648768239736005
y[1] (numeric) = 2.1972173631218101648768239736012
absolute error = 7e-31
relative error = 3.1858477533849396218737787496358e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 2.2092495976572514582858497035543
y[1] (numeric) = 2.209249597657251458285849703555
absolute error = 7e-31
relative error = 3.1684966729983750863157699189562e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 2.2214027581601698339210719946397
y[1] (numeric) = 2.2214027581601698339210719946404
absolute error = 7e-31
relative error = 3.1511620188126546400859322071257e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 2.2336780599567432511313258071563
y[1] (numeric) = 2.233678059956743251131325807157
absolute error = 7e-31
relative error = 3.1338446329797231075825879440414e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 2.2460767305873808195202647829927
y[1] (numeric) = 2.2460767305873808195202647829934
absolute error = 7e-31
relative error = 3.1165453542494966482061620112254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 2.258600009929477862811072376219
y[1] (numeric) = 2.2586000099294778628110723762197
absolute error = 7e-31
relative error = 3.0992650178101109601831839451739e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.000e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 2.2712491503214046916134410512278
y[1] (numeric) = 2.2712491503214046916134410512285
absolute error = 7e-31
relative error = 3.0820044551296493863510322595819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 2.2840254166877414840734205680624
y[1] (numeric) = 2.2840254166877414840734205680632
absolute error = 8e-31
relative error = 3.5025879929136151677814108967765e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 2.2969300866657717979985630881788
y[1] (numeric) = 2.2969300866657717979985630881796
absolute error = 8e-31
relative error = 3.4829096655757666668845434571187e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 2.3099644507332473639149892266262
y[1] (numeric) = 2.309964450733247363914989226627
absolute error = 8e-31
relative error = 3.4632567602763653397205265815810e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 2.3231298123374369356421517730364
y[1] (numeric) = 2.3231298123374369356421517730372
absolute error = 8e-31
relative error = 3.4436302084861678728109246436902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 2.3364274880254721033778956250755
y[1] (numeric) = 2.3364274880254721033778956250763
absolute error = 8e-31
relative error = 3.4240309365478509256501010510918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 2.349858807576003103983744313328
y[1] (numeric) = 2.3498588075760031039837443133288
absolute error = 8e-31
relative error = 3.4044598655067281027834298781228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 2.3634251141321777941611551872143
y[1] (numeric) = 2.3634251141321777941611551872151
absolute error = 8e-31
relative error = 3.3849179109436293385832598612343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 2.3771277643359570845268770678281
y[1] (numeric) = 2.3771277643359570845268770678289
absolute error = 8e-31
relative error = 3.3654059828100043249361676231270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 2.3909681284637802662427478049531
y[1] (numeric) = 2.3909681284637802662427478049539
absolute error = 8e-31
relative error = 3.3459249852653100775692951712745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 2.4049475905635937968456495337223
y[1] (numeric) = 2.404947590563593796845649533723
absolute error = 7e-31
relative error = 2.9106663394521485212063749887367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=100039828, alloc=4390108, time=3.78
x[1] = 0.35
y[1] (analytic) = 2.4190675485932572482703956619399
y[1] (numeric) = 2.4190675485932572482703956619406
absolute error = 7e-31
relative error = 2.8936769475786895954407589173619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 2.4333294145603402577756905512456
y[1] (numeric) = 2.4333294145603402577756905512463
absolute error = 7e-31
relative error = 2.8767169615893443008351049013768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 2.4477346146633244615847523355192
y[1] (numeric) = 2.4477346146633244615847523355199
absolute error = 7e-31
relative error = 2.8597871509705394997676304641332e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 2.46228458943422453155163160907
y[1] (numeric) = 2.4622845894342245315516316090707
absolute error = 7e-31
relative error = 2.8428882794610010730150505930305e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 2.4769807938826425770757438765387
y[1] (numeric) = 2.4769807938826425770757438765394
absolute error = 7e-31
relative error = 2.8260211049224851414020538736901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 2.4918246976412703178248529528372
y[1] (numeric) = 2.4918246976412703178248529528379
absolute error = 7e-31
relative error = 2.8091863792128359974164493841615e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 2.5068177851128535776050298262424
y[1] (numeric) = 2.5068177851128535776050298262431
absolute error = 7e-31
relative error = 2.7923848480614116034948236436945e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 2.5219615556186337959494448003237
y[1] (numeric) = 2.5219615556186337959494448003244
absolute error = 7e-31
relative error = 2.7756172509469159469181308267848e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 2.5372575235482814017008534659144
y[1] (numeric) = 2.5372575235482814017008534659151
absolute error = 7e-31
relative error = 2.7588843209776759571613466443033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 2.5527072185113360420500796461917
y[1] (numeric) = 2.5527072185113360420500796461924
absolute error = 7e-31
relative error = 2.7421867847743990916671686872495e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 2.5683121854901688111795997746932
y[1] (numeric) = 2.5683121854901688111795997746939
absolute error = 7e-31
relative error = 2.7255253623554460819156153688743e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 2.5840739849944817748625620134736
y[1] (numeric) = 2.5840739849944817748625620134743
absolute error = 7e-31
relative error = 2.7089007670246517048959108946619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 2.5999941932173602410984500463115
y[1] (numeric) = 2.5999941932173602410984500463121
absolute error = 6e-31
relative error = 2.3076974616529069776091007442583e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 8.165e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 2.616074402192893382142499105688
y[1] (numeric) = 2.6160744021928933821424991056886
absolute error = 6e-31
relative error = 2.2935127513845061385217032189685e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 2.6323162199553789701224181313345
y[1] (numeric) = 2.6323162199553789701224181313351
absolute error = 6e-31
relative error = 2.2793614059414592116886020881554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 2.6487212707001281468486507878142
y[1] (numeric) = 2.6487212707001281468486507878148
absolute error = 6e-31
relative error = 2.2652440127888726121665966055269e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 2.6652911949458863084291607887622
y[1] (numeric) = 2.6652911949458863084291607887629
absolute error = 7e-31
relative error = 2.6263546787209949669457931143939e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 2.6820276496988863469125541946667
y[1] (numeric) = 2.6820276496988863469125541946673
absolute error = 6e-31
relative error = 2.2371134021208265279753869078450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 2.6989323086185506544204144868253
y[1] (numeric) = 2.698932308618550654420414486826
absolute error = 7e-31
relative error = 2.5936182162282358935825954043757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 2.716006862184858460107349114715
y[1] (numeric) = 2.7160068621848584601073491147157
absolute error = 7e-31
relative error = 2.5773130758472884423752000028383e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 2.7332530178673952368219167671373
y[1] (numeric) = 2.733253017867395236821916767138
absolute error = 7e-31
relative error = 2.5610508629243952208324663532384e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 2.7506725002961010825499764350019
y[1] (numeric) = 2.7506725002961010825499764350025
absolute error = 6e-31
relative error = 2.1812847583106019425120464386986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
bytes used=104041152, alloc=4390108, time=3.94
x[1] = 0.57
y[1] (analytic) = 2.7682670514337351516208933928238
y[1] (numeric) = 2.7682670514337351516208933928245
absolute error = 7e-31
relative error = 2.5286577739581065573340633168984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 2.7860384307500733822634435579423
y[1] (numeric) = 2.786038430750073382263443557943
absolute error = 7e-31
relative error = 2.5125281556562805590067764624513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 2.8039884153978569404293370747409
y[1] (numeric) = 2.8039884153978569404293370747416
absolute error = 7e-31
relative error = 2.4964439801391877134801165170084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 2.8221188003905089748753676681629
y[1] (numeric) = 2.8221188003905089748753676681636
absolute error = 7e-31
relative error = 2.4804058564194318296362255451168e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 2.8404313987816374553277937710156
y[1] (numeric) = 2.8404313987816374553277937710164
absolute error = 8e-31
relative error = 2.8164735833547981204609268082138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 2.8589280418463420441623540602681
y[1] (numeric) = 2.8589280418463420441623540602688
absolute error = 7e-31
relative error = 2.4484701599832105601881721152734e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 2.8776105792643431324381749672586
y[1] (numeric) = 2.8776105792643431324381749672593
absolute error = 7e-31
relative error = 2.4325737646507887095049794423831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 2.8964808793049513533417815912859
y[1] (numeric) = 2.8964808793049513533417815912866
absolute error = 7e-31
relative error = 2.4167257757557653823639525457948e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 2.9155408290138960701466981926821
y[1] (numeric) = 2.9155408290138960701466981926828
absolute error = 7e-31
relative error = 2.4009267612855084984673667443527e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 2.9347923344020315216931251510197
y[1] (numeric) = 2.9347923344020315216931251510204
absolute error = 7e-31
relative error = 2.3851772808403020546652085005318e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 2.9542373206359394961594960015662
y[1] (numeric) = 2.9542373206359394961594960015669
absolute error = 7e-31
relative error = 2.3694778855793330196247101241461e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 2.9738777322304475935521277966183
y[1] (numeric) = 2.973877732230447593552127796619
absolute error = 7e-31
relative error = 2.3538291181695313034089810591313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 2.9937155332430823288996461769344
y[1] (numeric) = 2.9937155332430823288996461769351
absolute error = 7e-31
relative error = 2.3382315127372582057472608175789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 3.0137527074704765216245493885831
y[1] (numeric) = 3.0137527074704765216245493885838
absolute error = 7e-31
relative error = 2.3226855948228372542844816925909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 3.0339912586467506119945217716624
y[1] (numeric) = 3.0339912586467506119945217716632
absolute error = 8e-31
relative error = 2.6367907215290512834923960905733e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 3.0544332106438877429504601670086
y[1] (numeric) = 3.0544332106438877429504601670093
absolute error = 7e-31
relative error = 2.2917508805256768728407036343998e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 3.0750806076741226449863758349892
y[1] (numeric) = 3.07508060767412264498637583499
absolute error = 8e-31
relative error = 2.6015578193414918055644079052276e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 3.0959355144943645631383178428338
y[1] (numeric) = 3.0959355144943645631383178428345
absolute error = 7e-31
relative error = 2.2610290063303390185027080840986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 3.1170000166126746685453698198371
y[1] (numeric) = 3.1170000166126746685453698198378
absolute error = 7e-31
relative error = 2.2457491057722491878822391895639e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 3.138276220496818602495941263298
y[1] (numeric) = 3.1382762204968186024959412632987
absolute error = 7e-31
relative error = 2.2305238634768211229391395151407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 3.15976625378491500838755239034
y[1] (numeric) = 3.1597662537849150083875523903408
absolute error = 8e-31
relative error = 2.5318328501094749799584117440186e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 3.181472265498201116628849542537
y[1] (numeric) = 3.1814722654982011166288495425378
absolute error = 8e-31
relative error = 2.5145590884939692706336015843341e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 3.203396426255936659219646589984
y[1] (numeric) = 3.2033964262559366592196465899848
absolute error = 8e-31
