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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_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 2;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 2
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 2;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_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 add CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_y[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_y[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_y[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_y[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp1[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp1[kkk] := array_y[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp1[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp1[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_y[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp1[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_y[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp1[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_y[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp1[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_y[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp1[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_y[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp1[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(exp(x));
> end;
exact_soln_y := 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_1,
> array_const_0D0,
> #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_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/diff0postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = y;");
> 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,"glob_look_poles := false;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := 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_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_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);
> glob_look_poles := false;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 5;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = y;");
> 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,"2013-05-26T00:16:01-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"diff0")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = y;")
> ;
> 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,"diff0 diffeq.mxt")
> ;
> logitem_str(html_log_file,"diff0 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_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_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/diff0postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y;");
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, "glob_look_poles := false;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := 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_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_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);
glob_look_poles := false;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
16, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = y;");
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, "2013-05-26T00:16:01-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "diff0")
;
logitem_str(html_log_file, "diff ( y , x , 1 ) = y;");
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,
"diff0 diffeq.mxt");
logitem_str(html_log_file,
"diff0 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/diff0postode.ode#################
diff ( y , x , 1 ) = y;
!
#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);
glob_look_poles := false;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := 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 = 1.6707388510135145318336278216146e-185
estimated_step_error = 1.6707388510135145318336278216146e-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 = 1.1212138840850425077445713955373e-177
estimated_step_error = 1.1212138840850425077445713955373e-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 = 7.5243392848767301974381056101733e-170
estimated_step_error = 7.5243392848767301974381056101733e-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 = 5.0494989916234845162087581339871e-162
estimated_step_error = 5.0494989916234845162087581339871e-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 = 3.3886619129940291314972567327095e-154
estimated_step_error = 3.3886619129940291314972567327095e-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 = 2.2740931884165287534899973804412e-146
estimated_step_error = 2.2740931884165287534899973804412e-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 = 1.5261190094150109279521457218482e-138
estimated_step_error = 1.5261190094150109279521457218482e-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 = 1.0241623443297890615626508578017e-130
estimated_step_error = 1.0241623443297890615626508578017e-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 = 6.8730534396716051320554906013086e-123
estimated_step_error = 6.8730534396716051320554906013086e-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 = 4.6124499519984951434514169271138e-115
estimated_step_error = 4.6124499519984951434514169271138e-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 = 2.0773218772353800142339251534026e-99
estimated_step_error = 2.0773218772353800142339251534026e-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 = 9.3564906260931470770328224636151e-84
estimated_step_error = 9.3564906260931470770328224636151e-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 = 6.2799873957036472828680343021067e-76
estimated_step_error = 6.2799873957036472828680343021067e-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 = 2.8308322136530815525163584828253e-60
estimated_step_error = 2.8308322136530815525163584828253e-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 = 1.9020502070240742375686819415176e-52
estimated_step_error = 1.9020502070240742375686819415176e-52
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (analytic) = 0.0067379469990854670966360484231484
y[1] (numeric) = 0.0067379469990854670966360484231484
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0068056644922305447989653325038289
y[1] (numeric) = 0.0068056644922305447989653325038288
absolute error = 1e-34
relative error = 1.4693642349569479361641444906234e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.98
y[1] (analytic) = 0.006874062557496251537290648273441
y[1] (numeric) = 0.0068740625574962515372906482734409
absolute error = 1e-34
relative error = 1.4547438165360998102828140547844e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.97
y[1] (analytic) = 0.0069431480347461124600022155600681
y[1] (numeric) = 0.0069431480347461124600022155600681
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.007012927832585423976138302447481
y[1] (numeric) = 0.007012927832585423976138302447481
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.007083408929052120042216400047348
y[1] (numeric) = 0.0070834089290521200422164000473479
absolute error = 1e-34
relative error = 1.4117496392147684728431889649845e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.94
y[1] (analytic) = 0.0071545983723145817706798693520961
y[1] (numeric) = 0.007154598372314581770679869352096
absolute error = 1e-34
relative error = 1.3977024956000295070162563718432e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.93
y[1] (analytic) = 0.0072265032813764601415024147785109
y[1] (numeric) = 0.0072265032813764601415024147785109
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.92
y[1] (analytic) = 0.0072991308467885822998088990669439
y[1] (numeric) = 0.0072991308467885822998088990669439
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.91
y[1] (analytic) = 0.0073724883313680126307355188431553
y[1] (numeric) = 0.0073724883313680126307355188431552
absolute error = 1e-34
relative error = 1.3563941440846520375077355696288e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.9
y[1] (analytic) = 0.0074465830709243405182360464201282
y[1] (numeric) = 0.0074465830709243405182360464201282
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0075214224749932674172152602805094
y[1] (numeric) = 0.0075214224749932674172152602805093
absolute error = 1e-34
relative error = 1.3295357405128278224310585398182e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.88
y[1] (analytic) = 0.0075970140275775665983081021805795
y[1] (numeric) = 0.0075970140275775665983081021805795
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) 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=4000120, alloc=3079628, time=0.15
x[1] = -4.87
y[1] (analytic) = 0.0076733652878954896618965073036742
y[1] (numeric) = 0.0076733652878954896618965073036741
absolute error = 1e-34
relative error = 1.3032091689645883089187895918358e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.86
y[1] (analytic) = 0.0077504838911366946626389833199926
y[1] (numeric) = 0.0077504838911366946626389833199926
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0078283775492257714379553335142817
y[1] (numeric) = 0.0078283775492257714379553335142817
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0079070540515934404936356456816838
y[1] (numeric) = 0.0079070540515934404936356456816838
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.83
y[1] (analytic) = 0.0079865212659555025671047755708698
y[1] (numeric) = 0.0079865212659555025671047755708698
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0080667871390996167639477781226075
y[1] (numeric) = 0.0080667871390996167639477781226075
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0081478596976799859461655896794928
y[1] (numeric) = 0.0081478596976799859461655896794928
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0082297470490200288413620267660743
y[1] (numeric) = 0.0082297470490200288413620267660743
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0083124573819231191407419157932201
y[1] (numeric) = 0.0083124573819231191407419157932201
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0083959989674914726605057716667536
y[1] (numeric) = 0.0083959989674914726605057716667536
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0084803801599532644560395730107377
y[1] (numeric) = 0.0084803801599532644560395730107377
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.76
y[1] (analytic) = 0.0085656093974980586013003195423073
y[1] (numeric) = 0.0085656093974980586013003195423073
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0086516952031206341770715039572504
y[1] (numeric) = 0.0086516952031206341770715039572504
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.008738646185473291851390514541038
y[1] (numeric) = 0.008738646185473291851390514541038
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0088264710397267262835162690967764
y[1] (numeric) = 0.0088264710397267262835162690967764
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0089151785484395504393948730147636
y[1] (numeric) = 0.0089151785484395504393948730147636
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0090047775824365587717794540610285
y[1] (numeric) = 0.0090047775824365587717794540610284
absolute error = 1e-34
relative error = 1.1105215990569917948564300622207e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (analytic) = 0.009095277101695817092054074291388
y[1] (numeric) = 0.0090952771016958170920540742913879
absolute error = 1e-34
relative error = 1.0994717245212349887972870045537e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.69
y[1] (analytic) = 0.0091866861562446678434881455062114
y[1] (numeric) = 0.0091866861562446678434881455062114
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0092790138870647403771953472373895
y[1] (numeric) = 0.0092790138870647403771953472373895
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0093722695270060567325788209031947
y[1] (numeric) = 0.0093722695270060567325788209031947
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0094664624017103243336024420066738
y[1] (numeric) = 0.0094664624017103243336024420066738
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0095616019305435079309272106497248
y[1] (numeric) = 0.0095616019305435079309272106497248
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0096576976275377740478841198775054
y[1] (numeric) = 0.0096576976275377740478841198775053
absolute error = 1e-34
relative error = 1.0354434758328104540320567097554e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.63
y[1] (analytic) = 0.0097547591023429021255130554615014
y[1] (numeric) = 0.0097547591023429021255130554615014
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0098527960611872575085750762749145
y[1] (numeric) = 0.0098527960611872575085750762749144
absolute error = 1e-34
relative error = 1.0149403212954561532644134822903e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.61
y[1] (analytic) = 0.0099518183078484223706374899794548
y[1] (numeric) = 0.0099518183078484223706374899794547
absolute error = 1e-34
relative error = 1.0048414963638935731968466139449e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.6
y[1] (analytic) = 0.01005183574463358164213309433155
y[1] (numeric) = 0.01005183574463358164213309433155
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.01015285837336976198080338102878
y[1] (numeric) = 0.01015285837336976198080338102878
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.010254896296404022809247948309628
y[1] (numeric) = 0.010254896296404022809247948309629
absolute error = 1e-33
relative error = 9.7514394207054003787300140686583e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.57
y[1] (analytic) = 0.010357959717613699439517372557417
y[1] (numeric) = 0.010357959717613699439517372557418
absolute error = 1e-33
relative error = 9.6544109772844652775135092387329e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.56
y[1] (analytic) = 0.010462058943426799309903870272308
y[1] (numeric) = 0.010462058943426799309903870272309
absolute error = 1e-33
relative error = 9.5583479830066279217513027221683e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.55
y[1] (analytic) = 0.010567204383852653374403762509342
y[1] (numeric) = 0.010567204383852653374403762509343
absolute error = 1e-33
relative error = 9.4632408314924077656341598932635e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.54
y[1] (analytic) = 0.010673406553522925710849567049765
y[1] (numeric) = 0.010673406553522925710849567049766
absolute error = 1e-33
relative error = 9.3690800119473971633642818281705e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=8001580, alloc=4128012, time=0.31
TOP MAIN SOLVE Loop
x[1] = -4.53
y[1] (analytic) = 0.010780676072743085449540042413331
y[1] (numeric) = 0.010780676072743085449540042413332
absolute error = 1e-33
relative error = 9.2758561082111740027023002329752e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.52
y[1] (analytic) = 0.010889023668554446170437276243945
y[1] (numeric) = 0.010889023668554446170437276243946
absolute error = 1e-33
relative error = 9.1835597978156778159295456987862e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.51
y[1] (analytic) = 0.010998460175806878973755573558587
y[1] (numeric) = 0.010998460175806878973755573558587
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011108996538242306496143134286931
y[1] (numeric) = 0.011108996538242306496143134286931
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011220643809589086222761052959285
y[1] (numeric) = 0.011220643809589086222761052959285
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011333413154667392534502837576167
y[1] (numeric) = 0.011333413154667392534502837576167
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011447315850505708029480324387936
y[1] (numeric) = 0.011447315850505708029480324387936
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.0115623632874685357688385497119
y[1] (numeric) = 0.0115623632874685357688385497119
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011678566970395445219063923611468
y[1] (numeric) = 0.011678566970395445219063923611468
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011795938519751565796329144370652
y[1] (numeric) = 0.011795938519751565796329144370652
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.011914489672789643063188036071488
y[1] (numeric) = 0.011914489672789643063188036071488
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.012034232284723773784208362149973
y[1] (numeric) = 0.012034232284723773784208362149973
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.012155178329914937215026294018624
y[1] (numeric) = 0.012155178329914937215026294018623
absolute error = 1e-33
relative error = 8.2269463504201675475045050936082e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.4
y[1] (analytic) = 0.012277339903068441178939386236542
y[1] (numeric) = 0.012277339903068441178939386236541
absolute error = 1e-33
relative error = 8.1450868664968117444400811726179e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.39
y[1] (analytic) = 0.012400729220443402676643592581245
y[1] (numeric) = 0.012400729220443402676643592581245
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.012525358621074383978183200591659
y[1] (numeric) = 0.012525358621074383978183200591659
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.012651240568005306361740913045782
y[1] (numeric) = 0.012651240568005306361740913045782
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.012778387649535764891670220257723
y[1] (numeric) = 0.012778387649535764891670220257723
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.012906812580479868868286465541673
y[1] (numeric) = 0.012906812580479868868286465541673
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.01303652820343773383451062015432
y[1] (numeric) = 0.01303652820343773383451062015432
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.33
y[1] (analytic) = 0.013167547490079752289626012297322
y[1] (numeric) = 0.013167547490079752289626012297322
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.32
y[1] (analytic) = 0.013299883542443771538289615014963
y[1] (numeric) = 0.013299883542443771538289615014962
absolute error = 1e-33
relative error = 7.5188628292023087156815560466136e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.31
y[1] (analytic) = 0.013433549594245308393663779259903
y[1] (numeric) = 0.013433549594245308393663779259902
absolute error = 1e-33
relative error = 7.4440488940345450980176545280379e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.3
y[1] (analytic) = 0.013568559012200931757230574525767
y[1] (numeric) = 0.013568559012200931757230574525767
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.013704925297364945414649540973216
y[1] (numeric) = 0.013704925297364945414649540973216
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.013842662086479504717052344867598
y[1] (numeric) = 0.013842662086479504717052344867598
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.013981783153338302160567567778484
y[1] (numeric) = 0.013981783153338302160567567778484
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.014122302410163958233769990457622
y[1] (numeric) = 0.014122302410163958233769990457622
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.25
y[1] (analytic) = 0.014264233908999255273286945856002
y[1] (numeric) = 0.014264233908999255273286945856002
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.014407591843112353452106667326216
y[1] (numeric) = 0.014407591843112353452106667326216
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.01455239054841612942335848007191
y[1] (numeric) = 0.01455239054841612942335848007191
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.014698644504901779554612000009234
y[1] (numeric) = 0.014698644504901779554612000009234
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.014846368338086831114213443304338
y[1] (numeric) = 0.014846368338086831114213443304338
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.014995576820477706211984360228729
y[1] (numeric) = 0.014995576820477706211984360228729
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) 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=12002580, alloc=4193536, time=0.46
x[1] = -4.19
y[1] (analytic) = 0.015146284873046984751895670552491
y[1] (numeric) = 0.015146284873046984751895670552492
absolute error = 1e-33
relative error = 6.6022790960409921477070149341101e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.18
y[1] (analytic) = 0.015298507566725514124243324442973
y[1] (numeric) = 0.015298507566725514124243324442974
absolute error = 1e-33
relative error = 6.5365853214009918165243590001587e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.17
y[1] (analytic) = 0.015452260123909514849538235323269
y[1] (numeric) = 0.01545226012390951484953823532327
absolute error = 1e-33
relative error = 6.4715452107403041762380539262931e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.16
y[1] (analytic) = 0.015607557919982832885930799240113
y[1] (numeric) = 0.015607557919982832885930799240114
absolute error = 1e-33
relative error = 6.4071522599936628851995347043460e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = -4.15
y[1] (analytic) = 0.015764416484854490826669291011109
y[1] (numeric) = 0.01576441648485449082666929101111
absolute error = 1e-33
relative error = 6.3434000298123323081212027004719e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.14
y[1] (analytic) = 0.015922851504511691743993179926466
y[1] (numeric) = 0.015922851504511691743993179926466
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.016082878822588430981139928520603
y[1] (numeric) = 0.016082878822588430981139928520603
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.016244514441949872754951655944126
y[1] (numeric) = 0.016244514441949872754951655944126
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.016407774526292650008062244839057
y[1] (numeric) = 0.016407774526292650008062244839057
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.1
y[1] (analytic) = 0.016572675401761247541983698083451
y[1] (numeric) = 0.016572675401761247541983698083451
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.016739233558580630070752044475271
y[1] (numeric) = 0.016739233558580630070752044475271
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.08
y[1] (analytic) = 0.016907465652705278459298685859221
y[1] (numeric) = 0.016907465652705278459298685859221
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.017077388507484799051545224277218
y[1] (numeric) = 0.017077388507484799051545224277218
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.06
y[1] (analytic) = 0.017249019115346272650542591025329
y[1] (numeric) = 0.017249019115346272650542591025329
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -4.05
y[1] (analytic) = 0.017422374639493511386954453686733
y[1] (numeric) = 0.017422374639493511386954453686733
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.017597472415623393402987801591979
y[1] (numeric) = 0.01759747241562339340298780159198
absolute error = 1e-33
relative error = 5.6826342805469022397620692052799e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.03
y[1] (analytic) = 0.017774329953659446986669386435969
y[1] (numeric) = 0.01777432995365944698666938643597
absolute error = 1e-33
relative error = 5.6260911247127837742734388822999e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.02
y[1] (analytic) = 0.017952964939502857516326103956469
y[1] (numeric) = 0.017952964939502857516326103956469
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.018133395236801072317422942029974
y[1] (numeric) = 0.018133395236801072317422942029974
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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
y[1] (analytic) = 0.018315638888734180293718021273241
y[1] (numeric) = 0.018315638888734180293718021273241
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.018499714119819244972186498309335
y[1] (numeric) = 0.018499714119819244972186498309335
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.98
y[1] (analytic) = 0.018685639337732771396521439971349
y[1] (numeric) = 0.018685639337732771396521439971349
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.97
y[1] (analytic) = 0.018873433135151489117419746004876
y[1] (numeric) = 0.018873433135151489117419746004876
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.019063114291611635359486139800038
y[1] (numeric) = 0.019063114291611635359486139800037
absolute error = 1e-33
relative error = 5.2457325949099050312431513118507e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.95
y[1] (analytic) = 0.019254701775386924294621325355917
y[1] (numeric) = 0.019254701775386924294621325355916
absolute error = 1e-33
relative error = 5.1935366834831434039259902922699e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (analytic) = 0.01944821474538539022038662890417
y[1] (numeric) = 0.01944821474538539022038662890417
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.019643672553065294329243669573638
y[1] (numeric) = 0.019643672553065294329243669573637
absolute error = 1e-33
relative error = 5.0906977669201430973337148919991e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.92
y[1] (analytic) = 0.019841094744370286660942577359354
y[1] (numeric) = 0.019841094744370286660942577359353
absolute error = 1e-33
relative error = 5.0400444778065487352279404612568e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.91
y[1] (analytic) = 0.020040501061684016755866637553545
y[1] (numeric) = 0.020040501061684016755866637553544
absolute error = 1e-33
relative error = 4.9898951973407860929830291482880e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.9
y[1] (analytic) = 0.020241911445804388472027543743654
y[1] (numeric) = 0.020241911445804388472027543743652
absolute error = 2e-33
relative error = 9.8804898211060347759522973082439e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.89
y[1] (analytic) = 0.020445346037937656392838176734243
y[1] (numeric) = 0.020445346037937656392838176734241
absolute error = 2e-33
relative error = 9.7821773047463769328585629114430e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.88
y[1] (analytic) = 0.020650825181712563236965439216312
y[1] (numeric) = 0.02065082518171256323696543921631
absolute error = 2e-33
relative error = 9.6848430142690353208433533137167e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.87
y[1] (analytic) = 0.020858369425214719685682584903873
y[1] (numeric) = 0.020858369425214719685682584903872
absolute error = 1e-33
relative error = 4.7942386080819250133204185354246e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.86
y[1] (analytic) = 0.021067999523041430067399099544563
y[1] (numeric) = 0.021067999523041430067399099544561
absolute error = 2e-33
relative error = 9.4930702737707054322840223328278e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
bytes used=16003232, alloc=4193536, time=0.63
Order of 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] = -3.85
y[1] (analytic) = 0.021279736438377169383648947237348
y[1] (numeric) = 0.021279736438377169383648947237347
absolute error = 1e-33
relative error = 4.6993063231579280864830476241163e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.84
y[1] (analytic) = 0.021493601345089919225969350835525
y[1] (numeric) = 0.021493601345089919225969350835523
absolute error = 2e-33
relative error = 9.3050948879578418118326492822241e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.83
y[1] (analytic) = 0.021709615629848572219008746733589
y[1] (numeric) = 0.021709615629848572219008746733587
absolute error = 2e-33
relative error = 9.2125076468428948223772109164926e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.82
y[1] (analytic) = 0.021927800894261616732072734417763
