|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> 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 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 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,"");
> value3 := 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 (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
max_value3 := 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, "");
value3 := 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_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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 1
> if (iter >= 0) then # if number 2
> 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 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> 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 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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)) + 2
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 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> 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 1;
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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 1
> 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 1;
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #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]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> 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) > glob_small_float * glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #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 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> 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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> 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) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found_sing := 0;
> #TOP WHICH RADII EQ = 1
> if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found_sing := 1;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> 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 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no,
rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (
omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float)
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 glob_small_float*glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) 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
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float 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) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) 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 glob_small_float < omniabs(rcs) 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_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found_sing := 0;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1]
and 0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float
and array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found_sing := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
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_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp1[1] := (array_y[1] * (array_y[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[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 FULL FULL $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[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 mult FULL FULL $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[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 mult FULL FULL $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[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 mult FULL FULL $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_y,array_y,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[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 mult FULL FULL $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_y,array_y,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> 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 2
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, array_fact_2, glob_last;
array_tmp1[1] := array_y[1]*array_y[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[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] := ats(2, array_y, array_y, 1);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_y, array_y, 1);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_y, array_y, 1);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_y, array_y, 1);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_y, array_y, 1);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #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\n", 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 \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", 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\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", 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, " | \n")
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 Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
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,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_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, 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_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
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 16
> # Begin Function number 17
> 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 17
> # Begin Function number 18
> 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 18
> # Begin Function number 19
> 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 19
> # Begin Function number 20
> 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 20
> # Begin Function number 21
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 21
> # Begin Function number 22
> 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 22
> # Begin Function number 23
> 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");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> 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")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 23
> # Begin Function number 24
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 24
> # Begin Function number 25
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 25
> # Begin Function number 26
> 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 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> 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 26
> # Begin Function number 27
> 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 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> 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 27
> # Begin Function number 28
> 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 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> 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 28
> # Begin Function number 29
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 29
> # Begin Function number 30
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> 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 30
> # Begin Function number 31
> 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 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> 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 31
> # Begin Function number 32
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 33
> # Begin Function number 34
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 34
> # Begin Function number 35
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 35
> # Begin Function number 36
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 36
> # Begin Function number 37
> 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 37
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(1.0/(1.0 - x));
> end;
exact_soln_y := proc(x) return 1.0/(1.0 - x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> 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_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 := 0.1e-200;
> glob_smallish_float := 0.1e-100;
> 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/nonlinear1postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 0.5 ;");
> 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,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(1.0/(1.0 - x));");
> 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 := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> 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..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(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..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 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 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 0.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> 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);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> 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 3
> 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 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> 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 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> 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,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> 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 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
> ;
> 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 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> 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 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> 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 3
> 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 3;
> #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 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> 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 3
> 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 3;
> #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 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> 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 3
> 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 3;
> #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 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> 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 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = y * y;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T18:55:17-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"nonlinear1")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"nonlinear1 diffeq.mxt")
> ;
> logitem_str(html_log_file,"nonlinear1 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #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, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole,
array_1st_rel_error, array_last_rel_error, array_type_pole, array_y,
array_x, array_tmp0, array_tmp1, array_tmp2, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_real_pole, array_complex_pole, 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;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
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_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 := 0.1*10^(-200);
glob_smallish_float := 0.1*10^(-100);
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/nonlinear1postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 0.5 ;");
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, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(1.0/(1.0 - x));");
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 := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
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 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 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 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 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 <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 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 <= 1 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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 0.5;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
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);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. 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();
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, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = y * y;");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-01-28T18:55:17-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"nonlinear1");
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
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, " 165 | ");
logitem_str(html_log_file, "nonlinear1 diffeq.mxt");
logitem_str(html_log_file, "nonlinear1 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 12
> main();
##############ECHO OF PROBLEM#################
##############temp/nonlinear1postode.ode#################
diff ( y , x , 1 ) = y * y;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 0.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(1.0/(1.0 - x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.5
estimated_steps = 500
step_error = 2.0000000000000000000000000000000e-13
est_needed_step_err = 2.0000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.0005002500000000000000000000000e-78
max_value3 = 1.0005002500000000000000000000000e-78
value3 = 1.0005002500000000000000000000000e-78
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 1
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.001
y[1] (analytic) = 1.001001001001001001001001001001
y[1] (numeric) = 1.001001001001001001001001001001
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.999
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.002
y[1] (analytic) = 1.0020040080160320641282565130261
y[1] (numeric) = 1.0020040080160320641282565130261
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.998
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.003
y[1] (analytic) = 1.0030090270812437311935807422267
y[1] (numeric) = 1.0030090270812437311935807422267
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.997
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.004
y[1] (analytic) = 1.0040160642570281124497991967871
y[1] (numeric) = 1.0040160642570281124497991967872
absolute error = 1e-31
relative error = 9.9600000000000000000000000000005e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.996
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.005
y[1] (analytic) = 1.0050251256281407035175879396985
y[1] (numeric) = 1.0050251256281407035175879396985
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.995
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.006
y[1] (analytic) = 1.006036217303822937625754527163
y[1] (numeric) = 1.006036217303822937625754527163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.994
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.31
x[1] = 0.007
y[1] (analytic) = 1.0070493454179254783484390735146
y[1] (numeric) = 1.0070493454179254783484390735146
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.993
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.008
y[1] (analytic) = 1.0080645161290322580645161290323
y[1] (numeric) = 1.0080645161290322580645161290323
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.992
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.009
y[1] (analytic) = 1.0090817356205852674066599394551
y[1] (numeric) = 1.0090817356205852674066599394551
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.991
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 1.010101010101010101010101010101
y[1] (numeric) = 1.010101010101010101010101010101
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.99
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.011
