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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,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 2;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 2
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 2;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre cosh $eq_no = 1
> array_tmp4_g[1] := sinh(array_tmp3[1]);
> array_tmp4[1] := cosh(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1);
> array_tmp4[2] := att(1,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1);
> array_tmp4[3] := att(2,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1);
> array_tmp4[4] := att(3,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1);
> array_tmp4[5] := att(4,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> #emit cosh $eq_no = 1
> array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[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_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_g[1] := sinh(array_tmp3[1]);
array_tmp4[1] := cosh(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[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_tmp5[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(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2)));
> end;
exact_soln_y := proc(x)
return 20.0*sqrt(0.1*x + 0.2)*sinh(sqrt(0.1*x + 0.2))
- 20.0*cosh(sqrt(0.1*x + 0.2))
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> 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/cosh_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));");
> 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 := -1.0;");
> 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 := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4_g:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_0D1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D1[1] := 0.1;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D2[1] := 0.2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_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 ) = cosh(sqrt(0.1 * x + 0.2));");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T00:09:28-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cosh_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"cosh_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"cosh_sqrt maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, 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/cosh_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));");
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 := -1.0;");
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 := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0\
.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4_g := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_g[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_0D1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D1[term] := 0.; term := term + 1
end do;
array_const_0D1[1] := 0.1;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := -1.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_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 ) = cosh(sqrt(0.1 * x + 0.2));")
;
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T00:09:28-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"cosh_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file, "cosh_sqrt diffeq.mxt");
logitem_str(html_log_file, "cosh_sqrt 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/cosh_sqrtpostode.ode#################
diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 6
estimated_steps = 6000000
step_error = 1.6666666666666666666666666666667e-17
est_needed_step_err = 1.6666666666666666666666666666667e-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 = 2.9230751424511675824175824175824e-193
estimated_step_error = 2.9230751424511675824175824175824e-193
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.7999928490042378917378917378917e-185
estimated_step_error = 2.7999928490042378917378917378917e-185
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 = 3.1999940740896825396825396825397e-177
estimated_step_error = 3.1999940740896825396825396825397e-177
best_h = 8.000e-06
opt_iter = 4
bytes used=4000512, alloc=2948580, time=0.12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0553837607289987789987789987789e-169
estimated_step_error = 2.0553837607289987789987789987789e-169
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 = 1.5015197721744810744810744810745e-161
estimated_step_error = 1.5015197721744810744810744810745e-161
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.5785207980276760276760276760277e-154
estimated_step_error = 4.5785207980276760276760276760277e-154
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 = 4.9227851954708994708994708994709e-146
estimated_step_error = 4.9227851954708994708994708994709e-146
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.1266716947106227106227106227106e-138
estimated_step_error = 2.1266716947106227106227106227106e-138
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 = 8.6609505035409035409035409035409e-131
estimated_step_error = 8.6609505035409035409035409035409e-131
best_h = 0.000512
opt_iter = 10
bytes used=8001644, alloc=3996964, time=0.25
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.4341843959299959299959299959300e-122
estimated_step_error = 2.4341843959299959299959299959300e-122
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 = 5.2063515715099715099715099715100e-115
estimated_step_error = 5.2063515715099715099715099715100e-115
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 = 3.8176933613349613349613349613350e-107
estimated_step_error = 3.8176933613349613349613349613350e-107
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.6380042940170940170940170940172e-99
estimated_step_error = 2.6380042940170940170940170940172e-99
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.3580532643060643060643060643060e-91
estimated_step_error = 1.3580532643060643060643060643060e-91
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 = 4.8546723060643060643060643060643e-84
estimated_step_error = 4.8546723060643060643060643060643e-84
best_h = 0.032768
opt_iter = 16
bytes used=12002508, alloc=4193536, time=0.38
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5735845092389092389092389092390e-75
estimated_step_error = 1.5735845092389092389092389092390e-75
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 = 8.4987415547415547415547415547416e-68
estimated_step_error = 8.4987415547415547415547415547416e-68
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 = 1.5767116060236060236060236060236e-59
estimated_step_error = 1.5767116060236060236060236060236e-59
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = -18.974860763392397555820586777095
y[1] (numeric) = -18.974860763392397555820586777095
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = -18.964354040796229869016125972141
y[1] (numeric) = -18.964354040796229869016125972142
absolute error = 1e-30
relative error = 5.2730506815512625573464059010359e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00537
Order of pole (three term test) = -0.7228
Radius of convergence (six term test) for eq 1 = 0.2886
Order of pole (six term test) = -12.9
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (analytic) = -18.953842233607323295055774089317
y[1] (numeric) = -18.953842233607323295055774089319
absolute error = 2e-30
relative error = 1.0551950234416175369373711118540e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01056
Order of pole (three term test) = -2.708
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=16003660, alloc=4324584, time=0.51
x[1] = -0.97
y[1] (analytic) = -18.943325340983855447367567229042
y[1] (numeric) = -18.943325340983855447367567229044
absolute error = 2e-30
relative error = 1.0557808431199790747124488584556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = -18.93280336208391999718039639065
y[1] (numeric) = -18.932803362083919997180396390651
absolute error = 1e-30
relative error = 5.2818379870921065857851759094252e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6695
Order of pole (six term test) = -13.38
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = -18.922276296065526667537651949257
y[1] (numeric) = -18.922276296065526667537651949258
absolute error = 1e-30
relative error = 5.2847764420812739099150571467851e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01473
Order of pole (three term test) = 1.778
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = -18.911744142086601227310535893506
y[1] (numeric) = -18.911744142086601227310535893507
absolute error = 1e-30
relative error = 5.2877195909951982785103105986264e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = -18.901206899304985485211041809093
y[1] (numeric) = -18.901206899304985485211041809094
absolute error = 1e-30
relative error = 5.2906674442930462110705252901870e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02007
Order of pole (three term test) = -29.08
Radius of convergence (six term test) for eq 1 = 0.01656
Order of pole (six term test) = -11.51
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (analytic) = -18.890664566878437283804602592996
y[1] (numeric) = -18.890664566878437283804602592997
absolute error = 1e-30
relative error = 5.2936200124654675854327563488304e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03402
Order of pole (three term test) = -9.422
Radius of convergence (six term test) for eq 1 = 0.6727
Order of pole (six term test) = -9.998
TOP MAIN SOLVE Loop
bytes used=20004560, alloc=4324584, time=0.64
x[1] = -0.91
y[1] (analytic) = -18.880117143964630493522405883301
y[1] (numeric) = -18.880117143964630493522405883303
absolute error = 2e-30
relative error = 1.0593154612069427880805618460195e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02913
Order of pole (three term test) = -37.07
Radius of convergence (six term test) for eq 1 = 0.1457
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = -18.869564629721155006673377189548
y[1] (numeric) = -18.869564629721155006673377189548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1664
Order of pole (six term test) = -11.67
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = -18.859007023305516731455830708474
y[1] (numeric) = -18.859007023305516731455830708474
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.05497
Order of pole (six term test) = -11.52
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (analytic) = -18.848444323875137585968787810106
y[1] (numeric) = -18.848444323875137585968787810107
absolute error = 1e-30
relative error = 5.3054776448224425222501010237981e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.6774
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03566
Order of pole (three term test) = -16.67
Radius of convergence (six term test) for eq 1 = 0.1943
Order of pole (six term test) = -11.82
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = -18.837876530587355492222963179063
y[1] (numeric) = -18.837876530587355492222963179064
absolute error = 1e-30
relative error = 5.3084539458377079839422624088760e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (analytic) = -18.827303642599424370151418595992
y[1] (numeric) = -18.827303642599424370151418595994
absolute error = 2e-30
relative error = 1.0622870050678518334519972948037e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005029
Order of pole (three term test) = -26.31
NO COMPLEX POLE (six term test) for Equation 1
bytes used=24009796, alloc=4390108, time=0.78
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = -18.816725659068514131619884344055
y[1] (numeric) = -18.816725659068514131619884344055
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = -18.806142579151710674436748225331
y[1] (numeric) = -18.806142579151710674436748225331
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1998
Order of pole (six term test) = -11.38
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = -18.795554402006015876362712172093
y[1] (numeric) = -18.795554402006015876362712172093
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6517
Order of pole (six term test) = 2.69
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = -18.784961126788347589120116437807
y[1] (numeric) = -18.784961126788347589120116437806
absolute error = 1e-30
relative error = 5.3234073429832502414758965670331e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5688
Order of pole (six term test) = -13.51
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (analytic) = -18.774362752655539632401931352784
y[1] (numeric) = -18.774362752655539632401931352784
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1467
Order of pole (six term test) = -12.46
TOP MAIN SOLVE Loop
bytes used=28010924, alloc=4390108, time=0.92
x[1] = -0.8
y[1] (analytic) = -18.763759278764341787880416629394
y[1] (numeric) = -18.763759278764341787880416629393
absolute error = 1e-30
relative error = 5.3294224528436470444695848561762e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.494
Order of pole (six term test) = -1.94
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = -18.753150704271419793215448201704
y[1] (numeric) = -18.753150704271419793215448201705
absolute error = 1e-30
relative error = 5.3324372835772562655750475955565e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001448
Order of pole (three term test) = -24.42
Radius of convergence (six term test) for eq 1 = 0.213
Order of pole (six term test) = -11.43
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = -18.742537028333355336062512584502
y[1] (numeric) = -18.742537028333355336062512584501
absolute error = 1e-30
relative error = 5.3354569794275236869803269596291e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003546
Order of pole (three term test) = -0.5806
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = -18.731918250106646048080368736524
y[1] (numeric) = -18.731918250106646048080368736524
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08617
Order of pole (three term test) = -11.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = -18.721294368747705498938377412881
y[1] (numeric) = -18.72129436874770549893837741288
absolute error = 1e-30
relative error = 5.3415110104210783191541914631597e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1291
Order of pole (three term test) = -60.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (analytic) = -18.710665383412863190323497991485
y[1] (numeric) = -18.710665383412863190323497991485
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01584
Order of pole (three term test) = -27.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32011708, alloc=4455632, time=1.05
x[1] = -0.74
y[1] (analytic) = -18.700031293258364549946952758457
y[1] (numeric) = -18.700031293258364549946952758456
absolute error = 1e-30
relative error = 5.3475846340455839847198897747884e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3203
Order of pole (six term test) = -14.43
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = -18.689392097440370925550558637347
y[1] (numeric) = -18.689392097440370925550558637345
absolute error = 2e-30
relative error = 1.0701257641621808030485348967762e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 0.5903
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.164
Order of pole (six term test) = -11.93
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (analytic) = -18.678747795114959578912726347113
y[1] (numeric) = -18.678747795114959578912726347111
absolute error = 2e-30
relative error = 1.0707355878122936392320526108498e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4841
Order of pole (six term test) = -12.19
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = -18.668098385438123679854126973725
y[1] (numeric) = -18.668098385438123679854126973725
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02615
Order of pole (three term test) = -34.36
Radius of convergence (six term test) for eq 1 = 0.7819
Order of pole (six term test) = -22.11
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (analytic) = -18.657443867565772300243025940306
y[1] (numeric) = -18.657443867565772300243025940304
absolute error = 2e-30
relative error = 1.0719582029544859807536710527631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (analytic) = -18.646784240653730408000284360674
y[1] (numeric) = -18.646784240653730408000284360673
absolute error = 1e-30
relative error = 5.3628549946955432040903648982398e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3949
Order of pole (six term test) = -10.93
TOP MAIN SOLVE Loop
bytes used=36012400, alloc=4455632, time=1.19
x[1] = -0.68
y[1] (analytic) = -18.636119503857738861104027761244
y[1] (numeric) = -18.636119503857738861104027761243
absolute error = 1e-30
relative error = 5.3659239510295942590615105365752e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3028
Order of pole (six term test) = -12.41
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (analytic) = -18.625449656333454401593982156101
y[1] (numeric) = -18.6254496563334544015939821561
absolute error = 1e-30
relative error = 5.3689978950921969633726131221611e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2387
Order of pole (six term test) = -11.16
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (analytic) = -18.614774697236449649575477460205
y[1] (numeric) = -18.614774697236449649575477460204
absolute error = 1e-30
relative error = 5.3720768382357055779360974611067e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (analytic) = -18.604094625722213097223118225584
y[1] (numeric) = -18.604094625722213097223118225583
absolute error = 1e-30
relative error = 5.3751607918473478779377933958306e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005293
Order of pole (three term test) = -30.36
Radius of convergence (six term test) for eq 1 = 0.668
Order of pole (six term test) = -9.502
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (analytic) = -18.59340944094614910278412168542
y[1] (numeric) = -18.593409440946149102784121685418
absolute error = 2e-30
relative error = 1.0756499534698717827844863816556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07014
Order of pole (three term test) = 10.64
Radius of convergence (six term test) for eq 1 = 0.7399
Order of pole (six term test) = -15.43
TOP MAIN SOLVE Loop
bytes used=40013416, alloc=4455632, time=1.33
x[1] = -0.63
y[1] (analytic) = -18.58271914206357788458132309091
y[1] (numeric) = -18.582719142063577884581323090909
absolute error = 1e-30
relative error = 5.3813437761991153892081135175160e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01642
Order of pole (three term test) = -19.31
Radius of convergence (six term test) for eq 1 = 0.1577
Order of pole (six term test) = -11.67
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (analytic) = -18.572023728229735515015848325814
y[1] (numeric) = -18.572023728229735515015848325813
absolute error = 1e-30
relative error = 5.3844428298892706569452858394688e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05705
Order of pole (three term test) = -27.7
Radius of convergence (six term test) for eq 1 = 0.2046
Order of pole (six term test) = -10.82
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (analytic) = -18.56132319859977391456945378355
y[1] (numeric) = -18.561323198599773914569453783548
absolute error = 2e-30
relative error = 1.0775093879895780680312333826066e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (analytic) = -18.550617552328760845806533491746
y[1] (numeric) = -18.550617552328760845806533491743
absolute error = 3e-30
relative error = 1.6171968353815765734333275837999e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05468
Order of pole (three term test) = -20.53
Radius of convergence (six term test) for eq 1 = 0.3119
Order of pole (six term test) = -11.74
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (analytic) = -18.539906788571679907375793469138
y[1] (numeric) = -18.539906788571679907375793469135
absolute error = 3e-30
relative error = 1.6181311126381994707256833754039e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06049
Order of pole (three term test) = -33.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (analytic) = -18.529190906483430528011593299696
y[1] (numeric) = -18.529190906483430528011593299693
absolute error = 3e-30
relative error = 1.6190669172447725238688982281646e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03411
Order of pole (three term test) = -26.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=44014268, alloc=4455632, time=1.47
x[1] = -0.57
y[1] (analytic) = -18.518469905218827960534954908861
y[1] (numeric) = -18.518469905218827960534954908859
absolute error = 2e-30
relative error = 1.0800028351350805179935529445446e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1049
Order of pole (three term test) = 20.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (analytic) = -18.507743783932603275854238526798
y[1] (numeric) = -18.507743783932603275854238526795
absolute error = 3e-30
relative error = 1.6209431225238992241111042429010e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7059
Order of pole (six term test) = -14.67
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (analytic) = -18.497012541779403356965485823526
y[1] (numeric) = -18.497012541779403356965485823523
absolute error = 3e-30
relative error = 1.6218835302316346378872485919896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09573
Order of pole (three term test) = -23.46
Radius of convergence (six term test) for eq 1 = 0.3902
Order of pole (six term test) = -11.44
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (analytic) = -18.486276177913790892952430200843
y[1] (numeric) = -18.48627617791379089295243020084
absolute error = 3e-30
relative error = 1.6228254793597675924253764536607e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6708
Order of pole (six term test) = -12.72
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (analytic) = -18.475534691490244372986174225901
y[1] (numeric) = -18.475534691490244372986174225899
absolute error = 2e-30
relative error = 1.0825126489687964541494898087285e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4843
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (analytic) = -18.464788081663158080324534191337
y[1] (numeric) = -18.464788081663158080324534191335
absolute error = 2e-30
relative error = 1.0831426773785406208666073201362e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5304
Order of pole (six term test) = -12.68
TOP MAIN SOLVE Loop
bytes used=48015528, alloc=4455632, time=1.61
x[1] = -0.51
y[1] (analytic) = -18.454036347586842086311051786829
y[1] (numeric) = -18.454036347586842086311051786828
absolute error = 1e-30
relative error = 5.4188687025685080485302370465938e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004249
Order of pole (three term test) = -24.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (analytic) = -18.443279488415522244373672866982
y[1] (numeric) = -18.44327948841552224437367286698
absolute error = 2e-30
relative error = 1.0844058407596260383274651855921e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06227
Order of pole (three term test) = -29.53
Radius of convergence (six term test) for eq 1 = 0.05808
Order of pole (six term test) = -11.78
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (analytic) = -18.432517503303340184023093300395
y[1] (numeric) = -18.432517503303340184023093300393
absolute error = 2e-30
relative error = 1.0850389805090784335049681250908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1205
Order of pole (six term test) = -11.61
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (analytic) = -18.421750391404353304850771884829
y[1] (numeric) = -18.421750391404353304850771884828
absolute error = 1e-30
relative error = 5.4283658108113501875349284021554e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01143
Order of pole (three term test) = -24.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (analytic) = -18.410978151872534770526610313331
y[1] (numeric) = -18.41097815187253477052661031333
absolute error = 1e-30
relative error = 5.4315419406344387442873822317072e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
bytes used=52016620, alloc=4455632, time=1.74
y[1] (analytic) = -18.400200783861773502796300176202
y[1] (numeric) = -18.4002007838617735027963001762
absolute error = 2e-30
relative error = 1.0869446608181231982103762656251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5651
Order of pole (six term test) = -9.747
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (analytic) = -18.389418286525874175478336983693
y[1] (numeric) = -18.389418286525874175478336983691
absolute error = 2e-30
relative error = 1.0875819826587019600737499976334e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3831
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (analytic) = -18.378630659018557208460701194317
y[1] (numeric) = -18.378630659018557208460701194315
absolute error = 2e-30
relative error = 1.0882203560789129011247009864161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (analytic) = -18.367837900493458761697206233636
y[1] (numeric) = -18.367837900493458761697206233635
absolute error = 1e-30