y[1] (numeric) = 0.021927800894261616732072734417761
absolute error = 2e-33
relative error = 9.1208416641697474184511386451833e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.81
y[1] (analytic) = 0.022148178957037315729361418575537
y[1] (numeric) = 0.022148178957037315729361418575536
absolute error = 1e-33
relative error = 4.5150438866318718558957830086432e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.8
y[1] (analytic) = 0.022370771856165595778583322540823
y[1] (numeric) = 0.022370771856165595778583322540821
absolute error = 2e-33
relative error = 8.9402368986601646075115657458129e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.79
y[1] (analytic) = 0.022595601851121864408664981367371
y[1] (numeric) = 0.02259560185112186440866498136737
absolute error = 1e-33
relative error = 4.4256400275983368846390927167132e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.78
y[1] (analytic) = 0.022822691425092976200128506076269
y[1] (numeric) = 0.022822691425092976200128506076267
absolute error = 2e-33
relative error = 8.7632083471147938980185751680847e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.77
y[1] (analytic) = 0.023052063287225570206601134759146
y[1] (numeric) = 0.023052063287225570206601134759145
absolute error = 1e-33
relative error = 4.3380064835851617355166526689092e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.76
y[1] (analytic) = 0.023283740374897003543072542255544
y[1] (numeric) = 0.023283740374897003543072542255543
absolute error = 1e-33
relative error = 4.2948425978763024912247320706349e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.75
y[1] (analytic) = 0.023517745856009108236151185100433
y[1] (numeric) = 0.023517745856009108236151185100432
absolute error = 1e-33
relative error = 4.2521082000062783055518172621604e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.74
y[1] (analytic) = 0.023754103131305000713916177789828
y[1] (numeric) = 0.023754103131305000713916177789827
absolute error = 1e-33
relative error = 4.2097990164996900591474480707947e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.023992835836709175618244366562593
y[1] (numeric) = 0.023992835836709175618244366562592
absolute error = 1e-33
relative error = 4.1679108164029293227391075798772e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.72
y[1] (analytic) = 0.024233967845691117950943918083021
y[1] (numeric) = 0.024233967845691117950943918083019
absolute error = 2e-33
relative error = 8.2528788217221589409657370322528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.71
y[1] (analytic) = 0.024477523271652669916878719737107
y[1] (numeric) = 0.024477523271652669916878719737105
absolute error = 2e-33
relative error = 8.1707613053980533951534852129925e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.7
y[1] (analytic) = 0.024723526470339391202757382983403
y[1] (numeric) = 0.024723526470339391202757382983401
absolute error = 2e-33
relative error = 8.0894608720134781057788378478077e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.69
y[1] (analytic) = 0.024972002042276153829624202256009
y[1] (numeric) = 0.024972002042276153829624202256008
absolute error = 1e-33
relative error = 4.0044846957286720141620521375167e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.68
y[1] (analytic) = 0.025222974835227215140566987658226
y[1] (numeric) = 0.025222974835227215140566987658225
absolute error = 1e-33
relative error = 3.9646394072572595459984576852157e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.025476469946681014932990609886771
y[1] (numeric) = 0.02547646994668101493299060988677
absolute error = 1e-33
relative error = 3.9251905860304499894107543068852e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (analytic) = 0.025732512726359945217240155920177
y[1] (numeric) = 0.025732512726359945217240155920176
absolute error = 1e-33
relative error = 3.8861342871332465361740206261101e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.65
y[1] (analytic) = 0.025991128778755343580641039557388
y[1] (numeric) = 0.025991128778755343580641039557387
absolute error = 1e-33
relative error = 3.8474666049032124417053505344034e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (analytic) = 0.026252343965687963658404972329299
y[1] (numeric) = 0.026252343965687963658404972329297
absolute error = 2e-33
relative error = 7.6183673450798030533196970634895e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (analytic) = 0.026516184408894178760582617885181
y[1] (numeric) = 0.02651618440889417876058261788518
absolute error = 1e-33
relative error = 3.7712816617181749099682489560460e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (analytic) = 0.026782676492638177277580801992482
y[1] (numeric) = 0.026782676492638177277580801992481
absolute error = 1e-33
relative error = 3.7337567822053653046672257335396e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (analytic) = 0.027051846866350411085961666631689
y[1] (numeric) = 0.027051846866350411085961666631688
absolute error = 1e-33
relative error = 3.6966052814822505926329448641596e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (analytic) = 0.027323722447292560801563062435553
y[1] (numeric) = 0.027323722447292560801563062435553
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.027598330423249284378686303292207
y[1] (numeric) = 0.027598330423249284378686303292207
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.027875698255247018232454333197378
y[1] (numeric) = 0.027875698255247018232454333197378
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.028155853680300102766718216326597
y[1] (numeric) = 0.028155853680300102766718216326597
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.028438824714184506922353186544466
y[1] (numeric) = 0.028438824714184506922353186544466
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.028724639654239429120710530784324
y[1] (numeric) = 0.028724639654239429120710530784324
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.029013327082197054764654326721755
y[1] (numeric) = 0.029013327082197054764654326721755
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.029304915867040753275291277527036
y[1] (numeric) = 0.029304915867040753275291277527036
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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=20004504, alloc=4193536, time=0.79
TOP MAIN SOLVE Loop
x[1] = -3.52
y[1] (analytic) = 0.029599435167892000486479155483378
y[1] (numeric) = 0.029599435167892000486479155483378
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.029896914436926315091759081996662
y[1] (numeric) = 0.029896914436926315091759081996662
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.03019738342231850073978629236362
y[1] (numeric) = 0.03019738342231850073978629236362
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.49
y[1] (analytic) = 0.030500872171217488304923304969038
y[1] (numeric) = 0.030500872171217488304923304969038
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.48
y[1] (analytic) = 0.030807411032751075819701597717858
y[1] (numeric) = 0.030807411032751075819701597717858
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.031117030661060866545648996160059
y[1] (numeric) = 0.031117030661060866545648996160059
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.031429762018367708678818979536548
y[1] (numeric) = 0.031429762018367708678818979536548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.031745636378067943236546999279735
y[1] (numeric) = 0.031745636378067943236546999279735
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.032064685327860769752802700773639
y[1] (numeric) = 0.032064685327860769752802700773639
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.032386940772907042521313730362309
y[1] (numeric) = 0.032386940772907042521313730362309
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.032712434939019813268717778964307
y[1] (numeric) = 0.032712434939019813268717778964308
absolute error = 1e-33
relative error = 3.0569415021050210302281241122151e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.41
y[1] (analytic) = 0.033041200375886939314668971921217
y[1] (numeric) = 0.033041200375886939314668971921218
absolute error = 1e-33
relative error = 3.0265244259400081344601532358897e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (analytic) = 0.033373269960326079482400131470948
y[1] (numeric) = 0.033373269960326079482400131470949
absolute error = 1e-33
relative error = 2.9964100047397013348162753033730e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.39
y[1] (analytic) = 0.033708676899572403262044473705897
y[1] (numeric) = 0.033708676899572403262044473705898
absolute error = 1e-33
relative error = 2.9665952270368851659649508823945e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.38
y[1] (analytic) = 0.034047454734599342000372838954302
y[1] (numeric) = 0.034047454734599342000372838954304
absolute error = 2e-33
relative error = 5.8741542226578872307692797132173e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.37
y[1] (analytic) = 0.034389637343472714194832731190271
y[1] (numeric) = 0.034389637343472714194832731190272
absolute error = 1e-33
relative error = 2.9078527057797073771687539613153e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.36
y[1] (analytic) = 0.034735258944738560307213684105142
y[1] (numeric) = 0.034735258944738560307213684105143
absolute error = 1e-33
relative error = 2.8789190879242677752233921434877e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.35
y[1] (analytic) = 0.035084354100845025883243525465533
y[1] (numeric) = 0.035084354100845025883243525465534
absolute error = 1e-33
relative error = 2.8502733643767278370041893023457e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.34
y[1] (analytic) = 0.035436957721598635169279078156064
y[1] (numeric) = 0.035436957721598635169279078156065
absolute error = 1e-33
relative error = 2.8219126705408612926561105116599e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.33
y[1] (analytic) = 0.035793105067655300856333204591566
y[1] (numeric) = 0.035793105067655300856333204591567
absolute error = 1e-33
relative error = 2.7938341703236505652149863987642e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.32
y[1] (analytic) = 0.036152831754046419055321781687162
y[1] (numeric) = 0.036152831754046419055321781687163
absolute error = 1e-33
relative error = 2.7660350558516751054310906965868e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.31
y[1] (analytic) = 0.036516173753740402115966553357815
y[1] (numeric) = 0.036516173753740402115966553357816
absolute error = 1e-33
relative error = 2.7385125471903217098118984843308e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.3
y[1] (analytic) = 0.036883167401240005445603704741515
y[1] (numeric) = 0.036883167401240005445603704741517
absolute error = 2e-33
relative error = 5.4225277841315774853636744220463e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.29
y[1] (analytic) = 0.03725384939621580806357782134513
y[1] (numeric) = 0.037253849396215808063577821345132
absolute error = 2e-33
relative error = 5.3685727311797129248991451130798e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (analytic) = 0.037628256807176210242304583063831
y[1] (numeric) = 0.037628256807176210242304583063833
absolute error = 2e-33
relative error = 5.3151545399747918577721940654428e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (analytic) = 0.038006427075174315237824640905527
y[1] (numeric) = 0.038006427075174315237824640905529
absolute error = 2e-33
relative error = 5.2622678686531784841545449318298e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.26
y[1] (analytic) = 0.038388398017552065801110810213673
y[1] (numeric) = 0.038388398017552065801110810213675
absolute error = 2e-33
relative error = 5.2099074285036682696998087965271e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (analytic) = 0.038774207831722009886899835267596
y[1] (numeric) = 0.038774207831722009886899835267598
absolute error = 2e-33
relative error = 5.1580679834386124178160215338755e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.24
y[1] (analytic) = 0.039163895098987073739771090365755
y[1] (numeric) = 0.039163895098987073739771090365757
absolute error = 2e-33
relative error = 5.1067443494703047413650659008111e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (analytic) = 0.039557498788398724337963980110933
y[1] (numeric) = 0.039557498788398724337963980110935
absolute error = 2e-33
relative error = 5.0559313941925785720398025776285e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (analytic) = 0.039955058260653907014393566724384
y[1] (numeric) = 0.039955058260653907014393566724386
absolute error = 2e-33
relative error = 5.0056240362675618666778438545380e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (analytic) = 0.040356613272031147951873984794018
y[1] (numeric) = 0.04035661327203114795187398479402
absolute error = 2e-33
relative error = 4.9558172449175391855948958376315e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.2
y[1] (analytic) = 0.040762203978366215166079262144425
y[1] (numeric) = 0.040762203978366215166079262144427
absolute error = 2e-33
relative error = 4.9065060394218697287120527455928e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=24007636, alloc=4259060, time=0.95
x[1] = -3.19
y[1] (analytic) = 0.041171870939067735545652904773485
y[1] (numeric) = 0.041171870939067735545652904773487
absolute error = 2e-33
relative error = 4.8576854886189111208614196592343e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = -3.18
y[1] (analytic) = 0.041585655121173169514516615501986
y[1] (numeric) = 0.041585655121173169514516615501988
absolute error = 2e-33
relative error = 4.8093507104128991382335293903428e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (analytic) = 0.04200359790344554891722436736
y[1] (numeric) = 0.042003597903445548917224367360002
absolute error = 2e-33
relative error = 4.7614968712857340635282632804463e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (analytic) = 0.042425741080511387804564326734984
y[1] (numeric) = 0.042425741080511387804564326734986
absolute error = 2e-33
relative error = 4.7141191858136248480379449613901e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.15
y[1] (analytic) = 0.042852126867040179913935456956155
y[1] (numeric) = 0.042852126867040179913935456956157
absolute error = 2e-33
relative error = 4.6672129161885427446760175128420e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.14
y[1] (analytic) = 0.0432827979019659007977297661522
y[1] (numeric) = 0.043282797901965900797729766152202
absolute error = 2e-33
relative error = 4.6207733717444365569158169160030e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.13
y[1] (analytic) = 0.043717797252750936753450967773854
y[1] (numeric) = 0.043717797252750936753450967773856
absolute error = 2e-33
relative error = 4.5747959084881621247695137389124e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.12
y[1] (analytic) = 0.044157168419692866952015851600085
y[1] (numeric) = 0.044157168419692866952015851600087
absolute error = 2e-33
relative error = 4.5292759286350791403649275495235e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.11
y[1] (analytic) = 0.044600955340274529446040192435223
y[1] (numeric) = 0.044600955340274529446040192435225
absolute error = 2e-33
relative error = 4.4842088801492688524147677942923e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.1
y[1] (analytic) = 0.045049202393557806068335092178335
y[1] (numeric) = 0.045049202393557806068335092178338
absolute error = 3e-33
relative error = 6.6593853844324900214483923143772e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.09
y[1] (analytic) = 0.045501954404621565602765104519455
y[1] (numeric) = 0.045501954404621565602765104519458
absolute error = 3e-33
relative error = 6.5931233927290263319629533647492e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.08
y[1] (analytic) = 0.045959256649044209025483526378486
y[1] (numeric) = 0.045959256649044209025483526378489
absolute error = 3e-33
relative error = 6.5275207188591233533159164780318e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -3.07
y[1] (analytic) = 0.04642115485743126507480444643516
y[1] (numeric) = 0.046421154857431265074804446435163
absolute error = 3e-33
relative error = 6.4625708025007250180878560859277e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.06
y[1] (analytic) = 0.046887695219988488913041546839812
y[1] (numeric) = 0.046887695219988488913041546839815
absolute error = 3e-33
relative error = 6.3982671486080703757298276015944e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.05
y[1] (analytic) = 0.047358924391140921193990770239734
y[1] (numeric) = 0.047358924391140921193990770239737
absolute error = 3e-33
relative error = 6.3346033267621836039121365737307e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.04
y[1] (analytic) = 0.047834889494198369445812829108141
y[1] (numeric) = 0.047834889494198369445812829108144
absolute error = 3e-33
relative error = 6.2715729705278267522417635583600e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.03
y[1] (analytic) = 0.048315638126067778321341759738763
y[1] (numeric) = 0.048315638126067778321341759738765
absolute error = 2e-33
relative error = 4.1394465178779006087246279673231e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.02
y[1] (analytic) = 0.048801218362012959956771540059998
y[1] (numeric) = 0.04880121836201295995677154006
absolute error = 2e-33
relative error = 4.0982583368385881027302858516284e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.01
y[1] (analytic) = 0.049291678760462160415723095117485
y[1] (numeric) = 0.049291678760462160415723095117487
absolute error = 2e-33
relative error = 4.0574799850481861203163045311780e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3
y[1] (analytic) = 0.049787068367863942979342415650062
y[1] (numeric) = 0.049787068367863942979342415650063
absolute error = 1e-33
relative error = 2.0085536923187667740928529654582e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.99
y[1] (analytic) = 0.050287436723591873874805382467975
y[1] (numeric) = 0.050287436723591873874805382467976
absolute error = 1e-33
relative error = 1.9885682491564726876297103339624e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.98
y[1] (analytic) = 0.050792833864898500914889398847029
y[1] (numeric) = 0.050792833864898500914889398847029
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.051303310331919120450604117395944
y[1] (numeric) = 0.051303310331919120450604117395944
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.051818917172725833017746344162871
y[1] (numeric) = 0.051818917172725833017746344162871
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.05233970594843239308715550254932
y[1] (numeric) = 0.05233970594843239308715550254932
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.052865728738350363407898738216609
y[1] (numeric) = 0.052865728738350363407898738216609
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.053397038145197089563116793103992
y[1] (numeric) = 0.053397038145197089563116793103992
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.053933687300356015540326226409024
y[1] (numeric) = 0.053933687300356015540326226409024
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.054475729869189866352118623672859
y[1] (numeric) = 0.054475729869189866352118623672859
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.055023220056407229029946530834175
y[1] (numeric) = 0.055023220056407229029946530834175
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.055576212611483068653567657580483
y[1] (numeric) = 0.055576212611483068653567657580482
absolute error = 1e-33
relative error = 1.7993309601550314901100324712728e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.88
y[1] (analytic) = 0.056134762834133721472267406165369
y[1] (numeric) = 0.056134762834133721472267406165368
absolute error = 1e-33
relative error = 1.7814273179612198540477911123657e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.87
y[1] (analytic) = 0.056698926579846912621734357420589
y[1] (numeric) = 0.056698926579846912621734357420588
absolute error = 1e-33
relative error = 1.7637018199837320533566907580682e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.86
y[1] (analytic) = 0.057268760265467351442968764970189
y[1] (numeric) = 0.057268760265467351442968764970187
absolute error = 2e-33
relative error = 3.4923053873159980834090136499939e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=28008416, alloc=4259060, time=1.11
TOP MAIN SOLVE Loop
x[1] = -2.85
y[1] (analytic) = 0.057844320874838462967410626777401
y[1] (numeric) = 0.057844320874838462967410626777399
absolute error = 2e-33
relative error = 3.4575563681135278502086061506892e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.84
y[1] (analytic) = 0.058425665964500819746137305407264
y[1] (numeric) = 0.058425665964500819746137305407262
absolute error = 2e-33
relative error = 3.4231531074291755475615547432520e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.83
y[1] (analytic) = 0.059012853669447843871062325786974
y[1] (numeric) = 0.059012853669447843871062325786972
absolute error = 2e-33
relative error = 3.3890921649082032607691841402949e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.82
y[1] (analytic) = 0.059605942708939354763133904682846
y[1] (numeric) = 0.059605942708939354763133904682844
absolute error = 2e-33
relative error = 3.3553701344279746792214400208987e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.81
y[1] (analytic) = 0.060204992392373544087156671052436
y[1] (numeric) = 0.060204992392373544087156671052433
absolute error = 3e-33
relative error = 4.9829754656360099914812544465132e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.8
y[1] (analytic) = 0.060810062625217964995621388183941
y[1] (numeric) = 0.060810062625217964995621388183938
absolute error = 3e-33
relative error = 4.9333940313291149614494048032775e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.79
y[1] (analytic) = 0.06142121391500012880540956810663
y[1] (numeric) = 0.061421213915000128805409568106627
absolute error = 3e-33
relative error = 4.8843059405365282395847430436806e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.78
y[1] (analytic) = 0.062038507377358308172032829271555
y[1] (numeric) = 0.062038507377358308172032829271552
absolute error = 3e-33
relative error = 4.8357062844082636885318758500230e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.77
y[1] (analytic) = 0.06266200474215315184676677422468
y[1] (numeric) = 0.062662004742153151846766774224678
absolute error = 2e-33
relative error = 3.1917268019588057555974610704327e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.76
y[1] (analytic) = 0.063291768359640722183248129934537
y[1] (numeric) = 0.063291768359640722183248129934534
absolute error = 3e-33
relative error = 4.7399528844781192004577769969528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (analytic) = 0.063927861206707572702430025557952
y[1] (numeric) = 0.063927861206707572702430025557949
absolute error = 3e-33
relative error = 4.6927895652564514830638094138470e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.74
y[1] (analytic) = 0.06457034689316848922884781846213
y[1] (numeric) = 0.064570346893168489228847818462128
absolute error = 2e-33
relative error = 3.0973970192679869449433593486185e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.73
y[1] (analytic) = 0.065219289668127524377557230192989
y[1] (numeric) = 0.065219289668127524377557230192986
absolute error = 3e-33
relative error = 4.5998661059721587297369535680833e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.72
y[1] (analytic) = 0.065874754426402961500494365945365
y[1] (numeric) = 0.065874754426402961500494365945362
absolute error = 3e-33
relative error = 4.5540966734861687903373074942189e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.71
y[1] (analytic) = 0.066536806715016850594006408006172
y[1] (numeric) = 0.066536806715016850594006408006169
absolute error = 3e-33
relative error = 4.5087826544626206793462963949769e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.7
y[1] (analytic) = 0.067205512739749765126551700855966
y[1] (numeric) = 0.067205512739749765126551700855962
absolute error = 4e-33
relative error = 5.9518926899491336447475972077873e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.69
y[1] (analytic) = 0.067880939371761435267714313501548
y[1] (numeric) = 0.067880939371761435267714313501544
absolute error = 4e-33
relative error = 5.8926703681770284050869918546894e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.68
y[1] (analytic) = 0.06856315415427791958737319324403
y[1] (numeric) = 0.068563154154277919587373193244026
absolute error = 4e-33
relative error = 5.8340373183523158769724489116209e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.67
y[1] (analytic) = 0.069252225309345983947768489455882
y[1] (numeric) = 0.069252225309345983947768489455878
absolute error = 4e-33
relative error = 5.7759876771211525514273561322375e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.66
y[1] (analytic) = 0.06994822174465536303198292183827
y[1] (numeric) = 0.069948221744655363031982921838266
absolute error = 4e-33
relative error = 5.7185156394710404498438982044401e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.65
y[1] (analytic) = 0.070651213060429586740676278186658
y[1] (numeric) = 0.070651213060429586740676278186654
absolute error = 4e-33
relative error = 5.6616154581503210366586559231587e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.64
y[1] (analytic) = 0.071361269556386060545455089586297
y[1] (numeric) = 0.071361269556386060545455089586293
absolute error = 4e-33
relative error = 5.6052814430934452641067031190136e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.63
y[1] (analytic) = 0.072078462238766095812712906299841
y[1] (numeric) = 0.072078462238766095812712906299837
absolute error = 4e-33
relative error = 5.5495079608519622755797335267005e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.62
y[1] (analytic) = 0.072802862827435593106831936505778
y[1] (numeric) = 0.072802862827435593106831936505774
absolute error = 4e-33
relative error = 5.4942894340311698659843757446610e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.61
y[1] (analytic) = 0.073534543763057088546993623861712
y[1] (numeric) = 0.073534543763057088546993623861708
absolute error = 4e-33
relative error = 5.4396203407323703636772726029703e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.6
y[1] (analytic) = 0.074273578214333880428210570169976
y[1] (numeric) = 0.074273578214333880428210570169972
absolute error = 4e-33
relative error = 5.3854952140006761591003301330336e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.59
y[1] (analytic) = 0.075020040085326960525278698644646
y[1] (numeric) = 0.075020040085326960525278698644643
absolute error = 3e-33
relative error = 3.9989314809587322451566270529808e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.58
y[1] (analytic) = 0.075774004022845481778877516074428
y[1] (numeric) = 0.075774004022845481778877516074425
absolute error = 3e-33
relative error = 3.9591414478975072531743043613548e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.57
y[1] (analytic) = 0.076535545423911501416745827508484
y[1] (numeric) = 0.07653554542391150141674582750848
absolute error = 4e-33
relative error = 5.2263297763738233992888801956188e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.56
y[1] (analytic) = 0.077304740443299745990465661039762
y[1] (numeric) = 0.077304740443299745990465661039758
absolute error = 4e-33
relative error = 5.1743269262172305079387727300154e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.55
y[1] (analytic) = 0.078081666001153152310641239552787
y[1] (numeric) = 0.078081666001153152310641239552783
absolute error = 4e-33