y[1] (analytic) = 1.0111223458038422649140546006067
y[1] (numeric) = 1.0111223458038422649140546006067
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.989
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.012
y[1] (analytic) = 1.0121457489878542510121457489879
y[1] (numeric) = 1.0121457489878542510121457489879
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.988
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.013
y[1] (analytic) = 1.0131712259371833839918946301925
y[1] (numeric) = 1.0131712259371833839918946301925
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.987
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.014
y[1] (analytic) = 1.0141987829614604462474645030426
y[1] (numeric) = 1.0141987829614604462474645030426
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.986
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.015
y[1] (analytic) = 1.0152284263959390862944162436548
y[1] (numeric) = 1.0152284263959390862944162436548
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.985
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.016
y[1] (analytic) = 1.016260162601626016260162601626
y[1] (numeric) = 1.016260162601626016260162601626
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.984
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.017
y[1] (analytic) = 1.0172939979654120040691759918616
y[1] (numeric) = 1.0172939979654120040691759918616
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.983
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.018
y[1] (analytic) = 1.0183299389002036659877800407332
y[1] (numeric) = 1.0183299389002036659877800407331
absolute error = 1e-31
relative error = 9.8200000000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.982
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.019
y[1] (analytic) = 1.0193679918450560652395514780836
y[1] (numeric) = 1.0193679918450560652395514780835
absolute error = 1e-31
relative error = 9.8099999999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.981
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = 1.0204081632653061224489795918367
y[1] (numeric) = 1.0204081632653061224489795918366
absolute error = 1e-31
relative error = 9.8000000000000000000000000000003e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.98
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.021
y[1] (analytic) = 1.0214504596527068437180796731359
y[1] (numeric) = 1.0214504596527068437180796731357
absolute error = 2e-31
relative error = 1.9579999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.979
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.67
x[1] = 0.022
y[1] (analytic) = 1.0224948875255623721881390593047
y[1] (numeric) = 1.0224948875255623721881390593046
absolute error = 1e-31
relative error = 9.7800000000000000000000000000000e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.978
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.023
y[1] (analytic) = 1.0235414534288638689866939611054
y[1] (numeric) = 1.0235414534288638689866939611053
absolute error = 1e-31
relative error = 9.7700000000000000000000000000002e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.977
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.024
y[1] (analytic) = 1.0245901639344262295081967213115
y[1] (numeric) = 1.0245901639344262295081967213114
absolute error = 1e-31
relative error = 9.7599999999999999999999999999998e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.976
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.025
y[1] (analytic) = 1.025641025641025641025641025641
y[1] (numeric) = 1.025641025641025641025641025641
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.975
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.026
y[1] (analytic) = 1.0266940451745379876796714579055
y[1] (numeric) = 1.0266940451745379876796714579055
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.974
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.027
y[1] (analytic) = 1.0277492291880781089414182939363
y[1] (numeric) = 1.0277492291880781089414182939362
absolute error = 1e-31
relative error = 9.7299999999999999999999999999998e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.973
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.028
y[1] (analytic) = 1.0288065843621399176954732510288
y[1] (numeric) = 1.0288065843621399176954732510287
absolute error = 1e-31
relative error = 9.7200000000000000000000000000001e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.972
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.029
y[1] (analytic) = 1.029866117404737384140061791967
y[1] (numeric) = 1.0298661174047373841400617919669
absolute error = 1e-31
relative error = 9.7100000000000000000000000000004e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.971
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 1.0309278350515463917525773195876
y[1] (numeric) = 1.0309278350515463917525773195875
absolute error = 1e-31
relative error = 9.7000000000000000000000000000003e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.97
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.031
y[1] (analytic) = 1.0319917440660474716202270381837
y[1] (numeric) = 1.0319917440660474716202270381836
absolute error = 1e-31
relative error = 9.6899999999999999999999999999999e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.969
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.032
y[1] (analytic) = 1.0330578512396694214876033057851
y[1] (numeric) = 1.033057851239669421487603305785
absolute error = 1e-31
relative error = 9.6800000000000000000000000000002e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.968
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.033
y[1] (analytic) = 1.0341261633919338159255429162358
y[1] (numeric) = 1.0341261633919338159255429162357
absolute error = 1e-31
relative error = 9.6699999999999999999999999999998e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.967
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.034
y[1] (analytic) = 1.0351966873706004140786749482402
y[1] (numeric) = 1.0351966873706004140786749482401
absolute error = 1e-31
relative error = 9.6599999999999999999999999999997e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.966
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.035
y[1] (analytic) = 1.0362694300518134715025906735751
y[1] (numeric) = 1.0362694300518134715025906735751
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.965
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.036
y[1] (analytic) = 1.037344398340248962655601659751
y[1] (numeric) = 1.037344398340248962655601659751
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.964
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=1.05
x[1] = 0.037
y[1] (analytic) = 1.0384215991692627206645898234683
y[1] (numeric) = 1.0384215991692627206645898234683
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.963
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.038
y[1] (analytic) = 1.039501039501039501039501039501
y[1] (numeric) = 1.039501039501039501039501039501
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.962
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.039
y[1] (analytic) = 1.0405827263267429760665972944849
y[1] (numeric) = 1.0405827263267429760665972944849
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.961
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 1.0416666666666666666666666666667
y[1] (numeric) = 1.0416666666666666666666666666667
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.96
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.041
y[1] (analytic) = 1.0427528675703858185610010427529
y[1] (numeric) = 1.0427528675703858185610010427529
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.959
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.042
y[1] (analytic) = 1.0438413361169102296450939457202
y[1] (numeric) = 1.0438413361169102296450939457203
absolute error = 1e-31
relative error = 9.5800000000000000000000000000005e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.958
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.043
y[1] (analytic) = 1.0449320794148380355276907001045
y[1] (numeric) = 1.0449320794148380355276907001045
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.957
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.044
y[1] (analytic) = 1.0460251046025104602510460251046
y[1] (numeric) = 1.0460251046025104602510460251046
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.956
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.045
y[1] (analytic) = 1.0471204188481675392670157068063
y[1] (numeric) = 1.0471204188481675392670157068063
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.955
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.046
y[1] (analytic) = 1.0482180293501048218029350104822
y[1] (numeric) = 1.0482180293501048218029350104822
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.954
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.047
y[1] (analytic) = 1.0493179433368310598111227701994
y[1] (numeric) = 1.0493179433368310598111227701994
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.953
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.048
y[1] (analytic) = 1.0504201680672268907563025210084
y[1] (numeric) = 1.0504201680672268907563025210084
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.952
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.049
y[1] (analytic) = 1.0515247108307045215562565720294
y[1] (numeric) = 1.0515247108307045215562565720294
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.951
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = 1.0526315789473684210526315789474
y[1] (numeric) = 1.0526315789473684210526315789473
absolute error = 1e-31
relative error = 9.4999999999999999999999999999997e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.95
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.051
y[1] (analytic) = 1.0537407797681770284510010537408
y[1] (numeric) = 1.0537407797681770284510010537407
absolute error = 1e-31
relative error = 9.4899999999999999999999999999998e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.949
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.052
y[1] (analytic) = 1.0548523206751054852320675105485
y[1] (numeric) = 1.0548523206751054852320675105484
absolute error = 1e-31
relative error = 9.4800000000000000000000000000002e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.948
Order of pole = 651
memory used=15.2MB, alloc=3.9MB, time=1.43
TOP MAIN SOLVE Loop
x[1] = 0.053
y[1] (analytic) = 1.0559662090813093980992608236536
y[1] (numeric) = 1.0559662090813093980992608236535
absolute error = 1e-31
relative error = 9.4700000000000000000000000000004e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.947
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.054
y[1] (analytic) = 1.0570824524312896405919661733615
y[1] (numeric) = 1.0570824524312896405919661733614
absolute error = 1e-31
relative error = 9.4600000000000000000000000000002e-30 %
Correct digits = 31
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.946
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.055
y[1] (analytic) = 1.0582010582010582010582010582011
y[1] (numeric) = 1.0582010582010582010582010582009
absolute error = 2e-31
relative error = 1.8899999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.945
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.056
y[1] (analytic) = 1.0593220338983050847457627118644
y[1] (numeric) = 1.0593220338983050847457627118642
absolute error = 2e-31
relative error = 1.8880000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.944
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.057
y[1] (analytic) = 1.0604453870625662778366914103924
y[1] (numeric) = 1.0604453870625662778366914103922
absolute error = 2e-31
relative error = 1.8859999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.943
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.058
y[1] (analytic) = 1.0615711252653927813163481953291
y[1] (numeric) = 1.0615711252653927813163481953289
absolute error = 2e-31
relative error = 1.8840000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.942
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.059
y[1] (analytic) = 1.0626992561105207226354941551541
y[1] (numeric) = 1.0626992561105207226354941551539
absolute error = 2e-31
relative error = 1.8820000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.941
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 1.0638297872340425531914893617021
y[1] (numeric) = 1.0638297872340425531914893617019
absolute error = 2e-31
relative error = 1.8800000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.94
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.061
y[1] (analytic) = 1.0649627263045793397231096911608
y[1] (numeric) = 1.0649627263045793397231096911606
absolute error = 2e-31
relative error = 1.8780000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.939
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.062
y[1] (analytic) = 1.0660980810234541577825159914712
y[1] (numeric) = 1.066098081023454157782515991471
absolute error = 2e-31
relative error = 1.8760000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.938
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.063
y[1] (analytic) = 1.0672358591248665955176093916756
y[1] (numeric) = 1.0672358591248665955176093916753
absolute error = 3e-31
relative error = 2.8109999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.937
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.064
y[1] (analytic) = 1.0683760683760683760683760683761
y[1] (numeric) = 1.0683760683760683760683760683758
absolute error = 3e-31
relative error = 2.8079999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.936
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.065
y[1] (analytic) = 1.069518716577540106951871657754
y[1] (numeric) = 1.0695187165775401069518716577537
absolute error = 3e-31
relative error = 2.8050000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.935
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.066
y[1] (analytic) = 1.0706638115631691648822269807281
y[1] (numeric) = 1.0706638115631691648822269807277
absolute error = 4e-31
relative error = 3.7359999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.934
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.067
y[1] (analytic) = 1.0718113612004287245444801714898
y[1] (numeric) = 1.0718113612004287245444801714895
absolute error = 3e-31
relative error = 2.7990000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.933
memory used=19.0MB, alloc=4.0MB, time=1.80
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.068
y[1] (analytic) = 1.0729613733905579399141630901288
y[1] (numeric) = 1.0729613733905579399141630901284
absolute error = 4e-31
relative error = 3.7279999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.932
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.069
y[1] (analytic) = 1.0741138560687432867883995703545
y[1] (numeric) = 1.0741138560687432867883995703541
absolute error = 4e-31
relative error = 3.7239999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.931
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 1.0752688172043010752688172043011
y[1] (numeric) = 1.0752688172043010752688172043007
absolute error = 4e-31
relative error = 3.7199999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.93
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.071
y[1] (analytic) = 1.0764262648008611410118406889128
y[1] (numeric) = 1.0764262648008611410118406889124
absolute error = 4e-31
relative error = 3.7160000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.929
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.072
y[1] (analytic) = 1.0775862068965517241379310344828
y[1] (numeric) = 1.0775862068965517241379310344823
absolute error = 5e-31
relative error = 4.6399999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.928
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.073
y[1] (analytic) = 1.0787486515641855447680690399137