relative error = 5.4442989175831883293035790363478e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004935
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (analytic) = -18.357040010104130729203513488424
y[1] (numeric) = -18.357040010104130729203513488423
absolute error = 1e-30
relative error = 5.4475013370869015016888894502101e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4926
Order of pole (three term test) = -128.8
Radius of convergence (six term test) for eq 1 = 0.3998
Order of pole (six term test) = -11.96
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (analytic) = -18.346236987004040733052814261068
y[1] (numeric) = -18.346236987004040733052814261066
absolute error = 2e-30
relative error = 1.0901418102342970147502723689827e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0197
Order of pole (three term test) = -2.269
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=56017904, alloc=4455632, time=1.88
x[1] = -0.4
y[1] (analytic) = -18.335428830346572117371178669092
y[1] (numeric) = -18.335428830346572117371178669092
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (analytic) = -18.324615539285023942332571474698
y[1] (numeric) = -18.324615539285023942332571474696
absolute error = 2e-30
relative error = 1.0914280824677178983057829549571e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05764
Order of pole (three term test) = -42.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (analytic) = -18.313797112972610978153534829146
y[1] (numeric) = -18.313797112972610978153534829146
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (analytic) = -18.302973550562463699087537916942
y[1] (numeric) = -18.302973550562463699087537916942
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3471
Order of pole (six term test) = -11.24
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (analytic) = -18.292144851207628277418993484604
y[1] (numeric) = -18.292144851207628277418993484603
absolute error = 1e-30
relative error = 5.4668274723069506284098295288285e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0306
Order of pole (three term test) = -26.01
Radius of convergence (six term test) for eq 1 = 0.1539
Order of pole (six term test) = -11.51
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (analytic) = -18.281311014061066577456941238958
y[1] (numeric) = -18.281311014061066577456941238957
absolute error = 1e-30
relative error = 5.4700672136196917565774759678215e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01531
Order of pole (three term test) = -22.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=60019440, alloc=4521156, time=2.01
x[1] = -0.34
y[1] (analytic) = -18.270472038275656149528398099814
y[1] (numeric) = -18.270472038275656149528398099814
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.401
Order of pole (six term test) = -12.72
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (analytic) = -18.259627923004190223971375291892
y[1] (numeric) = -18.259627923004190223971375291891
absolute error = 1e-30
relative error = 5.4765628533983491715561693249545e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02814
Order of pole (three term test) = -20.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (analytic) = -18.248778667399377705127562260858
y[1] (numeric) = -18.248778667399377705127562260858
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.31
y[1] (analytic) = -18.23792427061384316533467739839
y[1] (numeric) = -18.23792427061384316533467739839
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (analytic) = -18.22706473180012683891848556109
y[1] (numeric) = -18.227064731800126838918485561088
absolute error = 2e-30
relative error = 1.0972693790408663315952966243978e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01433
Order of pole (three term test) = -27.43
Radius of convergence (six term test) for eq 1 = 0.3679
Order of pole (six term test) = -12.41
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (analytic) = -18.21620005011068461618448236814
y[1] (numeric) = -18.216200050110684616184482368139
absolute error = 1e-30
relative error = 5.4896191151234301258809224270333e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06662
Order of pole (three term test) = -7.164
Radius of convergence (six term test) for eq 1 = 0.4178
Order of pole (six term test) = -12.48
TOP MAIN SOLVE Loop
bytes used=64020232, alloc=4521156, time=2.15
x[1] = -0.28
y[1] (analytic) = -18.205330224697888037409245262597
y[1] (numeric) = -18.205330224697888037409245262596
absolute error = 1e-30
relative error = 5.4928967926292844726649112498043e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3502
Order of pole (six term test) = -12.39
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (analytic) = -18.19445525471402428683145132114
y[1] (numeric) = -18.194455254714024286831451321139
absolute error = 1e-30
relative error = 5.4961799405393505406270220450833e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01094
Order of pole (three term test) = -27.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (analytic) = -18.18357513931129618664256179719
y[1] (numeric) = -18.183575139311296186642561797189
absolute error = 1e-30
relative error = 5.4994685717116631320928017733220e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04141
Order of pole (three term test) = -29.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (analytic) = -18.172689877641822190977173382252
y[1] (numeric) = -18.17268987764182219097717338225
absolute error = 2e-30
relative error = 1.1005525398089992925715019752693e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2844
Order of pole (six term test) = -11.81
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (analytic) = -18.161799468857636379903036170341
y[1] (numeric) = -18.161799468857636379903036170339
absolute error = 2e-30
relative error = 1.1012124670958050755533131404518e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4584
Order of pole (six term test) = -11.55
TOP MAIN SOLVE Loop
bytes used=68021532, alloc=4521156, time=2.29
x[1] = -0.23
y[1] (analytic) = -18.15090391211068845341073831038
y[1] (numeric) = -18.150903912110688453410738310379
absolute error = 1e-30
relative error = 5.5093674939944873326603038826595e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (analytic) = -18.140003206552843725403057331419
y[1] (numeric) = -18.140003206552843725403057331419
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07137
Order of pole (three term test) = -24.23
Radius of convergence (six term test) for eq 1 = 0.3278
Order of pole (six term test) = -11.21
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (analytic) = -18.129097351335883117683978125549
y[1] (numeric) = -18.129097351335883117683978125548
absolute error = 1e-30
relative error = 5.5159944293989505310106944733101e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2745
Order of pole (six term test) = -12.36
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (analytic) = -18.118186345611503153947377573373
y[1] (numeric) = -18.118186345611503153947377573373
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5261
Order of pole (six term test) = -11.63
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (analytic) = -18.107270188531315953765375796921
y[1] (numeric) = -18.107270188531315953765375796922
absolute error = 1e-30
relative error = 5.5226436099317419288448990872297e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02276
Order of pole (three term test) = -0.3181
Radius of convergence (six term test) for eq 1 = 0.1843
Order of pole (six term test) = -12.53
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (analytic) = -18.096348879246849226576354024841
y[1] (numeric) = -18.09634887924684922657635402484
absolute error = 1e-30
relative error = 5.5259765750140585005892519231986e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2463
Order of pole (six term test) = -11.1
TOP MAIN SOLVE Loop
bytes used=72022508, alloc=4521156, time=2.42
x[1] = -0.17
y[1] (analytic) = -18.085422416909546265672639054744
y[1] (numeric) = -18.085422416909546265672639054744
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04096
Order of pole (three term test) = -17.03
Radius of convergence (six term test) for eq 1 = 0.3698
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (analytic) = -18.074490800670765942187854297595
y[1] (numeric) = -18.074490800670765942187854297594
absolute error = 1e-30
relative error = 5.5326593209634918488419883569738e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.111
Order of pole (three term test) = 45.86
Radius of convergence (six term test) for eq 1 = 1.359
Order of pole (six term test) = -12.36
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (analytic) = -18.063554029681782699083937388954
y[1] (numeric) = -18.063554029681782699083937388955
absolute error = 1e-30
relative error = 5.5360091284185482009872248077967e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4264
Order of pole (six term test) = -11.92
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (analytic) = -18.052612103093786545137824352002
y[1] (numeric) = -18.052612103093786545137824352002
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1295
Order of pole (three term test) = -63.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (analytic) = -18.041665020057883048927800297136
y[1] (numeric) = -18.041665020057883048927800297136
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (analytic) = -18.030712779725093332819516643072
y[1] (numeric) = -18.030712779725093332819516643072
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2329
Order of pole (six term test) = -12.23
TOP MAIN SOLVE Loop
bytes used=76023424, alloc=4521156, time=2.56
x[1] = -0.11
y[1] (analytic) = -18.019755381246354066951674844261
y[1] (numeric) = -18.019755381246354066951674844262
absolute error = 1e-30
relative error = 5.5494649002878640549070899718284e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4186
Order of pole (six term test) = -12.15
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (analytic) = -18.008792823772517463221376609506
y[1] (numeric) = -18.008792823772517463221376609507
absolute error = 1e-30
relative error = 5.5528430460921812436115228063383e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.09
y[1] (analytic) = -17.997825106454351269269140596623
y[1] (numeric) = -17.997825106454351269269140596623
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2959
Order of pole (three term test) = 12.01
Radius of convergence (six term test) for eq 1 = 0.3018
Order of pole (six term test) = -12.51
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (analytic) = -17.986852228442538762463585568025
y[1] (numeric) = -17.986852228442538762463585568025
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.006806
Order of pole (three term test) = -2.147
Radius of convergence (six term test) for eq 1 = 0.313
Order of pole (six term test) = -11.33
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (analytic) = -17.975874188887678743885779992075
y[1] (numeric) = -17.975874188887678743885779992074
absolute error = 1e-30
relative error = 5.5630117873109044194439746085453e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5284
Order of pole (six term test) = -11.71
TOP MAIN SOLVE Loop
bytes used=80024248, alloc=4521156, time=2.70
x[1] = -0.06
y[1] (analytic) = -17.964890986940285532313258075063
y[1] (numeric) = -17.964890986940285532313258075063
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2739
Order of pole (three term test) = -71.33
Radius of convergence (six term test) for eq 1 = 0.3814
Order of pole (six term test) = -11.9
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (analytic) = -17.953902621750788958203702208685
y[1] (numeric) = -17.953902621750788958203702208684
absolute error = 1e-30
relative error = 5.5698196713427657668908149671761e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (analytic) = -17.942909092469534357678291817842
y[1] (numeric) = -17.942909092469534357678291817841
absolute error = 1e-30
relative error = 5.5732322715701120136498543781684e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2419
Order of pole (three term test) = -39.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (analytic) = -17.931910398246782566504718593666
y[1] (numeric) = -17.931910398246782566504718593666
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (analytic) = -17.920906538232709914079868096589
y[1] (numeric) = -17.920906538232709914079868096589
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01783
Order of pole (three term test) = -29.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (analytic) = -17.909897511577408217412167714326
y[1] (numeric) = -17.909897511577408217412167714325
absolute error = 1e-30
relative error = 5.5835048712789944677960162367382e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02363
Order of pole (three term test) = -7.129
Radius of convergence (six term test) for eq 1 = 0.3494
Order of pole (six term test) = -11.56
TOP MAIN SOLVE Loop
bytes used=84025328, alloc=4521156, time=2.83
x[1] = 0
y[1] (analytic) = -17.898883317430884775103600959624
y[1] (numeric) = -17.898883317430884775103600959623
absolute error = 1e-30
relative error = 5.5869407172800931168569624150308e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04472
Order of pole (three term test) = -6.967
Radius of convergence (six term test) for eq 1 = 0.3643
Order of pole (six term test) = -11.1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = -17.88786395494306236133138809264
y[1] (numeric) = -17.887863954943062361331388092639
absolute error = 1e-30
relative error = 5.5903824096541382251171225029173e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005578
Order of pole (three term test) = -25.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = -17.876839423263779219829333052785
y[1] (numeric) = -17.876839423263779219829333052784
absolute error = 1e-30
relative error = 5.5938299624634080876726491598148e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.14
Order of pole (three term test) = -43.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = -17.865809721542789057868836684899
y[1] (numeric) = -17.865809721542789057868836684899
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03703
Order of pole (three term test) = -27.55
Radius of convergence (six term test) for eq 1 = 0.1744
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = -17.854774848929761040239576244611
y[1] (numeric) = -17.85477484892976104023957624461
absolute error = 1e-30
relative error = 5.6007427058647078401781373297503e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008072
Order of pole (three term test) = -24.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = -17.84373480457427978322985116772
y[1] (numeric) = -17.843734804574279783229851167718
absolute error = 2e-30
relative error = 1.1208415849619641846338796550107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1867
Order of pole (three term test) = -53.8
Radius of convergence (six term test) for eq 1 = 0.6529
Order of pole (six term test) = -9.572
TOP MAIN SOLVE Loop
bytes used=88026152, alloc=4521156, time=2.97
x[1] = 0.06
y[1] (analytic) = -17.832689587625845348606595088469
y[1] (numeric) = -17.832689587625845348606595088468
absolute error = 1e-30
relative error = 5.6076790608966965888822659040002e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00583
Order of pole (three term test) = -24.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = -17.821639197233873237595054091557
y[1] (numeric) = -17.821639197233873237595054091556
absolute error = 1e-30
relative error = 5.6111561284172540725012259202474e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07727
Order of pole (three term test) = -16.78
Radius of convergence (six term test) for eq 1 = 0.8015
Order of pole (six term test) = -9.878
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = -17.81058363254769438485813118272
y[1] (numeric) = -17.810583632547694384858131182719
absolute error = 1e-30
relative error = 5.6146391417099011362190273037582e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2799
Order of pole (six term test) = -12.54
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = -17.799522892716555152475396962759
y[1] (numeric) = -17.799522892716555152475396962757
absolute error = 2e-30
relative error = 1.1236256230319445952463500464499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = -17.788456976889617323921766489844
y[1] (numeric) = -17.788456976889617323921766489842
absolute error = 2e-30
relative error = 1.1243246126397344103672223289290e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01639
Order of pole (three term test) = -2.357
Radius of convergence (six term test) for eq 1 = 0.3001
Order of pole (six term test) = -11.55
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = -17.777385884215958098045842314954
y[1] (numeric) = -17.777385884215958098045842314952
bytes used=92027012, alloc=4521156, time=3.11
absolute error = 2e-30
relative error = 1.1250248000611517683768578108678e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = -17.766309613844570083047923675291
y[1] (numeric) = -17.76630961384457008304792367529
absolute error = 1e-30
relative error = 5.6286309410072435338858011121747e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03637
Order of pole (three term test) = -18.54
Radius of convergence (six term test) for eq 1 = 0.2475
Order of pole (six term test) = -11.65
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = -17.755228164924361290457681830526
y[1] (numeric) = -17.755228164924361290457681830525
absolute error = 1e-30
relative error = 5.6321438998768286510804927495099e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02074
Order of pole (three term test) = -30.43
Radius of convergence (six term test) for eq 1 = 0.09875
Order of pole (six term test) = -11.4
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = -17.744141536604155129111501526709
y[1] (numeric) = -17.744141536604155129111501526708
absolute error = 1e-30
relative error = 5.6356628915358526228414355527883e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03298
Order of pole (three term test) = -26.76
Radius of convergence (six term test) for eq 1 = 0.4097
Order of pole (six term test) = -11.22
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = -17.733049728032690399129488572706
y[1] (numeric) = -17.733049728032690399129488572704
absolute error = 2e-30
relative error = 1.1278375861306968607603144806453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03649
Order of pole (three term test) = -6.554
Radius of convergence (six term test) for eq 1 = 0.1761
Order of pole (six term test) = -11.83
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = -17.721952738358621285892143513994
y[1] (numeric) = -17.721952738358621285892143513992
absolute error = 2e-30
relative error = 1.1285438063893836894266422895711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08629
Order of pole (three term test) = 4.67
Radius of convergence (six term test) for eq 1 = 0.4092
Order of pole (six term test) = -12.23
TOP MAIN SOLVE Loop
bytes used=96027852, alloc=4521156, time=3.25
x[1] = 0.17
y[1] (analytic) = -17.710850566730517354016701388671
y[1] (numeric) = -17.710850566730517354016701388669
absolute error = 2e-30
relative error = 1.1292512420363144274890020518407e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.299
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03814
Order of pole (three term test) = -3.022
Radius of convergence (six term test) for eq 1 = 0.4895
Order of pole (six term test) = -12.24
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = -17.699743212296863541333137550514
y[1] (numeric) = -17.699743212296863541333137550513
absolute error = 1e-30
relative error = 5.6497994801712821887968887174386e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7357
Order of pole (six term test) = -11.39
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = -17.68863067420606015285983954394
y[1] (numeric) = -17.688630674206060152859839543938
absolute error = 2e-30
relative error = 1.1306697713557007026738741713971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01879
Order of pole (three term test) = -4.695
Radius of convergence (six term test) for eq 1 = 0.8626
Order of pole (six term test) = -9.641
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = -17.677512951606422854778945015693
y[1] (numeric) = -17.677512951606422854778945015692
absolute error = 1e-30
relative error = 5.6569043549145084663601838250640e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.002153
Order of pole (three term test) = -25.06
Radius of convergence (six term test) for eq 1 = 0.3562
Order of pole (six term test) = -11.06
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = -17.666390043646182668411345648138
y[1] (numeric) = -17.666390043646182668411345648137
absolute error = 1e-30
relative error = 5.6604659895395871727175383873576e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = -17.655261949473485964191357098956
y[1] (numeric) = -17.655261949473485964191357098954
absolute error = 2e-30
relative error = 1.1328067551326497682712764582078e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005884
Order of pole (three term test) = -1.095
Radius of convergence (six term test) for eq 1 = 0.3517
Order of pole (six term test) = -12.18
TOP MAIN SOLVE Loop
bytes used=100028816, alloc=4521156, time=3.39
x[1] = 0.23
y[1] (analytic) = -17.644128668236394455641054932112
y[1] (numeric) = -17.644128668236394455641054932111
absolute error = 1e-30
relative error = 5.6676077283444240725410574823604e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = -17.632990199082885193344276524943
y[1] (numeric) = -17.632990199082885193344276524942
absolute error = 1e-30
relative error = 5.6711878626916681641552069199931e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5622
Order of pole (three term test) = -119.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = -17.621846541160850558920288936173
y[1] (numeric) = -17.621846541160850558920288936172
absolute error = 1e-30
relative error = 5.6747741938633654226174687915256e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.115
Order of pole (six term test) = -11.8
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = -17.610697693618098258997122719726
y[1] (numeric) = -17.610697693618098258997122719725
absolute error = 1e-30
relative error = 5.6783667370679344842394676147807e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.046
Order of pole (six term test) = -10.22
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = -17.599543655602351319184571669164
y[1] (numeric) = -17.599543655602351319184571669163
absolute error = 1e-30
relative error = 5.6819655075640346528608652945226e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2819
Order of pole (six term test) = -11.6
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = -17.588384426261248078046858477586
y[1] (numeric) = -17.588384426261248078046858477584
absolute error = 2e-30
relative error = 1.1371141041321546519269546072306e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06673
Order of pole (three term test) = -3.054
NO COMPLEX POLE (six term test) for Equation 1
bytes used=104031632, alloc=4586680, time=3.53
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = -17.577220004742342181074966297828
y[1] (numeric) = -17.577220004742342181074966297827
absolute error = 1e-30
relative error = 5.6891817917179140508756494398206e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1272
Order of pole (three term test) = -44.94
Radius of convergence (six term test) for eq 1 = 0.8157
Order of pole (six term test) = -10.59
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = -17.566050390193102574658636187812
y[1] (numeric) = -17.566050390193102574658636187811
absolute error = 1e-30
relative error = 5.6927993361460866099209234810159e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1707
Order of pole (three term test) = 13.24
Radius of convergence (six term test) for eq 1 = 0.7138
Order of pole (six term test) = -14.9
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = -17.554875581760913500058030425856
y[1] (numeric) = -17.554875581760913500058030425854
absolute error = 2e-30
relative error = 1.1392846338813993637993971637661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4905
Order of pole (six term test) = -11.19
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = -17.543695578593074487375061680805
y[1] (numeric) = -17.543695578593074487375061680803
absolute error = 2e-30
relative error = 1.1400106614027276734239780747911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.805
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = -17.532510379836800349524388021811
y[1] (numeric) = -17.53251037983680034952438802181
absolute error = 1e-30
relative error = 5.7036897645305053101011028206684e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7044
Order of pole (six term test) = -12.32
TOP MAIN SOLVE Loop
bytes used=108032508, alloc=4586680, time=3.66
x[1] = 0.34
y[1] (analytic) = -17.521319984639221176204073752594
y[1] (numeric) = -17.521319984639221176204073752593
absolute error = 1e-30