relative error = 5.1228415130652128179765015011011e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.54
y[1] (analytic) = 0.078866399790674945840912822600043
y[1] (numeric) = 0.078866399790674945840912822600039
absolute error = 4e-33
relative error = 5.0718683883335504736577636224576e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.53
y[1] (analytic) = 0.079659020285898025765054906486419
y[1] (numeric) = 0.079659020285898025765054906486416
absolute error = 3e-33
relative error = 3.7660518410004694224096069600226e-30 %
Correct digits = 32
h = 0.01
bytes used=32010412, alloc=4259060, time=1.28
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.52
y[1] (analytic) = 0.080459606749532433672140001519296
y[1] (numeric) = 0.080459606749532433672140001519293
absolute error = 3e-33
relative error = 3.7285789990732630319589847395587e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.51
y[1] (analytic) = 0.081268239240891690613176081838195
y[1] (numeric) = 0.081268239240891690613176081838192
absolute error = 3e-33
relative error = 3.6914790181531234908883255482154e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.5
y[1] (analytic) = 0.08208499862389879516952867446716
y[1] (numeric) = 0.082084998623898795169528674467157
absolute error = 3e-33
relative error = 3.6547481882110420314210527853504e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.49
y[1] (analytic) = 0.0829099665751726831396061170947
y[1] (numeric) = 0.082909966575172683139606117094698
absolute error = 2e-33
relative error = 2.4122552240889435456194798699356e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.48
y[1] (analytic) = 0.08374322559219595749651539197509
y[1] (numeric) = 0.083743225592195957496515391975088
absolute error = 2e-33
relative error = 2.3882528835698206854411941532637e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.47
y[1] (analytic) = 0.084584859001564705396490765853959
y[1] (numeric) = 0.084584859001564705396490765853957
absolute error = 2e-33
relative error = 2.3644893703292721776872706601286e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.46
y[1] (analytic) = 0.085434950967321227226670949205396
y[1] (numeric) = 0.085434950967321227226670949205395
absolute error = 1e-33
relative error = 1.1704811539980854868983000160809e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.45
y[1] (analytic) = 0.086293586499370510972073516516155
y[1] (numeric) = 0.086293586499370510972073516516153
absolute error = 2e-33
relative error = 2.3176693438446778130181412386160e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.44
y[1] (analytic) = 0.087160851461981293556217037077254
y[1] (numeric) = 0.087160851461981293556217037077252
absolute error = 2e-33
relative error = 2.2946081485589666778734450604127e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.43
y[1] (analytic) = 0.088036832582372559268609219894026
y[1] (numeric) = 0.088036832582372559268609219894024
absolute error = 2e-33
relative error = 2.2717764160002912704519142306946e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.42
y[1] (analytic) = 0.08892161745938633393609926073676
y[1] (numeric) = 0.088921617459386333936099260736757
absolute error = 3e-33
relative error = 3.3737577944645538239884767616592e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.41
y[1] (analytic) = 0.089815294572247642124738879133905
y[1] (numeric) = 0.089815294572247642124738879133902
absolute error = 3e-33
relative error = 3.3401883435195913979681065414371e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.4
y[1] (analytic) = 0.090717953289412503375172220079691
y[1] (numeric) = 0.090717953289412503375172220079689
absolute error = 2e-33
relative error = 2.2046352761283203304475879539336e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.39
y[1] (analytic) = 0.091629683877504852278551514220294
y[1] (numeric) = 0.091629683877504852278551514220291
absolute error = 3e-33
relative error = 3.2740481829125921225813456274577e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.38
y[1] (analytic) = 0.092550577510343276092433546305981
y[1] (numeric) = 0.092550577510343276092433546305978
absolute error = 3e-33
relative error = 3.2414708591793775890585870987861e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.37
y[1] (analytic) = 0.093480726278058472577940827976991
y[1] (numeric) = 0.093480726278058472577940827976989
absolute error = 2e-33
relative error = 2.1394784568222104755862318476360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.36
y[1] (analytic) = 0.094420223196302339811569097857706
y[1] (numeric) = 0.094420223196302339811569097857704
absolute error = 2e-33
relative error = 2.1181902904867561032057988814206e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.35
y[1] (analytic) = 0.095369162215549618888296596799802
y[1] (numeric) = 0.0953691622155496188882965967998
absolute error = 2e-33
relative error = 2.0971139449455148657137415078217e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.34
y[1] (analytic) = 0.096327638230493019688016823959127
y[1] (numeric) = 0.096327638230493019688016823959125
absolute error = 2e-33
relative error = 2.0762473125463689591564339964852e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.33
y[1] (analytic) = 0.097295747089532769225700714551537
y[1] (numeric) = 0.097295747089532769225700714551536
absolute error = 1e-33
relative error = 1.0277941533043447753238138736105e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.32
y[1] (analytic) = 0.098273585604361531548031238823858
y[1] (numeric) = 0.098273585604361531548031238823857
absolute error = 1e-33
relative error = 1.0175674306073334882894211461532e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.31
y[1] (analytic) = 0.099261251559645657676487545571868
y[1] (numeric) = 0.099261251559645657676487545571867
absolute error = 1e-33
relative error = 1.0074424655013586200245455289684e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -2.3
y[1] (analytic) = 0.10025884372280373372994069379799
y[1] (numeric) = 0.10025884372280373372994069379799
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.10126646185388340508972204934667
y[1] (numeric) = 0.10126646185388340508972204934668
absolute error = 1e-32
relative error = 9.8749376811731831702012210539714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.28
y[1] (analytic) = 0.10228420671553746429781156759708
y[1] (numeric) = 0.10228420671553746429781156759709
absolute error = 1e-32
relative error = 9.7766804095289050835042636318180e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.27
y[1] (analytic) = 0.10331218008310020030524921533449
y[1] (numeric) = 0.1033121800831002003052492153345
absolute error = 1e-32
relative error = 9.6794008140728407194171550561079e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.26
y[1] (analytic) = 0.10435048475476501671409135863961
y[1] (numeric) = 0.10435048475476501671409135863962
absolute error = 1e-32
relative error = 9.5830891667643778717351852852972e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.25
y[1] (analytic) = 0.1053992245618643367832176892407
y[1] (numeric) = 0.1053992245618643367832176892407
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.10645850437925282319705588608135
y[1] (numeric) = 0.10645850437925282319705588608135
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.10752843013579495092785359655303
y[1] (numeric) = 0.10752843013579495092785359655303
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.10860910882495798195752363777457
y[1] (numeric) = 0.10860910882495798195752363777457
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.10970064851551140116536211079855
y[1] (numeric) = 0.10970064851551140116536211079855
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.11080315836233388333414442584994
y[1] (numeric) = 0.11080315836233388333414442584994
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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=36012392, alloc=4259060, time=1.45
TOP MAIN SOLVE Loop
x[1] = -2.19
y[1] (analytic) = 0.11191674861732887198030568405714
y[1] (numeric) = 0.11191674861732887198030568405715
absolute error = 1e-32
relative error = 8.9352131146987488146044744309989e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.18
y[1] (analytic) = 0.11304153064044986157518477972675
y[1] (numeric) = 0.11304153064044986157518477972675
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.11417761691083648569474211338224
y[1] (numeric) = 0.11417761691083648569474211338224
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.11532512103806252471584599172984
y[1] (numeric) = 0.11532512103806252471584599172984
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.15
y[1] (analytic) = 0.11648415777349695786927071418284
y[1] (numeric) = 0.11648415777349695786927071418283
absolute error = 1e-32
relative error = 8.5848583971778938662399876124014e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.14
y[1] (analytic) = 0.11765484302177919576407922068906
y[1] (numeric) = 0.11765484302177919576407922068906
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.11883729385240964091620546477244
y[1] (numeric) = 0.11883729385240964091620546477244
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.12003162851145673534694820266229
y[1] (numeric) = 0.12003162851145673534694820266229
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.12123796643338166596589195340782
y[1] (numeric) = 0.12123796643338166596589195340782
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.12245642825298191021864737607263
y[1] (numeric) = 0.12245642825298191021864737607262
absolute error = 1e-32
relative error = 8.1661699125676500734497274104784e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.09
y[1] (analytic) = 0.12368713581745481636392882592999
y[1] (numeric) = 0.12368713581745481636392882592998
absolute error = 1e-32
relative error = 8.0849151643050601749734407164419e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.08
y[1] (analytic) = 0.12493021219858242474804981448882
y[1] (numeric) = 0.12493021219858242474804981448881
absolute error = 1e-32
relative error = 8.0044689142963525442399839278696e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.07
y[1] (analytic) = 0.12618578170503874856911787447176
y[1] (numeric) = 0.12618578170503874856911787447175
absolute error = 1e-32
relative error = 7.9248231178494875453501560543463e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.06
y[1] (analytic) = 0.12745396989482074486926135072242
y[1] (numeric) = 0.12745396989482074486926135072241
absolute error = 1e-32
relative error = 7.8459698103184487735262954149554e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.05
y[1] (analytic) = 0.12873490358780421886234651674487
y[1] (numeric) = 0.12873490358780421886234651674486
absolute error = 1e-32
relative error = 7.7679011063067718162446641452443e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.04
y[1] (analytic) = 0.1300287108784259171980810770711
y[1] (numeric) = 0.13002871087842591719808107707109
absolute error = 1e-32
relative error = 7.6906091988789980356085715614842e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.03
y[1] (analytic) = 0.1313355211484930783823989120881
y[1] (numeric) = 0.13133552114849307838239891208809
absolute error = 1e-32
relative error = 7.6140863587799745166833496561362e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.02
y[1] (analytic) = 0.13265546508012172131984276473165
y[1] (numeric) = 0.13265546508012172131984276473164
absolute error = 1e-32
relative error = 7.5383249336619221111374286770602e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -2.01
y[1] (analytic) = 0.13398867466880496581758105037375
y[1] (numeric) = 0.13398867466880496581758105037375
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.13533528323661269189399949497248
y[1] (numeric) = 0.13533528323661269189399949497248
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.13669542544552385786879821340419
y[1] (numeric) = 0.13669542544552385786879821340418
absolute error = 1e-32
relative error = 7.3155337623095665114351708335139e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (analytic) = 0.13806923731089281047751353979537
y[1] (numeric) = 0.13806923731089281047751353979536
absolute error = 1e-32
relative error = 7.2427429851610122085124347531445e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (analytic) = 0.13945685621505093365269802453912
y[1] (numeric) = 0.13945685621505093365269802453912
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (analytic) = 0.14085842092104499614797146109596
y[1] (numeric) = 0.14085842092104499614797146109596
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (analytic) = 0.14227407158651357185115400886383
y[1] (numeric) = 0.14227407158651357185115400886383
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.14370394977770292044007644756961
y[1] (numeric) = 0.1437039497777029204400764475696
absolute error = 1e-32
relative error = 6.9587509706372721011318681258758e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (analytic) = 0.14514819848362372998081308368709
y[1] (numeric) = 0.14514819848362372998081308368708
absolute error = 1e-32
relative error = 6.8895102415812930672790192339938e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (analytic) = 0.14660696213035013715439445699501
y[1] (numeric) = 0.146606962130350137154394456995
absolute error = 1e-32
relative error = 6.8209584692907498349465988329417e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (analytic) = 0.14808038659546245502593840845419
y[1] (numeric) = 0.14808038659546245502593840845418
absolute error = 1e-32
relative error = 6.7530887985312866824806579188519e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (analytic) = 0.14956861922263505264101206910373
y[1] (numeric) = 0.14956861922263505264101206910372
absolute error = 1e-32
relative error = 6.6858944422792694160725307276931e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (analytic) = 0.1510718088363708452493410130273
y[1] (numeric) = 0.15107180883637084524934101302728
absolute error = 2e-32
relative error = 1.3238737362086154700935144993520e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (analytic) = 0.15259010575688386861716672808717
y[1] (numeric) = 0.15259010575688386861716672808715
absolute error = 2e-32
relative error = 1.3107009724382297094603236282640e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (analytic) = 0.15412366181513142569808582677398
y[1] (numeric) = 0.15412366181513142569808582677396
absolute error = 2e-32
relative error = 1.2976592798573422230058062648698e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (analytic) = 0.15567263036799730888956491174158
y[1] (numeric) = 0.15567263036799730888956491174156
absolute error = 2e-32
relative error = 1.2847473542858268086035888585819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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
bytes used=40013072, alloc=4259060, time=1.61
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (analytic) = 0.15723716631362761621000947490312
y[1] (numeric) = 0.1572371663136276162100094749031
absolute error = 2e-32
relative error = 1.2719639045203663408694443741274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = -1.84
y[1] (analytic) = 0.15881742610692069499078442639196
y[1] (numeric) = 0.15881742610692069499078442639194
absolute error = 2e-32
relative error = 1.2593076522053313634424029154049e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = -1.83
y[1] (analytic) = 0.16041356777517276209046378487805
y[1] (numeric) = 0.16041356777517276209046378487804
absolute error = 1e-32
relative error = 6.2338866585247173036960337699730e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.82
y[1] (analytic) = 0.16202575093388076520636901451425
y[1] (numeric) = 0.16202575093388076520636901451424
absolute error = 1e-32
relative error = 6.1718584498835531270637716458997e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (analytic) = 0.16365413680270406558269625733594
y[1] (numeric) = 0.16365413680270406558269625733592
absolute error = 2e-32
relative error = 1.2220894864461219649458081851989e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.8
y[1] (analytic) = 0.16529888822158653829680472043221
y[1] (numeric) = 0.1652988882215865382968047204322
absolute error = 1e-32
relative error = 6.0496474644129460837310239530279e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.79
y[1] (analytic) = 0.16696016966704070234712997508294
y[1] (numeric) = 0.16696016966704070234712997508292
absolute error = 2e-32
relative error = 1.1978904932766226657916933453631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (analytic) = 0.16863814726859550896930111283181
y[1] (numeric) = 0.16863814726859550896930111283179
absolute error = 2e-32
relative error = 1.1859712837182291823138143164094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.77
y[1] (analytic) = 0.17033298882540943297299990616306
y[1] (numeric) = 0.17033298882540943297299990616304
absolute error = 2e-32
relative error = 1.1741706722765202192232507831657e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.76
y[1] (analytic) = 0.17204486382305052842253994862595
y[1] (numeric) = 0.17204486382305052842253994862593
absolute error = 2e-32
relative error = 1.1624874788805177299760681248899e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (analytic) = 0.17377394345044512668071725866637
y[1] (numeric) = 0.17377394345044512668071725866636
absolute error = 1e-32
relative error = 5.7546026760057304368664997048427e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.17552040061699687169986069434221
y[1] (numeric) = 0.1755204006169968716998606943422
absolute error = 1e-32
relative error = 5.6973434226719910119370988363600e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (analytic) = 0.17728440996987780447787719425943
y[1] (numeric) = 0.17728440996987780447787719425942
absolute error = 1e-32
relative error = 5.6406539084283207976510967178079e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.72
y[1] (analytic) = 0.17906614791149322580214673433063
y[1] (numeric) = 0.17906614791149322580214673433062
absolute error = 1e-32
relative error = 5.5845284642760540076461854730192e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.71
y[1] (analytic) = 0.18086579261712208378209549065185
y[1] (numeric) = 0.18086579261712208378209549065185
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.18268352405273465022390083775894
y[1] (numeric) = 0.18268352405273465022390083775894
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.18451952399298926762981376590245
y[1] (numeric) = 0.18451952399298926762981376590245
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.18637397603940996651179598874008
y[1] (numeric) = 0.18637397603940996651179598874008
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.67
y[1] (analytic) = 0.18824706563874677079635117007879
y[1] (numeric) = 0.18824706563874677079635117007879
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 0.19013898010152052736639105829434
y[1] (numeric) = 0.19013898010152052736639105829433
absolute error = 1e-32
relative error = 5.2593108444468987342204704726538e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (analytic) = 0.19204990862075411423854479117333
y[1] (numeric) = 0.19204990862075411423854479117332
absolute error = 1e-32
relative error = 5.2069798271798487376573070927124e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.64
y[1] (analytic) = 0.19398004229089190051233849428734
y[1] (numeric) = 0.19398004229089190051233849428733
absolute error = 1e-32
relative error = 5.1551695122346810458097983038692e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (analytic) = 0.1959295741269093500530063600373
y[1] (numeric) = 0.19592957412690935005300636003728
absolute error = 2e-32
relative error = 1.0207749437073451471073308870245e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.19789869908361467988422621129413
y[1] (numeric) = 0.19789869908361467988422621129411
absolute error = 2e-32
relative error = 1.0106180633127734414812185849810e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (analytic) = 0.19988761407514450347270359213509
y[1] (numeric) = 0.19988761407514450347270359213508
absolute error = 1e-32
relative error = 5.0028112278335876995198834453143e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.6
y[1] (analytic) = 0.20189651799465540848517926764335
y[1] (numeric) = 0.20189651799465540848517926764334
absolute error = 1e-32
relative error = 4.9530324243951148036542863564240e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.59
y[1] (analytic) = 0.20392561173421343819204553635051
y[1] (numeric) = 0.2039256117342134381920455363505
absolute error = 1e-32
relative error = 4.9037489283266221980462867706038e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (analytic) = 0.20597509820488346548228634003843
y[1] (numeric) = 0.20597509820488346548228634003842
absolute error = 1e-32
relative error = 4.8549558112374333164794020642401e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (analytic) = 0.20804518235702046844388386572756
y[1] (numeric) = 0.20804518235702046844388386572756
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (analytic) = 0.21013607120076473665415913319392
y[1] (numeric) = 0.21013607120076473665415913319391
absolute error = 1e-32
relative error = 4.7588212451378540618839355044149e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.55
y[1] (analytic) = 0.21224797382674305771775499757972
y[1] (numeric) = 0.21224797382674305771775499757972
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.54
y[1] (analytic) = 0.21438110142697795418816641168331
y[1] (numeric) = 0.21438110142697795418816641168331
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.53
y[1] (analytic) = 0.21653566731600706181393452313687
y[1] (numeric) = 0.21653566731600706181393452313687
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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
bytes used=44016304, alloc=4259060, time=1.77
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (analytic) = 0.21871188695221476106492876641876
y[1] (numeric) = 0.21871188695221476106492876641877
absolute error = 1e-32
relative error = 4.5722251951421592069882364234397e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.51
y[1] (analytic) = 0.22090997795937819511964599676946
y[1] (numeric) = 0.22090997795937819511964599676947
absolute error = 1e-32
relative error = 4.5267307943142521840843397438117e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (analytic) = 0.22313016014842982893328047076401
y[1] (numeric) = 0.22313016014842982893328047076402
absolute error = 1e-32
relative error = 4.4816890703380648226020554601193e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.49
y[1] (analytic) = 0.22537265553943872566060700688087
y[1] (numeric) = 0.22537265553943872566060700688088
absolute error = 1e-32
relative error = 4.4370955190036646087089558540138e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (analytic) = 0.22763768838381273857963740579475
y[1] (numeric) = 0.22763768838381273857963740579476
absolute error = 1e-32
relative error = 4.3929456809187566857337876433173e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (analytic) = 0.22992548518672383875374438431145
y[1] (numeric) = 0.22992548518672383875374438431146
absolute error = 1e-32
relative error = 4.3492351410627409085081719198622e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (analytic) = 0.23223627472975882098370707068245
y[1] (numeric) = 0.23223627472975882098370707068246
absolute error = 1e-32
relative error = 4.3059595283452061041559898892827e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (analytic) = 0.23457028809379765313914891706098
y[1] (numeric) = 0.23457028809379765313914891706099
absolute error = 1e-32
relative error = 4.2631145151688173883886106755808e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.44
y[1] (analytic) = 0.2369277586821217567233665275514
y[1] (numeric) = 0.23692775868212175672336652755141
absolute error = 1e-32
relative error = 4.2206958169965528256733289292909e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.43
y[1] (analytic) = 0.2393089222437545295188628493952
y[1] (numeric) = 0.23930892224375452951886284939521
absolute error = 1e-32
relative error = 4.1786991919232461565803917643529e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.42
y[1] (analytic) = 0.24171401689703644438529978098548
y[1] (numeric) = 0.2417140168970364443852997809855
absolute error = 2e-32
relative error = 8.2742408805027854924486016180389e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (analytic) = 0.24414328315343708173939597312236
y[1] (numeric) = 0.24414328315343708173939597312237
absolute error = 1e-32
relative error = 4.0959554040711763340407372797126e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.4
y[1] (analytic) = 0.24659696394160647693986123983377
y[1] (numeric) = 0.24659696394160647693986123983378
absolute error = 1e-32
relative error = 4.0551999668446745872241088952286e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (analytic) = 0.24907530463166818773214892849983
y[1] (numeric) = 0.24907530463166818773214892849984
absolute error = 1e-32
relative error = 4.0148500529942018780345658588566e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (analytic) = 0.25157855305975651108001501486909
y[1] (numeric) = 0.25157855305975651108001501486911
absolute error = 2e-32
relative error = 7.9498032549894962378183355618793e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (analytic) = 0.25410695955280030312601482772834
y[1] (numeric) = 0.25410695955280030312601482772836
absolute error = 2e-32
relative error = 7.8707013909409457978421544447575e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.36
y[1] (analytic) = 0.25666077695355588068358670504276
y[1] (numeric) = 0.25666077695355588068358670504277
absolute error = 1e-32
relative error = 3.8961933017952145706641697713002e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (analytic) = 0.25924026064589150757173261071155
y[1] (numeric) = 0.25924026064589150757173261071156
absolute error = 1e-32
relative error = 3.8574255306969743381388389099302e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (analytic) = 0.26184566858032599426199965551435
y[1] (numeric) = 0.26184566858032599426199965551437
absolute error = 2e-32
relative error = 7.6380870107326715874363731201573e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (analytic) = 0.26447726129982396471900945771373
y[1] (numeric) = 0.26447726129982396471900945771374
absolute error = 1e-32
relative error = 3.7810433875687807458219777860330e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (analytic) = 0.2671353019658503699827155236038
y[1] (numeric) = 0.26713530196585036998271552360381
absolute error = 1e-32
relative error = 3.7434213772608625685580558298259e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (analytic) = 0.26982005638468685396545904076889
y[1] (numeric) = 0.2698200563846868539654590407689
absolute error = 1e-32
relative error = 3.7061737122101986903463250122245e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.3
y[1] (analytic) = 0.27253179303401260312233316756335
y[1] (numeric) = 0.27253179303401260312233316756336
absolute error = 1e-32
relative error = 3.6692966676192442204574899160115e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (analytic) = 0.27527078308975233810197363713616
y[1] (numeric) = 0.27527078308975233810197363713617
absolute error = 1e-32
relative error = 3.6327865557528090905156817025115e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (analytic) = 0.27803730045319413219931415601409
y[1] (numeric) = 0.2780373004531941321993141560141
absolute error = 1e-32
relative error = 3.5966397255692814623687184072408e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (analytic) = 0.28083162177837976841475013015476
y[1] (numeric) = 0.28083162177837976841475013015477