relative error = 2.4973493553372768697378322135591e-29 %
Correct digits = 31
bytes used=108042032, alloc=4390108, time=4.09
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 3.2255409284924676045795375313951
y[1] (numeric) = 3.2255409284924676045795375313959
absolute error = 8e-31
relative error = 2.4802041509791004589290075044125e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 3.2479079866764714191794502001334
y[1] (numeric) = 3.2479079866764714191794502001342
absolute error = 8e-31
relative error = 2.4631239655856947159787333460509e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 3.2704998375324057806850092252533
y[1] (numeric) = 3.2704998375324057806850092252541
absolute error = 8e-31
relative error = 2.4461092791357559329549303733660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 3.2933187402641828876675637932731
y[1] (numeric) = 3.2933187402641828876675637932739
absolute error = 8e-31
relative error = 2.4291605614093269782562023047042e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 3.3163669767810917335002471928655
y[1] (numeric) = 3.3163669767810917335002471928663
absolute error = 8e-31
relative error = 2.4122782719796897962037851755259e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 3.3396468519259909368547269375638
y[1] (numeric) = 3.3396468519259909368547269375646
absolute error = 8e-31
relative error = 2.3954628602082163991880978397113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 3.3631606937057949482718564674462
y[1] (numeric) = 3.363160693705794948271856467447
absolute error = 8e-31
relative error = 2.3787147652421481055030922595667e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 3.3869108535242766816189579740184
y[1] (numeric) = 3.3869108535242766816189579740192
absolute error = 8e-31
relative error = 2.3620344160152716114319706062681e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 3.4108997064172098508908849161329
y[1] (numeric) = 3.4108997064172098508908849161337
absolute error = 8e-31
relative error = 2.3454222312514593592754005299536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 3.4351296512898745267844969337052
y[1] (numeric) = 3.435129651289874526784496933706
absolute error = 8e-31
relative error = 2.3288786194710405741952880971134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 3.4596031111569496638001265636025
y[1] (numeric) = 3.4596031111569496638001265636032
absolute error = 7e-31
relative error = 2.0233534816249722557583123423977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 3.4843225333848165873226590099968
y[1] (numeric) = 3.4843225333848165873226590099975
absolute error = 7e-31
relative error = 2.0089988607340283542221724944078e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 3.5092903899362976712328533227943
y[1] (numeric) = 3.509290389936297671232853322795
absolute error = 7e-31
relative error = 1.9947052600930717991314493875672e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 3.5345091776178546801206156940979
y[1] (numeric) = 3.5345091776178546801206156940987
absolute error = 8e-31
relative error = 2.2633977160562197991883590368794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 3.5599814183292714961404455052082
y[1] (numeric) = 3.559981418329271496140445505209
absolute error = 8e-31
relative error = 2.2472027406689290172719188551525e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 3.5857096593158461989898093013769
y[1] (numeric) = 3.5857096593158461989898093013777
absolute error = 8e-31
relative error = 2.2310785758170952658776250881115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 3.6116964734231177184286012988948
y[1] (numeric) = 3.6116964734231177184286012988956
absolute error = 8e-31
relative error = 2.2150255590048813714952556068677e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 3.6379444593541525322172152885726
y[1] (numeric) = 3.6379444593541525322172152885734
absolute error = 8e-31
relative error = 2.1990440176814153480403665514739e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 3.6644562419294171383574280391061
y[1] (numeric) = 3.664456241929417138357428039107
absolute error = 9e-31
relative error = 2.4560260529298342067866609846145e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 3.691234472349262289099879404071
y[1] (numeric) = 3.6912344723492622890998794040719
absolute error = 9e-31
relative error = 2.4382086988562415139187155312927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 3.7182818284590452353602874713527
y[1] (numeric) = 3.7182818284590452353602874713536
absolute error = 9e-31
relative error = 2.4204727923299560867395668236034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 3.7456010150169164939897763166604
y[1] (numeric) = 3.7456010150169164939897763166613
absolute error = 9e-31
relative error = 2.4028186568502819387005291602730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=112044908, alloc=4390108, time=4.25
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 3.7731947639642979167991997771454
y[1] (numeric) = 3.7731947639642979167991997771464
absolute error = 1.0e-30
relative error = 2.6502740053348118933845158669641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 3.8010658346990791093697628196836
y[1] (numeric) = 3.8010658346990791093697628196845
absolute error = 9e-31
relative error = 2.3677569374992179072394802346049e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 3.8292170143515595195194860071813
y[1] (numeric) = 3.8292170143515595195194860071823
absolute error = 1.0e-30
relative error = 2.6114999391575100570062960717259e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 3.8576511180631637898643122162488
y[1] (numeric) = 3.8576511180631637898643122162497
absolute error = 9e-31
relative error = 2.3330259073606140558819393564214e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 3.8863709892679582462413752849215
y[1] (numeric) = 3.8863709892679582462413752849225
absolute error = 1.0e-30
relative error = 2.5730945469731423259602329086400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 3.9153794999769966738778707729755
y[1] (numeric) = 3.9153794999769966738778707729765
absolute error = 1.0e-30
relative error = 2.5540308417252404790846409451920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 3.9446795510655238161201013252344
y[1] (numeric) = 3.9446795510655238161201013252354
absolute error = 1.0e-30
relative error = 2.5350601666233783216092668440930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 3.9742740725630653163119065891359
y[1] (numeric) = 3.9742740725630653163119065891369
absolute error = 1.0e-30
relative error = 2.5161827839293577397920941555007e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 4.0041660239464331120584079535887
y[1] (numeric) = 4.0041660239464331120584079535897
absolute error = 1.0e-30
relative error = 2.4973989440488239579002315758794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 4.0343583944356755826586664593838
y[1] (numeric) = 4.0343583944356755826586664593848
absolute error = 1.0e-30
relative error = 2.4787088856042984122701949176428e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 4.0648542032930020449686230918988
y[1] (numeric) = 4.0648542032930020449686230918999
absolute error = 1.1e-30
relative error = 2.7061241190615711978036831856143e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 4.0956565001247114903930123270235
y[1] (numeric) = 4.0956565001247114903930123270246
absolute error = 1.1e-30
relative error = 2.6857721099572323404834482998643e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 4.1267683651861557561315562411795
y[1] (numeric) = 4.1267683651861557561315562411806
absolute error = 1.1e-30
relative error = 2.6655239709592465507085210727036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 4.1581929096897676272507006280068
y[1] (numeric) = 4.1581929096897676272507006280079
absolute error = 1.1e-30
relative error = 2.6453799135597781795570870848201e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 4.1899332761161846726477912360218
y[1] (numeric) = 4.1899332761161846726477912360229
absolute error = 1.1e-30
relative error = 2.6253401367279853827498401272717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 4.2219926385284999275505572724101
y[1] (numeric) = 4.2219926385284999275505572724112
absolute error = 1.1e-30
relative error = 2.6054048270045902760496954318382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 4.2543742028896708478820285629729
y[1] (numeric) = 4.254374202889670847882028562974
absolute error = 1.1e-30
relative error = 2.5855741585985881845702606715037e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 4.2870812073831182776508312036078
y[1] (numeric) = 4.287081207383118277650831203609
absolute error = 1.2e-30
relative error = 2.7991072292574864816100231764912e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 4.3201169227365474895307674296016
y[1] (numeric) = 4.3201169227365474895307674296028
absolute error = 1.2e-30
relative error = 2.7777025980117882848290481704386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 4.3534846525490236810035894273757
y[1] (numeric) = 4.3534846525490236810035894273769
absolute error = 1.2e-30
relative error = 2.7564126114407774422313658158449e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 4.3871877336213346338871451880633
y[1] (numeric) = 4.3871877336213346338871451880645
absolute error = 1.2e-30
relative error = 2.7352374068785951055180577864809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 4.4212295362896735737901523514522
y[1] (numeric) = 4.4212295362896735737901523514534
absolute error = 1.2e-30
relative error = 2.7141771087665543490579289285875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
bytes used=116045972, alloc=4390108, time=4.40
Radius of convergence (six term test) for eq 1 = 1.732e+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 4.455613464762675598057615494122
y[1] (numeric) = 4.4556134647626755980576154941232
absolute error = 1.2e-30
relative error = 2.6932318287711184195048436929841e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 4.4903429574618413761305460296723
y[1] (numeric) = 4.4903429574618413761305460296735
absolute error = 1.2e-30
relative error = 2.6724016659037062360057654280615e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 4.5254214873653821649737080556228
y[1] (numeric) = 4.525421487365382164973708055624
absolute error = 1.2e-30
relative error = 2.6516867066422538003685072937690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 4.5608525623555205243594713895519
y[1] (numeric) = 4.5608525623555205243594713895532
absolute error = 1.3e-30
relative error = 2.8503442771423322559018823191229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 4.5966397255692814623687184072408
y[1] (numeric) = 4.5966397255692814623687184072421
absolute error = 1.3e-30
relative error = 2.8281529064995375458940502300148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 4.6327865557528090905156817025115
y[1] (numeric) = 4.6327865557528090905156817025128
absolute error = 1.3e-30
relative error = 2.8060865406926895520212113299037e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 4.6692966676192442204574899160115
y[1] (numeric) = 4.6692966676192442204574899160128
absolute error = 1.3e-30
relative error = 2.7841452204467380361728498606404e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 4.7061737122101986903463250122245
y[1] (numeric) = 4.7061737122101986903463250122259
absolute error = 1.4e-30
relative error = 2.9748158177155483654392270797923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 4.7434213772608625685580558298259
y[1] (numeric) = 4.7434213772608625685580558298272
absolute error = 1.3e-30
relative error = 2.7406378152107126577206879094388e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 4.7810433875687807458219777860331
y[1] (numeric) = 4.7810433875687807458219777860344
absolute error = 1.3e-30
relative error = 2.7190717477698230190438578003670e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 4.8190435053663357937181865600786
y[1] (numeric) = 4.8190435053663357937181865600799
absolute error = 1.3e-30
relative error = 2.6976307612752629204391527297397e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 4.8574255306969743381388389099302
y[1] (numeric) = 4.8574255306969743381388389099315
absolute error = 1.3e-30
relative error = 2.6763148334123152764693635241454e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 4.8961933017952145706641697713002
y[1] (numeric) = 4.8961933017952145706641697713015
absolute error = 1.3e-30
relative error = 2.6551239296931930433579228102745e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 4.9353506954704728989210772223787
y[1] (numeric) = 4.93535069547047289892107722238
absolute error = 1.3e-30
relative error = 2.6340580036046956324990869913907e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 4.9749016274947481189091677809396
y[1] (numeric) = 4.9749016274947481189091677809409
absolute error = 1.3e-30
relative error = 2.6131169967568818585133721309813e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 5.0148500529942018780345658588566
y[1] (numeric) = 5.014850052994201878034565858858
absolute error = 1.4e-30
relative error = 2.7917085958813585820550696751392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 5.0551999668446745872241088952286