relative error = 5.7073325575738056887689259980873e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = -17.510124392147382327865916055014
y[1] (numeric) = -17.510124392147382327865916055013
absolute error = 1e-30
relative error = 5.7109817018116762115568267459673e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1086
Order of pole (three term test) = -11.44
Radius of convergence (six term test) for eq 1 = 1.291
Order of pole (six term test) = -11.92
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = -17.498923601508244429685437426803
y[1] (numeric) = -17.498923601508244429685437426801
absolute error = 2e-30
relative error = 1.1429274425928796015301573624021e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03154
Order of pole (three term test) = -22.4
Radius of convergence (six term test) for eq 1 = 0.3529
Order of pole (six term test) = -10.94
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = -17.487717611868683365531543898272
y[1] (numeric) = -17.48771761186868336553154389827
absolute error = 2e-30
relative error = 1.1436598213609226913858009573505e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.926
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.001863
Order of pole (three term test) = -24.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = -17.476506422375490271935849012847
y[1] (numeric) = -17.476506422375490271935849012844
absolute error = 3e-30
relative error = 1.7165902197472632308906367141958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4855
Order of pole (six term test) = -12.27
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = -17.465290032175371532061663556235
y[1] (numeric) = -17.465290032175371532061663556233
absolute error = 2e-30
relative error = 1.1451284211802419310874612009775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1891
Order of pole (three term test) = -74.22
Radius of convergence (six term test) for eq 1 = 0.1587
Order of pole (six term test) = -11.93
TOP MAIN SOLVE Loop
bytes used=112033604, alloc=4586680, time=3.80
x[1] = 0.4
y[1] (analytic) = -17.454068440414948769672651019096
y[1] (numeric) = -17.454068440414948769672651019093
absolute error = 3e-30
relative error = 1.7187969728899944264674958444753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = -17.442841646240758843101148777995
y[1] (numeric) = -17.442841646240758843101148777993
absolute error = 2e-30
relative error = 1.1466021652676273679445690154192e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = -17.431609648799253839216154979526
y[1] (numeric) = -17.431609648799253839216154979523
absolute error = 3e-30
relative error = 1.7210114616160245365063251700936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.16
Order of pole (three term test) = 60.26
Radius of convergence (six term test) for eq 1 = 0.4907
Order of pole (six term test) = -12.78
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = -17.420372447236801067390981112378
y[1] (numeric) = -17.420372447236801067390981112377
absolute error = 1e-30
relative error = 5.7404053962039073431827623716395e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02433
Order of pole (three term test) = -28.27
Radius of convergence (six term test) for eq 1 = 0.2178
Order of pole (six term test) = -11.57
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = -17.409130040699683053470570252235
y[1] (numeric) = -17.409130040699683053470570252233
absolute error = 2e-30
relative error = 1.1488224829869895312246183279082e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01288
Order of pole (three term test) = -19.49
Radius of convergence (six term test) for eq 1 = 0.7481
Order of pole (six term test) = -11.38
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = -17.397882428334097533738480964264
y[1] (numeric) = -17.397882428334097533738480964262
absolute error = 2e-30
relative error = 1.1495651888892011258003948435669e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.002972
Order of pole (three term test) = -25.58
NO COMPLEX POLE (six term test) for Equation 1
bytes used=116035392, alloc=4586680, time=3.94
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = -17.386629609286157448883536848099
y[1] (numeric) = -17.386629609286157448883536848096
absolute error = 3e-30
relative error = 1.7254638002972739166244488441520e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.488
Order of pole (six term test) = -14.15
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = -17.375371582701890937966141710078
y[1] (numeric) = -17.375371582701890937966141710076
absolute error = 2e-30
relative error = 1.1510545201756183808088972832204e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5671
Order of pole (six term test) = -11.55
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = -17.364108347727241332384260347618
y[1] (numeric) = -17.364108347727241332384260347615
absolute error = 3e-30
relative error = 1.7277017281412350250445013011428e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08117
Order of pole (three term test) = -34.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = -17.3528399035080671498390649305
y[1] (numeric) = -17.352839903508067149839064930497
absolute error = 3e-30
relative error = 1.7288236488561835085900098642197e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4822
Order of pole (six term test) = -11.64
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = -17.341566249190142088300246963939
y[1] (numeric) = -17.341566249190142088300246963937
absolute error = 2e-30
relative error = 1.1532983649002296897700828938851e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.704
Order of pole (six term test) = -12.68
TOP MAIN SOLVE Loop
bytes used=120037176, alloc=4586680, time=4.08
x[1] = 0.51
y[1] (analytic) = -17.330287383919155019970994818231
y[1] (numeric) = -17.330287383919155019970994818229
absolute error = 2e-30
relative error = 1.1540489523882957822569669929707e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06783
Order of pole (three term test) = -17.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = -17.319003306840709985252636809814
y[1] (numeric) = -17.319003306840709985252636809812
absolute error = 2e-30
relative error = 1.1548008650186204532733555543499e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01791
Order of pole (three term test) = 0.1918
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = -17.307714017100326186708949818565
y[1] (numeric) = -17.307714017100326186708949818562
absolute error = 3e-30
relative error = 1.7333311591790499767012508185656e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = -17.296419513843437983030133426156
y[1] (numeric) = -17.296419513843437983030133426154
absolute error = 2e-30
relative error = 1.1563086790299409951643180076143e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1012
Order of pole (three term test) = -27.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = -17.285119796215394882996449560301
y[1] (numeric) = -17.285119796215394882996449560298
absolute error = 3e-30
relative error = 1.7355968806515618616406292681682e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2726
Order of pole (three term test) = -16.12
Radius of convergence (six term test) for eq 1 = 0.3468
Order of pole (six term test) = -12.3
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = -17.273814863361461539441527629686
y[1] (numeric) = -17.273814863361461539441527629684
absolute error = 2e-30
relative error = 1.1578218336947039871486493371725e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4548
Order of pole (six term test) = -12.67
TOP MAIN SOLVE Loop
bytes used=124037876, alloc=4586680, time=4.21
x[1] = 0.57
y[1] (analytic) = -17.262504714426817743215335134456
y[1] (numeric) = -17.262504714426817743215335134453
absolute error = 3e-30
relative error = 1.7378706332765289333959342268418e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = -17.251189348556558417146813737014
y[1] (numeric) = -17.251189348556558417146813737011
absolute error = 3e-30
relative error = 1.7390105339322682767781201068911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2702
Order of pole (six term test) = -11.44
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = -17.239868764895693610006180778018
y[1] (numeric) = -17.239868764895693610006180778016
absolute error = 2e-30
relative error = 1.1601016384025244645722616301529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004605
Order of pole (three term test) = -0.6797
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = -17.228542962589148490466896222348
y[1] (numeric) = -17.228542962589148490466896222346
absolute error = 2e-30
relative error = 1.1608642729352633555549790886971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = -17.217211940781763341067295019881
y[1] (numeric) = -17.217211940781763341067295019879
absolute error = 2e-30
relative error = 1.1616282629725171175455952846891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = -17.205875698618293552171884865895
y[1] (numeric) = -17.205875698618293552171884865894
absolute error = 1e-30
relative error = 5.8119680597268544572070606421822e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05885
Order of pole (three term test) = -25.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=128038680, alloc=4586680, time=4.35
x[1] = 0.63
y[1] (analytic) = -17.19453423524340961593230934592
y[1] (numeric) = -17.194534235243409615932309345917
absolute error = 3e-30
relative error = 1.7447404849448841955594858589911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02044
Order of pole (three term test) = -23.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = -17.18318754980169712024797644983
y[1] (numeric) = -17.183187549801697120247976449827
absolute error = 3e-30
relative error = 1.7458926007210004252360455794416e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004615
Order of pole (three term test) = -24.78
Radius of convergence (six term test) for eq 1 = 0.3011
Order of pole (six term test) = -12.58
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = -17.171835641437656742726352440042
y[1] (numeric) = -17.17183564143765674272635244004
absolute error = 2e-30
relative error = 1.1646978469638767336276179999816e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01892
Order of pole (three term test) = -23.37
Radius of convergence (six term test) for eq 1 = 0.1941
Order of pole (six term test) = -11.57
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = -17.160478509295704244642921058588
y[1] (numeric) = -17.160478509295704244642921058585
absolute error = 3e-30
relative error = 1.7482029993364824855303640893384e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02114
Order of pole (three term test) = -25.31
Radius of convergence (six term test) for eq 1 = 0.6293
Order of pole (six term test) = -12.35
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = -17.149116152520170464900808057895
y[1] (numeric) = -17.149116152520170464900808057892
absolute error = 3e-30
relative error = 1.7493612926279767099179786829431e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01121
Order of pole (three term test) = -20.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=132039468, alloc=4586680, time=4.49
x[1] = 0.68
y[1] (analytic) = -17.137748570255301313990071040103
y[1] (numeric) = -17.137748570255301313990071040101
absolute error = 2e-30
relative error = 1.1670144370487785538083701616975e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9383
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = -17.126375761645257767946654589717
y[1] (numeric) = -17.126375761645257767946654589715
absolute error = 2e-30
relative error = 1.1677893956285988568965229040478e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0276
Order of pole (three term test) = -26.24
Radius of convergence (six term test) for eq 1 = 0.3914
Order of pole (six term test) = -11.42
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = -17.114997725834115862311010684406
y[1] (numeric) = -17.114997725834115862311010684403
absolute error = 3e-30
relative error = 1.7528486115260597365283192230790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6798
Order of pole (six term test) = -12.96
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = -17.103614461965866686086384368771
y[1] (numeric) = -17.103614461965866686086384368768
absolute error = 3e-30
relative error = 1.7540152151296703119024783295129e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1443
Order of pole (six term test) = -11.92
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = -17.092225969184416375696764675903
y[1] (numeric) = -17.092225969184416375696764675901
absolute error = 2e-30
relative error = 1.1701226063859681604826931715820e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = -17.080832246633586108944500781519
y[1] (numeric) = -17.080832246633586108944500781517
absolute error = 2e-30
relative error = 1.1709031334782732599942061053824e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1097
Order of pole (three term test) = -35.69
Radius of convergence (six term test) for eq 1 = 0.1432
Order of pole (six term test) = -12.07
TOP MAIN SOLVE Loop
bytes used=136040472, alloc=4586680, time=4.63
x[1] = 0.74
y[1] (analytic) = -17.069433293457112098967583375504
y[1] (numeric) = -17.069433293457112098967583375502
absolute error = 2e-30
relative error = 1.1716850616046054682666702730471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = -17.058029108798645588196591235676
y[1] (numeric) = -17.058029108798645588196591235672
absolute error = 4e-30
relative error = 2.3449367887036687180626619386838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04169
Order of pole (three term test) = 1.875
Radius of convergence (six term test) for eq 1 = 2.086
Order of pole (six term test) = -15.05
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = -17.046619691801752842311302988558
y[1] (numeric) = -17.046619691801752842311302988556
absolute error = 2e-30
relative error = 1.1732531353191752838763559080621e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2908
Order of pole (three term test) = -36.18
Radius of convergence (six term test) for eq 1 = 1.212
Order of pole (six term test) = -10.9
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = -17.035205041609915144196974042016
y[1] (numeric) = -17.035205041609915144196974042012
absolute error = 4e-30
relative error = 2.3480785762364849551791725200859e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.029
Order of pole (three term test) = 343.6
Radius of convergence (six term test) for eq 1 = 0.9533
Order of pole (six term test) = -12.45
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = -17.023785157366528787900278674497
y[1] (numeric) = -17.023785157366528787900278674492
absolute error = 5e-30
relative error = 2.9370671409327560947468188227370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.304
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = -17.012360038214905072584917265759
y[1] (numeric) = -17.012360038214905072584917265755
absolute error = 4e-30
relative error = 2.3512316874406551625289914109908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=140041408, alloc=4586680, time=4.76
x[1] = 0.8
y[1] (analytic) = -17.000929683298270296486888653848
y[1] (numeric) = -17.000929683298270296486888653844
absolute error = 4e-30
relative error = 2.3528125076181003527873181685829e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = -16.989494091759765750869427603131
y[1] (numeric) = -16.989494091759765750869427603127
absolute error = 4e-30
relative error = 2.3543961806020331143008597213012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01949
Order of pole (three term test) = -8.11
Radius of convergence (six term test) for eq 1 = 0.2653
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = -16.978053262742447713977607368223
y[1] (numeric) = -16.97805326274244771397760736822
absolute error = 3e-30
relative error = 1.7669870353059624248343943260477e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = -16.96660719538928744499260733859
y[1] (numeric) = -16.966607195389287444992607338587
absolute error = 3e-30
relative error = 1.7681790858075953753697188121896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02558
Order of pole (three term test) = -2.909
Radius of convergence (six term test) for eq 1 = 0.792
Order of pole (six term test) = -11.51
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = -16.955155888843171177985645748631
y[1] (numeric) = -16.955155888843171177985645748627
absolute error = 4e-30
relative error = 2.3591643900083981688611668590483e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04063
Order of pole (three term test) = -15.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=144042532, alloc=4586680, time=4.90
x[1] = 0.85
y[1] (analytic) = -16.943699342246900115871577438062
y[1] (numeric) = -16.943699342246900115871577438058
absolute error = 4e-30
relative error = 2.3607595479615969801633741083011e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2084
Order of pole (six term test) = -11.51
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = -16.932237554743190424362156647396
y[1] (numeric) = -16.932237554743190424362156647394
absolute error = 2e-30
relative error = 1.1811787978605015517590860635221e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7084
Order of pole (six term test) = -12.46
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = -16.92077052547467322591896483333
y[1] (numeric) = -16.920770525474673225918964833327
absolute error = 3e-30
relative error = 1.7729689055728399892201554157711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03333
Order of pole (three term test) = -20.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = -16.909298253583894593706003488816
y[1] (numeric) = -16.909298253583894593706003488813
absolute error = 3e-30
relative error = 1.7741717929448405881041987531013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08198
Order of pole (three term test) = -31.81
Radius of convergence (six term test) for eq 1 = 0.2372
Order of pole (six term test) = -12.07
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = -16.897820738213315545541951952668
y[1] (numeric) = -16.897820738213315545541951952664
absolute error = 4e-30
relative error = 2.3671691527382947208534619545464e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05752
Order of pole (three term test) = -15.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = -16.886337978505312037852090193456
y[1] (numeric) = -16.886337978505312037852090193452
absolute error = 4e-30
relative error = 2.3687788347548273583292801825750e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7434
Order of pole (six term test) = -11.48
TOP MAIN SOLVE Loop
bytes used=148043608, alloc=4586680, time=5.03
x[1] = 0.91
y[1] (analytic) = -16.874849973602174959619886552531
y[1] (numeric) = -16.874849973602174959619886552526
absolute error = 5e-30
relative error = 2.9629893052807268377092565104594e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02142
Order of pole (three term test) = -24.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = -16.863356722646110126338250430944
y[1] (numeric) = -16.863356722646110126338250430939
absolute error = 5e-30
relative error = 2.9650087359448481357355145653239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4119
Order of pole (three term test) = -53.22
Radius of convergence (six term test) for eq 1 = 0.2664
Order of pole (six term test) = -11.43
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = -16.851858224779238273960449905093
y[1] (numeric) = -16.85185822477923827396044990509
absolute error = 3e-30
relative error = 1.7802191069877105047142178569121e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = -16.840354479143595052850694255885
y[1] (numeric) = -16.840354479143595052850694255882
absolute error = 3e-30
relative error = 1.7814351851770301871704691235797e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06735
Order of pole (three term test) = -19.9
Radius of convergence (six term test) for eq 1 = 0.3506
Order of pole (six term test) = -11.97
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = -16.828845484881131021734381396194
y[1] (numeric) = -16.828845484881131021734381396189
absolute error = 5e-30
relative error = 2.9710891365019369497165517702449e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = -16.817331241133711641648010181442
y[1] (numeric) = -16.817331241133711641648010181438
absolute error = 4e-30
relative error = 2.3784986705954581868306955757369e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.035
Order of pole (three term test) = -26.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=152044924, alloc=4586680, time=5.17
x[1] = 0.97
y[1] (analytic) = -16.805811747043117269888757588104
y[1] (numeric) = -16.805811747043117269888757588099
absolute error = 5e-30
relative error = 2.9751612568668218564167579451328e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = -16.794287001751043153963720744886
y[1] (numeric) = -16.794287001751043153963720744883
absolute error = 3e-30
relative error = 1.7863217412487992818158780440648e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003087
Order of pole (three term test) = -0.8811
Radius of convergence (six term test) for eq 1 = 0.9427
Order of pole (six term test) = -13.32
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = -16.782757004399099425538823801448
y[1] (numeric) = -16.782757004399099425538823801445
absolute error = 3e-30
relative error = 1.7875489701803103239924930555818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05188
Order of pole (three term test) = -19.62
Radius of convergence (six term test) for eq 1 = 1.261
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = -16.771221754128811094387389619393
y[1] (numeric) = -16.77122175412881109438738961939
absolute error = 3e-30
relative error = 1.7887784467827736940823790110642e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = -16.759681250081618042338376270378
y[1] (numeric) = -16.759681250081618042338376270373
absolute error = 5e-30
relative error = 2.9833502949082939622923895125520e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03538
Order of pole (three term test) = -5.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=156045808, alloc=4586680, time=5.31
x[1] = 1.02
y[1] (analytic) = -16.748135491398875017224278326097
y[1] (numeric) = -16.748135491398875017224278326092
absolute error = 5e-30
relative error = 2.9854069442940593746879920641871e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1964
Order of pole (six term test) = -11.51
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = -16.736584477221851626828692924975
y[1] (numeric) = -16.736584477221851626828692924971
absolute error = 4e-30
relative error = 2.3899738954766535549217600322781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01223
Order of pole (three term test) = -1.335
Radius of convergence (six term test) for eq 1 = 0.7345
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = -16.725028206691732332833550600323
y[1] (numeric) = -16.725028206691732332833550600319
absolute error = 4e-30
relative error = 2.3916252639858558739508895048110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.59
Order of pole (three term test) = -3871
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = -16.713466678949616444766010854774
y[1] (numeric) = -16.713466678949616444766010854769
absolute error = 5e-30
relative error = 2.9915995861573301685096288522790e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08915
Order of pole (three term test) = -37.75
Radius of convergence (six term test) for eq 1 = 0.05455
Order of pole (six term test) = -12.04
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = -16.701899893136518113945022465788
y[1] (numeric) = -16.701899893136518113945022465783
absolute error = 5e-30
relative error = 2.9936713978597733909308987361620e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09741
Order of pole (three term test) = 11.74
Radius of convergence (six term test) for eq 1 = 0.483
Order of pole (six term test) = -12.35
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = -16.69032784839336632742754850702
y[1] (numeric) = -16.690327848393366327427548507015
absolute error = 5e-30
relative error = 2.9957470251138936162393437332025e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3836
Order of pole (three term test) = -82.58
Radius of convergence (six term test) for eq 1 = 0.1899
Order of pole (six term test) = -11.33
TOP MAIN SOLVE Loop
bytes used=160046780, alloc=4586680, time=5.44
x[1] = 1.08
y[1] (analytic) = -16.678750543861004901954456070335
y[1] (numeric) = -16.678750543861004901954456070329
absolute error = 6e-30
relative error = 3.5973917735752916134193325714446e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3127
Order of pole (six term test) = -11.95
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = -16.667167978680192477896070673262
y[1] (numeric) = -16.667167978680192477896070673258
absolute error = 4e-30
relative error = 2.3999278132413376432786364408377e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.81
Order of pole (three term test) = -1293
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = -16.655580151991602513197395336702
y[1] (numeric) = -16.655580151991602513197395336697