absolute error = 1e-32
relative error = 3.5608525623555205243594713895519e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.26
y[1] (analytic) = 0.28365402649977037417824200847591
y[1] (numeric) = 0.28365402649977037417824200847592
absolute error = 1e-32
relative error = 3.5254214873653821649737080556227e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.25
y[1] (analytic) = 0.28650479686019010032488542664784
y[1] (numeric) = 0.28650479686019010032488542664785
absolute error = 1e-32
relative error = 3.4903429574618413761305460296722e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -1.24
y[1] (analytic) = 0.28938421793905063871313218493106
y[1] (numeric) = 0.28938421793905063871313218493107
absolute error = 1e-32
relative error = 3.4556134647626755980576154941220e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (analytic) = 0.29229257768085940096094439190719
y[1] (numeric) = 0.2922925776808594009609443919072
absolute error = 1e-32
relative error = 3.4212295362896735737901523514522e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (analytic) = 0.29523016692401420914151228432029
y[1] (numeric) = 0.29523016692401420914151228432031
absolute error = 2e-32
relative error = 6.7743754672426692677742903761267e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (analytic) = 0.29819727942988737793160095037596
y[1] (numeric) = 0.29819727942988737793160095037598
absolute error = 2e-32
relative error = 6.7069693050980473620071788547515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (analytic) = 0.30119421191220209664497760708322
y[1] (numeric) = 0.30119421191220209664497760708324
absolute error = 2e-32
relative error = 6.6402338454730949790615348592033e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=48018648, alloc=4259060, time=1.94
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (analytic) = 0.30422126406670404881360317432948
y[1] (numeric) = 0.3042212640667040488136031743295
absolute error = 2e-32
relative error = 6.5741624147662365553016624072157e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (analytic) = 0.30727873860113123650327269691818
y[1] (numeric) = 0.30727873860113123650327269691821
absolute error = 3e-32
relative error = 9.7631226086690125436460856889187e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (analytic) = 0.31036694126548500637111111545746
y[1] (numeric) = 0.31036694126548500637111111545748
absolute error = 2e-32
relative error = 6.4439852770569998551011145448201e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (analytic) = 0.313486180882605304592756074811
y[1] (numeric) = 0.31348618088260530459275607481102
absolute error = 2e-32
relative error = 6.3798665522323693452955824720435e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (analytic) = 0.31663676937905321821019995242953
y[1] (numeric) = 0.31663676937905321821019995242955
absolute error = 2e-32
relative error = 6.3163858193795352545014012560135e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (analytic) = 0.31981902181630389118016142767382
y[1] (numeric) = 0.31981902181630389118016142767385
absolute error = 3e-32
relative error = 9.3803050955584672683946687235387e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (analytic) = 0.32303325642225293444058561264034
y[1] (numeric) = 0.32303325642225293444058561264037
absolute error = 3e-32
relative error = 9.2869695003741344711790369810705e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (analytic) = 0.32627979462303948066253482374258
y[1] (numeric) = 0.3262797946230394806625348237426
absolute error = 2e-32
relative error = 6.1297084065860040899372461837976e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (analytic) = 0.32955896107518906601946448381613
y[1] (numeric) = 0.32955896107518906601946448381615
absolute error = 2e-32
relative error = 6.0687167888713511653173329187675e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (analytic) = 0.33287108369807955328884690643132
y[1] (numeric) = 0.33287108369807955328884690643134
absolute error = 2e-32
relative error = 6.0083320478928662241168159071773e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.33621649370673334290550815089305
y[1] (numeric) = 0.33621649370673334290550815089308
absolute error = 3e-32
relative error = 8.9228222176891959489357197674078e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (analytic) = 0.33959552564493915121511021524765
y[1] (numeric) = 0.33959552564493915121511021524768
absolute error = 3e-32
relative error = 8.8340386531965714483603039757031e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (analytic) = 0.34300851741870666813320548939875
y[1] (numeric) = 0.34300851741870666813320548939879
absolute error = 4e-32
relative error = 1.1661517999907986695511483091902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (analytic) = 0.34645581033005743970350834809013
y[1] (numeric) = 0.34645581033005743970350834809017
absolute error = 4e-32
relative error = 1.1545483957071832984965501139686e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (analytic) = 0.34993774911115535467179887357682
y[1] (numeric) = 0.34993774911115535467179887357686
absolute error = 4e-32
relative error = 1.1430604472252655159457248864995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (analytic) = 0.35345468195878014815255826530895
y[1] (numeric) = 0.353454681958780148152558265309
absolute error = 5e-32
relative error = 1.4146085071757797597597430035907e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (analytic) = 0.35700696056914736976743061565135
y[1] (numeric) = 0.3570069605691473697674306156514
absolute error = 5e-32
relative error = 1.4005329173495395546848814098418e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (analytic) = 0.36059494017307829828134163465402
y[1] (numeric) = 0.36059494017307829828134163465407
absolute error = 5e-32
relative error = 1.3865973819821489583995998885727e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.36421897957152331975704629563735
y[1] (numeric) = 0.3642189795715233197570462956374
absolute error = 5e-32
relative error = 1.3728005075084582469948881583302e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = 0.36787944117144232159552377016146
y[1] (numeric) = 0.36787944117144232159552377016152
absolute error = 6e-32
relative error = 1.6309690970754271412161724828116e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = 0.3715766910220456905315241199082
y[1] (numeric) = 0.37157669102204569053152411990826
absolute error = 6e-32
relative error = 1.6147406834095573734599276424426e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (analytic) = 0.37531109885139953871426723247749
y[1] (numeric) = 0.37531109885139953871426723247755
absolute error = 6e-32
relative error = 1.5986737451576502830144568234637e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.97
y[1] (analytic) = 0.37908303810339881842640652774028
y[1] (numeric) = 0.37908303810339881842640652774034
absolute error = 6e-32
relative error = 1.5827666756124915193303291731435e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = 0.38289288597511202278354036275445
y[1] (numeric) = 0.38289288597511202278354036275452
absolute error = 7e-32
relative error = 1.8281875313961824029000209092264e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = 0.38674102345450120691546177403596
y[1] (numeric) = 0.38674102345450120691546177403603
absolute error = 7e-32
relative error = 1.8099967615210923392928665109638e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = 0.39062783535852110166269813792166
y[1] (numeric) = 0.39062783535852110166269813792173
absolute error = 7e-32
relative error = 1.7919869928304900472983118536457e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = 0.39455371037160112973145977023493
y[1] (numeric) = 0.39455371037160112973145977023501
absolute error = 8e-32
relative error = 2.0276073420942837440964925552784e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (analytic) = 0.39851904108451417254068141380442
y[1] (numeric) = 0.39851904108451417254068141380449
absolute error = 7e-32
relative error = 1.7565032729554083698629973259560e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.91
y[1] (analytic) = 0.40252422403363597467023206499273
y[1] (numeric) = 0.40252422403363597467023206499281
absolute error = 8e-32
relative error = 1.9874580267078532698581272079974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = 0.40656965974059911188345423964563
y[1] (numeric) = 0.4065696597405991118834542396457
absolute error = 7e-32
relative error = 1.7217221778098647646600885945217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = 0.41065575275234548815388001589018
y[1] (numeric) = 0.41065575275234548815388001589026
absolute error = 8e-32
relative error = 1.9481037210318996214275975469642e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.88
y[1] (analytic) = 0.41478291168158136697920371749923
y[1] (numeric) = 0.41478291168158136697920371749931
absolute error = 8e-32
relative error = 1.9287197651337678807127079329063e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = 0.41895154924763898251935527356051
y[1] (numeric) = 0.41895154924763898251935527356059
absolute error = 8e-32
relative error = 1.9095286828194213452951663792147e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=52019620, alloc=4259060, time=2.10
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (analytic) = 0.42316208231774881675383951790624
y[1] (numeric) = 0.42316208231774881675383951790632
absolute error = 8e-32
relative error = 1.8905285549646359586174851739569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = 0.42741493194872666992045084117638
y[1] (numeric) = 0.42741493194872666992045084117647
absolute error = 9e-32
relative error = 2.1056821667333918431692542438074e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = 0.43171052342907969297714640814387
y[1] (numeric) = 0.43171052342907969297714640814395
absolute error = 8e-32
relative error = 1.8530935814248733868001977542924e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = 0.43604928632153559272541260496991
y[1] (numeric) = 0.43604928632153559272541260496999
absolute error = 8e-32
relative error = 1.8346549922113463101340510346185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = 0.44043165450599926255107817544048
y[1] (numeric) = 0.44043165450599926255107817544057
absolute error = 9e-32
relative error = 2.0434498537791652026165083027280e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (analytic) = 0.4448580662229411344814454391058
y[1] (numeric) = 0.44485806622294113448144543910589
absolute error = 9e-32
relative error = 2.0231171880088242772615051801201e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (analytic) = 0.44932896411722159143010238501556
y[1] (numeric) = 0.44932896411722159143010238501566
absolute error = 1.0e-31
relative error = 2.2255409284924676045795375313951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.79
y[1] (analytic) = 0.45384479528235582210716058753149
y[1] (numeric) = 0.45384479528235582210716058753159
absolute error = 1.0e-31
relative error = 2.2033964262559366592196465899840e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = 0.45840601130522354511729747005864
y[1] (numeric) = 0.45840601130522354511729747005874
absolute error = 1.0e-31
relative error = 2.1814722654982011166288495425370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = 0.4630130683112280732552709485309
y[1] (numeric) = 0.463013068311228073255270948531
absolute error = 1.0e-31
relative error = 2.1597662537849150083875523903400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = 0.46766642700990923394296868513658
y[1] (numeric) = 0.46766642700990923394296868513669
absolute error = 1.1e-31
relative error = 2.3521038425465004627455353896278e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (analytic) = 0.47236655274101470713804655094327
y[1] (numeric) = 0.47236655274101470713804655094338
absolute error = 1.1e-31
relative error = 2.3287000182739421353999068018208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (analytic) = 0.47711391552103438788634007083472
y[1] (numeric) = 0.47711391552103438788634007083483
absolute error = 1.1e-31
relative error = 2.3055290659438010194521496271171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = 0.48190899009020242699308285662715
y[1] (numeric) = 0.48190899009020242699308285662726
absolute error = 1.1e-31
relative error = 2.2825886684415349094850134184882e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (analytic) = 0.48675225595997165005616764799563
y[1] (numeric) = 0.48675225595997165005616764799574
absolute error = 1.1e-31
relative error = 2.2598765317082765172455061837094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = 0.49164419746096510234291543504933
y[1] (numeric) = 0.49164419746096510234291543504944
absolute error = 1.1e-31
relative error = 2.2373903845114256731939739488287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (analytic) = 0.49658530379140951470480009339753
y[1] (numeric) = 0.49658530379140951470480009339764
absolute error = 1.1e-31
relative error = 2.2151279782175241737870043274414e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (analytic) = 0.50157606906605553391708136030312
y[1] (numeric) = 0.50157606906605553391708136030323
absolute error = 1.1e-31
relative error = 2.1930870865673905617896107946278e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (analytic) = 0.50661699236558960950714710972739
y[1] (numeric) = 0.5066169923655896095071471097275
absolute error = 1.1e-31
relative error = 2.1712655054534923529073405762802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (analytic) = 0.51170857778654247830142447010597
y[1] (numeric) = 0.51170857778654247830142447010608
absolute error = 1.1e-31
relative error = 2.1496610526995334457754456017228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (analytic) = 0.51685133449169923758090501839177
y[1] (numeric) = 0.51685133449169923758090501839188
absolute error = 1.1e-31
relative error = 2.1282715678422346738624376661216e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (analytic) = 0.52204577676101604789460813720885
y[1] (numeric) = 0.52204577676101604789460813720897
absolute error = 1.2e-31
relative error = 2.2986489948166752841760378312185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (analytic) = 0.52729242404304855724369460856631
y[1] (numeric) = 0.52729242404304855724369460856643
absolute error = 1.2e-31
relative error = 2.2757770551659416240101379095431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (analytic) = 0.53259180100689718952150601850198
y[1] (numeric) = 0.53259180100689718952150601850209
absolute error = 1.1e-31
relative error = 2.0653716371907774456819924639845e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (analytic) = 0.53794443759467449178166186125583
y[1] (numeric) = 0.53794443759467449178166186125595
absolute error = 1.2e-31
relative error = 2.2307136502156104529948248723217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (analytic) = 0.54335086907449978711266408781658
y[1] (numeric) = 0.5433508690744997871126640878167
absolute error = 1.2e-31
relative error = 2.2085176785379649463933525252188e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (analytic) = 0.54881163609402643262845891723257
y[1] (numeric) = 0.54881163609402643262845891723269
absolute error = 1.2e-31
relative error = 2.1865425604686107698504412017954e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (analytic) = 0.5543272847345070353453611638809
y[1] (numeric) = 0.55432728473450703534536116388102
absolute error = 1.2e-31
relative error = 2.1647860984774283285152044896890e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (analytic) = 0.55989836656540203251198326987287
y[1] (numeric) = 0.55989836656540203251198326987299
absolute error = 1.2e-31
relative error = 2.1432461169000880587161322695307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (analytic) = 0.56552543869953709729570933746478
y[1] (numeric) = 0.5655254386995370972957093374649
absolute error = 1.2e-31
relative error = 2.1219204617204821819450720713886e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (analytic) = 0.57120906384881488561224746683128
y[1] (numeric) = 0.57120906384881488561224746683141
absolute error = 1.3e-31
relative error = 2.2758742503849314073149693655024e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (analytic) = 0.57694981038048669531936996488157
y[1] (numeric) = 0.5769498103804866953193699648817
absolute error = 1.3e-31
relative error = 2.2532289232276138078684917972785e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (analytic) = 0.58274825237398966498765400477775
y[1] (numeric) = 0.58274825237398966498765400477788
absolute error = 1.3e-31
relative error = 2.2308089208403159981395538491295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=56020428, alloc=4259060, time=2.26
x[1] = -0.53
y[1] (analytic) = 0.58860496967835519601546430041177
y[1] (numeric) = 0.5886049696783551960154643004119
absolute error = 1.3e-31
relative error = 2.2086120012041158507465388328729e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (analytic) = 0.59452054797019433897822980533888
y[1] (numeric) = 0.59452054797019433897822980533901
absolute error = 1.3e-31
relative error = 2.1866359446085522509863204530667e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (analytic) = 0.60049557881226594279897068019951
y[1] (numeric) = 0.60049557881226594279897068019964
absolute error = 1.3e-31
relative error = 2.1648785534296522009579090253909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (analytic) = 0.60653065971263342360379953499118
y[1] (numeric) = 0.60653065971263342360379953499131
absolute error = 1.3e-31
relative error = 2.1433376519101665909032460241584e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (analytic) = 0.61262639418441606898857996801905
y[1] (numeric) = 0.61262639418441606898857996801918
absolute error = 1.3e-31
relative error = 2.1220110859419926611591435707348e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (analytic) = 0.61878339180614085287696198691059
y[1] (numeric) = 0.61878339180614085287696198691072
absolute error = 1.3e-31
relative error = 2.1008967228507613967852488373943e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (analytic) = 0.62500226828270079620157346192914
y[1] (numeric) = 0.62500226828270079620157346192928
absolute error = 1.4e-31
relative error = 2.2399918705043043375378300648361e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (analytic) = 0.63128364550692596929523453396175
y[1] (numeric) = 0.63128364550692596929523453396189
absolute error = 1.4e-31
relative error = 2.2177035789922744848075868188631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (analytic) = 0.63762815162177329314374343831222
y[1] (numeric) = 0.63762815162177329314374343831236
absolute error = 1.4e-31
relative error = 2.1956370596862363356514396845705e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (analytic) = 0.64403642108314135853218403000896
y[1] (numeric) = 0.6440364210831413585321840300091
absolute error = 1.4e-31
relative error = 2.1737901059158704588701115046684e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (analytic) = 0.6505090947233165446190154984879
y[1] (numeric) = 0.65050909472331654461901549848804
absolute error = 1.4e-31
relative error = 2.1521605329675939623811948522802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (analytic) = 0.65704681981505678160267362233996
y[1] (numeric) = 0.6570468198150567816026736223401
absolute error = 1.4e-31
relative error = 2.1307461778660873143292227204532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (analytic) = 0.66365025013631936591035353781475
y[1] (numeric) = 0.66365025013631936591035353781488
absolute error = 1.3e-31
relative error = 1.9588631206467096508865387741151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (analytic) = 0.67032004603563930074443292514783
y[1] (numeric) = 0.67032004603563930074443292514796
absolute error = 1.3e-31
relative error = 1.9393721069336514131723088386884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.39
y[1] (analytic) = 0.67705687449816469987507238709242
y[1] (numeric) = 0.67705687449816469987507238709255
absolute error = 1.3e-31
relative error = 1.9200750320474353501984670395003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (analytic) = 0.68386140921235585827440196628578
y[1] (numeric) = 0.68386140921235585827440196628591
absolute error = 1.3e-31
relative error = 1.9009699662644918910171210917910e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (analytic) = 0.69073433063735465955493996423945
y[1] (numeric) = 0.69073433063735465955493996423959
absolute error = 1.4e-31
relative error = 2.0268284605286542462186532697269e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (analytic) = 0.69767632607103105720912926383816
y[1] (numeric) = 0.6976763260710310572091292638383
absolute error = 1.4e-31
relative error = 2.0066611803844763608859667717439e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (analytic) = 0.70468808971871343435482069903088
y[1] (numeric) = 0.70468808971871343435482069903102
absolute error = 1.4e-31
relative error = 1.9866945680305601475785539267158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.34
y[1] (analytic) = 0.71177032276260971507995351075699
y[1] (numeric) = 0.71177032276260971507995351075713
absolute error = 1.4e-31
relative error = 1.9669266267890313155839093472112e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (analytic) = 0.71892373343192616955541847611042
y[1] (numeric) = 0.71892373343192616955541847611057
absolute error = 1.5e-31
relative error = 2.0864521926956703993641217074297e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 0.72614903707369092485504752942358
y[1] (numeric) = 0.72614903707369092485504752942373
absolute error = 1.5e-31
relative error = 2.0656916465039356267903156017422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.31
y[1] (analytic) = 0.73344695622428926389283166331544
y[1] (numeric) = 0.73344695622428926389283166331559
absolute error = 1.5e-31
relative error = 2.0451376711982666912417327808215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.3
y[1] (analytic) = 0.74081822068171786606687377931782
y[1] (numeric) = 0.74081822068171786606687377931797
absolute error = 1.5e-31
relative error = 2.0247882113640046559756164699920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (analytic) = 0.74826356757856521509435295127478
y[1] (numeric) = 0.74826356757856521509435295127494
absolute error = 1.6e-31
relative error = 2.1382839808407553654046330001209e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (analytic) = 0.75578374145572547213910080719431
y[1] (numeric) = 0.75578374145572547213910080719447
absolute error = 1.6e-31
relative error = 2.1170076997398990970274428368583e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (analytic) = 0.7633794943368531856805312195579
y[1] (numeric) = 0.76337949433685318568053121955806
absolute error = 1.6e-31
relative error = 2.0959431211731957822639827626020e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (analytic) = 0.77105158580356628365695599543358
y[1] (numeric) = 0.77105158580356628365695599543374
absolute error = 1.6e-31
relative error = 2.0750881386652348767977009410862e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (analytic) = 0.77880078307140486824517026697832
y[1] (numeric) = 0.77880078307140486824517026697848
absolute error = 1.6e-31
relative error = 2.0544406667003863745174729088999e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.24
y[1] (analytic) = 0.78662786106655340921908474751564
y[1] (numeric) = 0.7866278610665534092190847475158
absolute error = 1.6e-31
relative error = 2.0339986405142475065815056819644e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (analytic) = 0.79453360250333400817067609066369
y[1] (numeric) = 0.79453360250333400817067609066385
absolute error = 1.6e-31
relative error = 2.0137600158871645804977158019504e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (analytic) = 0.80251879796247848298425538299341
y[1] (numeric) = 0.80251879796247848298425538299357
absolute error = 1.6e-31
relative error = 1.9937227689398093112324236527883e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (analytic) = 0.81058424597018709983772915155069
y[1] (numeric) = 0.81058424597018709983772915155086
absolute error = 1.7e-31
relative error = 2.0972527019264635269232538721657e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (analytic) = 0.81873075307798185866993550861904
y[1] (numeric) = 0.81873075307798185866993550861921
bytes used=60021756, alloc=4259060, time=2.43
absolute error = 1.7e-31
relative error = 2.0763846888722887176658223908874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (analytic) = 0.82695913394336231750914679370833
y[1] (numeric) = 0.82695913394336231750914679370851
absolute error = 1.8e-31
relative error = 2.1766492757830526249145294663977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (analytic) = 0.83527021141127202131238497401878
y[1] (numeric) = 0.83527021141127202131238497401895
absolute error = 1.7e-31
relative error = 2.0352695173070772802906007551208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (analytic) = 0.84366481659638368202632265191542
y[1] (numeric) = 0.8436648165963836820263226519156
absolute error = 1.8e-31
relative error = 2.1335487323766579252519349758647e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (analytic) = 0.85214378896621133845634698146856
y[1] (numeric) = 0.85214378896621133845634698146874
absolute error = 1.8e-31
relative error = 2.1123195677852584230334999564055e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (analytic) = 0.86070797642505780722903376454331
y[1] (numeric) = 0.86070797642505780722903376454349
absolute error = 1.8e-31
relative error = 2.0913016369109096207099163857970e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (analytic) = 0.86935823539880581966308441617118
y[1] (numeric) = 0.86935823539880581966308441617137
absolute error = 1.9e-31
relative error = 2.1855202178287318094347720894802e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (analytic) = 0.87809543092056132373307240915739
y[1] (numeric) = 0.87809543092056132373307240915758
absolute error = 1.9e-31
relative error = 2.1637739283167814781698539449760e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (analytic) = 0.88692043671715751552756522876984
y[1] (numeric) = 0.88692043671715751552756522877003
absolute error = 1.9e-31
relative error = 2.1422440180008137758106045818122e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (analytic) = 0.89583413529652825067685458287651
y[1] (numeric) = 0.89583413529652825067685458287671
absolute error = 2.0e-31
relative error = 2.2325561409177425830014755381060e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (analytic) = 0.90483741803595957316424905944644
y[1] (numeric) = 0.90483741803595957316424905944664
absolute error = 2.0e-31
relative error = 2.2103418361512952496234156529805e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.09
y[1] (analytic) = 0.91393118527122818674735354649952
y[1] (numeric) = 0.91393118527122818674735354649973
absolute error = 2.1e-31
relative error = 2.2977659957809417515330850094443e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.08
y[1] (analytic) = 0.92311634638663578291075984957239
y[1] (numeric) = 0.9231163463866357829107598495726
absolute error = 2.1e-31
relative error = 2.2749028421174129643155742932173e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (analytic) = 0.93239381990594822885797263248497
y[1] (numeric) = 0.93239381990594822885797263248518
absolute error = 2.1e-31
relative error = 2.2522671806338546060115182947671e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = -0.06
y[1] (analytic) = 0.94176453358424870953715278327115
y[1] (numeric) = 0.94176453358424870953715278327136
absolute error = 2.1e-31