y[1] (numeric) = 1.0787486515641855447680690399132
absolute error = 5e-31
relative error = 4.6350000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.927
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.074
y[1] (analytic) = 1.0799136069114470842332613390929
y[1] (numeric) = 1.0799136069114470842332613390924
absolute error = 5e-31
relative error = 4.6299999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.926
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.075
y[1] (analytic) = 1.0810810810810810810810810810811
y[1] (numeric) = 1.0810810810810810810810810810806
absolute error = 5e-31
relative error = 4.6249999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.925
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.076
y[1] (analytic) = 1.0822510822510822510822510822511
y[1] (numeric) = 1.0822510822510822510822510822506
absolute error = 5e-31
relative error = 4.6199999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.924
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.077
y[1] (analytic) = 1.0834236186348862405200433369447
y[1] (numeric) = 1.0834236186348862405200433369443
absolute error = 4e-31
relative error = 3.6920000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.923
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.078
y[1] (analytic) = 1.0845986984815618221258134490239
y[1] (numeric) = 1.0845986984815618221258134490234
absolute error = 5e-31
relative error = 4.6099999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.922
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.079
y[1] (analytic) = 1.0857763300760043431053203040174
y[1] (numeric) = 1.0857763300760043431053203040169
absolute error = 5e-31
relative error = 4.6049999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.921
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 1.0869565217391304347826086956522
y[1] (numeric) = 1.0869565217391304347826086956517
absolute error = 5e-31
relative error = 4.5999999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.92
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.081
y[1] (analytic) = 1.0881392818280739934711643090316
y[1] (numeric) = 1.0881392818280739934711643090311
absolute error = 5e-31
relative error = 4.5949999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.919
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.082
y[1] (analytic) = 1.0893246187363834422657952069717
y[1] (numeric) = 1.0893246187363834422657952069712
memory used=22.8MB, alloc=4.0MB, time=2.19
absolute error = 5e-31
relative error = 4.5899999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.918
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.083
y[1] (analytic) = 1.0905125408942202835332606324973
y[1] (numeric) = 1.0905125408942202835332606324968
absolute error = 5e-31
relative error = 4.5849999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.917
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.084
y[1] (analytic) = 1.0917030567685589519650655021834
y[1] (numeric) = 1.0917030567685589519650655021829
absolute error = 5e-31
relative error = 4.5800000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.916
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.085
y[1] (analytic) = 1.0928961748633879781420765027322
y[1] (numeric) = 1.0928961748633879781420765027317
absolute error = 5e-31
relative error = 4.5750000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.915
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.086
y[1] (analytic) = 1.0940919037199124726477024070022
y[1] (numeric) = 1.0940919037199124726477024070016
absolute error = 6e-31
relative error = 5.4839999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.914
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.087
y[1] (analytic) = 1.0952902519167579408543263964951
y[1] (numeric) = 1.0952902519167579408543263964945
absolute error = 6e-31
relative error = 5.4779999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.913
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.088
y[1] (analytic) = 1.0964912280701754385964912280702
y[1] (numeric) = 1.0964912280701754385964912280696
absolute error = 6e-31
relative error = 5.4719999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.912
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.089
y[1] (analytic) = 1.0976948408342480790340285400659
y[1] (numeric) = 1.0976948408342480790340285400653
absolute error = 6e-31
relative error = 5.4659999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.911
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 1.0989010989010989010989010989011
y[1] (numeric) = 1.0989010989010989010989010989005
absolute error = 6e-31
relative error = 5.4600000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.91
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.091
y[1] (analytic) = 1.10011001100110011001100110011
y[1] (numeric) = 1.1001100110011001100110011001094
absolute error = 6e-31
relative error = 5.4540000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.909
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.092
y[1] (analytic) = 1.1013215859030837004405286343612
y[1] (numeric) = 1.1013215859030837004405286343606
absolute error = 6e-31
relative error = 5.4480000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.908
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.093
y[1] (analytic) = 1.1025358324145534729878721058434
y[1] (numeric) = 1.1025358324145534729878721058428
absolute error = 6e-31
relative error = 5.4420000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.907
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.094
y[1] (analytic) = 1.1037527593818984547461368653422
y[1] (numeric) = 1.1037527593818984547461368653415
absolute error = 7e-31
relative error = 6.3419999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.906
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.095
y[1] (analytic) = 1.1049723756906077348066298342541
y[1] (numeric) = 1.1049723756906077348066298342535
absolute error = 6e-31
relative error = 5.4300000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.905
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.096
y[1] (analytic) = 1.1061946902654867256637168141593
y[1] (numeric) = 1.1061946902654867256637168141586
absolute error = 7e-31
relative error = 6.3280000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.904
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.097
y[1] (analytic) = 1.1074197120708748615725359911406
y[1] (numeric) = 1.1074197120708748615725359911399
absolute error = 7e-31
relative error = 6.3210000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
memory used=26.7MB, alloc=4.1MB, time=2.57
Real estimate of pole used for equation 1
Radius of convergence = 0.903
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.098
y[1] (analytic) = 1.1086474501108647450110864745011
y[1] (numeric) = 1.1086474501108647450110864745004
absolute error = 7e-31
relative error = 6.3140000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.902
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.099
y[1] (analytic) = 1.1098779134295227524972253052164
y[1] (numeric) = 1.1098779134295227524972253052157
absolute error = 7e-31
relative error = 6.3070000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.901
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.1111111111111111111111111111111
y[1] (numeric) = 1.1111111111111111111111111111104
absolute error = 7e-31
relative error = 6.3000000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.9
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = 1.112347052280311457174638487208
y[1] (numeric) = 1.1123470522803114571746384872073
absolute error = 7e-31
relative error = 6.2930000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.899
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = 1.113585746102449888641425389755
y[1] (numeric) = 1.1135857461024498886414253897543
absolute error = 7e-31
relative error = 6.2860000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.898
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.103
y[1] (analytic) = 1.1148272017837235228539576365663
y[1] (numeric) = 1.1148272017837235228539576365656
absolute error = 7e-31
relative error = 6.2790000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.897
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.104
y[1] (analytic) = 1.1160714285714285714285714285714
y[1] (numeric) = 1.1160714285714285714285714285707
absolute error = 7e-31
relative error = 6.2720000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.896
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.105
y[1] (analytic) = 1.1173184357541899441340782122905
y[1] (numeric) = 1.1173184357541899441340782122898
absolute error = 7e-31
relative error = 6.2650000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.895
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = 1.1185682326621923937360178970917
y[1] (numeric) = 1.118568232662192393736017897091
absolute error = 7e-31
relative error = 6.2580000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.894
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = 1.1198208286674132138857782754759
y[1] (numeric) = 1.1198208286674132138857782754752
absolute error = 7e-31
relative error = 6.2510000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.893
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = 1.1210762331838565022421524663677
y[1] (numeric) = 1.121076233183856502242152466367
absolute error = 7e-31
relative error = 6.2440000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.892
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = 1.1223344556677890011223344556678
y[1] (numeric) = 1.1223344556677890011223344556671
absolute error = 7e-31
relative error = 6.2369999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.891
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.1235955056179775280898876404494
y[1] (numeric) = 1.1235955056179775280898876404487
absolute error = 7e-31
relative error = 6.2300000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.89
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.111
y[1] (analytic) = 1.1248593925759280089988751406074
y[1] (numeric) = 1.1248593925759280089988751406067
absolute error = 7e-31
relative error = 6.2230000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.889
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = 1.1261261261261261261261261261261
y[1] (numeric) = 1.1261261261261261261261261261254
absolute error = 7e-31
relative error = 6.2160000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.888
Order of pole = 651
memory used=30.5MB, alloc=4.1MB, time=2.95
TOP MAIN SOLVE Loop
x[1] = 0.113
y[1] (analytic) = 1.1273957158962795941375422773393
y[1] (numeric) = 1.1273957158962795941375422773386
absolute error = 7e-31
relative error = 6.2090000000000000000000000000003e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.887
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = 1.1286681715575620767494356659142
y[1] (numeric) = 1.1286681715575620767494356659135
absolute error = 7e-31
relative error = 6.2020000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.886
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = 1.1299435028248587570621468926554
y[1] (numeric) = 1.1299435028248587570621468926546
absolute error = 8e-31
relative error = 7.0799999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.885
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.116
y[1] (analytic) = 1.1312217194570135746606334841629
y[1] (numeric) = 1.1312217194570135746606334841621
absolute error = 8e-31
relative error = 7.0720000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.884
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = 1.1325028312570781426953567383918
y[1] (numeric) = 1.132502831257078142695356738391
absolute error = 8e-31
relative error = 7.0640000000000000000000000000003e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.883
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = 1.1337868480725623582766439909297
y[1] (numeric) = 1.1337868480725623582766439909289
absolute error = 8e-31
relative error = 7.0560000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.882
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.119
y[1] (analytic) = 1.1350737797956867196367763904654
y[1] (numeric) = 1.1350737797956867196367763904646
absolute error = 8e-31
relative error = 7.0479999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.881
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.1363636363636363636363636363636
y[1] (numeric) = 1.1363636363636363636363636363629
absolute error = 7e-31
relative error = 6.1600000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.88
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.121
y[1] (analytic) = 1.1376564277588168373151308304892
y[1] (numeric) = 1.1376564277588168373151308304885
absolute error = 7e-31
relative error = 6.1530000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.879
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.122
y[1] (analytic) = 1.1389521640091116173120728929385
y[1] (numeric) = 1.1389521640091116173120728929378
absolute error = 7e-31
relative error = 6.1460000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.878
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = 1.1402508551881413911060433295325
y[1] (numeric) = 1.1402508551881413911060433295318
absolute error = 7e-31
relative error = 6.1390000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.877
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = 1.1415525114155251141552511415525
y[1] (numeric) = 1.1415525114155251141552511415518
absolute error = 7e-31
relative error = 6.1320000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.876
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = 1.1428571428571428571428571428571
y[1] (numeric) = 1.1428571428571428571428571428564
absolute error = 7e-31
relative error = 6.1250000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.875
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = 1.1441647597254004576659038901602
y[1] (numeric) = 1.1441647597254004576659038901594
absolute error = 8e-31
relative error = 6.9919999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.874
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.127
y[1] (analytic) = 1.145475372279495990836197021764
y[1] (numeric) = 1.1454753722794959908361970217632
absolute error = 8e-31
relative error = 6.9840000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.873
Order of pole = 651
memory used=34.3MB, alloc=4.1MB, time=3.33
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = 1.146788990825688073394495412844
y[1] (numeric) = 1.1467889908256880733944954128432
absolute error = 8e-31
relative error = 6.9760000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.872
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = 1.1481056257175660160734787600459
y[1] (numeric) = 1.1481056257175660160734787600451
absolute error = 8e-31
relative error = 6.9680000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.871
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 1.1494252873563218390804597701149
y[1] (numeric) = 1.1494252873563218390804597701141
absolute error = 8e-31
relative error = 6.9600000000000000000000000000003e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.87
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = 1.1507479861910241657077100115075
y[1] (numeric) = 1.1507479861910241657077100115066
absolute error = 9e-31
relative error = 7.8209999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.869
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.132
y[1] (analytic) = 1.1520737327188940092165898617512
y[1] (numeric) = 1.1520737327188940092165898617503
absolute error = 9e-31
relative error = 7.8119999999999999999999999999997e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.868
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.133
y[1] (analytic) = 1.1534025374855824682814302191465
y[1] (numeric) = 1.1534025374855824682814302191456
absolute error = 9e-31