absolute error = 5e-30
relative error = 3.0019969009618206200661011346985e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1606
Order of pole (six term test) = -11.96
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = -16.643987062935823277322994317626
y[1] (numeric) = -16.643987062935823277322994317622
absolute error = 4e-30
relative error = 2.4032703131015545906761318590544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.07475
Order of pole (six term test) = -11.33
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = -16.632388710653357845201541481626
y[1] (numeric) = -16.63238871065335784520154148162
absolute error = 6e-30
relative error = 3.6074192976002822327606255962092e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = -16.620785094284624091170033300026
y[1] (numeric) = -16.620785094284624091170033300021
absolute error = 5e-30
relative error = 3.0082814810711594787356607102651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0116
Order of pole (three term test) = -1.796
Radius of convergence (six term test) for eq 1 = 0.6544
Order of pole (six term test) = -9.881
TOP MAIN SOLVE Loop
bytes used=164047556, alloc=4586680, time=5.58
x[1] = 1.14
y[1] (analytic) = -16.609176212969954682917666456428
y[1] (numeric) = -16.609176212969954682917666456422
absolute error = 6e-30
relative error = 3.6124609210387295162969409400557e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6179
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = -16.597562065849597075429380047394
y[1] (numeric) = -16.59756206584959707542938004739
absolute error = 4e-30
relative error = 2.4099924941568505847402344062650e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1681
Order of pole (three term test) = -55.79
Radius of convergence (six term test) for eq 1 = 0.8289
Order of pole (six term test) = -11.54
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = -16.58594265206371350492906236213
y[1] (numeric) = -16.585942652063713504929062362126
absolute error = 4e-30
relative error = 2.4116808335294094179366271902042e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6676
Order of pole (six term test) = -10.34
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = -16.574317970752380982822422225888
y[1] (numeric) = -16.574317970752380982822422225885
absolute error = 3e-30
relative error = 1.8100292303393144344714169945448e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7395
Order of pole (six term test) = -10.62
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = -16.562688021055591289639524891937
y[1] (numeric) = -16.562688021055591289639524891933
absolute error = 4e-30
relative error = 2.4150669232644687822783429991271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2284
Order of pole (three term test) = -88.35
Radius of convergence (six term test) for eq 1 = 0.8431
Order of pole (six term test) = -11.72
TOP MAIN SOLVE Loop
bytes used=168048392, alloc=4586680, time=5.72
x[1] = 1.19
y[1] (analytic) = -16.55105280211325096897699246683
y[1] (numeric) = -16.551052802113250968976992466826
absolute error = 4e-30
relative error = 2.4167646903339447794138152985101e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = -16.539412313065181321439868853802
y[1] (numeric) = -16.539412313065181321439868853798
absolute error = 4e-30
relative error = 2.4184656167258317998281661732266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = -16.527766553051118398583149199045
y[1] (numeric) = -16.52776655305111839858314919904
absolute error = 5e-30
relative error = 3.0252121385856408762225816523515e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05078
Order of pole (three term test) = -36.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = -16.516115521210712996852973825661
y[1] (numeric) = -16.516115521210712996852973825657
absolute error = 4e-30
relative error = 2.4218769812205698390548197424680e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = -16.504459216683530651527486640086
y[1] (numeric) = -16.50445921668353065152748664008
absolute error = 6e-30
relative error = 3.6353811544063804938531867999808e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.116
Order of pole (three term test) = 8.949
Radius of convergence (six term test) for eq 1 = 2.34
Order of pole (six term test) = -11.76
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = -16.492797638609051630657357995728
y[1] (numeric) = -16.492797638609051630657357995724
absolute error = 4e-30
relative error = 2.4253010845389520336529392155174e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=172049256, alloc=4586680, time=5.85
x[1] = 1.25
y[1] (analytic) = -16.481130786126670929005971998672
y[1] (numeric) = -16.481130786126670929005971998667
absolute error = 5e-30
relative error = 3.0337724182183253520716033299717e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1192
Order of pole (three term test) = -37.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = -16.469458658375698261989278240135
y[1] (numeric) = -16.46945865837569826198927824013
absolute error = 5e-30
relative error = 3.0359224936984816587153258769076e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02233
Order of pole (three term test) = -25.63
Radius of convergence (six term test) for eq 1 = 0.0354
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = -16.457781254495358059615307940556
y[1] (numeric) = -16.45778125449535805961530794055
absolute error = 6e-30
relative error = 3.6456919114544258195781408443986e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.78
Order of pole (three term test) = -1815
Radius of convergence (six term test) for eq 1 = 0.6782
Order of pole (six term test) = -9.858
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = -16.446098573624789460423354490017
y[1] (numeric) = -16.446098573624789460423354490011
absolute error = 6e-30
relative error = 3.6482816718747020769639522502355e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04345
Order of pole (three term test) = -25.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = -16.434410614903046305422818369828
y[1] (numeric) = -16.434410614903046305422818369823
absolute error = 5e-30
relative error = 3.0423969055914313128148206564768e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3257
Order of pole (three term test) = 28.5
Radius of convergence (six term test) for eq 1 = 0.3197
Order of pole (six term test) = -12.22
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = -16.422717377469097132031716440028
y[1] (numeric) = -16.422717377469097132031716440023
absolute error = 5e-30
relative error = 3.0445631408476137086688238911871e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8957
Order of pole (six term test) = -12.37
TOP MAIN SOLVE Loop
bytes used=176050004, alloc=4586680, time=5.99
x[1] = 1.31
y[1] (analytic) = -16.411018860461825168014855577587
y[1] (numeric) = -16.411018860461825168014855577581
absolute error = 6e-30
relative error = 3.6560801319017879782516246176186e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = -16.39931506302002832542167065009
y[1] (numeric) = -16.399315063020028325421670650085
absolute error = 5e-30
relative error = 3.0489078237632329511837120256985e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6609
Order of pole (six term test) = -12.41
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = -16.387605984282419194523726809684
y[1] (numeric) = -16.387605984282419194523726809679
absolute error = 5e-30
relative error = 3.0510862933826756245374273410436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.239
Order of pole (six term test) = -11.74
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = -16.375891623387625037751886092046
y[1] (numeric) = -16.375891623387625037751886092041
absolute error = 5e-30
relative error = 3.0532688631494906017341209400536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = -16.364171979474187783633138305171
y[1] (numeric) = -16.364171979474187783633138305166
absolute error = 5e-30
relative error = 3.0554555441433704518959987756386e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.606
Order of pole (six term test) = -8.465
TOP MAIN SOLVE Loop
bytes used=180051176, alloc=4586680, time=6.13
x[1] = 1.36
y[1] (analytic) = -16.352447051680564020727096192741
y[1] (numeric) = -16.352447051680564020727096192736
absolute error = 5e-30
relative error = 3.0576463474842090719572406563767e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8042
Order of pole (six term test) = -12.56
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = -16.340716839145124991562154856854
y[1] (numeric) = -16.34071683914512499156215485685
absolute error = 4e-30
relative error = 2.4478730274658272259131578333863e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = -16.328981341006156586571315424893
y[1] (numeric) = -16.328981341006156586571315424888
absolute error = 5e-30
relative error = 3.0620403658884399164555665751110e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02018
Order of pole (three term test) = 1.046
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = -16.317240556401859338027672945286
y[1] (numeric) = -16.317240556401859338027672945282
absolute error = 4e-30
relative error = 2.4513948827154181274170802334563e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.156
Order of pole (three term test) = -11.34
Radius of convergence (six term test) for eq 1 = 0.7809
Order of pole (six term test) = -12.2
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = -16.305494484470348413979568496975
y[1] (numeric) = -16.305494484470348413979568496971
absolute error = 4e-30
relative error = 2.4531608065058519144891167860359e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = -16.293743124349653612185405497309
y[1] (numeric) = -16.293743124349653612185405497306
absolute error = 3e-30
relative error = 1.8411975548557333831819255416512e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00397
Order of pole (three term test) = -23.59
Radius of convergence (six term test) for eq 1 = 0.7802
Order of pole (six term test) = -11.69
TOP MAIN SOLVE Loop
bytes used=184052172, alloc=4586680, time=6.27
x[1] = 1.42
y[1] (analytic) = -16.281986475177719354048130193184
y[1] (numeric) = -16.281986475177719354048130193181
absolute error = 3e-30
relative error = 1.8425270187845766091268895983100e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5979
Order of pole (six term test) = -11.22
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = -16.27022453609240467854937632017
y[1] (numeric) = -16.270224536092404678549376320166
absolute error = 4e-30
relative error = 2.4584786713463967814447461546249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03977
Order of pole (three term test) = -15.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = -16.258457306231483236183273914403
y[1] (numeric) = -16.258457306231483236183273914399
absolute error = 4e-30
relative error = 2.4602580212003843306956540906576e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6372
Order of pole (six term test) = -11.94
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = -16.246684784732643282889922262025
y[1] (numeric) = -16.246684784732643282889922262022
absolute error = 3e-30
relative error = 1.8465305628500677745701101316035e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.639
Order of pole (six term test) = -11.02
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = -16.234906970733487673988526970928
y[1] (numeric) = -16.234906970733487673988526970924
absolute error = 4e-30
relative error = 2.4638268683711966697649622776611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009289
Order of pole (three term test) = -25.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = -16.223123863371533858110201149559
y[1] (numeric) = -16.223123863371533858110201149556
absolute error = 3e-30
relative error = 1.8492122881298964674080111004077e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4921
Order of pole (six term test) = -11.39
TOP MAIN SOLVE Loop
bytes used=188052996, alloc=4586680, time=6.40
x[1] = 1.48
y[1] (analytic) = -16.211335461784213871130430677602
y[1] (numeric) = -16.211335461784213871130430677598
absolute error = 4e-30
relative error = 2.4674093071662101111315675870520e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = -16.199541765108874330101203553234
y[1] (numeric) = -16.19954176510887433010120355323
absolute error = 4e-30
relative error = 2.4692056466778192777686784966391e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0194
Order of pole (three term test) = -24.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = -16.187742772482776427182803301796
y[1] (numeric) = -16.187742772482776427182803301791
absolute error = 5e-30
relative error = 3.0887567650873480932103865289633e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4202
Order of pole (six term test) = -12.45
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = -16.175938483043095923575266430585
y[1] (numeric) = -16.17593848304309592357526643058
absolute error = 5e-30
relative error = 3.0910107659233480058642877345211e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4547
Order of pole (six term test) = -12.71
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = -16.164128895926923143449503914574
y[1] (numeric) = -16.164128895926923143449503914568
absolute error = 6e-30
relative error = 3.7119228871726547048905950121049e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4631
Order of pole (three term test) = -58.05
Radius of convergence (six term test) for eq 1 = 0.7276
Order of pole (six term test) = -11.99
TOP MAIN SOLVE Loop
bytes used=192053744, alloc=4586680, time=6.54
x[1] = 1.53
y[1] (analytic) = -16.152314010271262967878086697801
y[1] (numeric) = -16.152314010271262967878086697795
absolute error = 6e-30
relative error = 3.7146380364971839884152267875062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09735
Order of pole (three term test) = -20.48
Radius of convergence (six term test) for eq 1 = 0.7761
Order of pole (six term test) = -10.89
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = -16.140493825213034828765695195208
y[1] (numeric) = -16.140493825213034828765695195204
absolute error = 4e-30
relative error = 2.4782389208882863158524260755192e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07844
Order of pole (three term test) = 9.545
Radius of convergence (six term test) for eq 1 = 0.6923
Order of pole (six term test) = -12.4
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = -16.128668339889072702779232779686
y[1] (numeric) = -16.128668339889072702779232779682
absolute error = 4e-30
relative error = 2.4800559573212171281030821318688e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = -16.116837553436125105277603239084
y[1] (numeric) = -16.116837553436125105277603239078
absolute error = 6e-30
relative error = 3.7228147148016605091470400659026e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3903
Order of pole (six term test) = -11.99
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = -16.105001464990855084241152187956
y[1] (numeric) = -16.10500146499085508424115218795
absolute error = 6e-30
relative error = 3.7255507322013192904482169725521e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8336
Order of pole (three term test) = -119.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = -16.093160073689840214200772418816
y[1] (numeric) = -16.093160073689840214200772418811
absolute error = 5e-30
relative error = 3.1069100022029420187062722799402e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01016
Order of pole (three term test) = -0.1528
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=196054736, alloc=4586680, time=6.68
x[1] = 1.59
y[1] (analytic) = -16.081313378669572590166673177636
y[1] (numeric) = -16.081313378669572590166673177632
absolute error = 4e-30
relative error = 2.4873590270964081310469069446816e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07117
Order of pole (three term test) = -27.49
Radius of convergence (six term test) for eq 1 = 0.7437
Order of pole (six term test) = -10.81
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = -16.069461379066458821556813348372
y[1] (numeric) = -16.069461379066458821556813348368
absolute error = 4e-30
relative error = 2.4891935738498140441285259035288e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9879
Order of pole (six term test) = -12.34
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = -16.05760407401682002612499853127
y[1] (numeric) = -16.057604074016820026124998531265
absolute error = 5e-30
relative error = 3.1137895647150844042023640989329e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05945
Order of pole (three term test) = -36.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = -16.045741462656891823888641999707
y[1] (numeric) = -16.045741462656891823888641999704
absolute error = 3e-30
relative error = 1.8696549529866679680327354926441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.42
Order of pole (six term test) = -9.106
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = -16.033873544122824331056189520355
y[1] (numeric) = -16.033873544122824331056189520351
absolute error = 4e-30
relative error = 2.4947184403023995731967534907575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01383
Order of pole (three term test) = -22.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = -16.022000317550682153954208021369
y[1] (numeric) = -16.022000317550682153954208021366
absolute error = 3e-30
relative error = 1.8724253779434554956734604775838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=200058144, alloc=4586680, time=6.82
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = -16.01012178207644438295413809343
y[1] (numeric) = -16.010121782076444382954138093426
absolute error = 4e-30
relative error = 2.4984194714109270768036302636368e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.479
Order of pole (three term test) = -309.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = -15.998237936836004586398710308338
y[1] (numeric) = -15.998237936836004586398710308333
absolute error = 5e-30
relative error = 3.1253441908670958725488817850549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = -15.986348780965170804528025339951
y[1] (numeric) = -15.986348780965170804528025339947
absolute error = 4e-30
relative error = 2.5021348244089175013287590538364e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1699
Order of pole (six term test) = -12.02
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = -15.97445431359966554340529787222
y[1] (numeric) = -15.974454313599665543405297872214
absolute error = 6e-30
relative error = 3.7559968448449409084367434335695e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5806
Order of pole (six term test) = -11.27
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = -15.962554533875125768842264279046
y[1] (numeric) = -15.962554533875125768842264279041
absolute error = 5e-30
relative error = 3.1323307240010928560873031350723e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02596
Order of pole (three term test) = -21.87
Radius of convergence (six term test) for eq 1 = 0.7056
Order of pole (six term test) = -11.4
TOP MAIN SOLVE Loop
bytes used=204058848, alloc=4586680, time=6.95
x[1] = 1.7
y[1] (analytic) = -15.950649440927102900324254060774
y[1] (numeric) = -15.95064944092710290032425406077
absolute error = 4e-30
relative error = 2.5077348824033256239176412258646e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.535
Order of pole (six term test) = 0.6553
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = -15.938739033891062804934925022016
y[1] (numeric) = -15.938739033891062804934925022012
absolute error = 4e-30
relative error = 2.5096088162900898240001402503792e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.026
Order of pole (six term test) = -12.1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = -15.926823311902385791280662175595
y[1] (numeric) = -15.926823311902385791280662175591
absolute error = 4e-30
relative error = 2.5114863910185604975316035736031e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = -15.91490227409636660341464035736
y[1] (numeric) = -15.914902274096366603414640357355
absolute error = 5e-30
relative error = 3.1417095209803261984232331941447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = -15.902975919608214414760550536609
y[1] (numeric) = -15.902975919608214414760550536603
absolute error = 6e-30
relative error = 3.7728787557315347749927150269034e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03594
Order of pole (three term test) = -39.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = -15.891044247573052822035989806889
y[1] (numeric) = -15.891044247573052822035989806885
absolute error = 4e-30
relative error = 2.5171410624011677771227554551580e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.599
Order of pole (six term test) = -12.24
TOP MAIN SOLVE Loop
bytes used=208060064, alloc=4586680, time=7.09
x[1] = 1.76
y[1] (analytic) = -15.879107257125919839175515041926
y[1] (numeric) = -15.879107257125919839175515041923
absolute error = 3e-30
relative error = 1.8892749771267637202232844048191e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3072
Order of pole (six term test) = -11.13
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = -15.867164947401767891253360201413
y[1] (numeric) = -15.867164947401767891253360201409
absolute error = 4e-30
relative error = 2.5209292354744165739253720842908e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04588
Order of pole (three term test) = -24.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = -15.855217317535463808405817271434
y[1] (numeric) = -15.855217317535463808405817271429
absolute error = 5e-30
relative error = 3.1535360883827988944473048203458e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.373
Order of pole (three term test) = -321.3
Radius of convergence (six term test) for eq 1 = 1.336
Order of pole (six term test) = -14.07
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = -15.843264366661788819753280824264
y[1] (numeric) = -15.84326436666178881975328082426
absolute error = 4e-30
relative error = 2.5247322189592478106491931787360e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = -15.831306093915438547321956182299
y[1] (numeric) = -15.831306093915438547321956182293
absolute error = 6e-30
relative error = 3.7899589360514125899903556511445e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = -15.819342498431022999965231170839
y[1] (numeric) = -15.819342498431022999965231170834
absolute error = 5e-30
relative error = 3.1606876205480124209292802334903e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02851
Order of pole (three term test) = -25.27
NO COMPLEX POLE (six term test) for Equation 1
bytes used=212062592, alloc=4586680, time=7.23
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = -15.807373579343066567284711444525
y[1] (numeric) = -15.807373579343066567284711444522
absolute error = 3e-30
relative error = 1.8978484850388890549678593312350e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.061
Order of pole (six term test) = -13.03
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = -15.795399335786008013550919372129
y[1] (numeric) = -15.795399335786008013550919372124
absolute error = 5e-30
relative error = 3.1654786901601249312643271654565e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02097
Order of pole (three term test) = -26.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = -15.783419766894200471623656464452
y[1] (numeric) = -15.783419766894200471623656464446
absolute error = 6e-30
relative error = 3.8014575349412103369004617521510e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04698
Order of pole (three term test) = 2.083
Radius of convergence (six term test) for eq 1 = 0.3129
Order of pole (six term test) = -12.13
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = -15.771434871801911436872029330114
y[1] (numeric) = -15.771434871801911436872029330109
absolute error = 5e-30
relative error = 3.1702885886049644342859864763400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.123
Order of pole (six term test) = -13.39
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = -15.75944464964332276109413914394
y[1] (numeric) = -15.759444649643322761094139143934
absolute error = 6e-30
relative error = 3.8072407584081940426472382261476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4459
Order of pole (three term test) = -67.72
Radius of convergence (six term test) for eq 1 = 0.4663
Order of pole (six term test) = -11.78
TOP MAIN SOLVE Loop
bytes used=216063552, alloc=4586680, time=7.36
x[1] = 1.87
y[1] (analytic) = -15.747449099552530646436434612696
y[1] (numeric) = -15.747449099552530646436434612692
absolute error = 4e-30
relative error = 2.5400939382072118710655373447090e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.108
Order of pole (three term test) = -23.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = -15.735448220663545639312728422948
y[1] (numeric) = -15.735448220663545639312728422944
absolute error = 4e-30
relative error = 2.5420311794787404089503521054823e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08372
Order of pole (three term test) = 0.02676