relative error = 2.2298567477452552066718382420536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (analytic) = 0.95122942450071400909142531977965
y[1] (numeric) = 0.95122942450071400909142531977986
absolute error = 2.1e-31
relative error = 2.2076693023896504833647870363049e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (analytic) = 0.96078943915232320943921069132325
y[1] (numeric) = 0.96078943915232320943921069132346
absolute error = 2.1e-31
relative error = 2.1857026258040152761897939916254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (analytic) = 0.97044553354850817693252835195919
y[1] (numeric) = 0.97044553354850817693252835195941
absolute error = 2.2e-31
relative error = 2.2669999746977370823473678984286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (analytic) = 0.98019867330675530222081410422531
y[1] (numeric) = 0.98019867330675530222081410422553
absolute error = 2.2e-31
relative error = 2.2444429480588627823523166250629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (analytic) = 0.99004983374916805357390597718004
y[1] (numeric) = 0.99004983374916805357390597718026
absolute error = 2.2e-31
relative error = 2.2221103675851697265927640051863e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1.0000000000000000000000000000002
absolute error = 2e-31
relative error = 2.0000000000000000000000000000000e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 1.0100501670841680575421654569029
y[1] (numeric) = 1.0100501670841680575421654569031
absolute error = 2e-31
relative error = 1.9800996674983361071478119543600e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.02
y[1] (analytic) = 1.0202013400267558101601439204832
y[1] (numeric) = 1.0202013400267558101601439204834
absolute error = 2e-31
relative error = 1.9603973466135106044416282084505e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 1.0304545339535168556124399538312
y[1] (numeric) = 1.0304545339535168556124399538314
absolute error = 2e-31
relative error = 1.9408910670970163538650567039184e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 1.0408107741923882267570447579169
y[1] (numeric) = 1.0408107741923882267570447579171
absolute error = 2e-31
relative error = 1.9215788783046464188784213826464e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = 1.0512710963760240396975176363356
y[1] (numeric) = 1.0512710963760240396975176363359
absolute error = 3e-31
relative error = 2.8536882735021420272742759593391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 1.0618365465453596222246848771684
y[1] (numeric) = 1.0618365465453596222246848771686
absolute error = 2e-31
relative error = 1.8835290671684974190743055665423e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 1.0725081812542164790531039498891
y[1] (numeric) = 1.0725081812542164790531039498893
absolute error = 2e-31
relative error = 1.8647876398118964577159452649700e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 1.0832870676749585544359877586749
y[1] (numeric) = 1.0832870676749585544359877586751
absolute error = 2e-31
relative error = 1.8462326927732715658215196991448e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 1.0941742837052103578728976235449
y[1] (numeric) = 1.0941742837052103578728976235451
absolute error = 2e-31
relative error = 1.8278623705424563734947070929990e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.1051709180756476248117078264902
y[1] (numeric) = 1.1051709180756476248117078264905
absolute error = 3e-31
relative error = 2.7145122541078787194927471783394e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.116278070458871291500737769053
y[1] (numeric) = 1.1162780704588712915007377690532
absolute error = 2e-31
relative error = 1.7916682705930565013537091657530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.1274968515793756714792655693748
y[1] (numeric) = 1.1274968515793756714792655693751
absolute error = 3e-31
relative error = 2.6607613101514725465826956863096e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 1.138828383324621830615712602619
y[1] (numeric) = 1.1388283833246218306157126026192
absolute error = 2e-31
relative error = 1.7561908618411226474661448183147e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=64025240, alloc=4259060, time=2.60
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 1.1502737988572272681235642576211
y[1] (numeric) = 1.1502737988572272681235642576214
absolute error = 3e-31
relative error = 2.6080747061964174589892532485136e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.1618342427282831226166202143317
y[1] (numeric) = 1.1618342427282831226166202143319
absolute error = 2e-31
relative error = 1.7214159528501156144580675290865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 1.173510870991810235018611086892
y[1] (numeric) = 1.1735108709918102350186110868922
absolute error = 2e-31
relative error = 1.7042875779324226769126939629371e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 1.1853048513203655140288527643693
y[1] (numeric) = 1.1853048513203655140288527643695
absolute error = 2e-31
relative error = 1.6873296331927673640526453038308e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 1.1972173631218101648768239736005
y[1] (numeric) = 1.1972173631218101648768239736007
absolute error = 2e-31
relative error = 1.6705404228225440426247699480375e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 1.2092495976572514582858497035543
y[1] (numeric) = 1.2092495976572514582858497035545
absolute error = 2e-31
relative error = 1.6539182678867246350182935874166e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 1.2214027581601698339210719946397
y[1] (numeric) = 1.2214027581601698339210719946399
absolute error = 2e-31
relative error = 1.6374615061559637173398710172380e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 1.2336780599567432511313258071563
y[1] (numeric) = 1.2336780599567432511313258071565
absolute error = 2e-31
relative error = 1.6211684919403741996754583031014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 1.2460767305873808195202647829927
y[1] (numeric) = 1.2460767305873808195202647829929
absolute error = 2e-31
relative error = 1.6050375959249569659685107659868e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 1.258600009929477862811072376219
y[1] (numeric) = 1.2586000099294778628110723762192
absolute error = 2e-31
relative error = 1.5890672050066680163413521813274e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 1.2712491503214046916134410512278
y[1] (numeric) = 1.271249150321404691613441051228
absolute error = 2e-31
relative error = 1.5732557221331068184381694950312e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 1.2840254166877414840734205680624
y[1] (numeric) = 1.2840254166877414840734205680627
absolute error = 3e-31
relative error = 2.3364023492142146047355108009350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 1.2969300866657717979985630881788
y[1] (numeric) = 1.2969300866657717979985630881791
absolute error = 3e-31
relative error = 2.3131547574106988509708679863008e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 1.3099644507332473639149892266262
y[1] (numeric) = 1.3099644507332473639149892266265
absolute error = 3e-31
relative error = 2.2901384830105595570415936586738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 1.3231298123374369356421517730364
y[1] (numeric) = 1.3231298123374369356421517730367
absolute error = 3e-31
relative error = 2.2673512243671764164173024215830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 1.3364274880254721033778956250755
y[1] (numeric) = 1.3364274880254721033778956250758
absolute error = 3e-31
relative error = 2.2447907027356956452830588538244e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 1.349858807576003103983744313328
y[1] (numeric) = 1.3498588075760031039837443133283
absolute error = 3e-31
relative error = 2.2224546620451535982006213379535e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 1.3634251141321777941611551872143
y[1] (numeric) = 1.3634251141321777941611551872146
absolute error = 3e-31
relative error = 2.2003408686728677916784949899464e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 1.3771277643359570845268770678281
y[1] (numeric) = 1.3771277643359570845268770678284
absolute error = 3e-31
relative error = 2.1784471112210727745651425882708e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 1.3909681284637802662427478049531
y[1] (numeric) = 1.3909681284637802662427478049534
absolute error = 3e-31
relative error = 2.1567712002957785086662554283313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 1.4049475905635937968456495337223
y[1] (numeric) = 1.4049475905635937968456495337225
absolute error = 2e-31
relative error = 1.4235406455252194301599070215139e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 1.4190675485932572482703956619399
y[1] (numeric) = 1.4190675485932572482703956619401
absolute error = 2e-31
relative error = 1.4093761794374268687096413980617e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 1.4333294145603402577756905512456
y[1] (numeric) = 1.4333294145603402577756905512458
absolute error = 2e-31
relative error = 1.3953526521420621144182585276763e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 1.4477346146633244615847523355192
y[1] (numeric) = 1.4477346146633244615847523355194
absolute error = 2e-31
relative error = 1.3814686612747093191098799284789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 1.46228458943422453155163160907
y[1] (numeric) = 1.4622845894342245315516316090702
absolute error = 2e-31
relative error = 1.3677228184247117165488039325716e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 1.4769807938826425770757438765387
y[1] (numeric) = 1.4769807938826425770757438765389
absolute error = 2e-31
relative error = 1.3541137489963293997501447741848e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 1.4918246976412703178248529528372
y[1] (numeric) = 1.4918246976412703178248529528374
absolute error = 2e-31
relative error = 1.3406400920712786014888658502957e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 1.5068177851128535776050298262424
y[1] (numeric) = 1.5068177851128535776050298262426
absolute error = 2e-31
relative error = 1.3273005002726387318207070756295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 1.5219615556186337959494448003237
y[1] (numeric) = 1.5219615556186337959494448003239
absolute error = 2e-31
relative error = 1.3140936396301135632053472446799e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 1.5372575235482814017008534659144
y[1] (numeric) = 1.5372575235482814017008534659146
absolute error = 2e-31
relative error = 1.3010181894466330892380309969758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 1.5527072185113360420500796461917
y[1] (numeric) = 1.5527072185113360420500796461919
absolute error = 2e-31
relative error = 1.2880728421662827170643680600179e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.45
y[1] (analytic) = 1.5683121854901688111795997746932
y[1] (numeric) = 1.5683121854901688111795997746934
absolute error = 2e-31
relative error = 1.2752563032435465862874868766245e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 1.5840739849944817748625620134736
y[1] (numeric) = 1.5840739849944817748625620134738
absolute error = 2e-31
relative error = 1.2625672910138519385904690679235e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=68026292, alloc=4259060, time=2.75
x[1] = 0.47
y[1] (analytic) = 1.5999941932173602410984500463115
y[1] (numeric) = 1.5999941932173602410984500463116
absolute error = 1e-31
relative error = 6.2500226828270079620157346192913e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = 0.48
y[1] (analytic) = 1.616074402192893382142499105688
y[1] (numeric) = 1.6160744021928933821424991056881
absolute error = 1e-31
relative error = 6.1878339180614085287696198691057e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.49
y[1] (analytic) = 1.6323162199553789701224181313345
y[1] (numeric) = 1.6323162199553789701224181313346
absolute error = 1e-31
relative error = 6.1262639418441606898857996801905e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 1.6487212707001281468486507878142
y[1] (numeric) = 1.6487212707001281468486507878143
absolute error = 1e-31
relative error = 6.0653065971263342360379953499117e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = 0.51
y[1] (analytic) = 1.6652911949458863084291607887622
y[1] (numeric) = 1.6652911949458863084291607887624
absolute error = 2e-31
relative error = 1.2009911576245318855979413603990e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.52
y[1] (analytic) = 1.6820276496988863469125541946667
y[1] (numeric) = 1.6820276496988863469125541946668
absolute error = 1e-31
relative error = 5.9452054797019433897822980533887e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 1.6989323086185506544204144868253
y[1] (numeric) = 1.6989323086185506544204144868254
absolute error = 1e-31
relative error = 5.8860496967835519601546430041178e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 1.716006862184858460107349114715
y[1] (numeric) = 1.7160068621848584601073491147151
absolute error = 1e-31
relative error = 5.8274825237398966498765400477775e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 1.7332530178673952368219167671373
y[1] (numeric) = 1.7332530178673952368219167671374
absolute error = 1e-31
relative error = 5.7694981038048669531936996488158e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 1.7506725002961010825499764350019
y[1] (numeric) = 1.7506725002961010825499764350019
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 1.7682670514337351516208933928238
y[1] (numeric) = 1.7682670514337351516208933928239
absolute error = 1e-31
relative error = 5.6552543869953709729570933746479e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 1.7860384307500733822634435579423
y[1] (numeric) = 1.7860384307500733822634435579424
absolute error = 1e-31
relative error = 5.5989836656540203251198326987286e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.59
y[1] (analytic) = 1.8039884153978569404293370747409
y[1] (numeric) = 1.803988415397856940429337074741
absolute error = 1e-31
relative error = 5.5432728473450703534536116388089e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.6
y[1] (analytic) = 1.8221188003905089748753676681629
y[1] (numeric) = 1.822118800390508974875367668163
absolute error = 1e-31
relative error = 5.4881163609402643262845891723256e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 1.8404313987816374553277937710156
y[1] (numeric) = 1.8404313987816374553277937710158
absolute error = 2e-31
relative error = 1.0867017381489995742253281756332e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.62
y[1] (analytic) = 1.8589280418463420441623540602681
y[1] (numeric) = 1.8589280418463420441623540602682
absolute error = 1e-31
relative error = 5.3794443759467449178166186125583e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 1.8776105792643431324381749672586
y[1] (numeric) = 1.8776105792643431324381749672587
absolute error = 1e-31
relative error = 5.3259180100689718952150601850198e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.64
y[1] (analytic) = 1.8964808793049513533417815912859
y[1] (numeric) = 1.896480879304951353341781591286
absolute error = 1e-31
relative error = 5.2729242404304855724369460856631e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 1.9155408290138960701466981926821
y[1] (numeric) = 1.9155408290138960701466981926822
absolute error = 1e-31
relative error = 5.2204577676101604789460813720884e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.66
y[1] (analytic) = 1.9347923344020315216931251510197
y[1] (numeric) = 1.9347923344020315216931251510198
absolute error = 1e-31
relative error = 5.1685133449169923758090501839176e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 1.9542373206359394961594960015662
y[1] (numeric) = 1.9542373206359394961594960015663
absolute error = 1e-31
relative error = 5.1170857778654247830142447010598e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.68
y[1] (analytic) = 1.9738777322304475935521277966183
y[1] (numeric) = 1.9738777322304475935521277966184
absolute error = 1e-31
relative error = 5.0661699236558960950714710972739e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.69
y[1] (analytic) = 1.9937155332430823288996461769344
y[1] (numeric) = 1.9937155332430823288996461769345
absolute error = 1e-31
relative error = 5.0157606906605553391708136030312e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.7
y[1] (analytic) = 2.0137527074704765216245493885831
y[1] (numeric) = 2.0137527074704765216245493885832
absolute error = 1e-31
relative error = 4.9658530379140951470480009339752e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.71
y[1] (analytic) = 2.0339912586467506119945217716624
y[1] (numeric) = 2.0339912586467506119945217716626
absolute error = 2e-31
relative error = 9.8328839492193020468583087009868e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.72
y[1] (analytic) = 2.0544332106438877429504601670086
y[1] (numeric) = 2.0544332106438877429504601670087
absolute error = 1e-31
relative error = 4.8675225595997165005616764799562e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 2.0750806076741226449863758349892
y[1] (numeric) = 2.0750806076741226449863758349894
absolute error = 2e-31
relative error = 9.6381798018040485398616571325432e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.74
y[1] (analytic) = 2.0959355144943645631383178428338
y[1] (numeric) = 2.0959355144943645631383178428339
absolute error = 1e-31
relative error = 4.7711391552103438788634007083471e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.75
y[1] (analytic) = 2.1170000166126746685453698198371
y[1] (numeric) = 2.1170000166126746685453698198372
absolute error = 1e-31
relative error = 4.7236655274101470713804655094327e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 2.138276220496818602495941263298
y[1] (numeric) = 2.1382762204968186024959412632981
absolute error = 1e-31
relative error = 4.6766642700990923394296868513658e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 2.15976625378491500838755239034
y[1] (numeric) = 2.1597662537849150083875523903402
absolute error = 2e-31
relative error = 9.2602613662245614651054189706180e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.78
y[1] (analytic) = 2.181472265498201116628849542537
y[1] (numeric) = 2.1814722654982011166288495425372
absolute error = 2e-31
relative error = 9.1681202261044709023459494011727e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 2.203396426255936659219646589984
y[1] (numeric) = 2.2033964262559366592196465899842
absolute error = 2e-31
relative error = 9.0768959056471164421432117506297e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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
bytes used=72027264, alloc=4259060, time=2.91
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 2.2255409284924676045795375313951
y[1] (numeric) = 2.2255409284924676045795375313953
absolute error = 2e-31
relative error = 8.9865792823444318286020477003112e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 2.2479079866764714191794502001334
y[1] (numeric) = 2.2479079866764714191794502001336
absolute error = 2e-31
relative error = 8.8971613244588226896289087821160e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.82
y[1] (analytic) = 2.2704998375324057806850092252533
y[1] (numeric) = 2.2704998375324057806850092252535
absolute error = 2e-31
relative error = 8.8086330901199852510215635088098e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.83
y[1] (analytic) = 2.2933187402641828876675637932731
y[1] (numeric) = 2.2933187402641828876675637932733
absolute error = 2e-31
relative error = 8.7209857264307118545082520993982e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.84
y[1] (analytic) = 2.3163669767810917335002471928655
y[1] (numeric) = 2.3163669767810917335002471928657
absolute error = 2e-31
relative error = 8.6342104685815938595429281628774e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 2.3396468519259909368547269375638
y[1] (numeric) = 2.339646851925990936854726937564
absolute error = 2e-31
relative error = 8.5482986389745333984090168235276e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 2.3631606937057949482718564674462
y[1] (numeric) = 2.3631606937057949482718564674464
absolute error = 2e-31
relative error = 8.4632416463549763350767903581247e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 2.3869108535242766816189579740184
y[1] (numeric) = 2.3869108535242766816189579740186
absolute error = 2e-31
relative error = 8.3790309849527796503871054712100e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.88
y[1] (analytic) = 2.4108997064172098508908849161329
y[1] (numeric) = 2.4108997064172098508908849161331
absolute error = 2e-31
relative error = 8.2956582336316273395840743499846e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 2.4351296512898745267844969337052
y[1] (numeric) = 2.4351296512898745267844969337054
absolute error = 2e-31
relative error = 8.2131150550469097630776003178037e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 2.4596031111569496638001265636025
y[1] (numeric) = 2.4596031111569496638001265636026
absolute error = 1e-31
relative error = 4.0656965974059911188345423964562e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 0.91
y[1] (analytic) = 2.4843225333848165873226590099968
y[1] (numeric) = 2.4843225333848165873226590099969
absolute error = 1e-31
relative error = 4.0252422403363597467023206499273e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 2.5092903899362976712328533227943
y[1] (numeric) = 2.5092903899362976712328533227944
absolute error = 1e-31
relative error = 3.9851904108451417254068141380441e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 2.5345091776178546801206156940979
y[1] (numeric) = 2.5345091776178546801206156940981
absolute error = 2e-31
relative error = 7.8910742074320225946291954046987e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 2.5599814183292714961404455052082
y[1] (numeric) = 2.5599814183292714961404455052084
absolute error = 2e-31
relative error = 7.8125567071704220332539627584331e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 2.5857096593158461989898093013769
y[1] (numeric) = 2.5857096593158461989898093013771
absolute error = 2e-31
relative error = 7.7348204690900241383092354807192e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 2.6116964734231177184286012988948
y[1] (numeric) = 2.611696473423117718428601298895
absolute error = 2e-31
relative error = 7.6578577195022404556708072550891e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 2.6379444593541525322172152885726
y[1] (numeric) = 2.6379444593541525322172152885728
absolute error = 2e-31
relative error = 7.5816607620679763685281305548054e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 2.6644562419294171383574280391061
y[1] (numeric) = 2.6644562419294171383574280391064
absolute error = 3e-31
relative error = 1.1259332965541986161428016974325e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 2.691234472349262289099879404071
y[1] (numeric) = 2.6912344723492622890998794040713
absolute error = 3e-31
relative error = 1.1147300730661370715945723597246e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 2.7182818284590452353602874713527
y[1] (numeric) = 2.718281828459045235360287471353
absolute error = 3e-31
relative error = 1.1036383235143269647865713104844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 2.7456010150169164939897763166604
y[1] (numeric) = 2.7456010150169164939897763166607
absolute error = 3e-31
relative error = 1.0926569387145699592711388869120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 2.7731947639642979167991997771454
y[1] (numeric) = 2.7731947639642979167991997771458
absolute error = 4e-31
relative error = 1.4423797606923131931253665386161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 2.8010658346990791093697628196836
y[1] (numeric) = 2.8010658346990791093697628196839
absolute error = 3e-31
relative error = 1.0710208817074421093022918469540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 2.8292170143515595195194860071813
y[1] (numeric) = 2.8292170143515595195194860071817
absolute error = 4e-31
relative error = 1.4138187278351205926102330612358e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 2.8576511180631637898643122162488
y[1] (numeric) = 2.8576511180631637898643122162491
absolute error = 3e-31
relative error = 1.0498132473334660640153966207304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 2.8863709892679582462413752849215
y[1] (numeric) = 2.8863709892679582462413752849219
absolute error = 4e-31
relative error = 1.3858232413202297588140333923605e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 2.9153794999769966738778707729755
y[1] (numeric) = 2.9153794999769966738778707729759
absolute error = 4e-31
relative error = 1.3720340696748266725328219575950e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 2.9446795510655238161201013252344
y[1] (numeric) = 2.9446795510655238161201013252348
absolute error = 4e-31
relative error = 1.3583821025797566048604408609906e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 2.9742740725630653163119065891359
y[1] (numeric) = 2.9742740725630653163119065891363
absolute error = 4e-31
relative error = 1.3448659748269333716220326035722e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 3.0041660239464331120584079535887
y[1] (numeric) = 3.0041660239464331120584079535891
absolute error = 4e-31
relative error = 1.3314843347923182131553876257252e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 3.0343583944356755826586664593838
y[1] (numeric) = 3.0343583944356755826586664593842
absolute error = 4e-31
relative error = 1.3182358443007562640778579352645e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 3.0648542032930020449686230918988
y[1] (numeric) = 3.0648542032930020449686230918993
absolute error = 5e-31
relative error = 1.6313989731151974033126741187129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=76028920, alloc=4259060, time=3.07
x[1] = 1.13
y[1] (analytic) = 3.0956565001247114903930123270235
y[1] (numeric) = 3.095656500124711490393012327024
absolute error = 5e-31
relative error = 1.6151662821112646722029280632017e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 3.1267683651861557561315562411795
y[1] (numeric) = 3.12676836518615575613155624118
absolute error = 5e-31
relative error = 1.5990951090815194559008071383691e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 3.1581929096897676272507006280068
y[1] (numeric) = 3.1581929096897676272507006280073
absolute error = 5e-31
relative error = 1.5831838468952660910509997621476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 3.1899332761161846726477912360218
y[1] (numeric) = 3.1899332761161846726477912360223
absolute error = 5e-31
relative error = 1.5674309044130265229637803740550e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 3.2219926385284999275505572724101
y[1] (numeric) = 3.2219926385284999275505572724106
absolute error = 5e-31
relative error = 1.5518347063274250318555555772873e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.18
y[1] (analytic) = 3.2543742028896708478820285629729
y[1] (numeric) = 3.2543742028896708478820285629734
absolute error = 5e-31
relative error = 1.5363936930056561825163634845909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 3.2870812073831182776508312036078
y[1] (numeric) = 3.2870812073831182776508312036084
absolute error = 6e-31
relative error = 1.8253275844002242928816190459769e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 3.3201169227365474895307674296016
y[1] (numeric) = 3.3201169227365474895307674296022
absolute error = 6e-31
relative error = 1.8071652714732125798698656424994e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 3.3534846525490236810035894273757