relative error = 7.8029999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.867
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = 1.1547344110854503464203233256351
y[1] (numeric) = 1.1547344110854503464203233256342
absolute error = 9e-31
relative error = 7.7940000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.866
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.135
y[1] (analytic) = 1.1560693641618497109826589595376
y[1] (numeric) = 1.1560693641618497109826589595367
absolute error = 9e-31
relative error = 7.7849999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.865
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = 1.1574074074074074074074074074074
y[1] (numeric) = 1.1574074074074074074074074074065
absolute error = 9e-31
relative error = 7.7760000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.864
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = 1.158748551564310544611819235226
y[1] (numeric) = 1.158748551564310544611819235225
absolute error = 1.0e-30
relative error = 8.6299999999999999999999999999997e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.863
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.138
y[1] (analytic) = 1.1600928074245939675174013921114
y[1] (numeric) = 1.1600928074245939675174013921104
absolute error = 1.0e-30
relative error = 8.6199999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.862
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.139
y[1] (analytic) = 1.1614401858304297328687572590012
y[1] (numeric) = 1.1614401858304297328687572590002
absolute error = 1.0e-30
relative error = 8.6099999999999999999999999999997e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.861
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 1.1627906976744186046511627906977
y[1] (numeric) = 1.1627906976744186046511627906967
absolute error = 1.0e-30
relative error = 8.5999999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.86
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.141
y[1] (analytic) = 1.1641443538998835855646100116414
y[1] (numeric) = 1.1641443538998835855646100116405
absolute error = 9e-31
relative error = 7.7310000000000000000000000000003e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.859
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = 1.1655011655011655011655011655012
y[1] (numeric) = 1.1655011655011655011655011655002
absolute error = 1.0e-30
relative error = 8.5799999999999999999999999999997e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.858
Order of pole = 651
memory used=38.1MB, alloc=4.1MB, time=3.72
TOP MAIN SOLVE Loop
x[1] = 0.143
y[1] (analytic) = 1.1668611435239206534422403733956
y[1] (numeric) = 1.1668611435239206534422403733946
absolute error = 1.0e-30
relative error = 8.5699999999999999999999999999997e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.857
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.144
y[1] (analytic) = 1.1682242990654205607476635514019
y[1] (numeric) = 1.1682242990654205607476635514009
absolute error = 1.0e-30
relative error = 8.5599999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.856
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = 1.1695906432748538011695906432749
y[1] (numeric) = 1.1695906432748538011695906432739
absolute error = 1.0e-30
relative error = 8.5499999999999999999999999999997e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.855
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = 1.1709601873536299765807962529274
y[1] (numeric) = 1.1709601873536299765807962529264
absolute error = 1.0e-30
relative error = 8.5400000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.854
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = 1.1723329425556858147713950762016
y[1] (numeric) = 1.1723329425556858147713950762006
absolute error = 1.0e-30
relative error = 8.5300000000000000000000000000003e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.853
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = 1.1737089201877934272300469483568
y[1] (numeric) = 1.1737089201877934272300469483558
absolute error = 1.0e-30
relative error = 8.5200000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.852
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.149
y[1] (analytic) = 1.1750881316098707403055229142186
y[1] (numeric) = 1.1750881316098707403055229142176
absolute error = 1.0e-30
relative error = 8.5099999999999999999999999999998e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.851
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.1764705882352941176470588235294
y[1] (numeric) = 1.1764705882352941176470588235284
absolute error = 1.0e-30
relative error = 8.5000000000000000000000000000001e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.85
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = 1.1778563015312131919905771495878
y[1] (numeric) = 1.1778563015312131919905771495867
absolute error = 1.1e-30
relative error = 9.3389999999999999999999999999996e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.849
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.152
y[1] (analytic) = 1.1792452830188679245283018867925
y[1] (numeric) = 1.1792452830188679245283018867914
absolute error = 1.1e-30
relative error = 9.3279999999999999999999999999996e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.848
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = 1.180637544273907910271546635183
y[1] (numeric) = 1.1806375442739079102715466351819
absolute error = 1.1e-30
relative error = 9.3170000000000000000000000000000e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.847
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.154
y[1] (analytic) = 1.1820330969267139479905437352246
y[1] (numeric) = 1.1820330969267139479905437352235
absolute error = 1.1e-30
relative error = 9.3059999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.846
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.155
y[1] (analytic) = 1.183431952662721893491124260355
y[1] (numeric) = 1.1834319526627218934911242603539
absolute error = 1.1e-30
relative error = 9.2950000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.845
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = 1.1848341232227488151658767772512
y[1] (numeric) = 1.1848341232227488151658767772501
absolute error = 1.1e-30
relative error = 9.2839999999999999999999999999999e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.844
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = 1.1862396204033214709371293001186
y[1] (numeric) = 1.1862396204033214709371293001175
absolute error = 1.1e-30
relative error = 9.2730000000000000000000000000002e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.843
Order of pole = 651
memory used=41.9MB, alloc=4.1MB, time=4.11
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = 1.1876484560570071258907363420428
y[1] (numeric) = 1.1876484560570071258907363420416
absolute error = 1.2e-30
relative error = 1.0104000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.842
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = 1.1890606420927467300832342449465
y[1] (numeric) = 1.1890606420927467300832342449453
absolute error = 1.2e-30
relative error = 1.0092000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.841
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 1.1904761904761904761904761904762
y[1] (numeric) = 1.190476190476190476190476190475
absolute error = 1.2e-30
relative error = 1.0080000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.84
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.161
y[1] (analytic) = 1.1918951132300357568533969010727
y[1] (numeric) = 1.1918951132300357568533969010715
absolute error = 1.2e-30
relative error = 1.0068000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.839
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = 1.1933174224343675417661097852029
y[1] (numeric) = 1.1933174224343675417661097852017
absolute error = 1.2e-30
relative error = 1.0056000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.838
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = 1.1947431302270011947431302270012
y[1] (numeric) = 1.194743130227001194743130227
absolute error = 1.2e-30
relative error = 1.0044000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.837
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = 1.1961722488038277511961722488038
y[1] (numeric) = 1.1961722488038277511961722488026
absolute error = 1.2e-30
relative error = 1.0032000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.836
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.165
y[1] (analytic) = 1.1976047904191616766467065868263
y[1] (numeric) = 1.1976047904191616766467065868251
absolute error = 1.2e-30
relative error = 1.0020000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.835
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.166
y[1] (analytic) = 1.1990407673860911270983213429257
y[1] (numeric) = 1.1990407673860911270983213429244
absolute error = 1.3e-30
relative error = 1.0842000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.834
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = 1.2004801920768307322929171668667
y[1] (numeric) = 1.2004801920768307322929171668655
absolute error = 1.2e-30
relative error = 9.9960000000000000000000000000004e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.833
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.168
y[1] (analytic) = 1.2019230769230769230769230769231
y[1] (numeric) = 1.2019230769230769230769230769218
absolute error = 1.3e-30
relative error = 1.0816000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.832
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.169
y[1] (analytic) = 1.2033694344163658243080625752106
y[1] (numeric) = 1.2033694344163658243080625752093
absolute error = 1.3e-30
relative error = 1.0803000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.831
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 1.2048192771084337349397590361446
y[1] (numeric) = 1.2048192771084337349397590361433
absolute error = 1.3e-30
relative error = 1.0790000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.83
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.171
y[1] (analytic) = 1.2062726176115802171290711700844
y[1] (numeric) = 1.2062726176115802171290711700832
absolute error = 1.2e-30
relative error = 9.9480000000000000000000000000003e-29 %
Correct digits = 30
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.829
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.172
y[1] (analytic) = 1.2077294685990338164251207729469
y[1] (numeric) = 1.2077294685990338164251207729456
absolute error = 1.3e-30
relative error = 1.0764000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.828
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=4.49
x[1] = 0.173
y[1] (analytic) = 1.2091898428053204353083434099154
y[1] (numeric) = 1.2091898428053204353083434099141
absolute error = 1.3e-30
relative error = 1.0751000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.827
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = 1.2106537530266343825665859564165
y[1] (numeric) = 1.2106537530266343825665859564152
absolute error = 1.3e-30
relative error = 1.0738000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.826
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = 1.2121212121212121212121212121212
y[1] (numeric) = 1.2121212121212121212121212121199
absolute error = 1.3e-30
relative error = 1.0725000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.825
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.176
y[1] (analytic) = 1.2135922330097087378640776699029
y[1] (numeric) = 1.2135922330097087378640776699016
absolute error = 1.3e-30
relative error = 1.0712000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.824
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.177
y[1] (analytic) = 1.2150668286755771567436208991495
y[1] (numeric) = 1.2150668286755771567436208991481
absolute error = 1.4e-30
relative error = 1.1522000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.823
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = 1.216545012165450121654501216545
y[1] (numeric) = 1.2165450121654501216545012165437
absolute error = 1.3e-30
relative error = 1.0686000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.822
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.179
y[1] (analytic) = 1.2180267965895249695493300852619
y[1] (numeric) = 1.2180267965895249695493300852606
absolute error = 1.3e-30
relative error = 1.0673000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.821
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 1.2195121951219512195121951219512
y[1] (numeric) = 1.2195121951219512195121951219499
absolute error = 1.3e-30
relative error = 1.0660000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.82
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = 1.2210012210012210012210012210012
y[1] (numeric) = 1.2210012210012210012210012209999
absolute error = 1.3e-30
relative error = 1.0647000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.819
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.182
y[1] (analytic) = 1.2224938875305623471882640586797
y[1] (numeric) = 1.2224938875305623471882640586784
absolute error = 1.3e-30
relative error = 1.0634000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.818
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.183
y[1] (analytic) = 1.2239902080783353733170134638923
y[1] (numeric) = 1.223990208078335373317013463891
absolute error = 1.3e-30
relative error = 1.0621000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.817
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = 1.2254901960784313725490196078431
y[1] (numeric) = 1.2254901960784313725490196078418
absolute error = 1.3e-30
relative error = 1.0608000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.816
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.185
y[1] (analytic) = 1.2269938650306748466257668711656
y[1] (numeric) = 1.2269938650306748466257668711643
absolute error = 1.3e-30
relative error = 1.0595000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.815
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.186
y[1] (analytic) = 1.2285012285012285012285012285012
y[1] (numeric) = 1.2285012285012285012285012284999
absolute error = 1.3e-30
relative error = 1.0582000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.814
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.187
y[1] (analytic) = 1.2300123001230012300123001230012
y[1] (numeric) = 1.2300123001230012300123001229999
absolute error = 1.3e-30
relative error = 1.0569000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.813
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=4.88
x[1] = 0.188
y[1] (analytic) = 1.2315270935960591133004926108374
y[1] (numeric) = 1.2315270935960591133004926108361
absolute error = 1.3e-30
relative error = 1.0556000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.812
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.189
y[1] (analytic) = 1.2330456226880394574599260172626
y[1] (numeric) = 1.2330456226880394574599260172613
absolute error = 1.3e-30
relative error = 1.0543000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.811
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 1.2345679012345679012345679012346
y[1] (numeric) = 1.2345679012345679012345679012332
absolute error = 1.4e-30
relative error = 1.1340000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.81
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = 1.23609394313967861557478368356
y[1] (numeric) = 1.2360939431396786155747836835586
absolute error = 1.4e-30
relative error = 1.1326000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.809
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = 1.2376237623762376237623762376238
y[1] (numeric) = 1.2376237623762376237623762376224
absolute error = 1.4e-30
relative error = 1.1312000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.808
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.193
y[1] (analytic) = 1.2391573729863692688971499380421
y[1] (numeric) = 1.2391573729863692688971499380408