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = -15.723442012110292624322877155743
y[1] (numeric) = -15.723442012110292624322877155739
absolute error = 4e-30
relative error = 2.5439722402506875875148680344144e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = -15.711430473026610818171124652897
y[1] (numeric) = -15.711430473026610818171124652894
absolute error = 3e-30
relative error = 1.9094378485462549197765381701338e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = -15.699413602546253763584108819617
y[1] (numeric) = -15.699413602546253763584108819614
absolute error = 3e-30
relative error = 1.9108993978688710523777639510450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04181
Order of pole (three term test) = -22.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = -15.687391399802889323228531848186
y[1] (numeric) = -15.687391399802889323228531848181
absolute error = 5e-30
relative error = 3.1872730606204066247772945211661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.63
Order of pole (six term test) = -28.69
TOP MAIN SOLVE Loop
bytes used=220064556, alloc=4586680, time=7.50
x[1] = 1.93
y[1] (analytic) = -15.675363863930099673628493847471
y[1] (numeric) = -15.675363863930099673628493847467
absolute error = 4e-30
relative error = 2.5517748964055798518773934812024e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05525
Order of pole (three term test) = -2.555
Radius of convergence (six term test) for eq 1 = 0.822
Order of pole (six term test) = -12.09
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = -15.663330994061381299082489863012
y[1] (numeric) = -15.663330994061381299082489863007
absolute error = 5e-30
relative error = 3.1921690232401444276382529186464e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1077
Order of pole (three term test) = 14.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = -15.651292789330144985580070272372
y[1] (numeric) = -15.651292789330144985580070272368
absolute error = 4e-30
relative error = 2.5556994261374333459100982382022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03111
Order of pole (three term test) = -26.65
Radius of convergence (six term test) for eq 1 = 0.9129
Order of pole (six term test) = -11.48
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = -15.639249248869715814718164540567
y[1] (numeric) = -15.639249248869715814718164540562
absolute error = 5e-30
relative error = 3.1970844127069343786239427523858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = -15.627200371813333157617068320243
y[1] (numeric) = -15.62720037181333315761706832024
absolute error = 3e-30
relative error = 1.9197296563823920919253553664106e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04042
Order of pole (three term test) = -30.08
Radius of convergence (six term test) for eq 1 = 0.2396
Order of pole (six term test) = -11.17
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = -15.61514615729415066883609388141
y[1] (numeric) = -15.615146157294150668836093881406
absolute error = 4e-30
relative error = 2.5616154723800129650940501673004e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.147
Order of pole (six term test) = -9.621
bytes used=224065364, alloc=4586680, time=7.64
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = -15.603086604445236280288883855391
y[1] (numeric) = -15.603086604445236280288883855388
absolute error = 3e-30
relative error = 1.9226964997716003039572205308140e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.181
Order of pole (six term test) = -12.43
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = -15.59102171239957219515838827781
y[1] (numeric) = -15.591021712399572195158388277807
absolute error = 3e-30
relative error = 1.9241843513142526906421349143729e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 29.32
Order of pole (six term test) = -459.2
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = -15.578951480290054881811504915282
y[1] (numeric) = -15.578951480290054881811504915279
absolute error = 3e-30
relative error = 1.9256751674177143349641721156246e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07614
Order of pole (three term test) = -26.4
Radius of convergence (six term test) for eq 1 = 0.4869
Order of pole (six term test) = -11.6
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = -15.566875907249495067713382860592
y[1] (numeric) = -15.566875907249495067713382860589
absolute error = 3e-30
relative error = 1.9271689566195487017620687390263e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5896
Order of pole (six term test) = -12.11
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = -15.554794992410617733341389381074
y[1] (numeric) = -15.55479499241061773334138938107
absolute error = 4e-30
relative error = 2.5715543033203914694709520058536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02382
Order of pole (three term test) = 0.3144
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=228066096, alloc=4586680, time=7.78
x[1] = 2.04
y[1] (analytic) = -15.542708734906062106098740004929
y[1] (numeric) = -15.542708734906062106098740004925
absolute error = 4e-30
relative error = 2.5735539848448272579160261962056e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = -15.530617133868381654227791830233
y[1] (numeric) = -15.530617133868381654227791830229
absolute error = 4e-30
relative error = 2.5755576649153258715119572934092e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = -15.518520188430044080723000041343
y[1] (numeric) = -15.51852018843004408072300004134
absolute error = 3e-30
relative error = 1.9331740163193355351695445737074e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04031
Order of pole (three term test) = -26.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = -15.506417897723431317243537617461
y[1] (numeric) = -15.506417897723431317243537617458
absolute error = 3e-30
relative error = 1.9346828002361808057607725241436e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01084
Order of pole (three term test) = -23.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = -15.494310260880839518025578218066
y[1] (numeric) = -15.494310260880839518025578218063
absolute error = 3e-30
relative error = 1.9361946091748470818119983167809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7153
Order of pole (six term test) = -11.76
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = -15.482197277034479053794242229966
y[1] (numeric) = -15.482197277034479053794242229963
absolute error = 3e-30
relative error = 1.9377094519070950610759410776241e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=232067292, alloc=4586680, time=7.91
x[1] = 2.1
y[1] (analytic) = -15.470078945316474505675205960693
y[1] (numeric) = -15.47007894531647450567520596069
absolute error = 3e-30
relative error = 1.9392273372387941609858091576702e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = -15.457955264858864659105973962972
y[1] (numeric) = -15.457955264858864659105973962969
absolute error = 3e-30
relative error = 1.9407482740100883691645168228978e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.08214
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = -15.445826234793602497746814474995
y[1] (numeric) = -15.445826234793602497746814474992
absolute error = 3e-30
relative error = 1.9422722710955630626677023629017e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02533
Order of pole (three term test) = -22.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = -15.433691854252555197391357961238
y[1] (numeric) = -15.433691854252555197391357961235
absolute error = 3e-30
relative error = 1.9437993374044128025683619243676e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04448
Order of pole (three term test) = -0.3279
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = -15.421552122367504119876858738537
y[1] (numeric) = -15.421552122367504119876858738534
absolute error = 3e-30
relative error = 1.9453294818806101105424750554575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9313
Order of pole (six term test) = -11.78
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = -15.409407038270144806994119672169
y[1] (numeric) = -15.409407038270144806994119672165
absolute error = 4e-30
relative error = 2.5958169513374336455560169394890e-29 %
Correct digits = 31
h = 0.01
bytes used=236068352, alloc=4586680, time=8.05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = -15.397256601092086974397079926645
y[1] (numeric) = -15.397256601092086974397079926641
absolute error = 4e-30
relative error = 2.5978653883811292102589209070019e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09236
Order of pole (three term test) = -37.76
Radius of convergence (six term test) for eq 1 = 0.7792
Order of pole (six term test) = -11.39
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = -15.38510080996485450551206575597
y[1] (numeric) = -15.385100809964854505512065755968
absolute error = 2e-30
relative error = 1.2999589828521694100791772144688e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05169
Order of pole (three term test) = -25.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = -15.372939664019885445446704318079
y[1] (numeric) = -15.372939664019885445446704318077
absolute error = 2e-30
relative error = 1.3009873477100592416057152538510e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02841
Order of pole (three term test) = -1.207
Radius of convergence (six term test) for eq 1 = 1.122
Order of pole (six term test) = -12.13
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = -15.360773162388531994898500498166
y[1] (numeric) = -15.360773162388531994898500498163
absolute error = 3e-30
relative error = 1.9530266922667799658223719392743e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = -15.348601304202060504063076725665
y[1] (numeric) = -15.348601304202060504063076725662
absolute error = 3e-30
relative error = 1.9545754955395678632934237134757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=240069412, alloc=4586680, time=8.19
x[1] = 2.21
y[1] (analytic) = -15.336424088591651466542075769583
y[1] (numeric) = -15.33642408859165146654207576958
absolute error = 3e-30
relative error = 1.9561274405756804559120379931006e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5297
Order of pole (three term test) = -90.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = -15.324241514688399513250726496912
y[1] (numeric) = -15.32424151468839951325072649691
absolute error = 2e-30
relative error = 1.3051216910690066577304356349091e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5229
Order of pole (three term test) = -33.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = -15.312053581623313406325072578861
y[1] (numeric) = -15.312053581623313406325072578859
absolute error = 2e-30
relative error = 1.3061605285918606420605399518086e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1612
Order of pole (three term test) = -40.47
Radius of convergence (six term test) for eq 1 = 1.105
Order of pole (six term test) = -12.34
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = -15.299860288527316033028864129605
y[1] (numeric) = -15.299860288527316033028864129603
absolute error = 2e-30
relative error = 1.3072014791531860883384478706471e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3373
Order of pole (six term test) = -11.38
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = -15.287661634531244399660112262302
y[1] (numeric) = -15.2876616345312443996601122623
absolute error = 2e-30
relative error = 1.3082445489782876764297055235580e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1515
Order of pole (three term test) = -60.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = -15.275457618765849625457306547086
y[1] (numeric) = -15.275457618765849625457306547083
absolute error = 3e-30
relative error = 1.9639346164755875014172378905828e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09743
Order of pole (three term test) = -7.236
Radius of convergence (six term test) for eq 1 = 0.9217
Order of pole (six term test) = -11.87
TOP MAIN SOLVE Loop
bytes used=244070100, alloc=4586680, time=8.33
x[1] = 2.27
y[1] (analytic) = -15.263248240361796936505295355752
y[1] (numeric) = -15.263248240361796936505295355749
absolute error = 3e-30
relative error = 1.9655056071661510297655557267876e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = -15.25103349844966565964082907788
y[1] (numeric) = -15.251033498449665659640829077878
absolute error = 2e-30
relative error = 1.3113865366588492236455250542809e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = -15.23881339215994921635776619309
y[1] (numeric) = -15.238813392159949216357766193087
absolute error = 3e-30
relative error = 1.9686572194285397953559602255948e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = -15.226587920623055116711942184154
y[1] (numeric) = -15.226587920623055116711942184151
absolute error = 3e-30
relative error = 1.9702378600111503654707472705014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01437
Order of pole (three term test) = -26.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = -15.214357082969304953225701275712
y[1] (numeric) = -15.21435708296930495322570127571
absolute error = 2e-30
relative error = 1.3145478241987407485216332728629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1266
Order of pole (three term test) = -20.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
bytes used=248072208, alloc=4586680, time=8.46
y[1] (analytic) = -15.202120878328934394792090983276
y[1] (numeric) = -15.202120878328934394792090983275
absolute error = 1e-30
relative error = 6.5780295262980647271000235984385e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1496
Order of pole (three term test) = -21.59
Radius of convergence (six term test) for eq 1 = 0.844
Order of pole (six term test) = -11.71
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = -15.189879305832093180578719457258
y[1] (numeric) = -15.189879305832093180578719457256
absolute error = 2e-30
relative error = 1.3166661562821687654126368906878e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = -15.177632364608845113931275606732
y[1] (numeric) = -15.177632364608845113931275606731
absolute error = 1e-30
relative error = 6.5886429185872021792226013531138e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06083
Order of pole (three term test) = -26.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = -15.165380053789168056276711987674
y[1] (numeric) = -15.165380053789168056276711987671
absolute error = 3e-30
relative error = 1.9781897910632517537501754431879e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.438
Order of pole (three term test) = -29.16
Radius of convergence (six term test) for eq 1 = 1.924
Order of pole (six term test) = -10.21
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = -15.153122372502953921026090440341
y[1] (numeric) = -15.153122372502953921026090440338
absolute error = 3e-30
relative error = 1.9797899906383899201708509045415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04264
Order of pole (three term test) = -3.459
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = -15.140859319880008667477090460575
y[1] (numeric) = -15.140859319880008667477090460573
absolute error = 2e-30
relative error = 1.3209289893962570698798221930172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05496
Order of pole (three term test) = -20.74
Radius of convergence (six term test) for eq 1 = 0.5733
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
bytes used=252073504, alloc=4586680, time=8.60
x[1] = 2.38
y[1] (analytic) = -15.128590895050052294716180289695
y[1] (numeric) = -15.128590895050052294716180289692
absolute error = 3e-30
relative error = 1.9830002812631907239831503402290e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8717
Order of pole (six term test) = -11.3
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = -15.116317097142718835520450707703
y[1] (numeric) = -15.1163170971427188355204507077
absolute error = 3e-30
relative error = 1.9846103920160943098989343618293e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = -15.104037925287556350259111514545
y[1] (numeric) = -15.104037925287556350259111514543
absolute error = 2e-30
relative error = 1.3241492175092795580235258956378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.66
Order of pole (six term test) = -15.1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = -15.091753378614026920794650684109
y[1] (numeric) = -15.091753378614026920794650684106
absolute error = 3e-30
relative error = 1.9878405939572207314307623358137e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01783
Order of pole (three term test) = -26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = -15.079463456251506644383656175679
y[1] (numeric) = -15.079463456251506644383656175677
absolute error = 2e-30
relative error = 1.3263071367243230475998422972852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8816
Order of pole (six term test) = -11.69
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = -15.067168157329285627577300387588
y[1] (numeric) = -15.067168157329285627577300387585
absolute error = 3e-30
relative error = 1.9910841696823284879747377740864e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2421
Order of pole (three term test) = -64.98
Radius of convergence (six term test) for eq 1 = 1.182
Order of pole (six term test) = -12.24
TOP MAIN SOLVE Loop
bytes used=256074356, alloc=4586680, time=8.74
x[1] = 2.44
y[1] (analytic) = -15.05486748097656798012148723773
y[1] (numeric) = -15.054867480976567980121487237728
absolute error = 2e-30
relative error = 1.3284739985438021823489450951171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7603
Order of pole (three term test) = -109.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = -15.042561426322471808856661855696
y[1] (numeric) = -15.042561426322471808856661855694
absolute error = 2e-30
relative error = 1.3295607997320638046983030779062e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03477
Order of pole (three term test) = 0.5019
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = -15.030249992496029211617282871202
y[1] (numeric) = -15.030249992496029211617282871201
absolute error = 1e-30
relative error = 6.6532492839391086824575307521196e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = -15.017933178626186271130957283552
y[1] (numeric) = -15.01793317862618627113095728355
absolute error = 2e-30
relative error = 1.3317411765065240696180054396833e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1017
Order of pole (three term test) = -23.49
Radius of convergence (six term test) for eq 1 = 1.325
Order of pole (six term test) = -9.993
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = -15.005610983841803048917237896817
y[1] (numeric) = -15.005610983841803048917237896816
absolute error = 1e-30
relative error = 6.6641738285552673088784760585449e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6433
Order of pole (six term test) = -12.25
TOP MAIN SOLVE Loop
bytes used=260075292, alloc=4586680, time=8.88
x[1] = 2.49
y[1] (analytic) = -14.993283407271653579186083305472
y[1] (numeric) = -14.99328340727165357918608330547
absolute error = 2e-30
relative error = 1.3339306312518656554488538271073e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05278
Order of pole (three term test) = -4.304
Radius of convergence (six term test) for eq 1 = 0.6609
Order of pole (six term test) = -10.58
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = -14.980950448044425862735980415159
y[1] (numeric) = -14.980950448044425862735980415157
absolute error = 2e-30
relative error = 1.3350287800071288370548664069321e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2507
Order of pole (three term test) = -27.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = -14.96861210528872186085172948333
y[1] (numeric) = -14.96861210528872186085172948333
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1139
Order of pole (three term test) = -18.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = -14.956268378133057489201891664443
y[1] (numeric) = -14.956268378133057489201891664442
absolute error = 1e-30
relative error = 6.6861597740654260656020014058936e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0649
Order of pole (three term test) = 3.516
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = -14.943919265705862611735899044418
y[1] (numeric) = -14.943919265705862611735899044417
absolute error = 1e-30
relative error = 6.6916849737997155706314545321850e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.384
Order of pole (six term test) = -11.86
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = -14.931564767135481034580827149095
y[1] (numeric) = -14.931564767135481034580827149092
absolute error = 3e-30
relative error = 2.0091665185707991672952617790142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.863
Order of pole (six term test) = -10.77
TOP MAIN SOLVE Loop
bytes used=264076316, alloc=4586680, time=9.02
x[1] = 2.55
y[1] (analytic) = -14.919204881550170499937829911348
y[1] (numeric) = -14.919204881550170499937829911346
absolute error = 2e-30
relative error = 1.3405540146937048238222595283737e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.659
Order of pole (six term test) = -13.53
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = -14.906839608078102679978237081619
y[1] (numeric) = -14.906839608078102679978237081616
absolute error = 3e-30
relative error = 2.0124990131203146727800860439349e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = -14.894468945847363170739314066506
y[1] (numeric) = -14.894468945847363170739314066504
absolute error = 2e-30
relative error = 1.3427803349495101718627125501028e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.373
Order of pole (six term test) = -12.05
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = -14.882092893985951486019684180188
y[1] (numeric) = -14.882092893985951486019684180185
absolute error = 3e-30
relative error = 2.0158455006098902014888521488736e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7
Order of pole (six term test) = -12
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = -14.869711451621781051274413293314
y[1] (numeric) = -14.869711451621781051274413293312
absolute error = 2e-30
relative error = 1.3450160122521192916402448969340e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1036
Order of pole (three term test) = -28.74
Radius of convergence (six term test) for eq 1 = 0.8103
Order of pole (six term test) = -12.08
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = -14.857324617882679197509756864126
y[1] (numeric) = -14.857324617882679197509756864124
absolute error = 2e-30
relative error = 1.3461373776492341777147215615715e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.197
Order of pole (six term test) = -11.6
TOP MAIN SOLVE Loop
bytes used=268077464, alloc=4586680, time=9.16
x[1] = 2.61
y[1] (analytic) = -14.844932391896387155177569336463
y[1] (numeric) = -14.84493239189638715517756933646
absolute error = 3e-30
relative error = 2.0208916556855808638783792629091e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.177
Order of pole (six term test) = -12.51
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = -14.832534772790560048069375889385
y[1] (numeric) = -14.832534772790560048069375889381
absolute error = 4e-30
relative error = 2.6967743957949602104615968963447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01742
Order of pole (three term test) = -23.82
Radius of convergence (six term test) for eq 1 = 1.166
Order of pole (six term test) = -11.13
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = -14.820131759692766887210106523101
y[1] (numeric) = -14.820131759692766887210106523098
absolute error = 3e-30
relative error = 2.0242735008330265917149326198648e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.331
Order of pole (six term test) = -13.83
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = -14.807723351730490564751492465911
y[1] (numeric) = -14.807723351730490564751492465908
absolute error = 3e-30
relative error = 2.0259697785678902769152960585027e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03166
Order of pole (three term test) = -13.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = -14.795309548031127847865124886843
y[1] (numeric) = -14.79530954803112784786512488684
absolute error = 3e-30
relative error = 2.0276696410175630485493153471379e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3572
Order of pole (three term test) = -51.69
Radius of convergence (six term test) for eq 1 = 0.4596
Order of pole (six term test) = -11.71
TOP MAIN SOLVE Loop
bytes used=272078512, alloc=4586680, time=9.29
x[1] = 2.66
y[1] (analytic) = -14.782890347721989372635175898713
y[1] (numeric) = -14.782890347721989372635175898709
absolute error = 4e-30
relative error = 2.7058307989251852440211480330216e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1424
Order of pole (three term test) = -6.343
Radius of convergence (six term test) for eq 1 = 0.7858
Order of pole (six term test) = -9.893
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = -14.770465749930299637950781836278
y[1] (numeric) = -14.770465749930299637950781836273
absolute error = 5e-30