y[1] (numeric) = 5.05519996684467458722410889523
absolute error = 1.4e-30
relative error = 2.7694255601798555258391897182732e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 5.0959554040711763340407372797126
y[1] (numeric) = 5.095955404071176334040737279714
absolute error = 1.4e-30
relative error = 2.7472767891209078778577093904835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 5.1371204402513927462243008090194
y[1] (numeric) = 5.1371204402513927462243008090208
absolute error = 1.4e-30
relative error = 2.7252621702820907307424521094143e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 5.1786991919232461565803917643529
y[1] (numeric) = 5.1786991919232461565803917643543
absolute error = 1.4e-30
relative error = 2.7033815792650300215464535026078e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 5.2206958169965528256733289292909
y[1] (numeric) = 5.2206958169965528256733289292922
absolute error = 1.3e-30
relative error = 2.4900895312990773644806294561149e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 5.2631145151688173883886106755809
y[1] (numeric) = 5.2631145151688173883886106755822
absolute error = 1.3e-30
relative error = 2.4700203581990686770877020451460e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=120047580, alloc=4390108, time=4.55
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 5.3059595283452061041559898892827
y[1] (numeric) = 5.305959528345206104155989889284
absolute error = 1.3e-30
relative error = 2.4500752277796528032109570440386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 5.3492351410627409085081719198621
y[1] (numeric) = 5.3492351410627409085081719198635
absolute error = 1.4e-30
relative error = 2.6171965955526490675633083404731e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 5.3929456809187566857337876433172
y[1] (numeric) = 5.3929456809187566857337876433186
absolute error = 1.4e-30
relative error = 2.5959838701017516021572357463792e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 5.4370955190036646087089558540139
y[1] (numeric) = 5.4370955190036646087089558540152
absolute error = 1.3e-30
relative error = 2.3909824564535552690309687458675e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 5.4816890703380648226020554601193
y[1] (numeric) = 5.4816890703380648226020554601206
absolute error = 1.3e-30
relative error = 2.3715318094826324251061766774688e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 5.5267307943142521840843397438116
y[1] (numeric) = 5.5267307943142521840843397438129
absolute error = 1.3e-30
relative error = 2.3522043109778461660788126959587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 5.5722251951421592069882364234397
y[1] (numeric) = 5.572225195142159206988236423441
absolute error = 1.3e-30
relative error = 2.3329997522952484703572637050946e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 5.6181768222997808090795197077546
y[1] (numeric) = 5.6181768222997808090795197077559
absolute error = 1.3e-30
relative error = 2.3139179152212044448948089446887e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 5.6645902709881259027933867662438
y[1] (numeric) = 5.6645902709881259027933867662451
absolute error = 1.3e-30
relative error = 2.2949585721285172473810867656637e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 5.7114701825907413254726398125845
y[1] (numeric) = 5.7114701825907413254726398125859
absolute error = 1.4e-30
relative error = 2.4512077542965574537281264288757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 5.758821245137854061883935504415
y[1] (numeric) = 5.7588212451378540618839355044164
absolute error = 1.4e-30
relative error = 2.4310530582660704658254518293276e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 5.8066481937751781736211397590791
y[1] (numeric) = 5.8066481937751781736211397590805
absolute error = 1.4e-30
relative error = 2.4110294842742890739882539482373e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 5.8549558112374333164794020642401
y[1] (numeric) = 5.8549558112374333164794020642415
absolute error = 1.4e-30
relative error = 2.3911367483132426448456783236173e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 5.9037489283266221980462867706038
y[1] (numeric) = 5.9037489283266221980462867706051
absolute error = 1.3e-30
relative error = 2.2019906601422432594523346365093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 5.953032424395114803654286356424
y[1] (numeric) = 5.9530324243951148036542863564253
absolute error = 1.3e-30
relative error = 2.1837609932589817360485097333984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 6.0028112278335876995198834453142
y[1] (numeric) = 6.0028112278335876995198834453156
absolute error = 1.4e-30
relative error = 2.3322405900564350583413674864699e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 6.053090316563867207406092924905
y[1] (numeric) = 6.0530903165638672074060929249064
absolute error = 1.4e-30
relative error = 2.3128681826686045893025212740644e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 6.1038747185367257355366544351225
y[1] (numeric) = 6.1038747185367257355366544351239
absolute error = 1.4e-30
relative error = 2.2936250571270248021116406808447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 6.1551695122346810458097983038692
y[1] (numeric) = 6.1551695122346810458097983038706
absolute error = 1.4e-30
relative error = 2.2745108761297450696243490916640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 6.2069798271798487376573070927123
y[1] (numeric) = 6.2069798271798487376573070927138
absolute error = 1.5e-30
relative error = 2.4166342436487785578717889517530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -12.5
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 6.2593108444468987342204704726538
y[1] (numeric) = 6.2593108444468987342204704726553
absolute error = 1.5e-30
relative error = 2.3964299541550358074595878646936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 6.3121677971811670669190161888314
y[1] (numeric) = 6.3121677971811670669190161888329
absolute error = 1.5e-30
relative error = 2.3763626826743372365460717351472e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=124050504, alloc=4390108, time=4.71
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 6.3655559711219747700232352669232
y[1] (numeric) = 6.3655559711219747700232352669247
absolute error = 1.5e-30
relative error = 2.3564320332817908930244278396206e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 6.4194807051312062175548592062532
y[1] (numeric) = 6.4194807051312062175548592062547
absolute error = 1.5e-30
relative error = 2.3366376018562109874686490693819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 6.4739473917271997607908626630091
y[1] (numeric) = 6.4739473917271997607908626630106
absolute error = 1.5e-30
relative error = 2.3169789762530205650093064808711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 6.528961477624004055878852351461
y[1] (numeric) = 6.5289614776240040558788523514625
absolute error = 1.5e-30
relative error = 2.2974557364762926295692489673121e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 6.5845284642760540076461854730193
y[1] (numeric) = 6.5845284642760540076461854730208
absolute error = 1.5e-30
relative error = 2.2780674548498892098342886598898e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 6.640653908428320797651096717808
y[1] (numeric) = 6.6406539084283207976510967178095
absolute error = 1.5e-30
relative error = 2.2588136961876591018246572063660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 6.6973434226719910119370988363601
y[1] (numeric) = 6.6973434226719910119370988363616
absolute error = 1.5e-30
relative error = 2.2396940179626562608782118088272e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 6.7546026760057304368664997048427
y[1] (numeric) = 6.7546026760057304368664997048442
absolute error = 1.5e-30
relative error = 2.2207079704753420455927729777648e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 6.8124373944025886498803406244497
y[1] (numeric) = 6.8124373944025886498803406244512
absolute error = 1.5e-30
relative error = 2.2018550970207357371654805967865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 6.8708533613826010961162539158285
y[1] (numeric) = 6.87085336138260109611625391583
absolute error = 1.5e-30
relative error = 2.1831349340544789690005248007338e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 6.9298564185911459115690715820469
y[1] (numeric) = 6.9298564185911459115690715820484
absolute error = 1.5e-30
relative error = 2.1645470113577809028476749991272e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 6.9894524663831133289584667268155
y[1] (numeric) = 6.989452466383113328958466726817
absolute error = 1.5e-30
relative error = 2.1460908522012121785228664007476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 7.0496474644129460837310239530277
y[1] (numeric) = 7.0496474644129460837310239530292
absolute error = 1.5e-30
relative error = 2.1277659735073168439141716270643e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 7.1104474322306098247290409259947
y[1] (numeric) = 7.1104474322306098247290409259962
absolute error = 1.5e-30
relative error = 2.1095718860120126399822679206578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 7.1718584498835531270637716458996
y[1] (numeric) = 7.1718584498835531270637716459011
absolute error = 1.5e-30
relative error = 2.0915080944247511713392185109442e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 7.2338866585247173036960337699729
y[1] (numeric) = 7.2338866585247173036960337699744
absolute error = 1.5e-30
relative error = 2.0735740975874106362726477608739e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 7.2965382610266568172120145770248
y[1] (numeric) = 7.2965382610266568172120145770263
absolute error = 1.5e-30
relative error = 2.0557693886318949203379205879770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 7.3598195226018317043472218706367
y[1] (numeric) = 7.3598195226018317043472218706382
absolute error = 1.5e-30
relative error = 2.0380934551364139744561977865411e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 7.4237367714291340430179442929097
y[1] (numeric) = 7.4237367714291340430179442929112
absolute error = 1.5e-30
relative error = 2.0205457792804215014420733998626e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 7.4882963992867111150290313243491
y[1] (numeric) = 7.4882963992867111150290313243506
absolute error = 1.5e-30
relative error = 2.0031258379981870636747583985531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 7.5535048621911485473016181413198
y[1] (numeric) = 7.5535048621911485473016181413213
absolute error = 1.5e-30
relative error = 1.9858331031309807988779247283513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 7.6193686810430773504675724967601
y[1] (numeric) = 7.6193686810430773504675724967615
absolute error = 1.4e-30
relative error = 1.8374225721393266576731130248276e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=128051608, alloc=4390108, time=4.86
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 7.6858944422792694160725307276929
y[1] (numeric) = 7.6858944422792694160725307276943
absolute error = 1.4e-30
relative error = 1.8215186410819699301745638750378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -6.667e+29
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 7.7530887985312866824806579188518
y[1] (numeric) = 7.7530887985312866824806579188532
absolute error = 1.4e-30
relative error = 1.8057319300472996689436052947328e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 7.8209584692907498349465988329418
y[1] (numeric) = 7.8209584692907498349465988329432
absolute error = 1.4e-30
relative error = 1.7900619284671385958940052576832e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 7.8895102415812930672790192339938
y[1] (numeric) = 7.8895102415812930672790192339953
absolute error = 1.5e-30
relative error = 1.9012587018321117985758484380057e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 7.958750970637272101131868125876
y[1] (numeric) = 7.9587509706372721011318681258775
absolute error = 1.5e-30
relative error = 1.8847178477301849660884982728838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 8.0286875805892933342908819335644
y[1] (numeric) = 8.0286875805892933342908819335659
absolute error = 1.5e-30
relative error = 1.8683003728112463237545933847705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -6.667e+29
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 8.099327065156632671441435472082
y[1] (numeric) = 8.0993270651566326714414354720835
absolute error = 1.5e-30
relative error = 1.8520057134783598713176651764499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 8.1706764883466132798778341038975
y[1] (numeric) = 8.1706764883466132798778341038991
absolute error = 1.6e-30
relative error = 1.9582221891687818572070548016264e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 8.2427429851610122085124347531447
y[1] (numeric) = 8.2427429851610122085124347531463
absolute error = 1.6e-30
relative error = 1.9411014062677897478602786149431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 8.315533762309566511435170833514
y[1] (numeric) = 8.3155337623095665114351708335156
absolute error = 1.6e-30
relative error = 1.9241097994840129712596443233579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 8.389056098930650227230427460575