y[1] (numeric) = 3.3534846525490236810035894273763
absolute error = 6e-31
relative error = 1.7891836765793242675896057022558e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.22
y[1] (analytic) = 3.3871877336213346338871451880633
y[1] (numeric) = 3.3871877336213346338871451880639
absolute error = 6e-31
relative error = 1.7713810015440852548490737059218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.23
y[1] (analytic) = 3.4212295362896735737901523514522
y[1] (numeric) = 3.4212295362896735737901523514528
absolute error = 6e-31
relative error = 1.7537554660851564057656663514432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 3.455613464762675598057615494122
y[1] (numeric) = 3.4556134647626755980576154941226
absolute error = 6e-31
relative error = 1.7363053076343038322787931095864e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 3.4903429574618413761305460296723
y[1] (numeric) = 3.4903429574618413761305460296729
absolute error = 6e-31
relative error = 1.7190287811611406019493125598870e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 3.5254214873653821649737080556228
y[1] (numeric) = 3.5254214873653821649737080556234
absolute error = 6e-31
relative error = 1.7019241589986222450694520508554e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.27
y[1] (analytic) = 3.5608525623555205243594713895519
y[1] (numeric) = 3.5608525623555205243594713895526
absolute error = 7e-31
relative error = 1.9658213524486583789032509110833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 3.5966397255692814623687184072408
y[1] (numeric) = 3.5966397255692814623687184072415
absolute error = 7e-31
relative error = 1.9462611031723589253951990920986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 3.6327865557528090905156817025115
y[1] (numeric) = 3.6327865557528090905156817025122
absolute error = 7e-31
relative error = 1.9268954816282663667138154599531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 3.6692966676192442204574899160115
y[1] (numeric) = 3.6692966676192442204574899160122
absolute error = 7e-31
relative error = 1.9077225512380882218563321729434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.31
y[1] (analytic) = 3.7061737122101986903463250122245
y[1] (numeric) = 3.7061737122101986903463250122253
absolute error = 8e-31
relative error = 2.1585604510774948317236723261511e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.32
y[1] (analytic) = 3.7434213772608625685580558298259
y[1] (numeric) = 3.7434213772608625685580558298266
absolute error = 7e-31
relative error = 1.8699471137609525898790086652266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 3.7810433875687807458219777860331
y[1] (numeric) = 3.7810433875687807458219777860338
absolute error = 7e-31
relative error = 1.8513408290987677530330662039961e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.34
y[1] (analytic) = 3.8190435053663357937181865600786
y[1] (numeric) = 3.8190435053663357937181865600793
absolute error = 7e-31
relative error = 1.8329196800622819598339975886005e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 3.8574255306969743381388389099302
y[1] (numeric) = 3.8574255306969743381388389099309
absolute error = 7e-31
relative error = 1.8146818245212405530021282749808e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.36
y[1] (analytic) = 3.8961933017952145706641697713002
y[1] (numeric) = 3.8961933017952145706641697713009
absolute error = 7e-31
relative error = 1.7966254386748911647851069352993e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 3.9353506954704728989210772223787
y[1] (numeric) = 3.9353506954704728989210772223794
absolute error = 7e-31
relative error = 1.7787487168696021218821037940984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 3.9749016274947481189091677809396
y[1] (numeric) = 3.9749016274947481189091677809403
absolute error = 7e-31
relative error = 1.7610498714182955775601051040836e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 4.0148500529942018780345658588566
y[1] (numeric) = 4.0148500529942018780345658588574
absolute error = 8e-31
relative error = 1.9926024370533455018571914279986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 4.0551999668446745872241088952286
y[1] (numeric) = 4.0551999668446745872241088952294
absolute error = 8e-31
relative error = 1.9727757115328518155188899186702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 4.0959554040711763340407372797126
y[1] (numeric) = 4.0959554040711763340407372797134
absolute error = 8e-31
relative error = 1.9531462652274966539151677849789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 4.1371204402513927462243008090194
y[1] (numeric) = 4.1371204402513927462243008090202
absolute error = 8e-31
relative error = 1.9337121351762915550823982478839e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 4.1786991919232461565803917643529
y[1] (numeric) = 4.1786991919232461565803917643537
absolute error = 8e-31
relative error = 1.9144713779500362361509027951616e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 4.2206958169965528256733289292909
y[1] (numeric) = 4.2206958169965528256733289292916
absolute error = 7e-31
relative error = 1.6584943107748522970635656928598e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 4.2631145151688173883886106755809
y[1] (numeric) = 4.2631145151688173883886106755816
absolute error = 7e-31
relative error = 1.6419920166565835719740424194268e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
bytes used=80030636, alloc=4259060, time=3.24
y[1] (analytic) = 4.3059595283452061041559898892827
y[1] (numeric) = 4.3059595283452061041559898892834
absolute error = 7e-31
relative error = 1.6256539231083117468859494947771e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 4.3492351410627409085081719198621
y[1] (numeric) = 4.3492351410627409085081719198629
absolute error = 8e-31
relative error = 1.8394038814937907100299550744916e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 4.3929456809187566857337876433172
y[1] (numeric) = 4.392945680918756685733787643318
absolute error = 8e-31
relative error = 1.8211015070705019086370992463580e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 4.4370955190036646087089558540139
y[1] (numeric) = 4.4370955190036646087089558540146
absolute error = 7e-31
relative error = 1.5776085887760710796242490481661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 4.4816890703380648226020554601193
y[1] (numeric) = 4.48168907033806482260205546012
absolute error = 7e-31
relative error = 1.5619111210390088025329632953481e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 4.5267307943142521840843397438116
y[1] (numeric) = 4.5267307943142521840843397438123
absolute error = 7e-31
relative error = 1.5463698457156473658375219773862e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 4.5722251951421592069882364234397
y[1] (numeric) = 4.5722251951421592069882364234404
absolute error = 7e-31
relative error = 1.5309832086655033274545013649313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.333e+15
Order of pole (six term test) = 4.444e+29
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 4.6181768222997808090795197077546
y[1] (numeric) = 4.6181768222997808090795197077553
absolute error = 7e-31
relative error = 1.5157496712120494326975416619581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 4.6645902709881259027933867662438
y[1] (numeric) = 4.6645902709881259027933867662445
absolute error = 7e-31
relative error = 1.5006677099888456793171648817832e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 4.7114701825907413254726398125845
y[1] (numeric) = 4.7114701825907413254726398125852
absolute error = 7e-31
relative error = 1.4857358167872014040242849830581e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 4.758821245137854061883935504415
y[1] (numeric) = 4.7588212451378540618839355044157
absolute error = 7e-31
relative error = 1.4709524984053531565791139323574e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 4.8066481937751781736211397590791
y[1] (numeric) = 4.8066481937751781736211397590798
absolute error = 7e-31
relative error = 1.4563162764991432791071870600930e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 4.8549558112374333164794020642401
y[1] (numeric) = 4.8549558112374333164794020642408
absolute error = 7e-31
relative error = 1.4418256874341842583760043802690e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 4.9037489283266221980462867706038
y[1] (numeric) = 4.9037489283266221980462867706044
absolute error = 6e-31
relative error = 1.2235536704052806291522732181031e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 4.953032424395114803654286356424
y[1] (numeric) = 4.9530324243951148036542863564246
absolute error = 6e-31
relative error = 1.2113791079679324509110756058601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.61
y[1] (analytic) = 5.0028112278335876995198834453142
y[1] (numeric) = 5.0028112278335876995198834453149
absolute error = 7e-31
relative error = 1.3992132985260115243089251449456e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 5.053090316563867207406092924905
y[1] (numeric) = 5.0530903165638672074060929249057
absolute error = 7e-31
relative error = 1.3852908935853027591895834790589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 5.1038747185367257355366544351225
y[1] (numeric) = 5.1038747185367257355366544351232
absolute error = 7e-31
relative error = 1.3715070188883654503710445202611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 5.1551695122346810458097983038692
y[1] (numeric) = 5.1551695122346810458097983038699
absolute error = 7e-31
relative error = 1.3578602960362433035863694600114e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 5.2069798271798487376573070927123
y[1] (numeric) = 5.2069798271798487376573070927131
absolute error = 8e-31
relative error = 1.5363992689660329139083583293867e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 5.2593108444468987342204704726538
y[1] (numeric) = 5.2593108444468987342204704726546
absolute error = 8e-31
relative error = 1.5211118408121642189311284663547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 5.3121677971811670669190161888314
y[1] (numeric) = 5.3121677971811670669190161888322
absolute error = 8e-31
relative error = 1.5059765251099741663708093606303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 5.3655559711219747700232352669232
y[1] (numeric) = 5.365555971121974770023235266924
absolute error = 8e-31
relative error = 1.4909918083152797320943679099207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 5.4194807051312062175548592062532
y[1] (numeric) = 5.419480705131206217554859206254
absolute error = 8e-31
relative error = 1.4761561919439141410385101272196e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 5.4739473917271997607908626630091
y[1] (numeric) = 5.4739473917271997607908626630099
absolute error = 8e-31
relative error = 1.4614681924218772017912067020715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 5.528961477624004055878852351461
y[1] (numeric) = 5.5289614776240040558788523514618
absolute error = 8e-31
relative error = 1.4469263409369766702567639252148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 5.5845284642760540076461854730193
y[1] (numeric) = 5.5845284642760540076461854730201
absolute error = 8e-31
relative error = 1.4325291832919458064171738746450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 5.640653908428320797651096717808
y[1] (numeric) = 5.6406539084283207976510967178088
absolute error = 8e-31
relative error = 1.4182752797590224358230175540754e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 5.6973434226719910119370988363601
y[1] (numeric) = 5.6973434226719910119370988363609
absolute error = 8e-31
relative error = 1.4041632049359749735988855547377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 5.7546026760057304368664997048427
y[1] (numeric) = 5.7546026760057304368664997048435
absolute error = 8e-31
relative error = 1.3901915476035610134457380693310e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 5.8124373944025886498803406244497
y[1] (numeric) = 5.8124373944025886498803406244505
absolute error = 8e-31
relative error = 1.3763589105844042273803195890076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 5.8708533613826010961162539158285
y[1] (numeric) = 5.8708533613826010961162539158293
absolute error = 8e-31
relative error = 1.3626639106032754637839992493045e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 5.9298564185911459115690715820469
y[1] (numeric) = 5.9298564185911459115690715820477
absolute error = 8e-31
relative error = 1.3491051781487640717544089026545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 5.9894524663831133289584667268155
y[1] (numeric) = 5.9894524663831133289584667268163
absolute error = 8e-31
relative error = 1.3356813573363256187770398006635e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
bytes used=84031540, alloc=4259060, time=3.41
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 6.0496474644129460837310239530277
y[1] (numeric) = 6.0496474644129460837310239530285
absolute error = 8e-31
relative error = 1.3223911057726923063744377634577e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 6.1104474322306098247290409259947
y[1] (numeric) = 6.1104474322306098247290409259955
absolute error = 8e-31
relative error = 1.3092330944216325246615700586875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 6.1718584498835531270637716458996
y[1] (numeric) = 6.1718584498835531270637716459004
absolute error = 8e-31
relative error = 1.2962060074710461216509521161140e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 6.2338866585247173036960337699729
y[1] (numeric) = 6.2338866585247173036960337699737
absolute error = 8e-31
relative error = 1.2833085422013820967237102790244e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = 1.84
y[1] (analytic) = 6.2965382610266568172120145770248
y[1] (numeric) = 6.2965382610266568172120145770256
absolute error = 8e-31
relative error = 1.2705394088553655599262754111357e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.85
y[1] (analytic) = 6.3598195226018317043472218706367
y[1] (numeric) = 6.3598195226018317043472218706375
absolute error = 8e-31
relative error = 1.2578973305090209296800757992250e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 6.4237367714291340430179442929097
y[1] (numeric) = 6.4237367714291340430179442929105
absolute error = 8e-31
relative error = 1.2453810429439784711165192939326e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 6.4882963992867111150290313243491
y[1] (numeric) = 6.4882963992867111150290313243499
absolute error = 8e-31
relative error = 1.2329892945210514055846866141918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 6.5535048621911485473016181413198
y[1] (numeric) = 6.5535048621911485473016181413206
absolute error = 8e-31
relative error = 1.2207208460550709489373338246974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 6.6193686810430773504675724967601
y[1] (numeric) = 6.6193686810430773504675724967608
absolute error = 7e-31
relative error = 1.0575026618545959167453870911911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.9
y[1] (analytic) = 6.6858944422792694160725307276929
y[1] (numeric) = 6.6858944422792694160725307276936
absolute error = 7e-31
relative error = 1.0469803345584453684870844837261e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.91
y[1] (analytic) = 6.7530887985312866824806579188518
y[1] (numeric) = 6.7530887985312866824806579188525
absolute error = 7e-31
relative error = 1.0365627061682371851815688591793e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 6.8209584692907498349465988329418
y[1] (numeric) = 6.8209584692907498349465988329425
absolute error = 7e-31
relative error = 1.0262487349124509600807611989651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.93
y[1] (analytic) = 6.8895102415812930672790192339938
y[1] (numeric) = 6.8895102415812930672790192339946
absolute error = 8e-31
relative error = 1.1611855878689898398465046694967e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 6.958750970637272101131868125876
y[1] (numeric) = 6.9587509706372721011318681258768
absolute error = 8e-31
relative error = 1.1496315982216233635206115805569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 7.0286875805892933342908819335644
y[1] (numeric) = 7.0286875805892933342908819335652
absolute error = 8e-31
relative error = 1.1381925726921085748092320709106e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 7.099327065156632671441435472082
y[1] (numeric) = 7.0993270651566326714414354720828
absolute error = 8e-31
relative error = 1.1268673673683599691837716887677e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 7.1706764883466132798778341038975
y[1] (numeric) = 7.1706764883466132798778341038984
absolute error = 9e-31
relative error = 1.2551117059354584028742822208521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 1.98
y[1] (analytic) = 7.2427429851610122085124347531447
y[1] (numeric) = 7.2427429851610122085124347531456
absolute error = 9e-31
relative error = 1.2426231357980352942976218581583e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 7.315533762309566511435170833514
y[1] (numeric) = 7.3155337623095665114351708335149
absolute error = 9e-31
relative error = 1.2302588290097147208191839206377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 7.389056098930650227230427460575
y[1] (numeric) = 7.3890560989306502272304274605759
absolute error = 9e-31
relative error = 1.2180175491295142270459954547524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 7.4633173473191942823497647873654
y[1] (numeric) = 7.4633173473191942823497647873663
absolute error = 9e-31
relative error = 1.2058980720192446923582294533638e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 7.5383249336619221111374286770603
y[1] (numeric) = 7.5383249336619221111374286770613
absolute error = 1.0e-30
relative error = 1.3265546508012172131984276473165e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 7.6140863587799745166833496561362
y[1] (numeric) = 7.6140863587799745166833496561372
absolute error = 1.0e-30
relative error = 1.3133552114849307838239891208810e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 7.6906091988789980356085715614843
y[1] (numeric) = 7.6906091988789980356085715614853
absolute error = 1.0e-30
relative error = 1.3002871087842591719808107707110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.05
y[1] (analytic) = 7.7679011063067718162446641452442
y[1] (numeric) = 7.7679011063067718162446641452452
absolute error = 1.0e-30
relative error = 1.2873490358780421886234651674487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 7.8459698103184487735262954149556
y[1] (numeric) = 7.8459698103184487735262954149565
absolute error = 9e-31
relative error = 1.1470857290533867038233521565018e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 7.9248231178494875453501560543463
y[1] (numeric) = 7.9248231178494875453501560543472
absolute error = 9e-31
relative error = 1.1356720353453487371220608702458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 8.0044689142963525442399839278696
y[1] (numeric) = 8.0044689142963525442399839278705
absolute error = 9e-31
relative error = 1.1243719097872418227324483303994e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.09
y[1] (analytic) = 8.0849151643050601749734407164419
y[1] (numeric) = 8.0849151643050601749734407164428
absolute error = 9e-31
relative error = 1.1131842223570933472753594333699e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 8.1661699125676500734497274104786
y[1] (numeric) = 8.1661699125676500734497274104796
absolute error = 1.0e-30
relative error = 1.2245642825298191021864737607263e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 8.2482412846266610145855536665902
y[1] (numeric) = 8.2482412846266610145855536665912
absolute error = 1.0e-30
relative error = 1.2123796643338166596589195340782e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 8.3311374876876919375006494494469
y[1] (numeric) = 8.3311374876876919375006494494479
absolute error = 1.0e-30
relative error = 1.2003162851145673534694820266229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=88032252, alloc=4259060, time=3.57
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 8.414866811440129344772473954749
y[1] (numeric) = 8.41486681144012934477247395475
absolute error = 1.0e-30
relative error = 1.1883729385240964091620546477244e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 8.4994376288861231491839890633767
y[1] (numeric) = 8.4994376288861231491839890633777
absolute error = 1.0e-30
relative error = 1.1765484302177919576407922068906e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 8.5848583971778938662399876124018
y[1] (numeric) = 8.5848583971778938662399876124028
absolute error = 1.0e-30
relative error = 1.1648415777349695786927071418284e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 8.6711376584634548838689864354103
y[1] (numeric) = 8.6711376584634548838689864354113
absolute error = 1.0e-30
relative error = 1.1532512103806252471584599172984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 8.7582840407408343822424252687577
y[1] (numeric) = 8.7582840407408343822424252687588
absolute error = 1.1e-30
relative error = 1.2559537860192013426421632472047e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 8.8463062587208823266150074163392
y[1] (numeric) = 8.8463062587208823266150074163403
absolute error = 1.1e-30
relative error = 1.2434568370449484773270325769942e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 8.9352131146987488146044744309985
y[1] (numeric) = 8.9352131146987488146044744309996
absolute error = 1.1e-30
relative error = 1.2310842347906175917833625246286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 9.0250134994341209264717771668887
y[1] (numeric) = 9.0250134994341209264717771668898
absolute error = 1.1e-30
relative error = 1.2188347419856727166755886843493e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 9.115716393040306102820204373562
y[1] (numeric) = 9.1157163930403061028202043735632
absolute error = 1.2e-30
relative error = 1.3164077821861368139843453295826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 9.2073308658822509587921440290797
y[1] (numeric) = 9.2073308658822509587921440290808
absolute error = 1.1e-30
relative error = 1.1947001970745378015327600155203e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 9.2998660794835853373932485946047
y[1] (numeric) = 9.2998660794835853373932485946059
absolute error = 1.2e-30
relative error = 1.2903411616295394111342431586364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 9.3933312874427823071052091710137
y[1] (numeric) = 9.3933312874427823071052091710149
absolute error = 1.2e-30
relative error = 1.2775020525510338783646706329762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 9.4877358363585257205503690445117
y[1] (numeric) = 9.4877358363585257205503690445129
absolute error = 1.2e-30
relative error = 1.2647906947423720413986122708884e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 9.5830891667643778717351852852969
y[1] (numeric) = 9.5830891667643778717351852852981
absolute error = 1.2e-30
relative error = 1.2522058170571802005690963036754e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 9.6794008140728407194171550561075
y[1] (numeric) = 9.6794008140728407194171550561087
absolute error = 1.2e-30
relative error = 1.2397461609972024036629905840139e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 9.7766804095289050835042636318178
y[1] (numeric) = 9.776680409528905083504263631819
absolute error = 1.2e-30
relative error = 1.2274104805864495715737388111650e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 9.8749376811731831702012210539711
y[1] (numeric) = 9.8749376811731831702012210539723
absolute error = 1.2e-30
relative error = 1.2151975422466008610766645921601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 9.9741824548147207399576151569089
y[1] (numeric) = 9.9741824548147207399576151569101
absolute error = 1.2e-30
relative error = 1.2031061246736448047592883255758e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 10.074424655013586200245455289684
y[1] (numeric) = 10.074424655013586200245455289686
absolute error = 2e-30
relative error = 1.9852250311929131535297509114374e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 10.175674306073334882894211461532
y[1] (numeric) = 10.175674306073334882894211461534
absolute error = 2e-30
relative error = 1.9654717120872306309606247764772e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 10.277941533043447753238138736105
y[1] (numeric) = 10.277941533043447753238138736106
absolute error = 1e-30
relative error = 9.7295747089532769225700714551533e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 10.381236562731844795782169982426
y[1] (numeric) = 10.381236562731844795782169982427
absolute error = 1e-30
relative error = 9.6327638230493019688016823959127e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 10.485569724727574328568707539109
y[1] (numeric) = 10.48556972472757432856870753911
absolute error = 1e-30
relative error = 9.5369162215549618888296596799798e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 10.590951452433780516028994407103
y[1] (numeric) = 10.590951452433780516028994407105
absolute error = 2e-30
relative error = 1.8884044639260467962313819571542e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 10.69739228411105237793115923818
y[1] (numeric) = 10.697392284111052377931159238182
absolute error = 2e-30
relative error = 1.8696145255611694515588165595398e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 10.804902863931258630195290329287
y[1] (numeric) = 10.804902863931258630195290329289
absolute error = 2e-30
relative error = 1.8510115502068655218486709261196e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 10.913493943041973741937818758192
y[1] (numeric) = 10.913493943041973741937818758194
absolute error = 2e-30
relative error = 1.8325936775500970455710302844059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 11.023176380641601652237939769668
y[1] (numeric) = 11.023176380641601652237939769669
absolute error = 1e-30
relative error = 9.0717953289412503375172220079690e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 11.133961145065304659893688471457
y[1] (numeric) = 11.133961145065304659893688471458
absolute error = 1e-30
relative error = 8.9815294572247642124738879133906e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 11.245859314881846079961589205531
y[1] (numeric) = 11.245859314881846079961589205531
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 11.358882080001456352259571153473
y[1] (numeric) = 11.358882080001456352259571153474
absolute error = 1e-30
relative error = 8.8036832582372559268609219894027e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 11.473040742794833389367225302064
y[1] (numeric) = 11.473040742794833389367225302064
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
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) = 11.58834671922338906509070619308
y[1] (numeric) = 11.588346719223389065090706193081
absolute error = 1e-30
relative error = 8.6293586499370510972073516516157e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=92033232, alloc=4259060, time=3.73
x[1] = 2.46
y[1] (analytic) = 11.704811539980854868983000160809
y[1] (numeric) = 11.70481153998085486898300016081
absolute error = 1e-30
relative error = 8.5434950967321227226670949205396e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 11.822446851646360888436353300643
y[1] (numeric) = 11.822446851646360888436353300644
absolute error = 1e-30
relative error = 8.4584859001564705396490765853959e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 11.941264417849103427205970766319
y[1] (numeric) = 11.94126441784910342720597076632
absolute error = 1e-30