relative error = 3.3851336069233933965817927092852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2548
Order of pole (three term test) = -23.44
Radius of convergence (six term test) for eq 1 = 1.347
Order of pole (six term test) = -11.87
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = -14.7580357537831969993980887942
y[1] (numeric) = -14.758035753783196999398088794197
absolute error = 3e-30
relative error = 2.0327908470007298747208238284694e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005152
Order of pole (three term test) = -25.15
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = -14.745600358407733663151960409521
y[1] (numeric) = -14.745600358407733663151960409517
absolute error = 4e-30
relative error = 2.7126735451766508317904128289451e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07353
Order of pole (three term test) = 3.089
Radius of convergence (six term test) for eq 1 = 2.165
Order of pole (six term test) = -12.13
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = -14.733159562930875679867347873309
y[1] (numeric) = -14.733159562930875679867347873306
absolute error = 3e-30
relative error = 2.0362231109938568536893164309293e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.378
Order of pole (six term test) = -11.08
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = -14.720713366479502938570322156233
y[1] (numeric) = -14.72071336647950293857032215623
absolute error = 3e-30
relative error = 2.0379447145756482030476294133342e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=276079824, alloc=4586680, time=9.43
x[1] = 2.72
y[1] (analytic) = -14.708261768180409160548768432703
y[1] (numeric) = -14.708261768180409160548768432699
absolute error = 4e-30
relative error = 2.7195599745535727174534714132352e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5972
Order of pole (three term test) = -51.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = -14.695804767160301893242742688308
y[1] (numeric) = -14.695804767160301893242742688304
absolute error = 4e-30
relative error = 2.7218652284620187925994068852872e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0147
Order of pole (three term test) = -26.99
Radius of convergence (six term test) for eq 1 = 1.67
Order of pole (six term test) = -12.73
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = -14.683342362545802504134490495236
y[1] (numeric) = -14.683342362545802504134490495231
absolute error = 5e-30
relative error = 3.4052192454178385252803099888608e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01935
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = -14.670874553463446174638127940358
y[1] (numeric) = -14.670874553463446174638127940353
absolute error = 5e-30
relative error = 3.4081131167600491589660127153512e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09498
Order of pole (three term test) = -24.54
Radius of convergence (six term test) for eq 1 = 0.1947
Order of pole (six term test) = -11.53
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = -14.658401339039681893988984690692
y[1] (numeric) = -14.658401339039681893988984690688
absolute error = 4e-30
relative error = 2.7288105349843372595649686440402e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.779
Order of pole (six term test) = -11.91
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = -14.645922718400872453132609180923
y[1] (numeric) = -14.64592271840087245313260918092
absolute error = 3e-30
relative error = 2.0483516523208566781852866530671e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1018
Order of pole (three term test) = -5.771
Radius of convergence (six term test) for eq 1 = 1.385
Order of pole (six term test) = -12.3
TOP MAIN SOLVE Loop
bytes used=280080844, alloc=4586680, time=9.57
x[1] = 2.78
y[1] (analytic) = -14.633438690673294438613435907674
y[1] (numeric) = -14.633438690673294438613435907671
absolute error = 3e-30
relative error = 2.0500991348752956475387568110474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = -14.620949254983138226463114815221
y[1] (numeric) = -14.620949254983138226463114815218
absolute error = 3e-30
relative error = 2.0518503605212463228749975903750e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1562
Order of pole (three term test) = -33.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = -14.60845441045650797608850275735
y[1] (numeric) = -14.608454410456507976088502757347
absolute error = 3e-30
relative error = 2.0536053409268580372787664631649e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.914
Order of pole (six term test) = -8.971
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = -14.595954156219421624159317020035
y[1] (numeric) = -14.595954156219421624159317020032
absolute error = 3e-30
relative error = 2.0553640878090059050206169228624e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09754
Order of pole (three term test) = -8.875
Radius of convergence (six term test) for eq 1 = 1.555
Order of pole (six term test) = -10.49
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = -14.583448491397810878495450889634
y[1] (numeric) = -14.583448491397810878495450889632
absolute error = 2e-30
relative error = 1.3714177419556968834147580797593e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3826
Order of pole (three term test) = -69.95
Radius of convergence (six term test) for eq 1 = 0.1229
Order of pole (six term test) = -11.6
TOP MAIN SOLVE Loop
bytes used=284081984, alloc=4586680, time=9.71
x[1] = 2.83
y[1] (analytic) = -14.570937415117521211953951251293
y[1] (numeric) = -14.570937415117521211953951251289
absolute error = 4e-30
relative error = 2.7451905708207574424663456247061e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06851
Order of pole (three term test) = 1.737
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = -14.55842092650431185631565820223
y[1] (numeric) = -14.558420926504311856315658202227
absolute error = 3e-30
relative error = 2.0606630452196600538395640641544e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.44
Order of pole (six term test) = -11.87
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = -14.545899024683855796171506664629
y[1] (numeric) = -14.545899024683855796171506664626
absolute error = 3e-30
relative error = 2.0624369761601605436536157478789e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = -14.533371708781739762808489982775
y[1] (numeric) = -14.533371708781739762808489982772
absolute error = 3e-30
relative error = 2.0642147329014232396673970002415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03589
Order of pole (three term test) = 1.082
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = -14.52083897792346422809528548916
y[1] (numeric) = -14.520838977923464228095285489158
absolute error = 2e-30
relative error = 1.3773308849720525481919258007966e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.174
Order of pole (six term test) = -12.42
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = -14.508300831234443398367542024237
y[1] (numeric) = -14.508300831234443398367542024234
absolute error = 3e-30
relative error = 2.0677817718952992266027550535953e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1263
Order of pole (three term test) = -5.132
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=288083060, alloc=4586680, time=9.85
x[1] = 2.89
y[1] (analytic) = -14.495757267840005208312829394485
y[1] (numeric) = -14.495757267840005208312829394482
absolute error = 3e-30
relative error = 2.0695710783290635736629700556563e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = -14.483208286865391314855249753507
y[1] (numeric) = -14.483208286865391314855249753504
absolute error = 3e-30
relative error = 2.0713642589264257827040609053844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.947
Order of pole (six term test) = -7.509
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = -14.470653887435757091039710890817
y[1] (numeric) = -14.470653887435757091039710890814
absolute error = 3e-30
relative error = 2.0731613259057838767149600607920e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02423
Order of pole (three term test) = -26.65
Radius of convergence (six term test) for eq 1 = 0.3867
Order of pole (six term test) = -11.48
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = -14.458094068676171619915861413012
y[1] (numeric) = -14.458094068676171619915861413007
absolute error = 5e-30
relative error = 3.4582704858952516564471002810505e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03597
Order of pole (three term test) = -9.334
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = -14.445528829711617688421687802001
y[1] (numeric) = -14.445528829711617688421687801998
absolute error = 3e-30
relative error = 2.0767671681424281174314653860545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = -14.432958169666991781266773335009
y[1] (numeric) = -14.432958169666991781266773335006
absolute error = 3e-30
relative error = 2.0785759680956785368856392998253e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=292085076, alloc=4586680, time=9.99
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = -14.420382087667104074815218850979
y[1] (numeric) = -14.420382087667104074815218850974
absolute error = 5e-30
relative error = 3.4673145063723400884761239418466e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09714
Order of pole (three term test) = 10.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = -14.407800582836678430968225348102
y[1] (numeric) = -14.407800582836678430968225348099
absolute error = 3e-30
relative error = 2.0822053878048229404052613336876e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5081
Order of pole (six term test) = -12.42
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = -14.395213654300352391046338397158
y[1] (numeric) = -14.395213654300352391046338397154
absolute error = 4e-30
relative error = 2.7787013767628662385593739182202e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04829
Order of pole (three term test) = -27.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = -14.382621301182677169671354355293
y[1] (numeric) = -14.38262130118267716967135435529
absolute error = 3e-30
relative error = 2.0858506507108764697892801961180e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4445
Order of pole (three term test) = -31.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = -14.370023522608117648647888364991
y[1] (numeric) = -14.370023522608117648647888364987
absolute error = 4e-30
relative error = 2.7835723398134087294969543329937e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=296085908, alloc=4586680, time=10.12
x[1] = 3
y[1] (analytic) = -14.357420317701052370844604122844
y[1] (numeric) = -14.35742031770105237084460412284
absolute error = 4e-30
relative error = 2.7860158102834523996049307054497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1018
Order of pole (three term test) = -18.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = -14.344811685585773534075105402864
y[1] (numeric) = -14.34481168558577353407510540286
absolute error = 4e-30
relative error = 2.7884646293540096214528920731253e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = -14.332197625386486984978489318965
y[1] (numeric) = -14.332197625386486984978489318962
absolute error = 3e-30
relative error = 2.0931891105702646666976790798766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02787
Order of pole (three term test) = -21.39
Radius of convergence (six term test) for eq 1 = 1.285
Order of pole (six term test) = -11.76
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = -14.319578136227312212899561311325
y[1] (numeric) = -14.319578136227312212899561311321
absolute error = 4e-30
relative error = 2.7933783816440380488177461483347e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.965
Order of pole (six term test) = -12.5
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = -14.306953217232282343768711841282
y[1] (numeric) = -14.306953217232282343768711841278
absolute error = 4e-30
relative error = 2.7958433492199609639663660861474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.014
Order of pole (six term test) = -12.47
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = -14.294322867525344133981454779464
y[1] (numeric) = -14.294322867525344133981454779459
absolute error = 5e-30
relative error = 3.4978921676376041848385030734832e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.191
Order of pole (three term test) = 2.854
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=300086932, alloc=4586680, time=10.26
x[1] = 3.06
y[1] (analytic) = -14.281687086230357964277627471804
y[1] (numeric) = -14.2816870862303579642776274718
absolute error = 4e-30
relative error = 2.8007895536771611227587488628176e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1035
Order of pole (three term test) = -4.314
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = -14.269045872471097833620252468141
y[1] (numeric) = -14.269045872471097833620252468137
absolute error = 4e-30
relative error = 2.8032708253584753201445707133262e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.049
Order of pole (six term test) = -11.23
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = -14.256399225371251353074060898052
y[1] (numeric) = -14.256399225371251353074060898047
absolute error = 5e-30
relative error = 3.5071969583327902620320820059370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03917
Order of pole (three term test) = -0.0833
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = -14.243747144054419739683677478613
y[1] (numeric) = -14.243747144054419739683677478609
absolute error = 4e-30
relative error = 2.8082497951879660085307626614089e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0338
Order of pole (three term test) = -0.4396
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = -14.231089627644117810351467138762
y[1] (numeric) = -14.231089627644117810351467138759
absolute error = 3e-30
relative error = 2.1080606464402081438965302351453e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = -14.218426675263773975715043244917
bytes used=304089232, alloc=4586680, time=10.40
y[1] (numeric) = -14.218426675263773975715043244912
absolute error = 5e-30
relative error = 3.5165634807532192776756287906831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = -14.205758286036730234024437412528
y[1] (numeric) = -14.205758286036730234024437412524
absolute error = 4e-30
relative error = 2.8157595810508201189332450628660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1322
Order of pole (three term test) = 8.295
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = -14.193084459086242165018930888271
y[1] (numeric) = -14.193084459086242165018930888267
absolute error = 4e-30
relative error = 2.8182739358246036880120606551153e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02571
Order of pole (three term test) = -15.62
Radius of convergence (six term test) for eq 1 = 0.3418
Order of pole (six term test) = -11.56
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = -14.180405193535478923803547487485
y[1] (numeric) = -14.18040519353547892380354748748
absolute error = 5e-30
relative error = 3.5259923336177905378316918837703e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04475
Order of pole (three term test) = 0.4841
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = -14.167720488507523234725208071583
y[1] (numeric) = -14.167720488507523234725208071579
absolute error = 4e-30
relative error = 2.8233193923078121506594710313341e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03272
Order of pole (three term test) = -25.58
Radius of convergence (six term test) for eq 1 = 1.685
Order of pole (six term test) = -14.9
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = -14.155030343125371385248546550095
y[1] (numeric) = -14.15503034312537138524854655009
absolute error = 5e-30
relative error = 3.5323131627395868596518248629673e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=308090164, alloc=4586680, time=10.53
x[1] = 3.17
y[1] (analytic) = -14.142334756511933219831387391972
y[1] (numeric) = -14.142334756511933219831387391967
absolute error = 5e-30
relative error = 3.5354841234384699802410329672327e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = -14.129633727790032133799884630882
y[1] (numeric) = -14.129633727790032133799884630877
absolute error = 5e-30
relative error = 3.5386621453364686496040091022897e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.292
Order of pole (six term test) = -12.54
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = -14.116927256082405067223322349115
y[1] (numeric) = -14.116927256082405067223322349111
absolute error = 4e-30
relative error = 2.8334778011104109263339328632231e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = -14.104215340511702498788576624799
y[1] (numeric) = -14.104215340511702498788576624794
absolute error = 5e-30
relative error = 3.5450394646474530108553901552383e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7156
Order of pole (six term test) = -9.292
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = -14.091497980200488439674238927058
y[1] (numeric) = -14.091497980200488439674238927054
absolute error = 4e-30
relative error = 2.8385910466156767891181117811858e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = -14.078775174271240427424400943828
y[1] (numeric) = -14.078775174271240427424400943823
absolute error = 5e-30
relative error = 3.5514453055102607505676910159261e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=312091060, alloc=4586680, time=10.67
x[1] = 3.23
y[1] (analytic) = -14.066046921846349519822100826942
y[1] (numeric) = -14.066046921846349519822100826936
absolute error = 6e-30
relative error = 4.2655907756721906711498491253838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3059
Order of pole (three term test) = -65.78
Radius of convergence (six term test) for eq 1 = 1.394
Order of pole (six term test) = -12.23
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = -14.053313222048120288762430839189
y[1] (numeric) = -14.053313222048120288762430839184
absolute error = 5e-30
relative error = 3.5578798543787835738046469302719e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = -14.040574073998770814125306388005
y[1] (numeric) = -14.040574073998770814125306388
absolute error = 5e-30
relative error = 3.5611079530283013172751928797447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03064
Order of pole (three term test) = -23.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = -14.027829476820432677647896430434
y[1] (numeric) = -14.027829476820432677647896430428
absolute error = 6e-30
relative error = 4.2772119592089369606647338950342e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = -14.015079429635150956796715234053
y[1] (numeric) = -14.015079429635150956796715234048
absolute error = 5e-30
relative error = 3.5675859170854253452057767363361e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2998
Order of pole (six term test) = -11.84
TOP MAIN SOLVE Loop
bytes used=316091888, alloc=4586680, time=10.80
x[1] = 3.28
y[1] (analytic) = -14.002323931564884218639375478523
y[1] (numeric) = -14.002323931564884218639375478517
absolute error = 6e-30
relative error = 4.2850029961629709586701531443317e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.885
Order of pole (six term test) = -10.88
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = -13.98956298173150451371600268239
y[1] (numeric) = -13.989562981731504513716002682384
absolute error = 6e-30
relative error = 4.2889116749645406061047402755786e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3139
Order of pole (six term test) = -11.61
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = -13.976796579256797369910310939854
y[1] (numeric) = -13.976796579256797369910310939849
absolute error = 5e-30
relative error = 3.5773576381733890560394705971199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.106
Order of pole (three term test) = -22.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = -13.964024723262461786320339952126
y[1] (numeric) = -13.964024723262461786320339952119
absolute error = 7e-30
relative error = 5.0128814140086731347064840080918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.434
Order of pole (six term test) = -10.65
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = -13.951247412870110227128853338034
y[1] (numeric) = -13.951247412870110227128853338029
absolute error = 5e-30
relative error = 3.5839089165514115390135931610924e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9792
Order of pole (six term test) = -13.27
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = -13.938464647201268615473398208583
y[1] (numeric) = -13.938464647201268615473398208578
absolute error = 5e-30
relative error = 3.5871956679274282263410094652256e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.347
Order of pole (six term test) = -12.1
TOP MAIN SOLVE Loop
bytes used=320093344, alloc=4586680, time=10.93
x[1] = 3.34
y[1] (analytic) = -13.925676425377376327316025990059
y[1] (numeric) = -13.925676425377376327316025990052
absolute error = 7e-30
relative error = 5.0266858041047042188958057626629e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.541
Order of pole (six term test) = -15.48
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = -13.912882746519786185312674480386
y[1] (numeric) = -13.91288274651978618531267448038
absolute error = 6e-30
relative error = 4.3125498211367155713324294536022e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08453
Order of pole (three term test) = -23.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = -13.900083609749764452682211123396
y[1] (numeric) = -13.900083609749764452682211123391
absolute error = 5e-30
relative error = 3.5971006652743524363399214162301e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05768
Order of pole (three term test) = -27.67
Radius of convergence (six term test) for eq 1 = 0.5735
Order of pole (six term test) = -11.09
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = -13.887279014188490827075137485632
y[1] (numeric) = -13.887279014188490827075137485626
absolute error = 6e-30
relative error = 4.3205007934742734068653347239519e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04439
Order of pole (three term test) = -2.331
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = -13.874468958957058434441954920362
y[1] (numeric) = -13.874468958957058434441954920357
absolute error = 5e-30
relative error = 3.6037415304260042709129418269529e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.249
Order of pole (six term test) = -11.19
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = -13.861653443176473822901191403483
y[1] (numeric) = -13.861653443176473822901191403478
absolute error = 5e-30
relative error = 3.6070732979270203203009055778469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.568
Order of pole (six term test) = -13.3
bytes used=324094616, alloc=4586680, time=11.07
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = -13.848832465967656956607089525927
y[1] (numeric) = -13.848832465967656956607089525921
absolute error = 6e-30
relative error = 4.3324951866841455716273159142252e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = -13.836006026451441209616955627251
y[1] (numeric) = -13.836006026451441209616955627246
absolute error = 5e-30
relative error = 3.6137596286392799798844322274488e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.775
Order of pole (six term test) = -8.609
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = -13.823174123748573359758170055075
y[1] (numeric) = -13.823174123748573359758170055068
absolute error = 7e-30
relative error = 5.0639599395437098549507279038343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = -13.810336756979713582494858534978
y[1] (numeric) = -13.810336756979713582494858534972
absolute error = 6e-30
relative error = 4.3445718273072619323941537452857e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9409
Order of pole (six term test) = -11.21
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = -13.797493925265435444794224635572
y[1] (numeric) = -13.797493925265435444794224635567
absolute error = 5e-30
relative error = 3.6238464949378916065549323173324e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=328095596, alloc=4586680, time=11.20
x[1] = 3.45
y[1] (analytic) = -13.784645627726225898992543313339
y[1] (numeric) = -13.784645627726225898992543313334
absolute error = 5e-30
relative error = 3.6272241848155140720858270213150e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = -13.771791863482485276660815521927
y[1] (numeric) = -13.771791863482485276660815521922
absolute error = 5e-30
relative error = 3.6306096182429855180199956023313e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = -13.758932631654527282470083870545
y[1] (numeric) = -13.758932631654527282470083870541
absolute error = 4e-30
relative error = 2.9072022569522498308950510206909e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9112
Order of pole (six term test) = -11.96
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = -13.746067931362578988056409316106
y[1] (numeric) = -13.746067931362578988056409316102
absolute error = 4e-30