y[1] (numeric) = 8.3890560989306502272304274605766
absolute error = 1.6e-30
relative error = 1.9072467523538808950443337391617e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 8.4633173473191942823497647873654
y[1] (numeric) = 8.463317347319194282349764787367
absolute error = 1.6e-30
relative error = 1.8905116449483126645442153958760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 6.325e+15
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 8.5383249336619221111374286770603
y[1] (numeric) = 8.538324933661922111137428677062
absolute error = 1.7e-30
relative error = 1.9910228448882689008327422779350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 8.6140863587799745166833496561362
y[1] (numeric) = 8.6140863587799745166833496561379
absolute error = 1.7e-30
relative error = 1.9735116751729123058540922957532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 8.6906091988789980356085715614843
y[1] (numeric) = 8.690609198878998035608571561486
absolute error = 1.7e-30
relative error = 1.9561344447743468381026475098633e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 8.7679011063067718162446641452442
y[1] (numeric) = 8.7679011063067718162446641452459
absolute error = 1.7e-30
relative error = 1.9388904817564445560264606902608e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 8.8459698103184487735262954149556
y[1] (numeric) = 8.8459698103184487735262954149572
absolute error = 1.6e-30
relative error = 1.8087332811532635227228467303004e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 8.9248231178494875453501560543463
y[1] (numeric) = 8.9248231178494875453501560543479
absolute error = 1.6e-30
relative error = 1.7927526169118449521467964985130e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 9.0044689142963525442399839278696
y[1] (numeric) = 9.0044689142963525442399839278712
absolute error = 1.6e-30
relative error = 1.7768954673825211350374477495610e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 9.0849151643050601749734407164419
y[1] (numeric) = 9.0849151643050601749734407164435
absolute error = 1.6e-30
relative error = 1.7611611898000481822972765699160e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 9.1661699125676500734497274104786
y[1] (numeric) = 9.1661699125676500734497274104803
absolute error = 1.7e-30
relative error = 1.8546459603254199510848032309440e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 9.2482412846266610145855536665902
y[1] (numeric) = 9.2482412846266610145855536665919
absolute error = 1.7e-30
relative error = 1.8381873349540606189572868625910e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=132054448, alloc=4390108, time=5.02
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 9.3311374876876919375006494494469
y[1] (numeric) = 9.3311374876876919375006494494486
absolute error = 1.7e-30
relative error = 1.8218571982709789745349109134641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 9.414866811440129344772473954749
y[1] (numeric) = 9.4148668114401293447724739547508
absolute error = 1.8e-30
relative error = 1.9118698501531600663619671142209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 9.4994376288861231491839890633767
y[1] (numeric) = 9.4994376288861231491839890633785
absolute error = 1.8e-30
relative error = 1.8948490114051760398363528260256e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 9.5848583971778938662399876124018
y[1] (numeric) = 9.5848583971778938662399876124036
absolute error = 1.8e-30
relative error = 1.8779620161420233526582639445433e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 9.6711376584634548838689864354103
y[1] (numeric) = 9.6711376584634548838689864354121
absolute error = 1.8e-30
relative error = 1.8612081262484924918844011214117e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 9.7582840407408343822424252687577
y[1] (numeric) = 9.7582840407408343822424252687596
absolute error = 1.9e-30
relative error = 1.9470636354378498204130682184750e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 9.8463062587208823266150074163392
y[1] (numeric) = 9.8463062587208823266150074163411
absolute error = 1.9e-30
relative error = 1.9296576300550963339815588430711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 9.9352131146987488146044744309985
y[1] (numeric) = 9.9352131146987488146044744310004
absolute error = 1.9e-30
relative error = 1.9123897777180303280767462719076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 10.025013499434120926471777166889
y[1] (numeric) = 10.025013499434120926471777166891
absolute error = 2e-30
relative error = 1.9950097823937029398853866939930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 10.115716393040306102820204373562
y[1] (numeric) = 10.115716393040306102820204373564
absolute error = 2e-30
relative error = 1.9771214635633873824245698337483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 10.20733086588225095879214402908
y[1] (numeric) = 10.207330865882250958792144029082
absolute error = 2e-30
relative error = 1.9593760859510787073458172262453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 10.299866079483585337393248594605
y[1] (numeric) = 10.299866079483585337393248594607
absolute error = 2e-30
relative error = 1.9417728197299784654636807809679e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 10.393331287442782307105209171014
y[1] (numeric) = 10.393331287442782307105209171016
absolute error = 2e-30
relative error = 1.9243108342138569232387866587707e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 10.487735836358525720550369044512
y[1] (numeric) = 10.487735836358525720550369044514
absolute error = 2e-30
relative error = 1.9069892979821898793922952645667e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 10.583089166764377871735185285297
y[1] (numeric) = 10.583089166764377871735185285299
absolute error = 2e-30
relative error = 1.8898073790031859453434842247641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 10.679400814072840719417155056108
y[1] (numeric) = 10.67940081407284071941715505611
absolute error = 2e-30
relative error = 1.8727642447547138673311472163336e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 10.776680409528905083504263631818
y[1] (numeric) = 10.77668040952890508350426363182
absolute error = 2e-30
relative error = 1.8558590623431400217242219529765e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 10.874937681173183170201221053971
y[1] (numeric) = 10.874937681173183170201221053973
absolute error = 2e-30
relative error = 1.8390909986200867490350857047855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 10.974182454814720739957615156909
y[1] (numeric) = 10.974182454814720739957615156911
absolute error = 2e-30
relative error = 1.8224592202971227067860949395282e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 11.074424655013586200245455289684
y[1] (numeric) = 11.074424655013586200245455289687
absolute error = 3e-30
relative error = 2.7089443410875953753760213734310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 11.175674306073334882894211461532
y[1] (numeric) = 11.175674306073334882894211461535
absolute error = 3e-30
relative error = 2.6844017800068429902060699308180e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 11.277941533043447753238138736105
y[1] (numeric) = 11.277941533043447753238138736107
absolute error = 2e-30
relative error = 1.7733732650946658277891477139213e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=136055748, alloc=4390108, time=5.18
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 11.381236562731844795782169982426
y[1] (numeric) = 11.381236562731844795782169982428
absolute error = 2e-30
relative error = 1.7572782965860247817158552757443e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 11.485569724727574328568707539109
y[1] (numeric) = 11.485569724727574328568707539111
absolute error = 2e-30
relative error = 1.7413154488054251945533768750134e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 11.590951452433780516028994407103
y[1] (numeric) = 11.590951452433780516028994407106
absolute error = 3e-30
relative error = 2.5882258348775006207098090872434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 11.69739228411105237793115923818
y[1] (numeric) = 11.697392284111052377931159238183
absolute error = 3e-30
relative error = 2.5646741830441964199201416500130e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 11.804902863931258630195290329287
y[1] (numeric) = 11.80490286393125863019529032929
absolute error = 3e-30
relative error = 2.5413169719220735478436275797763e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 11.913493943041973741937818758192
y[1] (numeric) = 11.913493943041973741937818758195
absolute error = 3e-30
relative error = 2.5181529569267439294005944512303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 12.023176380641601652237939769668
y[1] (numeric) = 12.02317638064160165223793976967
absolute error = 2e-30
relative error = 1.6634539298784474132590487818768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 12.133961145065304659893688471457
y[1] (numeric) = 12.133961145065304659893688471459
absolute error = 2e-30
relative error = 1.6482663625582559524323354079179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 12.245859314881846079961589205531
y[1] (numeric) = 12.245859314881846079961589205532
absolute error = 1e-30
relative error = 8.1660255461594650803329554070764e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 12.358882080001456352259571153473
y[1] (numeric) = 12.358882080001456352259571153475
absolute error = 2e-30
relative error = 1.6182693443093069166805919077044e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 12.473040742794833389367225302064
y[1] (numeric) = 12.473040742794833389367225302065
absolute error = 1e-30
relative error = 8.0172912172812326446118707227730e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 12.58834671922338906509070619308
y[1] (numeric) = 12.588346719223389065090706193082
absolute error = 2e-30
relative error = 1.5887709836795674880324671641767e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 12.704811539980854868983000160809
y[1] (numeric) = 12.704811539980854868983000160811
absolute error = 2e-30
relative error = 1.5742067434107045710927910849835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 12.822446851646360888436353300643
y[1] (numeric) = 12.822446851646360888436353300645
absolute error = 2e-30
relative error = 1.5597647025873275036033128979139e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 12.941264417849103427205970766319
y[1] (numeric) = 12.941264417849103427205970766321
absolute error = 2e-30
relative error = 1.5454440427331976495508299090890e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 13.061276120444717728097399349678
y[1] (numeric) = 13.061276120444717728097399349681
absolute error = 3e-30
relative error = 2.2968659205543648675323097838826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 13.182493960703473438070175951168
y[1] (numeric) = 13.182493960703473438070175951171
absolute error = 3e-30
relative error = 2.2757454006373065357991852993874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 13.304930060510411636294418494051
y[1] (numeric) = 13.304930060510411636294418494054
absolute error = 3e-30
relative error = 2.2548032844637983888849396547795e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 13.428596663577543439863282465196
y[1] (numeric) = 13.428596663577543439863282465199
absolute error = 3e-30
relative error = 2.2340383549808421112214214940815e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 13.553506136668231408032023200075
y[1] (numeric) = 13.553506136668231408032023200079
absolute error = 4e-30
relative error = 2.9512658640986113806084854742601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 13.679670970833876184144409056144
y[1] (numeric) = 13.679670970833876184144409056148
absolute error = 4e-30
relative error = 2.9240469368951281799727923461024e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 13.807103782663032044941253752753
y[1] (numeric) = 13.807103782663032044941253752757
absolute error = 4e-30
relative error = 2.8970594144607087137569402459077e-29 %
Correct digits = 31
h = 0.01
bytes used=140056932, alloc=4390108, time=5.32
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 13.935817315543076269846931825039
y[1] (numeric) = 13.935817315543076269846931825043
absolute error = 4e-30
relative error = 2.8703016905500534874484851515217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 14.065824440934558498222200489047
y[1] (numeric) = 14.065824440934558498222200489051
absolute error = 4e-30
relative error = 2.8437721633714865673180153336380e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 14.197138159658357510581014537849
y[1] (numeric) = 14.197138159658357510581014537853
absolute error = 4e-30
relative error = 2.8174692357126830414356048904553e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 14.329771603195774150522090176603
y[1] (numeric) = 14.329771603195774150522090176606
absolute error = 3e-30
relative error = 2.0935434862974025240916514896076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 14.463738035001690397750825332584
y[1] (numeric) = 14.463738035001690397750825332588
absolute error = 4e-30
relative error = 2.7655368137338727141009256812650e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 14.599050851830925909193181507426