absolute error = 1.3e-30
relative error = 1.0491000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.807
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.194
y[1] (analytic) = 1.2406947890818858560794044665012
y[1] (numeric) = 1.2406947890818858560794044664999
absolute error = 1.3e-30
relative error = 1.0478000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.806
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = 1.2422360248447204968944099378882
y[1] (numeric) = 1.2422360248447204968944099378869
absolute error = 1.3e-30
relative error = 1.0465000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.805
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = 1.2437810945273631840796019900498
y[1] (numeric) = 1.2437810945273631840796019900484
absolute error = 1.4e-30
relative error = 1.1256000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.804
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.197
y[1] (analytic) = 1.24533001245330012453300124533
y[1] (numeric) = 1.2453300124533001245330012453287
absolute error = 1.3e-30
relative error = 1.0439000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.803
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.198
y[1] (analytic) = 1.2468827930174563591022443890274
y[1] (numeric) = 1.2468827930174563591022443890261
absolute error = 1.3e-30
relative error = 1.0426000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.802
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = 1.2484394506866416978776529338327
y[1] (numeric) = 1.2484394506866416978776529338314
absolute error = 1.3e-30
relative error = 1.0413000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.801
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 1.25
y[1] (numeric) = 1.2499999999999999999999999999987
absolute error = 1.3e-30
relative error = 1.0400000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.8
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = 1.2515644555694618272841051314143
y[1] (numeric) = 1.251564455569461827284105131413
absolute error = 1.3e-30
relative error = 1.0387000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.799
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = 1.2531328320802005012531328320802
y[1] (numeric) = 1.2531328320802005012531328320789
absolute error = 1.3e-30
relative error = 1.0374000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.798
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.1MB, time=5.25
x[1] = 0.203
y[1] (analytic) = 1.2547051442910915934755332496863
y[1] (numeric) = 1.254705144291091593475533249685
absolute error = 1.3e-30
relative error = 1.0361000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.797
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.204
y[1] (analytic) = 1.2562814070351758793969849246231
y[1] (numeric) = 1.2562814070351758793969849246218
absolute error = 1.3e-30
relative error = 1.0348000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.796
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.205
y[1] (analytic) = 1.2578616352201257861635220125786
y[1] (numeric) = 1.2578616352201257861635220125773
absolute error = 1.3e-30
relative error = 1.0335000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.795
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = 1.2594458438287153652392947103275
y[1] (numeric) = 1.2594458438287153652392947103261
absolute error = 1.4e-30
relative error = 1.1116000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.794
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = 1.2610340479192938209331651954603
y[1] (numeric) = 1.2610340479192938209331651954589
absolute error = 1.4e-30
relative error = 1.1102000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.793
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.208
y[1] (analytic) = 1.2626262626262626262626262626263
y[1] (numeric) = 1.2626262626262626262626262626249
absolute error = 1.4e-30
relative error = 1.1088000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.792
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = 1.2642225031605562579013906447535
y[1] (numeric) = 1.2642225031605562579013906447521
absolute error = 1.4e-30
relative error = 1.1074000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.791
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 1.2658227848101265822784810126582
y[1] (numeric) = 1.2658227848101265822784810126568
absolute error = 1.4e-30
relative error = 1.1060000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.79
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.211
y[1] (analytic) = 1.2674271229404309252217997465146
y[1] (numeric) = 1.2674271229404309252217997465131
absolute error = 1.5e-30
relative error = 1.1835000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.789
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = 1.2690355329949238578680203045685
y[1] (numeric) = 1.269035532994923857868020304567
absolute error = 1.5e-30
relative error = 1.1820000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.788
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = 1.2706480304955527318932655654384
y[1] (numeric) = 1.2706480304955527318932655654368
absolute error = 1.6e-30
relative error = 1.2592000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.787
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = 1.2722646310432569974554707379135
y[1] (numeric) = 1.2722646310432569974554707379119
absolute error = 1.6e-30
relative error = 1.2576000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.786
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.215
y[1] (analytic) = 1.2738853503184713375796178343949
y[1] (numeric) = 1.2738853503184713375796178343933
absolute error = 1.6e-30
relative error = 1.2560000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.785
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.216
y[1] (analytic) = 1.2755102040816326530612244897959
y[1] (numeric) = 1.2755102040816326530612244897943
absolute error = 1.6e-30
relative error = 1.2544000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.784
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.217
y[1] (analytic) = 1.2771392081736909323116219667944
y[1] (numeric) = 1.2771392081736909323116219667928
absolute error = 1.6e-30
relative error = 1.2528000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.783
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.1MB, time=5.64
x[1] = 0.218
y[1] (analytic) = 1.278772378516624040920716112532
y[1] (numeric) = 1.2787723785166240409207161125304
absolute error = 1.6e-30
relative error = 1.2512000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.782
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = 1.2804097311139564660691421254802
y[1] (numeric) = 1.2804097311139564660691421254786
absolute error = 1.6e-30
relative error = 1.2496000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.781
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 1.2820512820512820512820512820513
y[1] (numeric) = 1.2820512820512820512820512820497
absolute error = 1.6e-30
relative error = 1.2480000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.78
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = 1.2836970474967907573812580231065
y[1] (numeric) = 1.283697047496790757381258023105
absolute error = 1.5e-30
relative error = 1.1685000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.779
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.222
y[1] (analytic) = 1.2853470437017994858611825192802
y[1] (numeric) = 1.2853470437017994858611825192787
absolute error = 1.5e-30
relative error = 1.1670000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.778
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = 1.2870012870012870012870012870013
y[1] (numeric) = 1.2870012870012870012870012869998
absolute error = 1.5e-30
relative error = 1.1655000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.777
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = 1.2886597938144329896907216494845
y[1] (numeric) = 1.288659793814432989690721649483
absolute error = 1.5e-30
relative error = 1.1640000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.776
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = 1.2903225806451612903225806451613
y[1] (numeric) = 1.2903225806451612903225806451598
absolute error = 1.5e-30
relative error = 1.1625000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.775
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.226
y[1] (analytic) = 1.2919896640826873385012919896641
y[1] (numeric) = 1.2919896640826873385012919896626
absolute error = 1.5e-30
relative error = 1.1610000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.774
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.227
y[1] (analytic) = 1.2936610608020698576972833117723
y[1] (numeric) = 1.2936610608020698576972833117708
absolute error = 1.5e-30
relative error = 1.1595000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.773
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = 1.2953367875647668393782383419689
y[1] (numeric) = 1.2953367875647668393782383419674
absolute error = 1.5e-30
relative error = 1.1580000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.772
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = 1.2970168612191958495460440985733
y[1] (numeric) = 1.2970168612191958495460440985718
absolute error = 1.5e-30
relative error = 1.1565000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.771
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 1.2987012987012987012987012987013
y[1] (numeric) = 1.2987012987012987012987012986998
absolute error = 1.5e-30
relative error = 1.1550000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.77
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = 1.3003901170351105331599479843953
y[1] (numeric) = 1.3003901170351105331599479843938
absolute error = 1.5e-30
relative error = 1.1535000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.769
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.232
y[1] (analytic) = 1.3020833333333333333333333333333
y[1] (numeric) = 1.3020833333333333333333333333318
absolute error = 1.5e-30
relative error = 1.1520000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.768
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.1MB, time=6.03
x[1] = 0.233
y[1] (analytic) = 1.3037809647979139504563233376793
y[1] (numeric) = 1.3037809647979139504563233376777
absolute error = 1.6e-30
relative error = 1.2272000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.767
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = 1.3054830287206266318537859007833
y[1] (numeric) = 1.3054830287206266318537859007817
absolute error = 1.6e-30
relative error = 1.2256000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.766
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = 1.307189542483660130718954248366
y[1] (numeric) = 1.3071895424836601307189542483644
absolute error = 1.6e-30
relative error = 1.2240000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.765
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.236
y[1] (analytic) = 1.3089005235602094240837696335079
y[1] (numeric) = 1.3089005235602094240837696335062
absolute error = 1.7e-30
relative error = 1.2988000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.764
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.237
y[1] (analytic) = 1.3106159895150720838794233289646
y[1] (numeric) = 1.310615989515072083879423328963
absolute error = 1.6e-30
relative error = 1.2208000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.763
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = 1.3123359580052493438320209973753
y[1] (numeric) = 1.3123359580052493438320209973737
absolute error = 1.6e-30
relative error = 1.2192000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.762
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = 1.3140604467805519053876478318003
y[1] (numeric) = 1.3140604467805519053876478317986
absolute error = 1.7e-30
relative error = 1.2937000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.761
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 1.3157894736842105263157894736842
y[1] (numeric) = 1.3157894736842105263157894736825
absolute error = 1.7e-30
relative error = 1.2920000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.76
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = 1.3175230566534914361001317523057
y[1] (numeric) = 1.317523056653491436100131752304
absolute error = 1.7e-30
relative error = 1.2903000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.759
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = 1.3192612137203166226912928759894
y[1] (numeric) = 1.3192612137203166226912928759878
absolute error = 1.6e-30
relative error = 1.2128000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.758
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.243
y[1] (analytic) = 1.321003963011889035667107001321
y[1] (numeric) = 1.3210039630118890356671070013194
absolute error = 1.6e-30
relative error = 1.2112000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.757
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.244
y[1] (analytic) = 1.3227513227513227513227513227513
y[1] (numeric) = 1.3227513227513227513227513227497
absolute error = 1.6e-30
relative error = 1.2096000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.756
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = 1.3245033112582781456953642384106
y[1] (numeric) = 1.324503311258278145695364238409
absolute error = 1.6e-30
relative error = 1.2080000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.755
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.246
y[1] (analytic) = 1.3262599469496021220159151193634
y[1] (numeric) = 1.3262599469496021220159151193618
absolute error = 1.6e-30
relative error = 1.2064000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.754
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = 1.3280212483399734395750332005312
y[1] (numeric) = 1.3280212483399734395750332005296
absolute error = 1.6e-30
relative error = 1.2048000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.753
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.1MB, time=6.41
x[1] = 0.248
y[1] (analytic) = 1.3297872340425531914893617021277
y[1] (numeric) = 1.329787234042553191489361702126
absolute error = 1.7e-30
relative error = 1.2784000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.752
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = 1.3315579227696404793608521970706
y[1] (numeric) = 1.3315579227696404793608521970689
absolute error = 1.7e-30
relative error = 1.2767000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.751
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 1.3333333333333333333333333333333
y[1] (numeric) = 1.3333333333333333333333333333317
absolute error = 1.6e-30
relative error = 1.2000000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.75
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.251
y[1] (analytic) = 1.3351134846461949265687583444593
y[1] (numeric) = 1.3351134846461949265687583444576
absolute error = 1.7e-30
relative error = 1.2733000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.749
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = 1.3368983957219251336898395721925
y[1] (numeric) = 1.3368983957219251336898395721908
absolute error = 1.7e-30
relative error = 1.2716000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.748
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = 1.3386880856760374832663989290495
y[1] (numeric) = 1.3386880856760374832663989290478
absolute error = 1.7e-30
relative error = 1.2699000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.747
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.254
y[1] (analytic) = 1.3404825737265415549597855227882
y[1] (numeric) = 1.3404825737265415549597855227865
absolute error = 1.7e-30
relative error = 1.2682000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.746
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.255
y[1] (analytic) = 1.3422818791946308724832214765101