relative error = 2.9099230557952727931348483371599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1558
Order of pole (three term test) = -34.79
Radius of convergence (six term test) for eq 1 = 1.7
Order of pole (six term test) = -12.62
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = -13.733197761726780825885508873764
y[1] (numeric) = -13.733197761726780825885508873759
absolute error = 5e-30
relative error = 3.6408126401081633111514754570757e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004128
Order of pole (three term test) = -25.48
Radius of convergence (six term test) for eq 1 = 5.998
Order of pole (six term test) = -45.44
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = -13.720322121867186583117054330502
y[1] (numeric) = -13.720322121867186583117054330498
absolute error = 4e-30
relative error = 2.9153834468834201935878256473362e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=332096676, alloc=4586680, time=11.34
x[1] = 3.51
y[1] (analytic) = -13.707441010903763395468631946431
y[1] (numeric) = -13.707441010903763395468631946426
absolute error = 5e-30
relative error = 3.6476538516727407728977715473470e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = -13.694554427956391741079363128412
y[1] (numeric) = -13.694554427956391741079363128407
absolute error = 5e-30
relative error = 3.6510862958731100613310165000242e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.015
Order of pole (six term test) = -11.18
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = -13.681662372144865434373186060697
y[1] (numeric) = -13.681662372144865434373186060693
absolute error = 4e-30
relative error = 2.9236213343078737044471466992190e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.335
Order of pole (six term test) = -12.95
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = -13.668764842588891619921798277202
y[1] (numeric) = -13.668764842588891619921798277197
absolute error = 5e-30
relative error = 3.6579749945079821265572960867449e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.325
Order of pole (six term test) = -12.04
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = -13.655861838408090766307260160063
y[1] (numeric) = -13.655861838408090766307260160059
absolute error = 4e-30
relative error = 2.9291450421310745363687545200219e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=336097812, alloc=4586680, time=11.48
x[1] = 3.56
y[1] (analytic) = -13.642953358721996659984259349149
y[1] (numeric) = -13.642953358721996659984259349144
absolute error = 5e-30
relative error = 3.6648956193956928430338599411119e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = -13.63003940265005639914203604713
y[1] (numeric) = -13.630039402650056399142036047126
absolute error = 4e-30
relative error = 2.9346943774955554703232735514247e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1118
Order of pole (three term test) = -28.87
Radius of convergence (six term test) for eq 1 = 0.9624
Order of pole (six term test) = -11.56
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = -13.617119969311630387565969204799
y[1] (numeric) = -13.617119969311630387565969204795
absolute error = 4e-30
relative error = 2.9374787098994818565196736755281e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.38
Order of pole (three term test) = -124.4
Radius of convergence (six term test) for eq 1 = 1.343
Order of pole (six term test) = -12.17
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = -13.604195057825992328498823571244
y[1] (numeric) = -13.60419505782599232849882357124
absolute error = 4e-30
relative error = 2.9402695146589708249265313972418e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6656
Order of pole (six term test) = -11.57
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = -13.591264667312329218501657593551
y[1] (numeric) = -13.591264667312329218501657593546
absolute error = 5e-30
relative error = 3.6788335172555721670251734837759e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08331
Order of pole (three term test) = -25.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = -13.578328796889741341314392150653
y[1] (numeric) = -13.578328796889741341314392150648
absolute error = 5e-30
relative error = 3.6823382868334300860966927949575e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1716
Order of pole (six term test) = -11.42
TOP MAIN SOLVE Loop
bytes used=340098828, alloc=4586680, time=11.62
x[1] = 3.62
y[1] (analytic) = -13.565387445677242261716040105997
y[1] (numeric) = -13.565387445677242261716040105992
absolute error = 5e-30
relative error = 3.6858512298469618666132831236775e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.087
Order of pole (six term test) = -11.95
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = -13.552440612793758819384596663641
y[1] (numeric) = -13.552440612793758819384596663636
absolute error = 5e-30
relative error = 3.6893723742127347637607012369401e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09589
Order of pole (three term test) = 4.975
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = -13.539488297358131122756590512443
y[1] (numeric) = -13.539488297358131122756590512437
absolute error = 6e-30
relative error = 4.4314820975699203221462449668010e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.279
Order of pole (three term test) = -94.2
Radius of convergence (six term test) for eq 1 = 2.826
Order of pole (six term test) = -14.77
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = -13.526530498489112542886295742975
y[1] (numeric) = -13.526530498489112542886295742969
absolute error = 6e-30
relative error = 4.4357272551673087694593736603881e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = -13.51356721530536970730460452181
y[1] (numeric) = -13.513567215305369707304604521804
absolute error = 6e-30
relative error = 4.4399823558093845532087272626779e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1518
Order of pole (three term test) = 2.678
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = -13.50059844692548249387756050781
y[1] (numeric) = -13.500598446925482493877560507803
absolute error = 7e-30
relative error = 5.1849553392161838543448545332788e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=344099856, alloc=4586680, time=11.75
x[1] = 3.68
y[1] (analytic) = -13.48762419246794402466455299506
y[1] (numeric) = -13.487624192467944024664552995053
absolute error = 7e-30
relative error = 5.1899429433310382979062082876574e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.425
Order of pole (six term test) = -11.55
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = -13.474644451051160659776171767094
y[1] (numeric) = -13.474644451051160659776171767088
absolute error = 6e-30
relative error = 4.4528076579652818790626289298840e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6207
Order of pole (six term test) = -12.55
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = -13.461659221793451991231722647041
y[1] (numeric) = -13.461659221793451991231722647035
absolute error = 6e-30
relative error = 4.4571028735346637289437062760396e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1104
Order of pole (three term test) = -20
Radius of convergence (six term test) for eq 1 = 1.157
Order of pole (six term test) = -11.32
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = -13.448668503813050836816403728329
y[1] (numeric) = -13.448668503813050836816403728323
absolute error = 6e-30
relative error = 4.4614082043131945525435476689751e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03944
Order of pole (three term test) = -25.6
Radius of convergence (six term test) for eq 1 = 0.6724
Order of pole (six term test) = -11.36
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = -13.435672296228103233938142270589
y[1] (numeric) = -13.435672296228103233938142270584
absolute error = 5e-30
relative error = 3.7214364043425555964657275406013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1015
Order of pole (three term test) = -25.38
Radius of convergence (six term test) for eq 1 = 0.4979
Order of pole (six term test) = -11.54
TOP MAIN SOLVE Loop
bytes used=348100680, alloc=4586680, time=11.89
x[1] = 3.73
y[1] (analytic) = -13.4226705981566684334840922454
y[1] (numeric) = -13.422670598156668433484092245395
absolute error = 5e-30
relative error = 3.7250411260830974943450476355675e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03859
Order of pole (three term test) = -0.8814
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = -13.40966340871671889367679251649
y[1] (numeric) = -13.409663408716718893676792516484
absolute error = 6e-30
relative error = 4.4743852378127583470864004591393e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05008
Order of pole (three term test) = -5.915
Radius of convergence (six term test) for eq 1 = 1.558
Order of pole (six term test) = -10.75
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = -13.396650727026140273929985639053
y[1] (numeric) = -13.396650727026140273929985639047
absolute error = 6e-30
relative error = 4.4787313801469181749209409625960e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.529
Order of pole (six term test) = -10.42
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = -13.383632552202731428704097262807
y[1] (numeric) = -13.383632552202731428704097262801
absolute error = 6e-30
relative error = 4.4830878138629830788924090139958e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = -13.370608883364204401361376123416
y[1] (numeric) = -13.370608883364204401361376123411
absolute error = 5e-30
relative error = 3.7395454789056251745488692116781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06716
Order of pole (three term test) = -21.31
Radius of convergence (six term test) for eq 1 = 0.6192
Order of pole (six term test) = -11.63
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = -13.357579719628184418020694606929
y[1] (numeric) = -13.357579719628184418020694606925
absolute error = 4e-30
relative error = 2.9945544656733234912277247983492e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=352101988, alloc=4586680, time=12.03
x[1] = 3.79
y[1] (analytic) = -13.344545060112209881412009871857
y[1] (numeric) = -13.344545060112209881412009871851
absolute error = 6e-30
relative error = 4.4962192213913870042689393192831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2673
Order of pole (three term test) = -42.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = -13.331504903933732364730485513506
y[1] (numeric) = -13.331504903933732364730485513502
absolute error = 4e-30
relative error = 3.0004114530383726116077810857516e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07487
Order of pole (three term test) = 1.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = -13.318459250210116605490273755254
y[1] (numeric) = -13.318459250210116605490273755248
absolute error = 6e-30
relative error = 4.5050256094039871249600649060665e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = -13.305408098058640499377958151307
y[1] (numeric) = -13.305408098058640499377958151302
absolute error = 5e-30
relative error = 3.7578704562466879548280367808029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.284
Order of pole (six term test) = -12.77
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = -13.292351446596495094105656785677
y[1] (numeric) = -13.292351446596495094105656785672
absolute error = 5e-30
relative error = 3.7615616921415731655987828547940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.059
Order of pole (six term test) = -15.11
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = -13.27928929494078458326378595191
y[1] (numeric) = -13.279289294940784583263785951906
bytes used=356103232, alloc=4586680, time=12.16
absolute error = 4e-30
relative error = 3.0122093970224307275129232185869e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = -13.266221642208526300173484298269
y[1] (numeric) = -13.266221642208526300173484298265
absolute error = 4e-30
relative error = 3.0151765196454914164013152842052e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09486
Order of pole (three term test) = -29.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = -13.253148487516650711738697422952
y[1] (numeric) = -13.253148487516650711738697422947
absolute error = 5e-30
relative error = 3.7726884330237292266979743824008e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = -13.240069829982001412297922903997
y[1] (numeric) = -13.240069829982001412297922903993
absolute error = 4e-30
relative error = 3.0211321022960477929067490400825e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.719
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = -13.226985668721335117475615748503
y[1] (numeric) = -13.226985668721335117475615748499
absolute error = 4e-30
relative error = 3.0241206123471090770091070337371e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05413
Order of pole (three term test) = 0.3118
Radius of convergence (six term test) for eq 1 = 1.341
Order of pole (six term test) = -9.26
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = -13.213896002851321658033254245775
y[1] (numeric) = -13.213896002851321658033254245771
absolute error = 4e-30
relative error = 3.0271163017605646152659725876982e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.804
Order of pole (six term test) = -11.15
TOP MAIN SOLVE Loop
bytes used=360104096, alloc=4586680, time=12.30
x[1] = 3.9
y[1] (analytic) = -13.200800831488543973720066209037
y[1] (numeric) = -13.200800831488543973720066209033
absolute error = 4e-30
relative error = 3.0301191958434793180175339231698e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0539
Order of pole (three term test) = -28.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = -13.187700153749498107123415590334
y[1] (numeric) = -13.18770015374949810712341559033
absolute error = 4e-30
relative error = 3.0331293200222851105631112893130e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = -13.174593968750593197518849453245
y[1] (numeric) = -13.17459396875059319751884945324
absolute error = 5e-30
relative error = 3.7951833748043567163644386117262e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = -13.16148227560815147471980528803
y[1] (numeric) = -13.161482275608151474719805288024
absolute error = 6e-30
relative error = 4.5587570414615465629494124679156e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07444
Order of pole (three term test) = -23.12
Radius of convergence (six term test) for eq 1 = 1.07
Order of pole (six term test) = -11.65
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = -13.148365073438408252926978653846
y[1] (numeric) = -13.14836507343840825292697865384
absolute error = 6e-30
relative error = 4.5633049938055526205948351163085e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.106
Order of pole (three term test) = -446.2
Radius of convergence (six term test) for eq 1 = 1.536
Order of pole (six term test) = -12.06
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = -13.135242361357511924577351132644
y[1] (numeric) = -13.135242361357511924577351132639
absolute error = 5e-30
relative error = 3.8065532880531150336482083566330e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05336
Order of pole (three term test) = -32.29
Radius of convergence (six term test) for eq 1 = 0.6178
Order of pole (six term test) = -12.05
TOP MAIN SOLVE Loop
bytes used=364105464, alloc=4586680, time=12.44
x[1] = 3.96
y[1] (analytic) = -13.122114138481523954192878579374
y[1] (numeric) = -13.122114138481523954192878579369
absolute error = 5e-30
relative error = 3.8103616134058366631323737528974e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08588
Order of pole (three term test) = -0.1142
Radius of convergence (six term test) for eq 1 = 4.643
Order of pole (six term test) = -14.54
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = -13.108980403926418872228839653117
y[1] (numeric) = -13.108980403926418872228839653112
absolute error = 5e-30
relative error = 3.8141791702597964769121020679781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2529
Order of pole (three term test) = -17.12
Radius of convergence (six term test) for eq 1 = 1.124
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = -13.095841156808084268921844613775
y[1] (numeric) = -13.095841156808084268921844613769
absolute error = 6e-30
relative error = 4.5816071897610053222895788618467e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03692
Order of pole (three term test) = -12
Radius of convergence (six term test) for eq 1 = 1.834
Order of pole (six term test) = -11.2
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = -13.082696396242320788137504368922
y[1] (numeric) = -13.082696396242320788137504368916
absolute error = 6e-30
relative error = 4.5862105320454816927106970402732e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = -13.069546121344842121217759755467
y[1] (numeric) = -13.069546121344842121217759755461
absolute error = 6e-30
relative error = 4.5908250709647493920335233467571e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01876
Order of pole (three term test) = -0.7626
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=368106784, alloc=4586680, time=12.57
x[1] = 4.01
y[1] (analytic) = -13.056390331231275000827871040709
y[1] (numeric) = -13.056390331231275000827871040703
absolute error = 6e-30
relative error = 4.5954508465083347623202537512294e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1068
Order of pole (three term test) = -3.705
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = -13.043229025017159194803067627439
y[1] (numeric) = -13.043229025017159194803067627433
absolute error = 6e-30
relative error = 4.6000878988568604234588513697295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02123
Order of pole (three term test) = -1.319
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = -13.030062201817947499994857947682
y[1] (numeric) = -13.030062201817947499994857947678
absolute error = 4e-30
relative error = 3.0698241789221252380901723496962e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = -13.016889860749005736116999529723
y[1] (numeric) = -13.016889860749005736116999529718
absolute error = 5e-30
relative error = 3.8411633297113068322976466865018e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00728
Order of pole (three term test) = -0.885
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = -13.003712000925612739591129222994
y[1] (numeric) = -13.003712000925612739591129222989
absolute error = 5e-30
relative error = 3.8450559345240010885018146944726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001769
Order of pole (three term test) = -0.8946
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = -12.990528621462960357392053565493
y[1] (numeric) = -12.990528621462960357392053565488
absolute error = 5e-30
relative error = 3.8489580722211693124368243471891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2071
Order of pole (three term test) = -12.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=372107500, alloc=4652204, time=12.71
x[1] = 4.07
y[1] (analytic) = -12.977339721476153440892699278303
y[1] (numeric) = -12.977339721476153440892699278298
absolute error = 5e-30
relative error = 3.8528697770973181413506455190079e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.225
Order of pole (six term test) = -12.59
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = -12.964145300080209839708723871855
y[1] (numeric) = -12.964145300080209839708723871848
absolute error = 7e-30
relative error = 5.3995075170568249005625401658585e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.086
Order of pole (six term test) = -11.36
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = -12.950945356390060395542786348529
y[1] (numeric) = -12.950945356390060395542786348523
absolute error = 6e-30
relative error = 4.6328664316690753155831833871457e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = -12.937739889520548936028477986247
y[1] (numeric) = -12.93773988952054893602847798624
absolute error = 7e-30
relative error = 5.4105276963172957452808023174249e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1462
Order of pole (three term test) = -14.87
Radius of convergence (six term test) for eq 1 = 1.729
Order of pole (six term test) = -11.18
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = -12.924528898586432268573913187608
y[1] (numeric) = -12.924528898586432268573913187602
absolute error = 6e-30
relative error = 4.6423355520960037262863034210075e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1517
Order of pole (three term test) = -25.93
Radius of convergence (six term test) for eq 1 = 0.523
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = -12.911312382702380174204980379252
y[1] (numeric) = -12.911312382702380174204980379245
absolute error = 7e-30
relative error = 5.4216022295131526840603121116028e-29 %
bytes used=376109036, alloc=4652204, time=12.85
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.967
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7349
Order of pole (six term test) = -12.36
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = -12.898090340982975401408252945994
y[1] (numeric) = -12.898090340982975401408252945987
absolute error = 7e-30
relative error = 5.4271600019406621103404027502500e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = -12.884862772542713659973560184407
y[1] (numeric) = -12.8848627725427136599735601844
absolute error = 7e-30
relative error = 5.4327315110540458923237780770435e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7248
Order of pole (six term test) = -11.68
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = -12.871629676496003614836218260409
y[1] (numeric) = -12.871629676496003614836218260403
absolute error = 6e-30
relative error = 4.6614144057890250947333905557913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01477
Order of pole (three term test) = 0.3273
Radius of convergence (six term test) for eq 1 = 1.587
Order of pole (six term test) = -14.58
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = -12.858391051957166879918921155508
y[1] (numeric) = -12.858391051957166879918921155501
absolute error = 7e-30
relative error = 5.4439159391831801558693435412139e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1233
Order of pole (three term test) = -1.887
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = -12.84514689804043801197329158628
y[1] (numeric) = -12.845146898040438011973291586273
absolute error = 7e-30
relative error = 5.4495289587290504089272981569933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=380109828, alloc=4652204, time=12.99
x[1] = 4.18
y[1] (analytic) = -12.831897213859964504421091881723
y[1] (numeric) = -12.831897213859964504421091881715
absolute error = 8e-30
relative error = 6.2344639040274225066333432969343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.335
Order of pole (six term test) = -13.04
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = -12.818641998529806781195094803066
y[1] (numeric) = -12.81864199852980678119509480306
absolute error = 6e-30
relative error = 4.6806830245264286530534193215726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.083
Order of pole (six term test) = -5.793
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = -12.805381251163938190579614290675
y[1] (numeric) = -12.805381251163938190579614290669
absolute error = 6e-30
relative error = 4.6855301551093086361138878092084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02228
Order of pole (three term test) = -25.65
Radius of convergence (six term test) for eq 1 = 0.5509
Order of pole (six term test) = -12.1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = -12.792114970876244999050696122617
y[1] (numeric) = -12.792114970876244999050696122611
absolute error = 6e-30
relative error = 4.6903893638074509719922525784292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = -12.778843156780526385115968469543
y[1] (numeric) = -12.778843156780526385115968469537
absolute error = 6e-30
relative error = 4.6952606948746891046553172585362e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.595
Order of pole (six term test) = -7.626
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = -12.765565807990494433154152330457
y[1] (numeric) = -12.765565807990494433154152330451
absolute error = 6e-30
relative error = 4.7001441927817663978948335085088e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=384110788, alloc=4652204, time=13.13
x[1] = 4.24
y[1] (analytic) = -12.752282923619774127254231833997
y[1] (numeric) = -12.752282923619774127254231833991
absolute error = 6e-30
relative error = 4.7050399022176664736555037200333e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = -12.738994502781903345054284389824
y[1] (numeric) = -12.738994502781903345054284389819
absolute error = 5e-30
relative error = 3.9249565567424611279646444005305e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.258
Order of pole (six term test) = -12.74
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = -12.725700544590332851579970674735
y[1] (numeric) = -12.725700544590332851579970674731
absolute error = 4e-30
relative error = 3.1432454236874143253310641158582e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.423
Order of pole (six term test) = -10.22