y[1] (numeric) = 14.59905085183092590919318150743
absolute error = 4e-30
relative error = 2.7399041489730435800858492079938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 14.735723585077924664960939361653
y[1] (numeric) = 14.735723585077924664960939361657
absolute error = 4e-30
relative error = 2.7144917430797799632030266437959e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 14.873769902129905688949333816751
y[1] (numeric) = 14.873769902129905688949333816756
absolute error = 5e-30
relative error = 3.3616225293925019675439957511022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 15.013203607733613160266757797534
y[1] (numeric) = 15.013203607733613160266757797539
absolute error = 5e-30
relative error = 3.3304017787545331747081697597851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.000e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 15.154038645375802591646639807897
y[1] (numeric) = 15.154038645375802591646639807902
absolute error = 5e-30
relative error = 3.2994504745609389305243033806108e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 15.2962890986776011246097455111
y[1] (numeric) = 15.296289098677601124609745511106
absolute error = 6e-30
relative error = 3.9225200055343577445861957130013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 15.439969192802881378568390330594
y[1] (numeric) = 15.439969192802881378568390330599
absolute error = 5e-30
relative error = 3.2383484303392766995078352991235e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 15.585093295880789692431122279052
y[1] (numeric) = 15.585093295880789692431122279057
absolute error = 5e-30
relative error = 3.2081938202586971393420147604504e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 15.731675920442571012717479636724
y[1] (numeric) = 15.731675920442571012717479636729
absolute error = 5e-30
relative error = 3.1783009167527636270142434678787e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 15.879731724872834111868993019468
y[1] (numeric) = 15.879731724872834111868993019474
absolute error = 6e-30
relative error = 3.7784013634197893708493797105364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 16.029275514875402264487654649923
y[1] (numeric) = 16.029275514875402264487654649929
absolute error = 6e-30
relative error = 3.7431510827996637718655758982158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 16.18032224495389596779102498073
y[1] (numeric) = 16.180322244953895967791024980736
absolute error = 6e-30
relative error = 3.7082079758153150020872509107528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 16.332887019907195765789845226944
y[1] (numeric) = 16.332887019907195765789845226951
absolute error = 7e-30
relative error = 4.2858313973935603272659475536726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 16.486985096339934724716796743092
y[1] (numeric) = 16.486985096339934724716796743099
absolute error = 7e-30
relative error = 4.2457732320956490203609280428981e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 16.642631884188171610212698046157
y[1] (numeric) = 16.642631884188171610212698046163
absolute error = 6e-30
relative error = 3.6051990104404573211834067356944e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.472e+15
Order of pole (six term test) = -10.75
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 16.799842948260397334859256656509
y[1] (numeric) = 16.799842948260397334859256656516
absolute error = 7e-30
relative error = 4.1667056183551056468981723891514e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 16.958634009794028777987305352163
y[1] (numeric) = 16.95863400979402877798730535217
absolute error = 7e-30
relative error = 4.1276909425354233201902063161774e-29 %
Correct digits = 31
h = 0.01
bytes used=144057816, alloc=4390108, time=5.48
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 17.119020948027545628439586166743
y[1] (numeric) = 17.11902094802754562843958616675
absolute error = 7e-30
relative error = 4.0890188879677376164999124040392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 17.281019801788427465282476812269
y[1] (numeric) = 17.281019801788427465282476812275
absolute error = 6e-30
relative error = 3.4720173165816608155896559703238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 17.444646771097049871498016010925
y[1] (numeric) = 17.444646771097049871498016010931
absolute error = 6e-30
relative error = 3.4394505539321247724974704392328e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 17.609918218786699971604181488378
y[1] (numeric) = 17.609918218786699971604181488384
absolute error = 6e-30
relative error = 3.4071708485273090886203779979901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 17.776850672139873396107200104494
y[1] (numeric) = 17.7768506721398733961072001045
absolute error = 6e-30
relative error = 3.3751760143900421614796416799682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 17.945460824541016303845920701474
y[1] (numeric) = 17.945460824541016303845920701481
absolute error = 7e-30
relative error = 3.9007078550065799889487190428670e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 18.11576553714587773780777371626
y[1] (numeric) = 18.115765537145877737807773716266
absolute error = 6e-30
relative error = 3.3120322669760576414633456991519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 18.287781840567639251043030753446
y[1] (numeric) = 18.287781840567639251043030753452
absolute error = 6e-30
relative error = 3.2808790329564454320376899412194e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 18.46152693657999041704506824997
y[1] (numeric) = 18.461526936579990417045068249976
absolute error = 6e-30
relative error = 3.2500020288741640827339177807047e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 18.637018199837320533566907580682
y[1] (numeric) = 18.637018199837320533566907580688
absolute error = 6e-30
relative error = 3.2193991204303127273410491340570e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 18.814273179612198540477911123657
y[1] (numeric) = 18.814273179612198540477911123663
absolute error = 6e-30
relative error = 3.1890681838838233184528260365198e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 18.993309601550314901100324712728
y[1] (numeric) = 18.993309601550314901100324712734
absolute error = 6e-30
relative error = 3.1590071061181745918943573258470e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 19.174145369443060942676256574128
y[1] (numeric) = 19.174145369443060942676256574134
absolute error = 6e-30
relative error = 3.1292137847050640867973194993343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 19.356798567017922915376293819354
y[1] (numeric) = 19.35679856701792291537629381936
absolute error = 6e-30
relative error = 3.0996861279650906121781625618598e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 19.541287459746869810747657378403
y[1] (numeric) = 19.54128745974686981074765737841
absolute error = 7e-30
relative error = 3.5821590641964156747455181871680e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 19.727630496672915779890735060899
y[1] (numeric) = 19.727630496672915779890735060905
absolute error = 6e-30
relative error = 3.0414194958750397728433995373188e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 19.915846312255039809127950820668
y[1] (numeric) = 19.915846312255039809127950820674
absolute error = 6e-30
relative error = 3.0126763914159917417708270277570e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 20.105953728231647146669975298563
y[1] (numeric) = 20.10595372823164714666997529857
absolute error = 7e-30
relative error = 3.4815558090989707628780008997033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 20.297971755502758827974833963076
y[1] (numeric) = 20.297971755502758827974833963083
absolute error = 7e-30
relative error = 3.4486204258818654384591028599882e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 20.491919596031117520320945259013
y[1] (numeric) = 20.49191959603111752032094525902
absolute error = 7e-30
relative error = 3.4159806099159995529954637395678e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 20.687816644762399798762806219384
y[1] (numeric) = 20.687816644762399798762806219391
absolute error = 7e-30
relative error = 3.3836340103933646460342783298150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 20.885682491564726876297103339624
y[1] (numeric) = 20.885682491564726876297103339631
absolute error = 7e-30
relative error = 3.3515782894943212062788742536485e-29 %
Correct digits = 31
h = 0.01
bytes used=148059968, alloc=4390108, time=5.63
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 21.085536923187667740928529654582
y[1] (numeric) = 21.085536923187667740928529654589
absolute error = 7e-30
relative error = 3.3198111224296746615193706240226e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 21.28739992524093060158152265589
y[1] (numeric) = 21.287399925240930601581522655897
absolute error = 7e-30
relative error = 3.2883301974798474890456821794874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 21.491291684192940513651429258142
y[1] (numeric) = 21.491291684192940513651429258149
absolute error = 7e-30
relative error = 3.2571332160312029314071920074647e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 21.697232589389503043623139836616
y[1] (numeric) = 21.697232589389503043623139836623
absolute error = 7e-30
relative error = 3.2262178926095752474047066288611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 21.905243235092755840805878527866
y[1] (numeric) = 21.905243235092755840805878527874
absolute error = 8e-30
relative error = 3.6520936627554981350385947079987e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 22.115344422540612013040455245769
y[1] (numeric) = 22.115344422540612013040455245776
absolute error = 7e-30
relative error = 3.1652231438301242634154512337858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 22.327557162026901252432758671981
y[1] (numeric) = 22.327557162026901252432758671989
absolute error = 8e-30
relative error = 3.5830162439829391478124453191738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 22.541902675002416726959520286426
y[1] (numeric) = 22.541902675002416726959520286433
absolute error = 7e-30
relative error = 3.1053279312409459362671309487259e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 22.758402396197077844386388260106
y[1] (numeric) = 22.758402396197077844386388260114
absolute error = 8e-30
relative error = 3.5151852316913060557662270198029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 22.977077975763421106543177882497
y[1] (numeric) = 22.977077975763421106543177882505
absolute error = 8e-30
relative error = 3.4817307964217749155595242127412e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 23.197951281441633404827974381257
y[1] (numeric) = 23.197951281441633404827974381265
absolute error = 8e-30
relative error = 3.4485803952868898043016994936912e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 23.421044400746344262073838971462
y[1] (numeric) = 23.421044400746344262073838971469
absolute error = 7e-30
relative error = 2.9887650952819743734591839044445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 23.646379643175395701824637747618
y[1] (numeric) = 23.646379643175395701824637747625
absolute error = 7e-30
relative error = 2.9602840289423656913898845976937e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 23.873979542440810623847568694562
y[1] (numeric) = 23.87397954244081062384756869457
absolute error = 8e-30
relative error = 3.3509285646234166940947659197587e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 24.103866858722182784579084580015
y[1] (numeric) = 24.103866858722182784579084580023
absolute error = 8e-30
relative error = 3.3189695441356680486142655530596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 24.33606458094271372338008756421
y[1] (numeric) = 24.336064580942713723380087564218
absolute error = 8e-30
relative error = 3.2873022560372008616002533817217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 24.57059592906812424018972480695
y[1] (numeric) = 24.570595929068124240189724806959
absolute error = 9e-30
relative error = 3.6629148214319839466890068433622e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 24.807484356428670317641316402232
y[1] (numeric) = 24.80748435642867031764131640224
absolute error = 8e-30
relative error = 3.2248332338167376616895489255528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 25.046753552064495691167646951714
y[1] (numeric) = 25.046753552064495691167646951723
absolute error = 9e-30
relative error = 3.5932800557532410745399294111043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 25.288427443094555604307098296172
y[1] (numeric) = 25.288427443094555604307098296181
absolute error = 9e-30
relative error = 3.5589401595857659144249370261236e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 25.532530197109348643560263727964
y[1] (numeric) = 25.532530197109348643560263727973
absolute error = 9e-30
relative error = 3.5249150517087922792531099610029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 25.779086224587695927974479188157
y[1] (numeric) = 25.779086224587695927974479188166
absolute error = 9e-30
relative error = 3.4912021014212437175972878799743e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=152065048, alloc=4390108, time=5.78