relative error = 8.3743225592195957496515391975087e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 12.061276120444717728097399349678
y[1] (numeric) = 12.06127612044471772809739934968
absolute error = 2e-30
relative error = 1.6581993315034536627921223418940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 12.182493960703473438070175951168
y[1] (numeric) = 12.18249396070347343807017595117
absolute error = 2e-30
relative error = 1.6416999724779759033905734893432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 12.304930060510411636294418494051
y[1] (numeric) = 12.304930060510411636294418494053
absolute error = 2e-30
relative error = 1.6253647848178338122635216367639e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 12.428596663577543439863282465196
y[1] (numeric) = 12.428596663577543439863282465198
absolute error = 2e-30
relative error = 1.6091921349906486734428000303859e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 12.553506136668231408032023200075
y[1] (numeric) = 12.553506136668231408032023200078
absolute error = 3e-30
relative error = 2.3897706085769407729516471945927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 12.679670970833876184144409056144
y[1] (numeric) = 12.679670970833876184144409056147
absolute error = 3e-30
relative error = 2.3659919937202483752273846780013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 12.807103782663032044941253752753
y[1] (numeric) = 12.807103782663032044941253752756
absolute error = 3e-30
relative error = 2.3424499800345945693192371865835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 12.935817315543076269846931825039
y[1] (numeric) = 12.935817315543076269846931825042
absolute error = 3e-30
relative error = 2.3191422132989923797139698311928e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 13.065824440934558498222200489047
y[1] (numeric) = 13.06582444093455849822220048905
absolute error = 3e-30
relative error = 2.2960663627173450425023748252545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 13.197138159658357510581014537849
y[1] (numeric) = 13.197138159658357510581014537852
absolute error = 3e-30
relative error = 2.2732201206853644533663254822329e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 13.329771603195774150522090176603
y[1] (numeric) = 13.329771603195774150522090176605
absolute error = 2e-30
relative error = 1.5004008017065392105055739728929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 13.463738035001690397750825332584
y[1] (numeric) = 13.463738035001690397750825332587
absolute error = 3e-30
relative error = 2.2282073464300164128463171050993e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 13.599050851830925909193181507426
y[1] (numeric) = 13.599050851830925909193181507429
absolute error = 3e-30
relative error = 2.2060363128917126564098087158513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 13.735723585077924664960939361653
y[1] (numeric) = 13.735723585077924664960939361656
absolute error = 3e-30
relative error = 2.1840858848230677932049580951733e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 13.873769902129905688949333816751
y[1] (numeric) = 13.873769902129905688949333816755
absolute error = 4e-30
relative error = 2.8831384895506438325085162519937e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 14.013203607733613160266757797534
y[1] (numeric) = 14.013203607733613160266757797538
absolute error = 4e-30
relative error = 2.8544507822554424218182035834519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 14.154038645375802591646639807897
y[1] (numeric) = 14.154038645375802591646639807901
absolute error = 4e-30
relative error = 2.8260485224171834696270511274663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 14.2962890986776011246097455111
y[1] (numeric) = 14.296289098677601124609745511105
absolute error = 5e-30
relative error = 3.4974110872327681515991460919136e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 14.439969192802881378568390330594
y[1] (numeric) = 14.439969192802881378568390330598
absolute error = 4e-30
relative error = 2.7700890123738393579107395782352e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 14.585093295880789692431122279052
y[1] (numeric) = 14.585093295880789692431122279056
absolute error = 4e-30
relative error = 2.7425261661711167834949277297612e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 14.731675920442571012717479636724
y[1] (numeric) = 14.731675920442571012717479636728
absolute error = 4e-30
relative error = 2.7152375748704574107085725400619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 14.879731724872834111868993019468
y[1] (numeric) = 14.879731724872834111868993019473
absolute error = 5e-30
relative error = 3.3602756369874882563275850427984e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 15.029275514875402264487654649923
y[1] (numeric) = 15.029275514875402264487654649928
absolute error = 5e-30
relative error = 3.3268403357508425297003204003086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 15.18032224495389596779102498073
y[1] (numeric) = 15.180322244953895967791024980735
absolute error = 5e-30
relative error = 3.2937377213201480750247182972682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 15.332887019907195765789845226944
y[1] (numeric) = 15.33288701990719576578984522695
absolute error = 6e-30
relative error = 3.9131573800876514626534338115794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 15.486985096339934724716796743092
y[1] (numeric) = 15.486985096339934724716796743098
absolute error = 6e-30
relative error = 3.8742208135901093537308691077279e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 15.642631884188171610212698046157
y[1] (numeric) = 15.642631884188171610212698046162
absolute error = 5e-30
relative error = 3.1963930603353786351215012778975e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 15.799842948260397334859256656509
y[1] (numeric) = 15.799842948260397334859256656515
absolute error = 6e-30
relative error = 3.7975061015784433309948877960723e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 15.958634009794028777987305352163
y[1] (numeric) = 15.958634009794028777987305352169
absolute error = 6e-30
relative error = 3.7597202845291891108060064534809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = 2.78
y[1] (analytic) = 16.119020948027545628439586166743
y[1] (numeric) = 16.119020948027545628439586166749
absolute error = 6e-30
relative error = 3.7223104426414984903219697562933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=96034244, alloc=4259060, time=3.90
x[1] = 2.79
y[1] (analytic) = 16.281019801788427465282476812269
y[1] (numeric) = 16.281019801788427465282476812274
absolute error = 5e-30
relative error = 3.0710606957500064402704784053314e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 16.444646771097049871498016010925
y[1] (numeric) = 16.44464677109704987149801601093
absolute error = 5e-30
relative error = 3.0405031312608982497810694091970e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 16.609918218786699971604181488378
y[1] (numeric) = 16.609918218786699971604181488383
absolute error = 5e-30
relative error = 3.0102496196186772043578335526217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 16.776850672139873396107200104494
y[1] (numeric) = 16.776850672139873396107200104499
absolute error = 5e-30
relative error = 2.9802971354469677381566952341422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.83
y[1] (analytic) = 16.945460824541016303845920701474
y[1] (numeric) = 16.94546082454101630384592070148
absolute error = 6e-30
relative error = 3.5407712201668706322637395472185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 17.11576553714587773780777371626
y[1] (numeric) = 17.115765537145877737807773716265
absolute error = 5e-30
relative error = 2.9212832982250409873068652703632e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.85
y[1] (analytic) = 17.287781840567639251043030753446
y[1] (numeric) = 17.287781840567639251043030753451
absolute error = 5e-30
relative error = 2.8922160437419231483705313388701e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 17.46152693657999041704506824997
y[1] (numeric) = 17.461526936579990417045068249975
absolute error = 5e-30
relative error = 2.8634380132733675721484382485094e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 17.637018199837320533566907580682
y[1] (numeric) = 17.637018199837320533566907580687
absolute error = 5e-30
relative error = 2.8349463289923456310867178710295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.88
y[1] (analytic) = 17.814273179612198540477911123657
y[1] (numeric) = 17.814273179612198540477911123662
absolute error = 5e-30
relative error = 2.8067381417066860736133703082684e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 17.993309601550314901100324712728
y[1] (numeric) = 17.993309601550314901100324712733
absolute error = 5e-30
relative error = 2.7788106305741534326783828790241e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 18.174145369443060942676256574128
y[1] (numeric) = 18.174145369443060942676256574133
absolute error = 5e-30
relative error = 2.7511610028203614514973265417088e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.91
y[1] (analytic) = 18.356798567017922915376293819354
y[1] (numeric) = 18.356798567017922915376293819359
absolute error = 5e-30
relative error = 2.7237864934594933176059311836429e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.92
y[1] (analytic) = 18.541287459746869810747657378403
y[1] (numeric) = 18.541287459746869810747657378409
absolute error = 6e-30
relative error = 3.2360212380213609324195735845415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.93
y[1] (analytic) = 18.727630496672915779890735060899
y[1] (numeric) = 18.727630496672915779890735060904
absolute error = 5e-30
relative error = 2.6698519072598544781558396551995e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.94
y[1] (analytic) = 18.915846312255039809127950820668
y[1] (numeric) = 18.915846312255039809127950820673
absolute error = 5e-30
relative error = 2.6432864369175181703949369108304e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.95
y[1] (analytic) = 19.105953728231647146669975298563
y[1] (numeric) = 19.105953728231647146669975298569
absolute error = 6e-30
relative error = 3.1403823569059435852293301529592e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.96
y[1] (analytic) = 19.297971755502758827974833963076
y[1] (numeric) = 19.297971755502758827974833963082
absolute error = 6e-30
relative error = 3.1091350303635499810647806497723e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.97
y[1] (analytic) = 19.491919596031117520320945259013
y[1] (numeric) = 19.491919596031117520320945259019
absolute error = 6e-30
relative error = 3.0781986199151472270362470437567e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 2.98
y[1] (analytic) = 19.687816644762399798762806219384
y[1] (numeric) = 19.68781664476239979876280621939
absolute error = 6e-30
relative error = 3.0475700318939100548933639308218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 19.885682491564726876297103339624
y[1] (numeric) = 19.88568249156472687629710333963
absolute error = 6e-30
relative error = 3.0172462034155124324883229480786e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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
y[1] (analytic) = 20.085536923187667740928529654582
y[1] (numeric) = 20.085536923187667740928529654588
absolute error = 6e-30
relative error = 2.9872241020718365787605449390037e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.01
y[1] (analytic) = 20.28739992524093060158152265589
y[1] (numeric) = 20.287399925240930601581522655896
absolute error = 6e-30
relative error = 2.9575007256277296249433857070491e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.02
y[1] (analytic) = 20.491291684192940513651429258142
y[1] (numeric) = 20.491291684192940513651429258148
absolute error = 6e-30
relative error = 2.9280731017207775974062924035999e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 20.697232589389503043623139836616
y[1] (numeric) = 20.697232589389503043623139836622
absolute error = 6e-30
relative error = 2.8989382875640666992805055843257e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.04
y[1] (analytic) = 20.905243235092755840805878527866
y[1] (numeric) = 20.905243235092755840805878527873
absolute error = 7e-30
relative error = 3.3484422645938858612068980375700e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.05
y[1] (analytic) = 21.115344422540612013040455245769
y[1] (numeric) = 21.115344422540612013040455245775
absolute error = 6e-30
relative error = 2.8415354634684552716394462143840e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 21.327557162026901252432758671981
y[1] (numeric) = 21.327557162026901252432758671988
absolute error = 7e-30
relative error = 3.2821386653991942239129082787869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.07
y[1] (analytic) = 21.541902675002416726959520286426
y[1] (numeric) = 21.541902675002416726959520286432
absolute error = 6e-30
relative error = 2.7852692914458759044882667861096e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 21.758402396197077844386388260106
y[1] (numeric) = 21.758402396197077844386388260113
absolute error = 7e-30
relative error = 3.2171479654330946317838468464940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 21.977077975763421106543177882497
y[1] (numeric) = 21.977077975763421106543177882504
absolute error = 7e-30
relative error = 3.1851368083235095921935573163619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 22.197951281441633404827974381257
y[1] (numeric) = 22.197951281441633404827974381264
absolute error = 7e-30
relative error = 3.1534441675490464247834564524835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.11
y[1] (analytic) = 22.421044400746344262073838971462
y[1] (numeric) = 22.421044400746344262073838971468
absolute error = 6e-30
relative error = 2.6760573204164717667624115461133e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=100034980, alloc=4259060, time=4.07
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 22.646379643175395701824637747618
y[1] (numeric) = 22.646379643175395701824637747624
absolute error = 6e-30
relative error = 2.6494301051815720171209510960050e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 22.873979542440810623847568694562
y[1] (numeric) = 22.873979542440810623847568694569
absolute error = 7e-30
relative error = 3.0602458076925655727415677441698e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.14
y[1] (analytic) = 23.103866858722182784579084580015
y[1] (numeric) = 23.103866858722182784579084580022
absolute error = 7e-30
relative error = 3.0297958531376130558410836306540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 23.33606458094271372338008756421
y[1] (numeric) = 23.336064580942713723380087564217
absolute error = 7e-30
relative error = 2.9996488806928125939754819869308e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.16
y[1] (analytic) = 23.57059592906812424018972480695
y[1] (numeric) = 23.570595929068124240189724806958
absolute error = 8e-30
relative error = 3.3940592864409110243651461387988e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 23.807484356428670317641316402232
y[1] (numeric) = 23.807484356428670317641316402239
absolute error = 7e-30
relative error = 2.9402518532411884242057057151999e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.18
y[1] (analytic) = 24.046753552064495691167646951714
y[1] (numeric) = 24.046753552064495691167646951722
absolute error = 8e-30
relative error = 3.3268524096938535611613292401589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.19
y[1] (analytic) = 24.288427443094555604307098296172
y[1] (numeric) = 24.28842744309455560430709829618
absolute error = 8e-30
relative error = 3.2937496751254188436522323818788e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.2
y[1] (analytic) = 24.532530197109348643560263727964
y[1] (numeric) = 24.532530197109348643560263727972
absolute error = 8e-30
relative error = 3.2609763182692972132863409715540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.21
y[1] (analytic) = 24.779086224587695927974479188157
y[1] (numeric) = 24.779086224587695927974479188165
absolute error = 8e-30
relative error = 3.2285290617624918361499187835215e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 25.02812018133780933338921927269
y[1] (numeric) = 25.028120181337809333389219272697
absolute error = 7e-30
relative error = 2.7968540782457734910075496707069e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.23
y[1] (analytic) = 25.279656970962892860199012888142
y[1] (numeric) = 25.27965697096289286019901288815
absolute error = 8e-30
relative error = 3.1645999030718979470371184088747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 25.533721747351523706825329504055
y[1] (numeric) = 25.533721747351523706825329504063
absolute error = 8e-30
relative error = 3.1331116079189658991816872292604e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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) = 25.790339917193062089080107669377
y[1] (numeric) = 25.790339917193062089080107669385
absolute error = 8e-30
relative error = 3.1019366265377607909519868214077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 26.049537142518341348499043982636
y[1] (numeric) = 26.049537142518341348499043982644
absolute error = 8e-30
relative error = 3.0710718414041652640888648170938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 26.311339343265892420772724659149
y[1] (numeric) = 26.311339343265892420772724659157
absolute error = 8e-30
relative error = 3.0405141660139452190259712724422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 26.575772699873959288860970327214
y[1] (numeric) = 26.575772699873959288860970327222
absolute error = 8e-30
relative error = 3.0102605445740968193843666451065e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 26.842863655898564624495725565399
y[1] (numeric) = 26.842863655898564624495725565407
absolute error = 8e-30
relative error = 2.9803079516972646450862257076104e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 27.112638920657887426818372110231
y[1] (numeric) = 27.11263892065788742681837211024
absolute error = 9e-30
relative error = 3.3194850661116004901043334267364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 27.385125471903217098118984843308
y[1] (numeric) = 27.385125471903217098118984843317
absolute error = 9e-30
relative error = 3.2864556378366361904369898022033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 27.660350558516751054310906965868
y[1] (numeric) = 27.660350558516751054310906965877
absolute error = 9e-30
relative error = 3.2537548578641777149789603518446e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 27.938341703236505652149863987642
y[1] (numeric) = 27.938341703236505652149863987651
absolute error = 9e-30
relative error = 3.2213794560889770770699884132410e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 28.2191267054086129265611051166
y[1] (numeric) = 28.219126705408612926561105116609
absolute error = 9e-30
relative error = 3.1893261949438771652351170340457e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 28.502733643767278370041893023457
y[1] (numeric) = 28.502733643767278370041893023467
absolute error = 1.0e-29
relative error = 3.5084354100845025883243525465533e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.36
y[1] (analytic) = 28.789190879242677752233921434877
y[1] (numeric) = 28.789190879242677752233921434887
absolute error = 1.0e-29
relative error = 3.4735258944738560307213684105142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 29.078527057797073771687539613154
y[1] (numeric) = 29.078527057797073771687539613163
absolute error = 9e-30
relative error = 3.0950673609125442775349458071243e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 29.370771113289436153846398566086
y[1] (numeric) = 29.370771113289436153846398566096
absolute error = 1.0e-29
relative error = 3.4047454734599342000372838954303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 29.665952270368851659649508823945
y[1] (numeric) = 29.665952270368851659649508823955
absolute error = 1.0e-29
relative error = 3.3708676899572403262044473705896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 29.96410004739701334816275303373
y[1] (numeric) = 29.964100047397013348162753033741
absolute error = 1.1e-29
relative error = 3.6710596956358687430640144618043e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 30.265244259400081344601532358897
y[1] (numeric) = 30.265244259400081344601532358908
absolute error = 1.1e-29
relative error = 3.6345320413475633246135869113339e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.42
y[1] (analytic) = 30.569415021050210302281241122151
y[1] (numeric) = 30.569415021050210302281241122162
absolute error = 1.1e-29
relative error = 3.5983678432921794595589556860738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 30.876642749677041713726379239121
y[1] (numeric) = 30.876642749677041713726379239132
absolute error = 1.1e-29
relative error = 3.5625634850197746773445103398540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 31.186958168309462222678998645337
y[1] (numeric) = 31.186958168309462222678998645348
absolute error = 1.1e-29
relative error = 3.5271153860646846728082970851003e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=104035732, alloc=4259060, time=4.23
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 31.500392308747932115372491603845
y[1] (numeric) = 31.500392308747932115372491603856
absolute error = 1.1e-29
relative error = 3.4920200015874737560201699207708e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 31.81697651466769122648013054928
y[1] (numeric) = 31.816976514667691226480130549291
absolute error = 1.1e-29
relative error = 3.4572738220204479546700877490203e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.47
y[1] (analytic) = 32.136742444753152582914967864034
y[1] (numeric) = 32.136742444753152582914967864044
absolute error = 1.0e-29
relative error = 3.1117030661060866545648996160059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 32.459722075863797227457478986324
y[1] (numeric) = 32.459722075863797227457478986335
absolute error = 1.1e-29
relative error = 3.3888152136026183401671757489644e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 32.785947706231886814331566095013
y[1] (numeric) = 32.785947706231886814331566095024
absolute error = 1.1e-29
relative error = 3.3550959388339237135415635465942e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 33.115451958692313750653249350389
y[1] (numeric) = 33.115451958692313750653249350399
absolute error = 1.0e-29
relative error = 3.0197383422318500739786292363619e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 33.448267783944911871457741316409
y[1] (numeric) = 33.448267783944911871457741316419
absolute error = 1.0e-29
relative error = 2.9896914436926315091759081996661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 33.78442846384955388209100856303
y[1] (numeric) = 33.78442846384955388209100856304
absolute error = 1.0e-29
relative error = 2.9599435167892000486479155483378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 34.123967614754365080455983293164
y[1] (numeric) = 34.123967614754365080455983293174
absolute error = 1.0e-29
relative error = 2.9304915867040753275291277527036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 34.466919190857386183259170295692
y[1] (numeric) = 34.466919190857386183259170295702
absolute error = 1.0e-29
relative error = 2.9013327082197054764654326721755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 34.813317487602021425341668911734
y[1] (numeric) = 34.813317487602021425341668911744
absolute error = 1.0e-29
relative error = 2.8724639654239429120710530784324e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 35.163197145106611479734092630969
y[1] (numeric) = 35.163197145106611479734092630979
absolute error = 1.0e-29
relative error = 2.8438824714184506922353186544466e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.57
y[1] (analytic) = 35.516593151628474158585378769949
y[1] (numeric) = 35.516593151628474158585378769959
absolute error = 1.0e-29
relative error = 2.8155853680300102766718216326597e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 35.873540847062759301922291319834
y[1] (numeric) = 35.873540847062759301922291319844
absolute error = 1.0e-29
relative error = 2.7875698255247018232454333197378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 36.234075926476467742644215040193
y[1] (numeric) = 36.234075926476467742644215040204
absolute error = 1.1e-29
relative error = 3.0358163465574212816554933621428e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.6
y[1] (analytic) = 36.598234443677987752594765899184
y[1] (numeric) = 36.598234443677987752594765899195
absolute error = 1.1e-29
relative error = 3.0056094692021816881719368679108e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 36.966052814822505926329448641597
y[1] (numeric) = 36.966052814822505926329448641608
absolute error = 1.1e-29
relative error = 2.9757031552985452194557833294857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 37.337567822053653046672257335396
y[1] (numeric) = 37.337567822053653046672257335408
absolute error = 1.2e-29
relative error = 3.2139211791165812733096962390979e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.63
y[1] (analytic) = 37.71281661718174909968248956046
y[1] (numeric) = 37.712816617181749099682489560472
absolute error = 1.2e-29
relative error = 3.1819421290673014512699141462217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 38.091836725399015266598485317448
y[1] (numeric) = 38.09183672539901526659848531746
absolute error = 1.2e-29
relative error = 3.1502812758825556390085966795158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 38.474666049032124417053505344034
y[1] (numeric) = 38.474666049032124417053505344046
absolute error = 1.2e-29
relative error = 3.1189354534506412296769247468865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.66
y[1] (analytic) = 38.861342871332465361740206261101
y[1] (numeric) = 38.861342871332465361740206261113
absolute error = 1.2e-29
relative error = 3.0879015271631934260688187104212e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 39.251905860304499894107543068851
y[1] (numeric) = 39.251905860304499894107543068864
absolute error = 1.3e-29
relative error = 3.3119410930685319412887792852803e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 39.646394072572595459984576852157
y[1] (numeric) = 39.64639407257259545998457685217
absolute error = 1.3e-29
relative error = 3.2789867285795379682737083955694e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.69
y[1] (analytic) = 40.044846957286720141620521375166
y[1] (numeric) = 40.04484695728672014162052137518
absolute error = 1.4e-29
relative error = 3.4960802859186615361473883158413e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 40.447304360067390528894189239039
y[1] (numeric) = 40.447304360067390528894189239053
absolute error = 1.4e-29
relative error = 3.4612937058475147683860336176764e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.71
y[1] (analytic) = 40.853806526990266975767426064963
y[1] (numeric) = 40.853806526990266975767426064977
absolute error = 1.4e-29
relative error = 3.4268532580313737883630207631949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 41.264394108610794704828685161265
y[1] (numeric) = 41.264394108610794704828685161279
absolute error = 1.4e-29
relative error = 3.3927554983967565131321485316229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 3.73
y[1] (analytic) = 41.679108164029293227391075798772
y[1] (numeric) = 41.679108164029293227391075798786
absolute error = 1.4e-29