y[1] (numeric) = 1.3422818791946308724832214765084
absolute error = 1.7e-30
relative error = 1.2665000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.745
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = 1.3440860215053763440860215053763
y[1] (numeric) = 1.3440860215053763440860215053747
absolute error = 1.6e-30
relative error = 1.1904000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.744
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = 1.3458950201884253028263795423957
y[1] (numeric) = 1.345895020188425302826379542394
absolute error = 1.7e-30
relative error = 1.2631000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.743
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = 1.3477088948787061994609164420485
y[1] (numeric) = 1.3477088948787061994609164420468
absolute error = 1.7e-30
relative error = 1.2614000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.742
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.259
y[1] (analytic) = 1.3495276653171390013495276653171
y[1] (numeric) = 1.3495276653171390013495276653154
absolute error = 1.7e-30
relative error = 1.2597000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.741
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 1.3513513513513513513513513513514
y[1] (numeric) = 1.3513513513513513513513513513496
absolute error = 1.8e-30
relative error = 1.3320000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.74
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.261
y[1] (analytic) = 1.3531799729364005412719891745602
y[1] (numeric) = 1.3531799729364005412719891745585
absolute error = 1.7e-30
relative error = 1.2563000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.739
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = 1.3550135501355013550135501355014
y[1] (numeric) = 1.3550135501355013550135501354996
absolute error = 1.8e-30
relative error = 1.3284000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.738
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.1MB, time=6.79
x[1] = 0.263
y[1] (analytic) = 1.3568521031207598371777476255088
y[1] (numeric) = 1.3568521031207598371777476255071
absolute error = 1.7e-30
relative error = 1.2529000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.737
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = 1.3586956521739130434782608695652
y[1] (numeric) = 1.3586956521739130434782608695635
absolute error = 1.7e-30
relative error = 1.2512000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.736
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.265
y[1] (analytic) = 1.3605442176870748299319727891156
y[1] (numeric) = 1.3605442176870748299319727891139
absolute error = 1.7e-30
relative error = 1.2495000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.735
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.266
y[1] (analytic) = 1.3623978201634877384196185286104
y[1] (numeric) = 1.3623978201634877384196185286086
absolute error = 1.8e-30
relative error = 1.3212000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.734
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = 1.3642564802182810368349249658936
y[1] (numeric) = 1.3642564802182810368349249658918
absolute error = 1.8e-30
relative error = 1.3194000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.733
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = 1.3661202185792349726775956284153
y[1] (numeric) = 1.3661202185792349726775956284135
absolute error = 1.8e-30
relative error = 1.3176000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.732
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.269
y[1] (analytic) = 1.3679890560875512995896032831737
y[1] (numeric) = 1.3679890560875512995896032831719
absolute error = 1.8e-30
relative error = 1.3158000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.731
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 1.369863013698630136986301369863
y[1] (numeric) = 1.3698630136986301369863013698612
absolute error = 1.8e-30
relative error = 1.3140000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.73
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = 1.3717421124828532235939643347051
y[1] (numeric) = 1.3717421124828532235939643347033
absolute error = 1.8e-30
relative error = 1.3122000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.729
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.272
y[1] (analytic) = 1.3736263736263736263736263736264
y[1] (numeric) = 1.3736263736263736263736263736246
absolute error = 1.8e-30
relative error = 1.3104000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.728
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = 1.3755158184319119669876203576341
y[1] (numeric) = 1.3755158184319119669876203576323
absolute error = 1.8e-30
relative error = 1.3086000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.727
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.274
y[1] (analytic) = 1.3774104683195592286501377410468
y[1] (numeric) = 1.377410468319559228650137741045
absolute error = 1.8e-30
relative error = 1.3068000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.726
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = 1.3793103448275862068965517241379
y[1] (numeric) = 1.3793103448275862068965517241361
absolute error = 1.8e-30
relative error = 1.3050000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.725
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.276
y[1] (analytic) = 1.3812154696132596685082872928177
y[1] (numeric) = 1.3812154696132596685082872928158
absolute error = 1.9e-30
relative error = 1.3756000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.724
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.277
y[1] (analytic) = 1.3831258644536652835408022130014
y[1] (numeric) = 1.3831258644536652835408022129995
absolute error = 1.9e-30
relative error = 1.3737000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.723
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.1MB, time=7.18
x[1] = 0.278
y[1] (analytic) = 1.3850415512465373961218836565097
y[1] (numeric) = 1.3850415512465373961218836565078
absolute error = 1.9e-30
relative error = 1.3718000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.722
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = 1.3869625520110957004160887656033
y[1] (numeric) = 1.3869625520110957004160887656014
absolute error = 1.9e-30
relative error = 1.3699000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.721
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 1.3888888888888888888888888888889
y[1] (numeric) = 1.388888888888888888888888888887
absolute error = 1.9e-30
relative error = 1.3680000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.72
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.281
y[1] (analytic) = 1.3908205841446453407510431154381
y[1] (numeric) = 1.3908205841446453407510431154362
absolute error = 1.9e-30
relative error = 1.3661000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.719
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = 1.3927576601671309192200557103064
y[1] (numeric) = 1.3927576601671309192200557103045
absolute error = 1.9e-30
relative error = 1.3642000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.718
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.283
y[1] (analytic) = 1.3947001394700139470013947001395
y[1] (numeric) = 1.3947001394700139470013947001376
absolute error = 1.9e-30
relative error = 1.3623000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.717
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.284
y[1] (analytic) = 1.3966480446927374301675977653631
y[1] (numeric) = 1.3966480446927374301675977653613
absolute error = 1.8e-30
relative error = 1.2888000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.716
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = 1.3986013986013986013986013986014
y[1] (numeric) = 1.3986013986013986013986013985996
absolute error = 1.8e-30
relative error = 1.2870000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.715
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = 1.4005602240896358543417366946779
y[1] (numeric) = 1.4005602240896358543417366946761
absolute error = 1.8e-30
relative error = 1.2852000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.714
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.287
y[1] (analytic) = 1.4025245441795231416549789621318
y[1] (numeric) = 1.4025245441795231416549789621301
absolute error = 1.7e-30
relative error = 1.2121000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.713
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.288
y[1] (analytic) = 1.4044943820224719101123595505618
y[1] (numeric) = 1.4044943820224719101123595505601
absolute error = 1.7e-30
relative error = 1.2104000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.712
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.289
y[1] (analytic) = 1.4064697609001406469760900140647
y[1] (numeric) = 1.406469760900140646976090014063
absolute error = 1.7e-30
relative error = 1.2087000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.711
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 1.4084507042253521126760563380282
y[1] (numeric) = 1.4084507042253521126760563380265
absolute error = 1.7e-30
relative error = 1.2070000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.71
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = 1.4104372355430183356840620592384
y[1] (numeric) = 1.4104372355430183356840620592367
absolute error = 1.7e-30
relative error = 1.2053000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.709
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.292
y[1] (analytic) = 1.4124293785310734463276836158192
y[1] (numeric) = 1.4124293785310734463276836158175
absolute error = 1.7e-30
relative error = 1.2036000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.708
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.293
y[1] (analytic) = 1.4144271570014144271570014144272
y[1] (numeric) = 1.4144271570014144271570014144254
absolute error = 1.8e-30
memory used=76.2MB, alloc=4.1MB, time=7.57
relative error = 1.2726000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.707
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.294
y[1] (analytic) = 1.416430594900849858356940509915
y[1] (numeric) = 1.4164305949008498583569405099133
absolute error = 1.7e-30
relative error = 1.2002000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.706
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = 1.4184397163120567375886524822695
y[1] (numeric) = 1.4184397163120567375886524822678
absolute error = 1.7e-30
relative error = 1.1985000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.705
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = 1.4204545454545454545454545454545
y[1] (numeric) = 1.4204545454545454545454545454528
absolute error = 1.7e-30
relative error = 1.1968000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.704
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.297
y[1] (analytic) = 1.4224751066856330014224751066856
y[1] (numeric) = 1.4224751066856330014224751066839
absolute error = 1.7e-30
relative error = 1.1951000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.703
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.298
y[1] (analytic) = 1.4245014245014245014245014245014
y[1] (numeric) = 1.4245014245014245014245014244997
absolute error = 1.7e-30
relative error = 1.1934000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.702
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = 1.4265335235378031383737517831669
y[1] (numeric) = 1.4265335235378031383737517831652
absolute error = 1.7e-30
relative error = 1.1917000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.701
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 1.4285714285714285714285714285714
y[1] (numeric) = 1.4285714285714285714285714285697
absolute error = 1.7e-30
relative error = 1.1900000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.7
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.301
y[1] (analytic) = 1.4306151645207439198855507868383
y[1] (numeric) = 1.4306151645207439198855507868366
absolute error = 1.7e-30
relative error = 1.1883000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.699
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = 1.4326647564469914040114613180516
y[1] (numeric) = 1.4326647564469914040114613180498
absolute error = 1.8e-30
relative error = 1.2564000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.698
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.303
y[1] (analytic) = 1.4347202295552367288378766140603
y[1] (numeric) = 1.4347202295552367288378766140585
absolute error = 1.8e-30
relative error = 1.2546000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.697
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = 1.4367816091954022988505747126437
y[1] (numeric) = 1.4367816091954022988505747126419
absolute error = 1.8e-30
relative error = 1.2528000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.696
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.305
y[1] (analytic) = 1.4388489208633093525179856115108
y[1] (numeric) = 1.438848920863309352517985611509
absolute error = 1.8e-30
relative error = 1.2510000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.695
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.306
y[1] (analytic) = 1.440922190201729106628242074928
y[1] (numeric) = 1.4409221902017291066282420749262
absolute error = 1.8e-30
relative error = 1.2492000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.694
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = 1.4430014430014430014430014430014
y[1] (numeric) = 1.4430014430014430014430014429997
absolute error = 1.7e-30
relative error = 1.1781000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.693
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = 1.445086705202312138728323699422
y[1] (numeric) = 1.4450867052023121387283236994202
absolute error = 1.8e-30
relative error = 1.2456000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.692
Order of pole = 651
memory used=80.1MB, alloc=4.1MB, time=7.96
TOP MAIN SOLVE Loop
x[1] = 0.309
y[1] (analytic) = 1.4471780028943560057887120115774
y[1] (numeric) = 1.4471780028943560057887120115757
absolute error = 1.7e-30
relative error = 1.1747000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.691
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 1.4492753623188405797101449275362
y[1] (numeric) = 1.4492753623188405797101449275345
absolute error = 1.7e-30
relative error = 1.1730000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.69
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.311
y[1] (analytic) = 1.4513788098693759071117561683599
y[1] (numeric) = 1.4513788098693759071117561683582
absolute error = 1.7e-30
relative error = 1.1713000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.689
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = 1.4534883720930232558139534883721
y[1] (numeric) = 1.4534883720930232558139534883703
absolute error = 1.8e-30
relative error = 1.2384000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.688
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = 1.4556040756914119359534206695779
y[1] (numeric) = 1.4556040756914119359534206695761
absolute error = 1.8e-30
relative error = 1.2366000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.687
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.314
y[1] (analytic) = 1.4577259475218658892128279883382
y[1] (numeric) = 1.4577259475218658892128279883364
absolute error = 1.8e-30
relative error = 1.2348000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.686
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.315
y[1] (analytic) = 1.459854014598540145985401459854
y[1] (numeric) = 1.4598540145985401459854014598522
absolute error = 1.8e-30
relative error = 1.2330000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.685
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.316
y[1] (analytic) = 1.4619883040935672514619883040936
y[1] (numeric) = 1.4619883040935672514619883040917
absolute error = 1.9e-30