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 26.02812018133780933338921927269
y[1] (numeric) = 26.028120181337809333389219272698
absolute error = 8e-30
relative error = 3.0735988401252306951883064335115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 26.279656970962892860199012888142
y[1] (numeric) = 26.279656970962892860199012888151
absolute error = 9e-30
relative error = 3.4247022363892894705570869978231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 26.533721747351523706825329504055
y[1] (numeric) = 26.533721747351523706825329504064
absolute error = 9e-30
relative error = 3.3919101457745328775697473000280e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 26.790339917193062089080107669377
y[1] (numeric) = 26.790339917193062089080107669386
absolute error = 9e-30
relative error = 3.3594198609716514177942749434649e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 27.049537142518341348499043982636
y[1] (numeric) = 27.049537142518341348499043982645
absolute error = 9e-30
relative error = 3.3272288367009337315639429512170e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 27.311339343265892420772724659149
y[1] (numeric) = 27.311339343265892420772724659158
absolute error = 9e-30
relative error = 3.2953345447040896342412907919181e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 27.575772699873959288860970327214
y[1] (numeric) = 27.575772699873959288860970327223
absolute error = 9e-30
relative error = 3.2637344737183507250926980434198e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 27.842863655898564624495725565399
y[1] (numeric) = 27.842863655898564624495725565408
absolute error = 9e-30
relative error = 3.2324261294485535284205265739128e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 28.112638920657887426818372110231
y[1] (numeric) = 28.112638920657887426818372110241
absolute error = 1.0e-29
relative error = 3.5571189272636172777356474040628e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 28.385125471903217098118984843308
y[1] (numeric) = 28.385125471903217098118984843318
absolute error = 1.0e-29
relative error = 3.5229719205921487725076433812097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 28.660350558516751054310906965868
y[1] (numeric) = 28.660350558516751054310906965878
absolute error = 1.0e-29
relative error = 3.4891408531736837377969116147084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 28.938341703236505652149863987642
y[1] (numeric) = 28.938341703236505652149863987652
absolute error = 1.0e-29
relative error = 3.4556230286276513396808558380102e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 29.2191267054086129265611051166
y[1] (numeric) = 29.21912670540861292656110511661
absolute error = 1.0e-29
relative error = 3.4224157692395877742103838228075e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 4.564e+15
Order of pole (six term test) = -6.458e+29
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 29.502733643767278370041893023457
y[1] (numeric) = 29.502733643767278370041893023468
absolute error = 1.1e-29
relative error = 3.7284680575095963525619921094800e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 29.789190879242677752233921434877
y[1] (numeric) = 29.789190879242677752233921434888
absolute error = 1.1e-29
relative error = 3.6926145609630770595620255687588e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 30.078527057797073771687539613154
y[1] (numeric) = 30.078527057797073771687539613164
absolute error = 1.0e-29
relative error = 3.3246308839474108401937615014541e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 30.370771113289436153846398566086
y[1] (numeric) = 30.370771113289436153846398566097
absolute error = 1.1e-29
relative error = 3.6219034277949875839972035830613e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 30.665952270368851659649508823945
y[1] (numeric) = 30.665952270368851659649508823956
absolute error = 1.1e-29
relative error = 3.5870400837442154641389726851017e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 30.96410004739701334816275303373
y[1] (numeric) = 30.964100047397013348162753033742
absolute error = 1.2e-29
relative error = 3.8754557638140611686530745352397e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 31.265244259400081344601532358897
y[1] (numeric) = 31.265244259400081344601532358909
absolute error = 1.2e-29
relative error = 3.8381276987439906989000478635566e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 31.569415021050210302281241122151
y[1] (numeric) = 31.569415021050210302281241122163
absolute error = 1.2e-29
relative error = 3.8011474054867677378416049672895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 31.876642749677041713726379239121
y[1] (numeric) = 31.876642749677041713726379239133
absolute error = 1.2e-29
relative error = 3.7645118697832688262669037909821e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
bytes used=156066888, alloc=4390108, time=5.94
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 32.186958168309462222678998645337
y[1] (numeric) = 32.186958168309462222678998645349
absolute error = 1.2e-29
relative error = 3.7282180991600888994078568225087e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 32.500392308747932115372491603845
y[1] (numeric) = 32.500392308747932115372491603857
absolute error = 1.2e-29
relative error = 3.6922631228577610999836166311139e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 32.81697651466769122648013054928
y[1] (numeric) = 32.816976514667691226480130549292
absolute error = 1.2e-29
relative error = 3.6566439917572990005261509280186e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 33.136742444753152582914967864034
y[1] (numeric) = 33.136742444753152582914967864045
absolute error = 1.1e-29
relative error = 3.3195779634463531602612582487487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 33.459722075863797227457478986324
y[1] (numeric) = 33.459722075863797227457478986336
absolute error = 1.2e-29
relative error = 3.5864015764363480972435767195133e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 33.785947706231886814331566095013
y[1] (numeric) = 33.785947706231886814331566095025
absolute error = 1.2e-29
relative error = 3.5517725014967023044440827778158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 34.115451958692313750653249350389
y[1] (numeric) = 34.1154519586923137506532493504
absolute error = 1.1e-29
relative error = 3.2243453826491950751818513925599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 34.448267783944911871457741316409
y[1] (numeric) = 34.44826778394491187145774131642
absolute error = 1.1e-29
relative error = 3.1931939419974844177882543581868e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 34.78442846384955388209100856303
y[1] (numeric) = 34.784428463849553882091008563041
absolute error = 1.1e-29
relative error = 3.1623345519193970608418659919516e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 35.123967614754365080455983293164
y[1] (numeric) = 35.123967614754365080455983293175
absolute error = 1.1e-29
relative error = 3.1317646459106972034722128608836e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 35.466919190857386183259170295692
y[1] (numeric) = 35.466919190857386183259170295703
absolute error = 1.1e-29
relative error = 3.1014816767156829688751008959524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 35.813317487602021425341668911734
y[1] (numeric) = 35.813317487602021425341668911745
absolute error = 1.1e-29
relative error = 3.0714831162480320866020833144505e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 36.163197145106611479734092630969
y[1] (numeric) = 36.16319714510661147973409263098
absolute error = 1.1e-29
relative error = 3.0417664555105450640368842518309e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 36.516593151628474158585378769949
y[1] (numeric) = 36.51659315162847415858537876996
absolute error = 1.1e-29
relative error = 3.0123292045138252370976503618120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.270e+15
Order of pole (six term test) = -3.333e+29
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 36.873540847062759301922291319834
y[1] (numeric) = 36.873540847062759301922291319845
absolute error = 1.1e-29
relative error = 2.9831688921939343690501970508438e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 37.234075926476467742644215040193
y[1] (numeric) = 37.234075926476467742644215040205
absolute error = 1.2e-29
relative error = 3.2228542541771582761379822230451e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 37.598234443677987752594765899184
y[1] (numeric) = 37.598234443677987752594765899196
absolute error = 1.2e-29
relative error = 3.1916392292239026212161011121533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 37.966052814822505926329448641597
y[1] (numeric) = 37.966052814822505926329448641609
absolute error = 1.2e-29
relative error = 3.1607183550340064177293187974797e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 38.337567822053653046672257335396
y[1] (numeric) = 38.337567822053653046672257335409
absolute error = 1.3e-29
relative error = 3.3909297690297820971361853627484e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 38.71281661718174909968248956046
y[1] (numeric) = 38.712816617181749099682489560473
absolute error = 1.3e-29
relative error = 3.3580610082063271597647603128708e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 39.091836725399015266598485317448
y[1] (numeric) = 39.091836725399015266598485317461
absolute error = 1.3e-29
relative error = 3.3255024805609993691373433055222e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 39.474666049032124417053505344034
y[1] (numeric) = 39.474666049032124417053505344047
absolute error = 1.3e-29
relative error = 3.2932514194933248241483596484685e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=160067788, alloc=4390108, time=6.09
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 39.861342871332465361740206261101
y[1] (numeric) = 39.861342871332465361740206261114
absolute error = 1.3e-29
relative error = 3.2613050799523760235751456754522e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 40.251905860304499894107543068851
y[1] (numeric) = 40.251905860304499894107543068865
absolute error = 1.4e-29
relative error = 3.4780961797405167657214917912561e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 40.646394072572595459984576852157
y[1] (numeric) = 40.646394072572595459984576852171
absolute error = 1.4e-29
relative error = 3.4443399763835214574573544217082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 41.044846957286720141620521375166
y[1] (numeric) = 41.044846957286720141620521375181
absolute error = 1.5e-29
relative error = 3.6545391472916771586862757393923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 41.447304360067390528894189239039
y[1] (numeric) = 41.447304360067390528894189239054
absolute error = 1.5e-29
relative error = 3.6190532126503801920570372205792e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 41.853806526990266975767426064963
y[1] (numeric) = 41.853806526990266975767426064978
absolute error = 1.5e-29
relative error = 3.5839034115874141604274871000755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 42.264394108610794704828685161265
y[1] (numeric) = 42.26439410861079470482868516128
absolute error = 1.5e-29
relative error = 3.5490867233191814013457110931118e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 42.679108164029293227391075798772
y[1] (numeric) = 42.679108164029293227391075798787
absolute error = 1.5e-29
relative error = 3.5146001510505472899362566672851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 43.097990164996900591474480707947
y[1] (numeric) = 43.097990164996900591474480707962
absolute error = 1.5e-29
relative error = 3.4804407218466120624872497672857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 7.071
Order of pole (six term test) = 1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 43.521082000062783055518172621604
y[1] (numeric) = 43.521082000062783055518172621619
absolute error = 1.5e-29
relative error = 3.4466054865038422430855830035238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 43.948425978763024912247320706349
y[1] (numeric) = 43.948425978763024912247320706365
absolute error = 1.6e-29
relative error = 3.6406309540486384853653736048456e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 44.380064835851617355166526689092
y[1] (numeric) = 44.380064835851617355166526689108
absolute error = 1.6e-29
relative error = 3.6052223130315697320226482904391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 44.816041735573969490092875840424
y[1] (numeric) = 44.81604173557396949009287584044
absolute error = 1.6e-29
relative error = 3.5701501918451576681804795270083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 45.256400275983368846390927167131
y[1] (numeric) = 45.256400275983368846390927167147
absolute error = 1.6e-29
relative error = 3.5354115445392300686674375872220e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 45.701184493300823037557828729065
y[1] (numeric) = 45.701184493300823037557828729081
absolute error = 1.6e-29
relative error = 3.5010033497808758323602075177078e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 46.150438866318718558957830086431
y[1] (numeric) = 46.150438866318718558957830086447