relative error = 3.3589970171392845865542113187630e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 42.097990164996900591474480707947
y[1] (numeric) = 42.097990164996900591474480707961
absolute error = 1.4e-29
relative error = 3.3255744383827000999482648905759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 42.521082000062783055518172621604
y[1] (numeric) = 42.521082000062783055518172621618
absolute error = 1.4e-29
relative error = 3.2924844198412751530611659140606e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 42.948425978763024912247320706349
y[1] (numeric) = 42.948425978763024912247320706364
absolute error = 1.5e-29
relative error = 3.4925610562345505314608813383316e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 43.380064835851617355166526689092
y[1] (numeric) = 43.380064835851617355166526689107
absolute error = 1.5e-29
relative error = 3.4578094930838355309901702138719e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=108036712, alloc=4259060, time=4.39
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 43.816041735573969490092875840424
y[1] (numeric) = 43.81604173557396949009287584044
absolute error = 1.6e-29
relative error = 3.6516306280148761920205609722030e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 44.256400275983368846390927167131
y[1] (numeric) = 44.256400275983368846390927167147
absolute error = 1.6e-29
relative error = 3.6152962961794983053863970187794e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 44.701184493300823037557828729065
y[1] (numeric) = 44.701184493300823037557828729081
absolute error = 1.6e-29
relative error = 3.5793234969864953245733316065316e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 45.150438866318718558957830086431
y[1] (numeric) = 45.150438866318718558957830086447
absolute error = 1.6e-29
relative error = 3.5437086331259705166978269720860e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 45.604208320848737092255693225917
y[1] (numeric) = 45.604208320848737092255693225933
absolute error = 1.6e-29
relative error = 3.5084481430818586771316375068420e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 46.062538234214474111886054582464
y[1] (numeric) = 46.06253823421447411188605458248
absolute error = 1.6e-29
relative error = 3.4735385007757715550413994773742e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 46.525474439789209059163246411121
y[1] (numeric) = 46.525474439789209059163246411138
absolute error = 1.7e-29
relative error = 3.6539122286652862684147896420392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 46.993063231579280864830476241162
y[1] (numeric) = 46.993063231579280864830476241179
absolute error = 1.7e-29
relative error = 3.6175551945241187952203210303493e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 47.46535136885352716142011166414
y[1] (numeric) = 47.465351368853527161420111664157
absolute error = 1.7e-29
relative error = 3.5815599189170431114578469225756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 47.942386080819250133204185354246
y[1] (numeric) = 47.942386080819250133204185354263
absolute error = 1.7e-29
relative error = 3.5459228022865023465660394336584e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = 48.424215071345176604216766568584
y[1] (numeric) = 48.424215071345176604216766568602
absolute error = 1.8e-29
relative error = 3.7171485327082613826537790589361e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 48.910886523731884664292814557216
y[1] (numeric) = 48.910886523731884664292814557233
absolute error = 1.7e-29
relative error = 3.4757088264494015867824900448212e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 49.40244910553017387976148654122
y[1] (numeric) = 49.402449105530173879761486541238
absolute error = 1.8e-29
relative error = 3.6435440602447899249649578738577e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 49.89895197340786092983029148288
y[1] (numeric) = 49.898951973407860929830291482897
absolute error = 1.7e-29
relative error = 3.4068851804862828484973283841026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 50.400444778065487352279404612568
y[1] (numeric) = 50.400444778065487352279404612585
absolute error = 1.7e-29
relative error = 3.3729861065429487323602381510902e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 50.906977669201430973337148919991
y[1] (numeric) = 50.906977669201430973337148920009
absolute error = 1.8e-29
relative error = 3.5358610595517529792638605232548e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 51.418601300526917537017237808153
y[1] (numeric) = 51.418601300526917537017237808171
absolute error = 1.8e-29
relative error = 3.5006786541693702396695932027507e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 51.9353668348314340392599029227
y[1] (numeric) = 51.935366834831434039259902922718
absolute error = 1.8e-29
relative error = 3.4658463195696463730318385640650e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 52.457325949099050312431513118509
y[1] (numeric) = 52.457325949099050312431513118527
absolute error = 1.8e-29
relative error = 3.4313605724900943647075051640067e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 52.984530839676160496604750057851
y[1] (numeric) = 52.984530839676160496604750057869
absolute error = 1.8e-29
relative error = 3.3972179643272680411355542808777e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 53.517034227491161176072934038621
y[1] (numeric) = 53.51703422749116117607293403864
absolute error = 1.9e-29
relative error = 3.5502714741692265653390735945564e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 54.054889363326588153261897764787
y[1] (numeric) = 54.054889363326588153261897764806
absolute error = 1.9e-29
relative error = 3.5149456827656565447154346787737e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 54.598150033144239078110261202861
y[1] (numeric) = 54.59815003314423907811026120288
absolute error = 1.9e-29
relative error = 3.4799713888594942558064240419158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 55.146870563463814449618662535082
y[1] (numeric) = 55.146870563463814449618662535101
absolute error = 1.9e-29
relative error = 3.4453450949922037403103589856951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 55.701105826795614858150315907712
y[1] (numeric) = 55.701105826795614858150315907732
absolute error = 2.0e-29
relative error = 3.5905929879005715032652207912938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 56.260911247127837742734388822998
y[1] (numeric) = 56.260911247127837742734388823018
absolute error = 2.0e-29
relative error = 3.5548659907318893973338772871938e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 56.826342805469022397620692052799
y[1] (numeric) = 56.82634280546902239762069205282
absolute error = 2.1e-29
relative error = 3.6954692072809126146274383343156e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 57.397457045446197477205057110728
y[1] (numeric) = 57.397457045446197477205057110749
absolute error = 2.1e-29
relative error = 3.6586986742936373912604352742138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 57.974311078959290818741032291737
y[1] (numeric) = 57.974311078959290818741032291758
absolute error = 2.1e-29
relative error = 3.6222940142227172566139441153191e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 58.556962591892367028532192341085
y[1] (numeric) = 58.556962591892367028532192341106
absolute error = 2.1e-29
relative error = 3.5862515865718078008244970982158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 59.145469849882263960123061503388
y[1] (numeric) = 59.14546984988226396012306150341
absolute error = 2.2e-29
relative error = 3.7196424435951612610457108890287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 59.739891704145204952943682133229
y[1] (numeric) = 59.739891704145204952943682133251
absolute error = 2.2e-29
relative error = 3.6826313828877386155654497845596e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 60.340287597361969497487219708124
y[1] (numeric) = 60.340287597361969497487219708146
absolute error = 2.2e-29
relative error = 3.6459885883874744592364135783592e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=112038128, alloc=4324584, time=4.56
x[1] = 4.11
y[1] (analytic) = 60.946717569622210848991447239727
y[1] (numeric) = 60.946717569622210848991447239749
absolute error = 2.2e-29
relative error = 3.6097103957843830017736938645926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 61.559242264428515026339091755126
y[1] (numeric) = 61.559242264428515026339091755148
absolute error = 2.2e-29
relative error = 3.5737931772289720060893643077077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 62.177922934760801607080332059943
y[1] (numeric) = 62.177922934760801607080332059966
absolute error = 2.3e-29
relative error = 3.6990621291953391256621835597386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 62.802821449201672763710634207787
y[1] (numeric) = 62.80282144920167276371063420781
absolute error = 2.3e-29
relative error = 3.6622558460376891011184313830871e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 63.434000298123323081212027004718
y[1] (numeric) = 63.434000298123323081212027004741
absolute error = 2.3e-29
relative error = 3.6258157915165328901339369325551e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 64.071522599936628851995347043461
y[1] (numeric) = 64.071522599936628851995347043484
absolute error = 2.3e-29
relative error = 3.5897383215960515637640838252260e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 64.71545210740304176238053926293
y[1] (numeric) = 64.715452107403041762380539262953
absolute error = 2.3e-29
relative error = 3.5540198284991884153937941243519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 65.365853214009918165243590001587
y[1] (numeric) = 65.36585321400991816524359000161
absolute error = 2.3e-29
relative error = 3.5186567403468682485759646218838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 66.022790960409921477070149341099
y[1] (numeric) = 66.022790960409921477070149341122
absolute error = 2.3e-29
relative error = 3.4836455208008064929360042270730e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 66.686331040925141645021734653992
y[1] (numeric) = 66.686331040925141645021734654015
absolute error = 2.3e-29
relative error = 3.4489826687098724287564028526076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = 4.21
y[1] (analytic) = 67.356539810116582101381339598584
y[1] (numeric) = 67.356539810116582101381339598607
absolute error = 2.3e-29
relative error = 3.4146647177599711562690919599977e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 68.033484289419671159548483832735
y[1] (numeric) = 68.033484289419671159548483832758
absolute error = 2.3e-29
relative error = 3.3806882361274092975607600021238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 68.717232173846461408252914213396
y[1] (numeric) = 68.717232173846461408252914213419
absolute error = 2.3e-29
relative error = 3.3470498261357097673724504165392e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 69.407851838755187329511563631169
y[1] (numeric) = 69.407851838755187329511563631192
absolute error = 2.3e-29
relative error = 3.3137461239158412939845334850296e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 70.105412346687858101731879995094
y[1] (numeric) = 70.105412346687858101731879995117
absolute error = 2.3e-29
relative error = 3.2807737990698287128559975468804e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 70.809983454276569352939848696489
y[1] (numeric) = 70.809983454276569352939848696512
absolute error = 2.3e-29
relative error = 3.2481295543377103937670978052529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 71.521635619219224501063310332678
y[1] (numeric) = 71.521635619219224501063310332701
absolute error = 2.3e-29
relative error = 3.2158101252678094969305405890512e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 72.240440007325363259217722516329
y[1] (numeric) = 72.240440007325363259217722516353
absolute error = 2.4e-29
relative error = 3.3222389007550811320925627682235e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 72.96646849963280189471643767276
y[1] (numeric) = 72.966468499632801894716437672785
absolute error = 2.5e-29
relative error = 3.4262313243412363536623852433041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 73.699793699595796911761951170653
y[1] (numeric) = 73.699793699595796911761951170677
absolute error = 2.4e-29
relative error = 3.2564541629282236217353378861842e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 4.31
y[1] (analytic) = 74.440488940345450980176545280381
y[1] (numeric) = 74.440488940345450980176545280406
absolute error = 2.5e-29
relative error = 3.3583873985613270984159448149756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 75.188628292023087156815560466137
y[1] (numeric) = 75.188628292023087156815560466162
absolute error = 2.5e-29
relative error = 3.3249708856109428845724037537407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 75.944286569187324743196600893995
y[1] (numeric) = 75.94428656918732474319660089402
absolute error = 2.5e-29
relative error = 3.2918868725199380724065030743306e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 76.70753933829559749310302086642
y[1] (numeric) = 76.707539338295597493103020866445
absolute error = 2.5e-29
relative error = 3.2591320508594334586276550385800e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 77.478462925260862328217071820222
y[1] (numeric) = 77.478462925260862328217071820247
absolute error = 2.5e-29
relative error = 3.2267031451199672170716163854182e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 78.257134423084254238951551456582
y[1] (numeric) = 78.257134423084254238951551456607
absolute error = 2.5e-29
relative error = 3.1945969123839412229175550644307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 79.043631699564450642330605120616
y[1] (numeric) = 79.043631699564450642330605120642
absolute error = 2.6e-29
relative error = 3.2893225476813796540526373919033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 79.838033405084516139779959223782
y[1] (numeric) = 79.838033405084516139779959223809
absolute error = 2.7e-29
relative error = 3.3818468276900836741094641597479e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 4.39
y[1] (analytic) = 80.640418980477006365791424660798
y[1] (numeric) = 80.640418980477006365791424660825
absolute error = 2.7e-29
relative error = 3.3481968895197187226937699969362e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 81.450868664968117444400811726181
y[1] (numeric) = 81.450868664968117444400811726208
absolute error = 2.7e-29
relative error = 3.3148817738284791183136342838662e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 82.269463504201675475045050936085
y[1] (numeric) = 82.269463504201675475045050936112
absolute error = 2.7e-29
relative error = 3.2818981490770330480570993850284e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 83.096285358343768453433785661304
y[1] (numeric) = 83.096285358343768453433785661331
absolute error = 2.7e-29
relative error = 3.2492427168754189217362577804927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 83.931416910268831097381406177663
y[1] (numeric) = 83.93141691026883109738140617769
absolute error = 2.7e-29
relative error = 3.2169122116532036270607697393018e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=116040144, alloc=4324584, time=4.73
x[1] = 4.44
y[1] (analytic) = 84.774941673828001192903868431231
y[1] (numeric) = 84.774941673828001192903868431259
absolute error = 2.8e-29
relative error = 3.3028627855304384229721604237826e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 85.626944002200574303105227123016
y[1] (numeric) = 85.626944002200574303105227123044
absolute error = 2.8e-29
relative error = 3.2699987517107246613378986112110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 86.4875090963293919922843405557
y[1] (numeric) = 86.487509096329391992284340555729
absolute error = 2.9e-29
relative error = 3.3530853533658753729631794164511e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 87.356723013441007111113671531353
y[1] (numeric) = 87.356723013441007111113671531383
absolute error = 3.0e-29
relative error = 3.4341947551517124088440973163808e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 88.234672675651478166518863585011
y[1] (numeric) = 88.234672675651478166518863585041
absolute error = 3.0e-29
relative error = 3.4000239464002177603508512728501e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 89.121445878658653362867599725013
y[1] (numeric) = 89.121445878658653362867599725044
absolute error = 3.1e-29
relative error = 3.4783995809726167290559264173783e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 4.5
y[1] (analytic) = 90.017131300521813550115456745574
y[1] (numeric) = 90.017131300521813550115456745605
absolute error = 3.1e-29
relative error = 3.4437889268551150138043716289485e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of 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] = 4.51
y[1] (analytic) = 90.92181851052955205051996320841
y[1] (numeric) = 90.921818510529552050519963208441
absolute error = 3.1e-29
relative error = 3.4095226545001324818642278031618e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 91.835597978156778159295456987861
y[1] (numeric) = 91.835597978156778159295456987892
absolute error = 3.1e-29
relative error = 3.3755973372518783128355556356230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 92.758561082111740027023002329753
y[1] (numeric) = 92.758561082111740027023002329784
absolute error = 3.1e-29
relative error = 3.3420095825503564893574131481326e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 93.690800119473971633642818281708
y[1] (numeric) = 93.690800119473971633642818281738
absolute error = 3.0e-29
relative error = 3.2020219660568777132548701149294e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 94.632408314924077656341598932635
y[1] (numeric) = 94.632408314924077656341598932666
absolute error = 3.1e-29
relative error = 3.2758333589943225460651663778960e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 95.583479830066279217513027221686
y[1] (numeric) = 95.583479830066279217513027221717
absolute error = 3.1e-29
relative error = 3.2432382724623077860701997844154e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 96.54410977284465277513509238733
y[1] (numeric) = 96.544109772844652775135092387362
absolute error = 3.2e-29
relative error = 3.3145471096363838206455592183734e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 97.51439420705400378730014068658
y[1] (numeric) = 97.514394207054003787300140686612
absolute error = 3.2e-29
relative error = 3.2815668148492872989593434590811e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 98.494430161946326246189866862324
y[1] (numeric) = 98.494430161946326246189866862357
absolute error = 3.3e-29
relative error = 3.3504432632120214536651157394973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 99.484315641933808735454053487567
y[1] (numeric) = 99.4843156419338087354540534876
absolute error = 3.3e-29
relative error = 3.3171057957290819419039211294115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 100.48414963638935731968466139449
y[1] (numeric) = 100.48414963638935731968466139453
absolute error = 4e-29
relative error = 3.9807273231393689482549959917821e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 101.49403212954561532644134822903
y[1] (numeric) = 101.49403212954561532644134822907
absolute error = 4e-29
relative error = 3.9411184244749030034300305099659e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 102.51406411049346993105582833176
y[1] (numeric) = 102.5140641104934699310558283318
absolute error = 4e-29
relative error = 3.9019036409371608502052221846007e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 103.54434758328104540320567097554
y[1] (numeric) = 103.54434758328104540320567097558
absolute error = 4e-29
relative error = 3.8630790510151096191536479510022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 104.58498557711419292299805009791
y[1] (numeric) = 104.58498557711419292299805009795
absolute error = 4e-29
relative error = 3.8246407722174031723708842598898e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = 105.63608215665949702404549041811
y[1] (numeric) = 105.63608215665949702404549041816
absolute error = 5e-29
relative error = 4.7332312008551621668012210033370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 106.69774243245082897276378483542
y[1] (numeric) = 106.69774243245082897276378483546
absolute error = 4e-29
relative error = 3.7489078108024226930315283612777e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 107.77007257140048774790216962363
y[1] (numeric) = 107.77007257140048774790216962368
absolute error = 5e-29
relative error = 4.6395069435323701885976736186949e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 108.85317980741597974316302378673
y[1] (numeric) = 108.85317980741597974316302378678
absolute error = 5e-29
relative error = 4.5933430781223339217440727531059e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 109.94717245212349887972870045537
y[1] (numeric) = 109.94717245212349887972870045541
absolute error = 4e-29
relative error = 3.6381108406783268368216297165551e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order 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] = 4.71
y[1] (analytic) = 111.05215990569917948564300622207
y[1] (numeric) = 111.05215990569917948564300622211
absolute error = 4e-29
relative error = 3.6019110329746235087117816244113e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 112.1682526678092050763613407161
y[1] (numeric) = 112.16825266780920507636134071615
absolute error = 5e-29
relative error = 4.4575892742197752196974365073820e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 113.29556234865986705646433913828
y[1] (numeric) = 113.29556234865986705646433913832
absolute error = 4e-29
relative error = 3.5305884158906905134065076387104e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 114.43420168015867835761360206601
y[1] (numeric) = 114.43420168015867835761360206605
absolute error = 4e-29
relative error = 3.4954584741893167405562058164152e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 115.58428452718765813341426713653
y[1] (numeric) = 115.58428452718765813341426713657
absolute error = 4e-29
relative error = 3.4606780812482536708286015829001e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 116.74592589898991484904834409238
y[1] (numeric) = 116.74592589898991484904834409242
absolute error = 4e-29
relative error = 3.4262437589992234405201278169228e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 117.91924196067066643347662739359
y[1] (numeric) = 117.91924196067066643347662739364
absolute error = 5e-29
relative error = 4.2401900799766322280197865053689e-29 %
Correct digits = 31
h = 0.01
bytes used=120041584, alloc=4324584, time=4.90
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 119.10435004481384760580862199534
y[1] (numeric) = 119.10435004481384760580862199539
absolute error = 5e-29
relative error = 4.1979994837457363302528858333768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 120.30136866321546604625365765727
y[1] (numeric) = 120.30136866321546604625365765732
absolute error = 5e-29
relative error = 4.1562286909615595703709578966102e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 121.51041751873488075704811629788
y[1] (numeric) = 121.51041751873488075704811629793
absolute error = 5e-29
relative error = 4.1148735245100144206810133830373e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 122.73161751726518775107096333766
y[1] (numeric) = 122.73161751726518775107096333771
absolute error = 5e-29
relative error = 4.0739298488399929730827948397465e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 123.96509077982391011669179924248
y[1] (numeric) = 123.96509077982391011669179924253
absolute error = 5e-29
relative error = 4.0333935695498083819738890613037e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 125.21096065476520153793352471171
y[1] (numeric) = 125.21096065476520153793352471176
absolute error = 5e-29
relative error = 3.9932606329777512835523877854349e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 126.46935173011478450047850596726
y[1] (numeric) = 126.46935173011478450047850596731
absolute error = 5e-29
relative error = 3.9535270257967202468178228408419e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 127.74038984602885668761799019549
y[1] (numeric) = 127.74038984602885668761799019554
absolute error = 5e-29
relative error = 3.9141887746128857189776667571407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 129.0242021073782114671668226883
y[1] (numeric) = 129.02420210737821146716682268836
absolute error = 6e-29
relative error = 4.6502903346820167975833899919957e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 130.32091689645883089187895918358
y[1] (numeric) = 130.32091689645883089187895918364
absolute error = 6e-29
relative error = 4.6040191727372937971379043822046e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 131.63066388583022228325601109699
y[1] (numeric) = 131.63066388583022228325601109705
absolute error = 6e-29
relative error = 4.5582084165465399589848613083478e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 132.95357405128278224310585398182
y[1] (numeric) = 132.95357405128278224310585398188
absolute error = 6e-29
relative error = 4.5128534849959604503291561683056e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 134.28977968493548484005862777435
y[1] (numeric) = 134.28977968493548484005862777441
absolute error = 6e-29
relative error = 4.4679498425546043109416278520770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 135.63941440846520375077355696288
y[1] (numeric) = 135.63941440846520375077355696294
absolute error = 6e-29
relative error = 4.4234929988208075784413113058933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 137.00261318646899129907518322816
y[1] (numeric) = 137.00261318646899129907518322822
absolute error = 6e-29
relative error = 4.3794785080731493798853394401663e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 138.37951233996065063205819382868
y[1] (numeric) = 138.37951233996065063205819382874
absolute error = 6e-29
relative error = 4.3359019688258760849014488671065e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 139.77024956000295070162563718432
y[1] (numeric) = 139.77024956000295070162563718438
absolute error = 6e-29
relative error = 4.2927590233887490624079216112576e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 141.17496392147684728431889649845
y[1] (numeric) = 141.17496392147684728431889649851
absolute error = 6e-29
relative error = 4.2500453574312720253298400284088e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 142.59379589698908697301579351366
y[1] (numeric) = 142.59379589698908697301579351371
absolute error = 5e-29
relative error = 3.5064639162927119880691512237404e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 144.02688737091958491248570083683
y[1] (numeric) = 144.02688737091958491248570083689
absolute error = 6e-29
relative error = 4.1658888208476674760013293360410e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 145.47438165360998102828140547844
y[1] (numeric) = 145.47438165360998102828140547849
absolute error = 5e-29
relative error = 3.4370312787481257686453241367204e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 146.93642349569479361641444906234
y[1] (numeric) = 146.93642349569479361641444906239
absolute error = 5e-29
relative error = 3.4028322461152723994826662519144e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = y;
Iterations = 1000
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Time to Timeout = 2 Minutes 55 Seconds
Percent Done = 100.1 %
> quit
bytes used=122773428, alloc=4324584, time=5.00