relative error = 1.2996000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.684
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.317
y[1] (analytic) = 1.4641288433382137628111273792094
y[1] (numeric) = 1.4641288433382137628111273792075
absolute error = 1.9e-30
relative error = 1.2977000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.683
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.318
y[1] (analytic) = 1.4662756598240469208211143695015
y[1] (numeric) = 1.4662756598240469208211143694996
absolute error = 1.9e-30
relative error = 1.2958000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.682
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.319
y[1] (analytic) = 1.4684287812041116005873715124816
y[1] (numeric) = 1.4684287812041116005873715124798
absolute error = 1.8e-30
relative error = 1.2258000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.681
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 1.4705882352941176470588235294118
y[1] (numeric) = 1.4705882352941176470588235294099
absolute error = 1.9e-30
relative error = 1.2920000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.68
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.321
y[1] (analytic) = 1.4727540500736377025036818851252
y[1] (numeric) = 1.4727540500736377025036818851233
absolute error = 1.9e-30
relative error = 1.2901000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.679
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.322
y[1] (analytic) = 1.4749262536873156342182890855457
y[1] (numeric) = 1.4749262536873156342182890855438
absolute error = 1.9e-30
relative error = 1.2882000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.678
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.323
y[1] (analytic) = 1.477104874446085672082717872969
y[1] (numeric) = 1.4771048744460856720827178729671
absolute error = 1.9e-30
relative error = 1.2863000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.677
Order of pole = 651
memory used=83.9MB, alloc=4.1MB, time=8.35
TOP MAIN SOLVE Loop
x[1] = 0.324
y[1] (analytic) = 1.4792899408284023668639053254438
y[1] (numeric) = 1.4792899408284023668639053254419
absolute error = 1.9e-30
relative error = 1.2844000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.676
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.325
y[1] (analytic) = 1.4814814814814814814814814814815
y[1] (numeric) = 1.4814814814814814814814814814796
absolute error = 1.9e-30
relative error = 1.2825000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.675
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.326
y[1] (analytic) = 1.4836795252225519287833827893175
y[1] (numeric) = 1.4836795252225519287833827893156
absolute error = 1.9e-30
relative error = 1.2806000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.674
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.327
y[1] (analytic) = 1.4858841010401188707280832095097
y[1] (numeric) = 1.4858841010401188707280832095077
absolute error = 2.0e-30
relative error = 1.3460000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.673
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.328
y[1] (analytic) = 1.4880952380952380952380952380952
y[1] (numeric) = 1.4880952380952380952380952380933
absolute error = 1.9e-30
relative error = 1.2768000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.672
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.329
y[1] (analytic) = 1.4903129657228017883755588673621
y[1] (numeric) = 1.4903129657228017883755588673602
absolute error = 1.9e-30
relative error = 1.2749000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.671
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 1.4925373134328358208955223880597
y[1] (numeric) = 1.4925373134328358208955223880577
absolute error = 2.0e-30
relative error = 1.3400000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.67
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.331
y[1] (analytic) = 1.4947683109118086696562032884903
y[1] (numeric) = 1.4947683109118086696562032884883
absolute error = 2.0e-30
relative error = 1.3380000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.669
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.332
y[1] (analytic) = 1.4970059880239520958083832335329
y[1] (numeric) = 1.4970059880239520958083832335309
absolute error = 2.0e-30
relative error = 1.3360000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.668
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.333
y[1] (analytic) = 1.4992503748125937031484257871064
y[1] (numeric) = 1.4992503748125937031484257871044
absolute error = 2.0e-30
relative error = 1.3340000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.667
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.334
y[1] (analytic) = 1.5015015015015015015015015015015
y[1] (numeric) = 1.5015015015015015015015015014994
absolute error = 2.1e-30
relative error = 1.3986000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.666
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.335
y[1] (analytic) = 1.5037593984962406015037593984962
y[1] (numeric) = 1.5037593984962406015037593984941
absolute error = 2.1e-30
relative error = 1.3965000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.665
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.336
y[1] (analytic) = 1.5060240963855421686746987951807
y[1] (numeric) = 1.5060240963855421686746987951786
absolute error = 2.1e-30
relative error = 1.3944000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.664
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.337
y[1] (analytic) = 1.5082956259426847662141779788839
y[1] (numeric) = 1.5082956259426847662141779788817
absolute error = 2.2e-30
relative error = 1.4586000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.663
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.338
y[1] (analytic) = 1.5105740181268882175226586102719
y[1] (numeric) = 1.5105740181268882175226586102697
absolute error = 2.2e-30
relative error = 1.4564000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.662
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.1MB, time=8.73
x[1] = 0.339
y[1] (analytic) = 1.5128593040847201210287443267776
y[1] (numeric) = 1.5128593040847201210287443267754
absolute error = 2.2e-30
relative error = 1.4542000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.661
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 1.5151515151515151515151515151515
y[1] (numeric) = 1.5151515151515151515151515151493
absolute error = 2.2e-30
relative error = 1.4520000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.66
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.341
y[1] (analytic) = 1.517450682852807283763277693475
y[1] (numeric) = 1.5174506828528072837632776934727
absolute error = 2.3e-30
relative error = 1.5157000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.659
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.342
y[1] (analytic) = 1.5197568389057750759878419452888
y[1] (numeric) = 1.5197568389057750759878419452865
absolute error = 2.3e-30
relative error = 1.5134000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.658
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.343
y[1] (analytic) = 1.52207001522070015220700152207
y[1] (numeric) = 1.5220700152207001522070015220678
absolute error = 2.2e-30
relative error = 1.4454000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.657
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.344
y[1] (analytic) = 1.524390243902439024390243902439
y[1] (numeric) = 1.5243902439024390243902439024368
absolute error = 2.2e-30
relative error = 1.4432000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.656
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.345
y[1] (analytic) = 1.5267175572519083969465648854962
y[1] (numeric) = 1.526717557251908396946564885494
absolute error = 2.2e-30
relative error = 1.4410000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.655
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.346
y[1] (analytic) = 1.5290519877675840978593272171254
y[1] (numeric) = 1.5290519877675840978593272171232
absolute error = 2.2e-30
relative error = 1.4388000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.654
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.347
y[1] (analytic) = 1.531393568147013782542113323124
y[1] (numeric) = 1.5313935681470137825421133231219
absolute error = 2.1e-30
relative error = 1.3713000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.653
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.348
y[1] (analytic) = 1.5337423312883435582822085889571
y[1] (numeric) = 1.5337423312883435582822085889549
absolute error = 2.2e-30
relative error = 1.4344000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.652
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.349
y[1] (analytic) = 1.5360983102918586789554531490015
y[1] (numeric) = 1.5360983102918586789554531489994
absolute error = 2.1e-30
relative error = 1.3671000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.651
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 1.5384615384615384615384615384615
y[1] (numeric) = 1.5384615384615384615384615384594
absolute error = 2.1e-30
relative error = 1.3650000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.65
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.351
y[1] (analytic) = 1.5408320493066255778120184899846
y[1] (numeric) = 1.5408320493066255778120184899824
absolute error = 2.2e-30
relative error = 1.4278000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.649
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.352
y[1] (analytic) = 1.5432098765432098765432098765432
y[1] (numeric) = 1.543209876543209876543209876541
absolute error = 2.2e-30
relative error = 1.4256000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.648
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.353
y[1] (analytic) = 1.5455950540958268933539412673879
y[1] (numeric) = 1.5455950540958268933539412673857
absolute error = 2.2e-30
relative error = 1.4234000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.647
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.1MB, time=9.12
x[1] = 0.354
y[1] (analytic) = 1.5479876160990712074303405572755
y[1] (numeric) = 1.5479876160990712074303405572733
absolute error = 2.2e-30
relative error = 1.4212000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.646
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.355
y[1] (analytic) = 1.5503875968992248062015503875969
y[1] (numeric) = 1.5503875968992248062015503875947
absolute error = 2.2e-30
relative error = 1.4190000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.645
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.356
y[1] (analytic) = 1.5527950310559006211180124223602
y[1] (numeric) = 1.552795031055900621118012422358
absolute error = 2.2e-30
relative error = 1.4168000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.644
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.357
y[1] (analytic) = 1.5552099533437013996889580093313
y[1] (numeric) = 1.555209953343701399688958009329
absolute error = 2.3e-30
relative error = 1.4789000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.643
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.358
y[1] (analytic) = 1.5576323987538940809968847352025
y[1] (numeric) = 1.5576323987538940809968847352002
absolute error = 2.3e-30
relative error = 1.4766000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.642
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.359
y[1] (analytic) = 1.56006240249609984399375975039
y[1] (numeric) = 1.5600624024960998439937597503877
absolute error = 2.3e-30
relative error = 1.4743000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.641
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 1.5625
y[1] (numeric) = 1.5624999999999999999999999999977
absolute error = 2.3e-30
relative error = 1.4720000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.64
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.361
y[1] (analytic) = 1.5649452269170579029733959311424
y[1] (numeric) = 1.5649452269170579029733959311401
absolute error = 2.3e-30
relative error = 1.4697000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.639
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.362
y[1] (analytic) = 1.5673981191222570532915360501567
y[1] (numeric) = 1.5673981191222570532915360501544
absolute error = 2.3e-30
relative error = 1.4674000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.638
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.363
y[1] (analytic) = 1.5698587127158555729984301412873
y[1] (numeric) = 1.5698587127158555729984301412849
absolute error = 2.4e-30
relative error = 1.5288000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.637
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.364
y[1] (analytic) = 1.5723270440251572327044025157233
y[1] (numeric) = 1.5723270440251572327044025157209
absolute error = 2.4e-30
relative error = 1.5264000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.636
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.365
y[1] (analytic) = 1.5748031496062992125984251968504
y[1] (numeric) = 1.574803149606299212598425196848
absolute error = 2.4e-30
relative error = 1.5240000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.635
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.366
y[1] (analytic) = 1.5772870662460567823343848580442
y[1] (numeric) = 1.5772870662460567823343848580418
absolute error = 2.4e-30
relative error = 1.5216000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.634
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.367
y[1] (analytic) = 1.5797788309636650868878357030016
y[1] (numeric) = 1.5797788309636650868878357029992
absolute error = 2.4e-30
relative error = 1.5192000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.633
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.368
y[1] (analytic) = 1.5822784810126582278481012658228
y[1] (numeric) = 1.5822784810126582278481012658204
absolute error = 2.4e-30
relative error = 1.5168000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.632
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.1MB, time=9.51
x[1] = 0.369
y[1] (analytic) = 1.5847860538827258320126782884311
y[1] (numeric) = 1.5847860538827258320126782884287
absolute error = 2.4e-30
relative error = 1.5144000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.631
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 1.5873015873015873015873015873016
y[1] (numeric) = 1.5873015873015873015873015872992
absolute error = 2.4e-30
relative error = 1.5120000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.63
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.371
y[1] (analytic) = 1.5898251192368839427662957074722
y[1] (numeric) = 1.5898251192368839427662957074698
absolute error = 2.4e-30
relative error = 1.5096000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.629
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.372
y[1] (analytic) = 1.5923566878980891719745222929936
y[1] (numeric) = 1.5923566878980891719745222929912
absolute error = 2.4e-30
relative error = 1.5072000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.628
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.373
y[1] (analytic) = 1.5948963317384370015948963317384
y[1] (numeric) = 1.594896331738437001594896331736
absolute error = 2.4e-30
relative error = 1.5048000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.627
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.374
y[1] (analytic) = 1.5974440894568690095846645367412
y[1] (numeric) = 1.5974440894568690095846645367388
absolute error = 2.4e-30
relative error = 1.5024000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.626
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.375
y[1] (analytic) = 1.6
y[1] (numeric) = 1.5999999999999999999999999999976
absolute error = 2.4e-30
relative error = 1.5000000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.625
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.376