absolute error = 1.6e-29
relative error = 3.4669226107136848093065546069869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 46.604208320848737092255693225917
y[1] (numeric) = 46.604208320848737092255693225933
absolute error = 1.6e-29
relative error = 3.4331663548165631487500593298207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 47.062538234214474111886054582464
y[1] (numeric) = 47.06253823421447411188605458248
absolute error = 1.6e-29
relative error = 3.3997316337621579880977300155795e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 47.525474439789209059163246411121
y[1] (numeric) = 47.525474439789209059163246411138
absolute error = 1.7e-29
relative error = 3.5770289934796073401794726438903e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 47.993063231579280864830476241162
y[1] (numeric) = 47.993063231579280864830476241179
absolute error = 1.7e-29
relative error = 3.5421785681756722734504968635106e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 48.46535136885352716142011166414
y[1] (numeric) = 48.465351368853527161420111664157
absolute error = 1.7e-29
relative error = 3.5076605285740536976729841226902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 48.942386080819250133204185354246
y[1] (numeric) = 48.942386080819250133204185354263
absolute error = 1.7e-29
relative error = 3.4734718433890127518201001460762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=164071484, alloc=4390108, time=6.25
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 49.424215071345176604216766568584
y[1] (numeric) = 49.424215071345176604216766568602
absolute error = 1.8e-29
relative error = 3.6419394772413721657358728586142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 49.910886523731884664292814557216
y[1] (numeric) = 49.910886523731884664292814557233
absolute error = 1.7e-29
relative error = 3.4060705357170429519002251561011e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 50.40244910553017387976148654122
y[1] (numeric) = 50.402449105530173879761486541238
absolute error = 1.8e-29
relative error = 3.5712550321339511794343750434182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 50.89895197340786092983029148288
y[1] (numeric) = 50.898951973407860929830291482897
absolute error = 1.7e-29
relative error = 3.3399508911070789548644673065608e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 51.400444778065487352279404612568
y[1] (numeric) = 51.400444778065487352279404612585
absolute error = 1.7e-29
relative error = 3.3073643765928155109855324463920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 51.906977669201430973337148919991
y[1] (numeric) = 51.906977669201430973337148920009
absolute error = 1.8e-29
relative error = 3.4677418736865022188217848814775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 52.418601300526917537017237808153
y[1] (numeric) = 52.418601300526917537017237808171
absolute error = 1.8e-29
relative error = 3.4338955167464687813396771345014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 52.9353668348314340392599029227
y[1] (numeric) = 52.935366834831434039259902922718
absolute error = 1.8e-29
relative error = 3.4003731486670292981389875116192e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 53.457325949099050312431513118509
y[1] (numeric) = 53.457325949099050312431513118527
absolute error = 1.8e-29
relative error = 3.3671717917838285058064536887918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 53.984530839676160496604750057851
y[1] (numeric) = 53.984530839676160496604750057869
absolute error = 1.8e-29
relative error = 3.3342884933938933964787082801824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 54.517034227491161176072934038621
y[1] (numeric) = 54.51703422749116117607293403864
absolute error = 1.9e-29
relative error = 3.4851492325712245132497976567815e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 55.054889363326588153261897764787
y[1] (numeric) = 55.054889363326588153261897764806
absolute error = 1.9e-29
relative error = 3.4511012954021783782040521082132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 55.598150033144239078110261202861
y[1] (numeric) = 55.59815003314423907811026120288
absolute error = 1.9e-29
relative error = 3.4173798927973960250906962104123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 56.146870563463814449618662535082
y[1] (numeric) = 56.146870563463814449618662535101
absolute error = 1.9e-29
relative error = 3.3839820116998256119837521021831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 56.701105826795614858150315907712
y[1] (numeric) = 56.701105826795614858150315907732
absolute error = 2.0e-29
relative error = 3.5272680679445352783561807091599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 57.260911247127837742734388822998
y[1] (numeric) = 57.260911247127837742734388823017
absolute error = 1.9e-29
relative error = 3.3181448891023411806883972933450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 57.826342805469022397620692052799
y[1] (numeric) = 57.826342805469022397620692052819
absolute error = 2.0e-29
relative error = 3.4586313139810852412877329778303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 58.397457045446197477205057110728
y[1] (numeric) = 58.397457045446197477205057110748
absolute error = 2.0e-29
relative error = 3.4248066631455469039591874086291e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 58.974311078959290818741032291737
y[1] (numeric) = 58.974311078959290818741032291757
absolute error = 2.0e-29
relative error = 3.3913071020401543355775633331218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 59.556962591892367028532192341085
y[1] (numeric) = 59.556962591892367028532192341105
absolute error = 2.0e-29
relative error = 3.3581296173627646082843204492176e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 60.145469849882263960123061503388
y[1] (numeric) = 60.145469849882263960123061503409
absolute error = 2.1e-29
relative error = 3.4915347826551408921847902640468e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 60.739891704145204952943682133229
y[1] (numeric) = 60.73989170414520495294368213325
absolute error = 2.1e-29
relative error = 3.4573654003678197506278924924702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=168072392, alloc=4390108, time=6.40
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 61.340287597361969497487219708124
y[1] (numeric) = 61.340287597361969497487219708145
absolute error = 2.1e-29
relative error = 3.4235248680025974157301129425905e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 61.946717569622210848991447239727
y[1] (numeric) = 61.946717569622210848991447239748
absolute error = 2.1e-29
relative error = 3.3900101286880939258849493499002e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 62.559242264428515026339091755126
y[1] (numeric) = 62.559242264428515026339091755147
absolute error = 2.1e-29
relative error = 3.3568181518625427221373270883619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 63.177922934760801607080332059943
y[1] (numeric) = 63.177922934760801607080332059965
absolute error = 2.2e-29
relative error = 3.4822290727597650420917922384768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 63.802821449201672763710634207787
y[1] (numeric) = 63.802821449201672763710634207809
absolute error = 2.2e-29
relative error = 3.4481233745306843449001398821709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -2.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 64.434000298123323081212027004718
y[1] (numeric) = 64.43400029812332308121202700474
absolute error = 2.2e-29
relative error = 3.4143464472499564049308251711730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 65.071522599936628851995347043461
y[1] (numeric) = 65.071522599936628851995347043483
absolute error = 2.2e-29
relative error = 3.3808952243606214803962675572578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 65.71545210740304176238053926293
y[1] (numeric) = 65.715452107403041762380539262952
absolute error = 2.2e-29
relative error = 3.3477666659043854247729412873043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 66.365853214009918165243590001587
y[1] (numeric) = 66.365853214009918165243590001609
absolute error = 2.2e-29
relative error = 3.3149577583304197328476669376578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 67.022790960409921477070149341099
y[1] (numeric) = 67.022790960409921477070149341121
absolute error = 2.2e-29
relative error = 3.2824655143047246042041633873069e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 67.686331040925141645021734653992
y[1] (numeric) = 67.686331040925141645021734654014
absolute error = 2.2e-29
relative error = 3.2502869725200727051174801907145e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 68.356539810116582101381339598584
y[1] (numeric) = 68.356539810116582101381339598606
absolute error = 2.2e-29
relative error = 3.2184191975065507624153195367248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 69.033484289419671159548483832735
y[1] (numeric) = 69.033484289419671159548483832757
absolute error = 2.2e-29
relative error = 3.1868592794427155858443074606375e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 69.717232173846461408252914213396
y[1] (numeric) = 69.717232173846461408252914213418
absolute error = 2.2e-29
relative error = 3.1556043339673805887075971370533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 70.407851838755187329511563631169
y[1] (numeric) = 70.407851838755187329511563631191
absolute error = 2.2e-29
relative error = 3.1246515019920483598799202545181e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -6.667e+29
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 71.105412346687858101731879995094
y[1] (numeric) = 71.105412346687858101731879995116
absolute error = 2.2e-29
relative error = 3.0939979495140043336200550876426e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 71.809983454276569352939848696489
y[1] (numeric) = 71.809983454276569352939848696511
absolute error = 2.2e-29
relative error = 3.0636408674300861067519775326919e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 72.521635619219224501063310332678
y[1] (numeric) = 72.5216356192192245010633103327
absolute error = 2.2e-29
relative error = 3.0335774713511424656386878338847e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 73.240440007325363259217722516329
y[1] (numeric) = 73.240440007325363259217722516352
absolute error = 2.3e-29
relative error = 3.1403415923907046036002494721500e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 73.96646849963280189471643767276
y[1] (numeric) = 73.966468499632801894716437672784
absolute error = 2.4e-29
relative error = 3.2447135150327131361544992484284e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 74.699793699595796911761951170653
y[1] (numeric) = 74.699793699595796911761951170676
absolute error = 2.3e-29
relative error = 3.0789911003628988296847753122322e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 75.440488940345450980176545280381
y[1] (numeric) = 75.440488940345450980176545280405
absolute error = 2.4e-29
relative error = 3.1813155425037070475221023468405e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=172074784, alloc=4390108, time=6.55
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 76.188628292023087156815560466137
y[1] (numeric) = 76.188628292023087156815560466161
absolute error = 2.4e-29
relative error = 3.1500764009046726058380643972197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 76.944286569187324743196600893995
y[1] (numeric) = 76.944286569187324743196600894019
absolute error = 2.4e-29
relative error = 3.1191399738848062449360180284551e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 77.70753933829559749310302086642
y[1] (numeric) = 77.707539338295597493103020866444
absolute error = 2.4e-29
relative error = 3.0885034070526013512235390122310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 78.478462925260862328217071820222
y[1] (numeric) = 78.478462925260862328217071820246
absolute error = 2.4e-29
relative error = 3.0581638713867845577766928415376e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 79.257134423084254238951551456582
y[1] (numeric) = 79.257134423084254238951551456606
absolute error = 2.4e-29
relative error = 3.0281185630412868071731129131408e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 80.043631699564450642330605120616
y[1] (numeric) = 80.043631699564450642330605120641
absolute error = 2.5e-29
relative error = 3.1232965657823887795065843615735e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 80.838033405084516139779959223782
y[1] (numeric) = 80.838033405084516139779959223808
absolute error = 2.6e-29
relative error = 3.2163078324422304775594254175814e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 81.640418980477006365791424660798
y[1] (numeric) = 81.640418980477006365791424660824
absolute error = 2.6e-29
relative error = 3.1846970317750919416303836578775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 82.450868664968117444400811726181
y[1] (numeric) = 82.450868664968117444400811726207
absolute error = 2.6e-29
relative error = 3.1533930959113023461401331560851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 83.269463504201675475045050936085
y[1] (numeric) = 83.269463504201675475045050936111
absolute error = 2.6e-29