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = -12.712401048158426293082684438092
y[1] (numeric) = -12.712401048158426293082684438086
absolute error = 6e-30
relative error = 4.7198007498899557580340789826229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4726
Order of pole (three term test) = -21.87
Radius of convergence (six term test) for eq 1 = 0.245
Order of pole (six term test) = -11.68
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = -12.699096012599460190877362111169
y[1] (numeric) = -12.699096012599460190877362111164
absolute error = 5e-30
relative error = 3.9372881306190846134442086217875e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4023
Order of pole (three term test) = -35.99
Radius of convergence (six term test) for eq 1 = 0.7502
Order of pole (six term test) = -11.86
TOP MAIN SOLVE Loop
bytes used=388111496, alloc=4652204, time=13.26
x[1] = 4.29
y[1] (analytic) = -12.685785437026623935179952205052
y[1] (numeric) = -12.685785437026623935179952205048
absolute error = 4e-30
relative error = 3.1531354679269632617615195965647e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2634
Order of pole (three term test) = -9.082
Radius of convergence (six term test) for eq 1 = 1.395
Order of pole (six term test) = -12.22
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = -12.672469320553019778944544481648
y[1] (numeric) = -12.672469320553019778944544481643
absolute error = 5e-30
relative error = 3.9455609427995858631599941811448e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = -12.65914766229166283170015888243
y[1] (numeric) = -12.659147662291662831700158882426
absolute error = 4e-30
relative error = 3.1597703942698833825550899341912e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0706
Order of pole (three term test) = -23.61
Radius of convergence (six term test) for eq 1 = 0.2879
Order of pole (six term test) = -11.99
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = -12.645820461355481053387194199534
y[1] (numeric) = -12.64582046135548105338719419953
absolute error = 4e-30
relative error = 3.1631004190069354592177251087316e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6059
Order of pole (six term test) = -11.12
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = -12.632487716857315248193536473774
y[1] (numeric) = -12.632487716857315248193536473768
absolute error = 6e-30
relative error = 4.7496582893908943124909631660856e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.932
Order of pole (six term test) = -14.4
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = -12.619149427909919058390327104198
y[1] (numeric) = -12.619149427909919058390327104192
absolute error = 6e-30
relative error = 4.7546786209930523953876770907279e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7883
Order of pole (six term test) = -11.94
TOP MAIN SOLVE Loop
bytes used=392112328, alloc=4652204, time=13.40
x[1] = 4.35
y[1] (analytic) = -12.605805593625958958167390653792
y[1] (numeric) = -12.605805593625958958167390653787
absolute error = 5e-30
relative error = 3.9664263920809761347209878409632e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = -12.592456213118014247468322335908
y[1] (numeric) = -12.592456213118014247468322335903
absolute error = 5e-30
relative error = 3.9706312377654490353954981247447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3373
Order of pole (three term test) = -41.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = -12.579101285498577045825235166024
y[1] (numeric) = -12.579101285498577045825235166019
absolute error = 5e-30
relative error = 3.9748467609240839850929354696510e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = -12.565740809880052286193166763446
y[1] (numeric) = -12.565740809880052286193166763442
absolute error = 4e-30
relative error = 3.1832584011719580079160467389417e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6719
Order of pole (three term test) = 69.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = -12.552374785374757708784145787539
y[1] (numeric) = -12.552374785374757708784145787534
absolute error = 5e-30
relative error = 3.9833099994956232396475599116770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05364
Order of pole (three term test) = -3.562
Radius of convergence (six term test) for eq 1 = 1.927
Order of pole (six term test) = -10.53
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = -12.53900321109492385490091799307
y[1] (numeric) = -12.539003211094923854900917993065
absolute error = 5e-30
relative error = 3.9875577953244600730190846191008e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.754
Order of pole (three term test) = 97.72
Radius of convergence (six term test) for eq 1 = 1.926
Order of pole (six term test) = -11.77
bytes used=396116248, alloc=4652204, time=13.54
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = -12.525626086152694060770331889296
y[1] (numeric) = -12.525626086152694060770331889291
absolute error = 5e-30
relative error = 3.9918164294618297245836966390579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0984
Order of pole (three term test) = -22.21
Radius of convergence (six term test) for eq 1 = 0.5341
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = -12.512243409660124451376383987353
y[1] (numeric) = -12.512243409660124451376383987348
absolute error = 5e-30
relative error = 3.9960859426213937363048443072434e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04381
Order of pole (three term test) = -35.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = -12.498855180729183934292923620568
y[1] (numeric) = -12.498855180729183934292923620562
absolute error = 6e-30
relative error = 4.8004396508656560439518615382125e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5382
Order of pole (three term test) = -61
Radius of convergence (six term test) for eq 1 = 3.648
Order of pole (six term test) = -5.677
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = -12.485461398471754193516017322268
y[1] (numeric) = -12.485461398471754193516017322262
absolute error = 6e-30
relative error = 4.8055893238630429574575348178303e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.195
Order of pole (six term test) = -13.47
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = -12.472062061999629683295972745709
y[1] (numeric) = -12.472062061999629683295972745703
absolute error = 6e-30
relative error = 4.8107521997353080122845284990513e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=400117204, alloc=4652204, time=13.67
x[1] = 4.46
y[1] (analytic) = -12.458657170424517621969022110681
y[1] (numeric) = -12.458657170424517621969022110676
absolute error = 5e-30
relative error = 4.0132736069417258579296839734630e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00441
Order of pole (three term test) = -0.8822
Radius of convergence (six term test) for eq 1 = 2.679
Order of pole (six term test) = -15.56
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = -12.445246722858037985788665161417
y[1] (numeric) = -12.445246722858037985788665161412
absolute error = 5e-30
relative error = 4.0175981331222296510569331107016e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2641
Order of pole (three term test) = -21.2
Radius of convergence (six term test) for eq 1 = 1.028
Order of pole (six term test) = -11.71
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = -12.431830718411723502756671620366
y[1] (numeric) = -12.431830718411723502756671620361
absolute error = 5e-30
relative error = 4.0219337869481497337568800334450e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6463
Order of pole (six term test) = -12.09
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = -12.41840915619701964645374312245
y[1] (numeric) = -12.418409156197019646453743122445
absolute error = 5e-30
relative error = 4.0262806105924654571413214168748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04203
Order of pole (three term test) = -29.84
Radius of convergence (six term test) for eq 1 = 1.292
Order of pole (six term test) = -10.11
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = -12.404982035325284629869834614379
y[1] (numeric) = -12.404982035325284629869834614375
absolute error = 4e-30
relative error = 3.2245109171535463783364090716400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.476
Order of pole (six term test) = -11.64
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = -12.391549354907789399234135203621
y[1] (numeric) = -12.391549354907789399234135203616
absolute error = 5e-30
relative error = 4.0350079370984412712267230493404e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1257
Order of pole (three term test) = -19.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=404118280, alloc=4652204, time=13.81
x[1] = 4.52
y[1] (analytic) = -12.378111114055717627844708441606
y[1] (numeric) = -12.3781111140557176278447084416
absolute error = 6e-30
relative error = 4.8472662304564542644731024296064e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.545
Order of pole (six term test) = -17.48
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = -12.364667311880165709897792025771
y[1] (numeric) = -12.364667311880165709897792025765
absolute error = 6e-30
relative error = 4.8525365451888108408563481447607e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06454
Order of pole (three term test) = 4.561
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = -12.351217947492142754316756905024
y[1] (numeric) = -12.35121794749214275431675690502
absolute error = 4e-30
relative error = 3.2385470137478882067588703612560e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03089
Order of pole (three term test) = -28.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = -12.337763020002570578580725773216
y[1] (numeric) = -12.337763020002570578580725773211
absolute error = 5e-30
relative error = 4.0525985074391210406860688557258e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = -12.324302528522283702552850935196
y[1] (numeric) = -12.324302528522283702552850935191
absolute error = 5e-30
relative error = 4.0570247187850501058817001784777e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.207
Order of pole (three term test) = -56.58
Radius of convergence (six term test) for eq 1 = 4.025
Order of pole (six term test) = -14.03
TOP MAIN SOLVE Loop
bytes used=408119336, alloc=4652204, time=13.95
x[1] = 4.57
y[1] (analytic) = -12.310836472162029342308251530069
y[1] (numeric) = -12.310836472162029342308251530065
absolute error = 4e-30
relative error = 3.2491699561155164314136843963271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.106
Order of pole (six term test) = -13.31
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = -12.297364850032467403961610096211
y[1] (numeric) = -12.297364850032467403961610096206
absolute error = 5e-30
relative error = 4.0659117306638251365997560332008e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01508
Order of pole (three term test) = -26.3
Radius of convergence (six term test) for eq 1 = 1.315
Order of pole (six term test) = -11.43
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = -12.283887661244170477494428462634
y[1] (numeric) = -12.283887661244170477494428462629
absolute error = 5e-30
relative error = 4.0703726197163677540622541846013e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.212
Order of pole (six term test) = 6.922
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = -12.270404904907623830581942951301
y[1] (numeric) = -12.270404904907623830581942951296
absolute error = 5e-30
relative error = 4.0748451569028657564553619254753e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.465
Order of pole (six term test) = -11.41
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = -12.256916580133225402419698874957
y[1] (numeric) = -12.256916580133225402419698874953
absolute error = 4e-30
relative error = 3.2634635096427509308092102285807e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03177
Order of pole (three term test) = -0.3235
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = -12.243422686031285797549784315071
y[1] (numeric) = -12.243422686031285797549784315067
absolute error = 4e-30
relative error = 3.2670602841831664761464484362061e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.767
Order of pole (three term test) = -216.2
Radius of convergence (six term test) for eq 1 = 1.644
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
bytes used=412120252, alloc=4652204, time=14.08
x[1] = 4.63
y[1] (analytic) = -12.229923221712028279686723164464
y[1] (numeric) = -12.229923221712028279686723164459
absolute error = 5e-30
relative error = 4.0883331067225341177989458821275e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = -12.216418186285588765543027419214
y[1] (numeric) = -12.216418186285588765543027419209
absolute error = 5e-30
relative error = 4.0928526870610130940349574702213e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07329
Order of pole (three term test) = -13.24
Radius of convergence (six term test) for eq 1 = 2.292
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = -12.202907578862015818654408704418
y[1] (numeric) = -12.202907578862015818654408704414
absolute error = 4e-30
relative error = 3.2779073136051897125651858954511e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5537
Order of pole (three term test) = -96.09
Radius of convergence (six term test) for eq 1 = 1.744
Order of pole (six term test) = -12.05
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = -12.189391398551270643204649018391
y[1] (numeric) = -12.189391398551270643204649018386
absolute error = 5e-30
relative error = 4.1019275175578152994687400495766e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.758
Order of pole (six term test) = -12.7
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = -12.175869644463227077850130679871
y[1] (numeric) = -12.175869644463227077850130679865
absolute error = 6e-30
relative error = 4.9277794319425878319177624507158e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = -12.162342315707671589544025462836
y[1] (numeric) = -12.162342315707671589544025462831
absolute error = 5e-30
relative error = 4.1110502156665146091297109586531e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06715
Order of pole (three term test) = -49.38
Radius of convergence (six term test) for eq 1 = 0.9833
Order of pole (six term test) = -11.91
bytes used=416122328, alloc=4652204, time=14.22
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = -12.1488094113943032673601429035
y[1] (numeric) = -12.148809411394303267360142903494
absolute error = 6e-30
relative error = 4.9387555577031541388878720916337e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5838
Order of pole (three term test) = -67.96
Radius of convergence (six term test) for eq 1 = 1.413
Order of pole (six term test) = -11.85
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = -12.135270930632733816316437764046
y[1] (numeric) = -12.135270930632733816316437764042
absolute error = 4e-30
relative error = 3.2961769233374995935127827896610e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.38
Order of pole (six term test) = -12.66
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = -12.121726872532487551198176637726
y[1] (numeric) = -12.121726872532487551198176637721
absolute error = 5e-30
relative error = 4.1248248311301814098942566260635e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6638
Order of pole (six term test) = -12.03
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = -12.108177236203001390380763679835
y[1] (numeric) = -12.10817723620300139038076367983
absolute error = 5e-30
relative error = 4.1294407097462904857025149878435e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = -12.094622020753624849652225449213
y[1] (numeric) = -12.094622020753624849652225449208
absolute error = 5e-30
relative error = 4.1340688377200284754100395715536e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.979
Order of pole (six term test) = -12.02
TOP MAIN SOLVE Loop
bytes used=420123008, alloc=4652204, time=14.36
x[1] = 4.74
y[1] (analytic) = -12.081061225293620036035354844792
y[1] (numeric) = -12.081061225293620036035354844786
absolute error = 6e-30
relative error = 4.9664511156007116787432298412926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2355
Order of pole (three term test) = -44.29
Radius of convergence (six term test) for eq 1 = 2.094
Order of pole (six term test) = -10.96
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = -12.067494848932161641609514121788
y[1] (numeric) = -12.067494848932161641609514121783
absolute error = 5e-30
relative error = 4.1433620337881843730289919852927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1447
Order of pole (three term test) = -41.54
Radius of convergence (six term test) for eq 1 = 1.604
Order of pole (six term test) = -12.19
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = -12.053922890778336937332096972127
y[1] (numeric) = -12.053922890778336937332096972122
absolute error = 5e-30
relative error = 4.1480271985356492698056014019432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = -12.040345349941145766859649653644
y[1] (numeric) = -12.040345349941145766859649653638
absolute error = 6e-30
relative error = 4.9832457671401663830327700164648e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.476
Order of pole (six term test) = -13.95
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = -12.026762225529500540368651152661
y[1] (numeric) = -12.026762225529500540368651152657
absolute error = 4e-30
relative error = 3.3259159239958222189782678968921e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = -12.013173516652226228375952364519
y[1] (numeric) = -12.013173516652226228375952364514
absolute error = 5e-30
relative error = 4.1620975448903497562836131510929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.107
Order of pole (three term test) = 0.079
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=424124148, alloc=4652204, time=14.49
x[1] = 4.8
y[1] (analytic) = -11.999579222418060355558874276597
y[1] (numeric) = -11.999579222418060355558874276591
absolute error = 6e-30
relative error = 5.0001753301403908947520590495095e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1356
Order of pole (three term test) = -3.435
Radius of convergence (six term test) for eq 1 = 2.07
Order of pole (six term test) = -11.58
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = -11.985979341935652994574965138439
y[1] (numeric) = -11.985979341935652994574965138435
absolute error = 4e-30
relative error = 3.3372325163327267912817552988136e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0491
Order of pole (three term test) = -25.15
Radius of convergence (six term test) for eq 1 = 0.9337
Order of pole (six term test) = -12.14
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = -11.972373874313566759881416603553
y[1] (numeric) = -11.972373874313566759881416603547
absolute error = 6e-30
relative error = 5.0115374469493073601232676421781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.178
Order of pole (six term test) = -17.76
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = -11.958762818660276801554138827396
y[1] (numeric) = -11.95876281866027680155413882739
absolute error = 6e-30
relative error = 5.0172414078132636387758546486737e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0747
Order of pole (three term test) = -29.85
Radius of convergence (six term test) for eq 1 = 1.206
Order of pole (six term test) = -11.56
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = -11.945146174084170799106494506214
y[1] (numeric) = -11.94514617408417079910649450621
absolute error = 4e-30
relative error = 3.3486404784884754860267539905455e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.046
Order of pole (six term test) = -11.44
TOP MAIN SOLVE Loop
bytes used=428124952, alloc=4652204, time=14.63
x[1] = 4.85
y[1] (analytic) = -11.931523939693548955307691841226
y[1] (numeric) = -11.931523939693548955307691841222
absolute error = 4e-30
relative error = 3.3524636251140410468144407392032e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02969
Order of pole (three term test) = -24.47
Radius of convergence (six term test) for eq 1 = 5.356
Order of pole (six term test) = -3.222
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = -11.917896114596623990000836412746
y[1] (numeric) = -11.917896114596623990000836412742
absolute error = 4e-30
relative error = 3.3562970859436669730444093754960e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7048
Order of pole (six term test) = -11.45
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = -11.904262697901521133920641948833
y[1] (numeric) = -11.904262697901521133920641948829
absolute error = 4e-30
relative error = 3.3601409020527734716410933522626e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3024
Order of pole (three term test) = 2.002
Radius of convergence (six term test) for eq 1 = 1.109
Order of pole (six term test) = -12.55
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = -11.890623688716278122510799973012
y[1] (numeric) = -11.890623688716278122510799973006
absolute error = 6e-30
relative error = 5.0459926721032789817292726537925e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7584
Order of pole (six term test) = -11.92
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = -11.876979086148845189741008315634
y[1] (numeric) = -11.87697908614884518974100831563
absolute error = 4e-30
relative error = 3.3678597655062596676009767798090e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = -11.863328889307085061923658473478
y[1] (numeric) = -11.863328889307085061923658473473
absolute error = 5e-30
relative error = 4.2146686201262693683886474235490e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=432125788, alloc=4652204, time=14.77
x[1] = 4.91
y[1] (analytic) = -11.849673097298772951530181802096
y[1] (numeric) = -11.849673097298772951530181802091
absolute error = 5e-30
relative error = 4.2195256855986935971805285642678e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.289
Order of pole (six term test) = -11.92
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = -11.836011709231596551007054525536
y[1] (numeric) = -11.836011709231596551007054525533
absolute error = 3e-30
relative error = 2.5346375736179145984906360252477e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003795
Order of pole (three term test) = -25.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = -11.822344724213156026591461547974
y[1] (numeric) = -11.822344724213156026591461547969
absolute error = 5e-30
relative error = 4.2292794844322037034989140113203e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.103
Order of pole (three term test) = -29.15
Radius of convergence (six term test) for eq 1 = 2.167
Order of pole (six term test) = -13.59
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = -11.808672141350964012126619051796
y[1] (numeric) = -11.808672141350964012126619051792
absolute error = 4e-30
relative error = 3.3873410592822017439897255864291e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04788
Order of pole (three term test) = -4.734
Radius of convergence (six term test) for eq 1 = 1.012
Order of pole (six term test) = -11.32
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = -11.794993959752445602876755866769
y[1] (numeric) = -11.794993959752445602876755866765
absolute error = 4e-30
relative error = 3.3912692229000110151779700321343e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2006
Order of pole (three term test) = -32.85
Radius of convergence (six term test) for eq 1 = 1.082
Order of pole (six term test) = -12.12
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = -11.781310178524938349341753594776
y[1] (numeric) = -11.781310178524938349341753594773
absolute error = 3e-30
relative error = 2.5464060911225500025004385051016e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
bytes used=436128504, alloc=4652204, time=14.91
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = -11.767620796775692251071445474747
y[1] (numeric) = -11.767620796775692251071445474742
absolute error = 5e-30
relative error = 4.2489472480027495053650880686218e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = -11.753925813611869750479573972297
y[1] (numeric) = -11.753925813611869750479573972293
absolute error = 4e-30
relative error = 3.4031182971800959466079575491530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0482
Order of pole (three term test) = -2.676
Radius of convergence (six term test) for eq 1 = 2.016
Order of pole (six term test) = -11.06
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = -11.740225228140545726657407078693
y[1] (numeric) = -11.740225228140545726657407078689
absolute error = 4e-30
relative error = 3.4070896616295433227372949875541e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06092
Order of pole (three term test) = -8.865
Radius of convergence (six term test) for eq 1 = 1.8
Order of pole (six term test) = -10.5
Finished!
diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));
Iterations = 600
Total Elapsed Time = 14 Seconds
Elapsed Time(since restart) = 14 Seconds
Time to Timeout = 2 Minutes 45 Seconds
Percent Done = 100.2 %
> quit
bytes used=438326596, alloc=4652204, time=14.98