relative error = 3.1223931205811205617027293715537e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 84.096285358343768453433785661304
y[1] (numeric) = 84.09628535834376845343378566133
absolute error = 2.6e-29
relative error = 3.0916942275406177525840415398897e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 84.931416910268831097381406177663
y[1] (numeric) = 84.931416910268831097381406177689
absolute error = 2.6e-29
relative error = 3.0612935643672758913787973072229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 85.774941673828001192903868431231
y[1] (numeric) = 85.774941673828001192903868431258
absolute error = 2.7e-29
relative error = 3.1477724698049371839415060751534e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 86.626944002200574303105227123016
y[1] (numeric) = 86.626944002200574303105227123043
absolute error = 2.7e-29
relative error = 3.1168131706590182960750391642527e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 87.4875090963293919922843405557
y[1] (numeric) = 87.487509096329391992284340555728
absolute error = 2.8e-29
relative error = 3.2004568754118023304795998614792e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 88.356723013441007111113671531353
y[1] (numeric) = 88.356723013441007111113671531382
absolute error = 2.9e-29
relative error = 3.2821497913167807424814849345847e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 89.234672675651478166518863585011
y[1] (numeric) = 89.23467267565147816651886358504
absolute error = 2.9e-29
relative error = 3.2498578333344325070926508820687e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 90.121445878658653362867599725013
y[1] (numeric) = 90.121445878658653362867599725043
absolute error = 3.0e-29
relative error = 3.3288413992372703177097986704246e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 91.017131300521813550115456745574
y[1] (numeric) = 91.017131300521813550115456745604
absolute error = 3.0e-29
relative error = 3.2960827891779540115906135490725e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 91.92181851052955205051996320841
y[1] (numeric) = 91.92181851052955205051996320844
absolute error = 3.0e-29
relative error = 3.2636430051221767452658766652161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 92.835597978156778159295456987861
y[1] (numeric) = 92.835597978156778159295456987891
absolute error = 3.0e-29
relative error = 3.2315190135424860051557294887603e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 93.758561082111740027023002329753
y[1] (numeric) = 93.758561082111740027023002329783
absolute error = 3.0e-29
relative error = 3.1997078084129984063338637490120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=176075680, alloc=4390108, time=6.71
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 94.690800119473971633642818281708
y[1] (numeric) = 94.690800119473971633642818281737
absolute error = 2.9e-29
relative error = 3.0625995306207051852282804543815e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -14
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 95.632408314924077656341598932635
y[1] (numeric) = 95.632408314924077656341598932665
absolute error = 3.0e-29
relative error = 3.1370118695754208173547698481061e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 96.583479830066279217513027221686
y[1] (numeric) = 96.583479830066279217513027221715
absolute error = 2.9e-29
relative error = 3.0025838840166066844192535781206e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 97.54410977284465277513509238733
y[1] (numeric) = 97.54410977284465277513509238736
absolute error = 3.0e-29
relative error = 3.0755316820115890865006131533809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 98.51439420705400378730014068658
y[1] (numeric) = 98.51439420705400378730014068661
absolute error = 3.0e-29
relative error = 3.0452402657978164132264776789400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 99.494430161946326246189866862324
y[1] (numeric) = 99.494430161946326246189866862355
absolute error = 3.1e-29
relative error = 3.1157523038768638696059638217712e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 100.48431564193380873545405348757
y[1] (numeric) = 100.4843156419338087354540534876
absolute error = 3e-29
relative error = 2.9855405600712964718847115348311e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 101.48414963638935731968466139449
y[1] (numeric) = 101.48414963638935731968466139453
absolute error = 4e-29
relative error = 3.9415022092925067751637193043035e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 102.49403212954561532644134822903
y[1] (numeric) = 102.49403212954561532644134822907
absolute error = 4e-29
relative error = 3.9026662498205427146554496179528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 103.51406411049346993105582833176
y[1] (numeric) = 103.5140641104934699310558283318
absolute error = 4e-29
relative error = 3.8642092109631606748734455838612e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 104.54434758328104540320567097554
y[1] (numeric) = 104.54434758328104540320567097558
absolute error = 4e-29
relative error = 3.8261274688366686161522124380556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 105.58498557711419292299805009791
y[1] (numeric) = 105.58498557711419292299805009795
absolute error = 4e-29
relative error = 3.7884174327784441208818848887336e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 106.63608215665949702404549041811
y[1] (numeric) = 106.63608215665949702404549041816
absolute error = 5e-29
relative error = 4.6888444313384281106888871963906e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 107.69774243245082897276378483542
y[1] (numeric) = 107.69774243245082897276378483546
absolute error = 4e-29
relative error = 3.7140982806662290063571859641367e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 108.77007257140048774790216962363
y[1] (numeric) = 108.77007257140048774790216962368
absolute error = 5e-29
relative error = 4.5968526836440462635764269311536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 109.85317980741597974316302378673
y[1] (numeric) = 109.85317980741597974316302378678
absolute error = 5e-29
relative error = 4.5515296041184412638681836556445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 110.94717245212349887972870045537
y[1] (numeric) = 110.94717245212349887972870045541
absolute error = 4e-29
relative error = 3.6053194611391298072076912660271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 112.05215990569917948564300622207
y[1] (numeric) = 112.05215990569917948564300622211
absolute error = 4e-29
relative error = 3.5697660833725282110255788635110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 113.1682526678092050763613407161
y[1] (numeric) = 113.16825266780920507636134071615
absolute error = 5e-29
relative error = 4.4182002303038595694893558957638e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 114.29556234865986705646433913828
y[1] (numeric) = 114.29556234865986705646433913832
absolute error = 4e-29
relative error = 3.4996984290588256697721364528658e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 115.43420168015867835761360206601
y[1] (numeric) = 115.43420168015867835761360206605
absolute error = 4e-29
relative error = 3.4651775139252658911206908959668e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 116.58428452718765813341426713653
y[1] (numeric) = 116.58428452718765813341426713657
absolute error = 4e-29
relative error = 3.4309941654847939952923967596822e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=180076540, alloc=4390108, time=6.86
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 117.74592589898991484904834409238
y[1] (numeric) = 117.74592589898991484904834409242
absolute error = 4e-29
relative error = 3.3971451406577406332341385774294e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 118.91924196067066643347662739359
y[1] (numeric) = 118.91924196067066643347662739364
absolute error = 5e-29
relative error = 4.2045340329814877349699951381052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 120.10435004481384760580862199534
y[1] (numeric) = 120.10435004481384760580862199539
absolute error = 5e-29
relative error = 4.1630465492168923637445831271902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 121.30136866321546604625365765727
y[1] (numeric) = 121.30136866321546604625365765732
absolute error = 5e-29
relative error = 4.1219650323007819670778640852655e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 122.51041751873488075704811629788
y[1] (numeric) = 122.51041751873488075704811629793
absolute error = 5e-29
relative error = 4.0812855765799475900677125165314e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 123.73161751726518775107096333766
y[1] (numeric) = 123.73161751726518775107096333771
absolute error = 5e-29
relative error = 4.0410043126626975666829139821401e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 124.96509077982391011669179924248
y[1] (numeric) = 124.96509077982391011669179924253
absolute error = 5e-29
relative error = 4.0011174071081209860528705311807e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 126.21096065476520153793352471171
y[1] (numeric) = 126.21096065476520153793352471176
absolute error = 5e-29
relative error = 3.9616210621174927030561975215969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 127.46935173011478450047850596726
y[1] (numeric) = 127.46935173011478450047850596731
absolute error = 5e-29
relative error = 3.9225115152278162172395272411631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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 = 5.000e+15
Order of pole (six term test) = -5.000e+29
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 128.74038984602885668761799019549
y[1] (numeric) = 128.74038984602885668761799019554
absolute error = 5e-29
relative error = 3.8837850390075004653590765754106e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 130.0242021073782114671668226883
y[1] (numeric) = 130.02420210737821146716682268836
absolute error = 6e-29
relative error = 4.6145255289049995625937325764961e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 131.32091689645883089187895918358
y[1] (numeric) = 131.32091689645883089187895918364
absolute error = 6e-29
relative error = 4.5689598746334938174978331404115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 132.63066388583022228325601109699
y[1] (numeric) = 132.63066388583022228325601109705
absolute error = 6e-29
relative error = 4.5238407350240355514140069609247e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 133.95357405128278224310585398182
y[1] (numeric) = 133.95357405128278224310585398188
absolute error = 6e-29
relative error = 4.4791638017086130014401484411752e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 135.28977968493548484005862777435
y[1] (numeric) = 135.28977968493548484005862777441
absolute error = 6e-29
relative error = 4.4349248065691838212207653368866e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 136.63941440846520375077355696288
y[1] (numeric) = 136.63941440846520375077355696294
absolute error = 6e-29
relative error = 4.3911195213877342155635992394432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 138.00261318646899129907518322816
y[1] (numeric) = 138.00261318646899129907518322822
absolute error = 6e-29
relative error = 4.3477437574988569753555115311410e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 139.37951233996065063205819382868
y[1] (numeric) = 139.37951233996065063205819382874
absolute error = 6e-29
relative error = 4.3047933654448413239300499559873e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 140.77024956000295070162563718432
y[1] (numeric) = 140.77024956000295070162563718438
absolute error = 6e-29
relative error = 4.2622642346332672320226152505882e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 142.17496392147684728431889649845
y[1] (numeric) = 142.17496392147684728431889649851
absolute error = 6e-29
relative error = 4.2201522929970966124981245140926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 143.59379589698908697301579351366
y[1] (numeric) = 143.59379589698908697301579351371
absolute error = 5e-29
relative error = 3.4820445888810446399878325310093e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 145.02688737091958491248570083683
y[1] (numeric) = 145.02688737091958491248570083689
absolute error = 6e-29
relative error = 4.1371638795876856342397163284808e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=184077460, alloc=4390108, time=7.02
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 146.47438165360998102828140547844
y[1] (numeric) = 146.47438165360998102828140547849
absolute error = 5e-29
relative error = 3.4135662110690814494335035558578e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 147.93642349569479361641444906234
y[1] (numeric) = 147.93642349569479361641444906239
absolute error = 5e-29
relative error = 3.3798302553566253194622954099052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18
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+16
Order of pole (six term test) = -1.000e+30
Finished!
diff ( y , x , 2 ) = diff ( y , x , 1 ) ;
Iterations = 1000
Total Elapsed Time = 6 Seconds
Elapsed Time(since restart) = 6 Seconds
Time to Timeout = 2 Minutes 53 Seconds
Percent Done = 100.1 %
> quit
bytes used=184512676, alloc=4390108, time=7.04