y[1] (analytic) = 1.6025641025641025641025641025641
y[1] (numeric) = 1.6025641025641025641025641025617
absolute error = 2.4e-30
relative error = 1.4976000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.624
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.377
y[1] (analytic) = 1.6051364365971107544141252006421
y[1] (numeric) = 1.6051364365971107544141252006396
absolute error = 2.5e-30
relative error = 1.5575000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.623
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.378
y[1] (analytic) = 1.6077170418006430868167202572347
y[1] (numeric) = 1.6077170418006430868167202572323
absolute error = 2.4e-30
relative error = 1.4928000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.622
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.379
y[1] (analytic) = 1.6103059581320450885668276972625
y[1] (numeric) = 1.61030595813204508856682769726
absolute error = 2.5e-30
relative error = 1.5525000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.621
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 1.6129032258064516129032258064516
y[1] (numeric) = 1.6129032258064516129032258064491
absolute error = 2.5e-30
relative error = 1.5500000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.62
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.381
y[1] (analytic) = 1.6155088852988691437802907915994
y[1] (numeric) = 1.6155088852988691437802907915968
absolute error = 2.6e-30
relative error = 1.6094000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.619
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.382
y[1] (analytic) = 1.6181229773462783171521035598706
y[1] (numeric) = 1.618122977346278317152103559868
absolute error = 2.6e-30
relative error = 1.6068000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.618
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.383
y[1] (analytic) = 1.6207455429497568881685575364668
y[1] (numeric) = 1.6207455429497568881685575364642
absolute error = 2.6e-30
relative error = 1.6042000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.617
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.1MB, time=9.90
x[1] = 0.384
y[1] (analytic) = 1.6233766233766233766233766233766
y[1] (numeric) = 1.623376623376623376623376623374
absolute error = 2.6e-30
relative error = 1.6016000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.616
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.385
y[1] (analytic) = 1.6260162601626016260162601626016
y[1] (numeric) = 1.626016260162601626016260162599
absolute error = 2.6e-30
relative error = 1.5990000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.615
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.386
y[1] (analytic) = 1.6286644951140065146579804560261
y[1] (numeric) = 1.6286644951140065146579804560234
absolute error = 2.7e-30
relative error = 1.6578000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.614
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.387
y[1] (analytic) = 1.6313213703099510603588907014682
y[1] (numeric) = 1.6313213703099510603588907014655
absolute error = 2.7e-30
relative error = 1.6551000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.613
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.388
y[1] (analytic) = 1.6339869281045751633986928104575
y[1] (numeric) = 1.6339869281045751633986928104548
absolute error = 2.7e-30
relative error = 1.6524000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.612
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.389
y[1] (analytic) = 1.6366612111292962356792144026187
y[1] (numeric) = 1.6366612111292962356792144026159
absolute error = 2.8e-30
relative error = 1.7108000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.611
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 1.6393442622950819672131147540984
y[1] (numeric) = 1.6393442622950819672131147540956
absolute error = 2.8e-30
relative error = 1.7080000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.61
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.391
y[1] (analytic) = 1.6420361247947454844006568144499
y[1] (numeric) = 1.6420361247947454844006568144471
absolute error = 2.8e-30
relative error = 1.7052000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.609
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.392
y[1] (analytic) = 1.6447368421052631578947368421053
y[1] (numeric) = 1.6447368421052631578947368421024
absolute error = 2.9e-30
relative error = 1.7632000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.608
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.393
y[1] (analytic) = 1.6474464579901153212520593080725
y[1] (numeric) = 1.6474464579901153212520593080696
absolute error = 2.9e-30
relative error = 1.7603000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.607
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.394
y[1] (analytic) = 1.650165016501650165016501650165
y[1] (numeric) = 1.6501650165016501650165016501621
absolute error = 2.9e-30
relative error = 1.7574000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.606
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.395
y[1] (analytic) = 1.6528925619834710743801652892562
y[1] (numeric) = 1.6528925619834710743801652892533
absolute error = 2.9e-30
relative error = 1.7545000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.605
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.396
y[1] (analytic) = 1.6556291390728476821192052980132
y[1] (numeric) = 1.6556291390728476821192052980103
absolute error = 2.9e-30
relative error = 1.7516000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.604
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.397
y[1] (analytic) = 1.658374792703150912106135986733
y[1] (numeric) = 1.65837479270315091210613598673
absolute error = 3.0e-30
relative error = 1.8090000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.603
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.398
y[1] (analytic) = 1.661129568106312292358803986711
y[1] (numeric) = 1.661129568106312292358803986708
absolute error = 3.0e-30
relative error = 1.8060000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.602
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.1MB, time=10.28
x[1] = 0.399
y[1] (analytic) = 1.6638935108153078202995008319468
y[1] (numeric) = 1.6638935108153078202995008319438
absolute error = 3.0e-30
relative error = 1.8030000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.601
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 1.6666666666666666666666666666667
y[1] (numeric) = 1.6666666666666666666666666666637
absolute error = 3.0e-30
relative error = 1.8000000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.6
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.401
y[1] (analytic) = 1.669449081803005008347245409015
y[1] (numeric) = 1.669449081803005008347245409012
absolute error = 3.0e-30
relative error = 1.7970000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.599
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.402
y[1] (analytic) = 1.6722408026755852842809364548495
y[1] (numeric) = 1.6722408026755852842809364548465
absolute error = 3.0e-30
relative error = 1.7940000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.598
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.403
y[1] (analytic) = 1.6750418760469011725293132328308
y[1] (numeric) = 1.6750418760469011725293132328278
absolute error = 3.0e-30
relative error = 1.7910000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.597
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.404
y[1] (analytic) = 1.6778523489932885906040268456376
y[1] (numeric) = 1.6778523489932885906040268456346
absolute error = 3.0e-30
relative error = 1.7880000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.596
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.405
y[1] (analytic) = 1.6806722689075630252100840336134
y[1] (numeric) = 1.6806722689075630252100840336105
absolute error = 2.9e-30
relative error = 1.7255000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.595
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.406
y[1] (analytic) = 1.6835016835016835016835016835017
y[1] (numeric) = 1.6835016835016835016835016834987
absolute error = 3.0e-30
relative error = 1.7820000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.594
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.407
y[1] (analytic) = 1.6863406408094435075885328836425
y[1] (numeric) = 1.6863406408094435075885328836395
absolute error = 3.0e-30
relative error = 1.7790000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.593
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.408
y[1] (analytic) = 1.6891891891891891891891891891892
y[1] (numeric) = 1.6891891891891891891891891891862
absolute error = 3.0e-30
relative error = 1.7760000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.592
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.409
y[1] (analytic) = 1.692047377326565143824027072758
y[1] (numeric) = 1.692047377326565143824027072755
absolute error = 3.0e-30
relative error = 1.7730000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.591
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 1.694915254237288135593220338983
y[1] (numeric) = 1.69491525423728813559322033898
absolute error = 3.0e-30
relative error = 1.7700000000000000000000000000001e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.59
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.411
y[1] (analytic) = 1.697792869269949066213921901528
y[1] (numeric) = 1.697792869269949066213921901525
absolute error = 3.0e-30
relative error = 1.7670000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.589
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.412
y[1] (analytic) = 1.7006802721088435374149659863946
y[1] (numeric) = 1.7006802721088435374149659863915
absolute error = 3.1e-30
relative error = 1.8228000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.588
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.413
y[1] (analytic) = 1.7035775127768313458262350936968
y[1] (numeric) = 1.7035775127768313458262350936937
absolute error = 3.1e-30
relative error = 1.8197000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.587
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.1MB, time=10.66
x[1] = 0.414
y[1] (analytic) = 1.7064846416382252559726962457338
y[1] (numeric) = 1.7064846416382252559726962457307
absolute error = 3.1e-30
relative error = 1.8166000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.586
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.415
y[1] (analytic) = 1.7094017094017094017094017094017
y[1] (numeric) = 1.7094017094017094017094017093986
absolute error = 3.1e-30
relative error = 1.8135000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.585
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.416
y[1] (analytic) = 1.7123287671232876712328767123288
y[1] (numeric) = 1.7123287671232876712328767123256
absolute error = 3.2e-30
relative error = 1.8688000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.584
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.417
y[1] (analytic) = 1.7152658662092624356775300171527
y[1] (numeric) = 1.7152658662092624356775300171495
absolute error = 3.2e-30
relative error = 1.8656000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.583
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.418
y[1] (analytic) = 1.718213058419243986254295532646
y[1] (numeric) = 1.7182130584192439862542955326429
absolute error = 3.1e-30
relative error = 1.8042000000000000000000000000001e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.582
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.419
y[1] (analytic) = 1.7211703958691910499139414802065
y[1] (numeric) = 1.7211703958691910499139414802034
absolute error = 3.1e-30
relative error = 1.8011000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.581
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 1.7241379310344827586206896551724
y[1] (numeric) = 1.7241379310344827586206896551693
absolute error = 3.1e-30
relative error = 1.7980000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.58
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.421
y[1] (analytic) = 1.7271157167530224525043177892919
y[1] (numeric) = 1.7271157167530224525043177892888
absolute error = 3.1e-30
relative error = 1.7949000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.579
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.422
y[1] (analytic) = 1.7301038062283737024221453287197
y[1] (numeric) = 1.7301038062283737024221453287166
absolute error = 3.1e-30
relative error = 1.7918000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.578
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.423
y[1] (analytic) = 1.7331022530329289428076256499133
y[1] (numeric) = 1.7331022530329289428076256499102
absolute error = 3.1e-30
relative error = 1.7887000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.577
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.424
y[1] (analytic) = 1.7361111111111111111111111111111
y[1] (numeric) = 1.736111111111111111111111111108
absolute error = 3.1e-30
relative error = 1.7856000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.576
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.425
y[1] (analytic) = 1.7391304347826086956521739130435
y[1] (numeric) = 1.7391304347826086956521739130404
absolute error = 3.1e-30
relative error = 1.7825000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.575
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.426
y[1] (analytic) = 1.7421602787456445993031358885017
y[1] (numeric) = 1.7421602787456445993031358884987
absolute error = 3.0e-30
relative error = 1.7220000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.574
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.427
y[1] (analytic) = 1.7452006980802792321116928446771
y[1] (numeric) = 1.7452006980802792321116928446741
absolute error = 3.0e-30
relative error = 1.7190000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.573
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.428
y[1] (analytic) = 1.7482517482517482517482517482517
y[1] (numeric) = 1.7482517482517482517482517482487
absolute error = 3.0e-30
relative error = 1.7160000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.572
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.429
y[1] (analytic) = 1.7513134851138353765323992994746
y[1] (numeric) = 1.7513134851138353765323992994715
memory used=110.6MB, alloc=4.1MB, time=11.05
absolute error = 3.1e-30
relative error = 1.7701000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.571
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 1.7543859649122807017543859649123
y[1] (numeric) = 1.7543859649122807017543859649092
absolute error = 3.1e-30
relative error = 1.7670000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.57
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.431
y[1] (analytic) = 1.7574692442882249560632688927944
y[1] (numeric) = 1.7574692442882249560632688927913
absolute error = 3.1e-30
relative error = 1.7639000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.569
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.432
y[1] (analytic) = 1.7605633802816901408450704225352
y[1] (numeric) = 1.7605633802816901408450704225321
absolute error = 3.1e-30
relative error = 1.7608000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.568
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.433
y[1] (analytic) = 1.7636684303350970017636684303351
y[1] (numeric) = 1.763668430335097001763668430332
absolute error = 3.1e-30
relative error = 1.7577000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.567
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.434
y[1] (analytic) = 1.7667844522968197879858657243816
y[1] (numeric) = 1.7667844522968197879858657243785
absolute error = 3.1e-30
relative error = 1.7546000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.566
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.435
y[1] (analytic) = 1.7699115044247787610619469026549
y[1] (numeric) = 1.7699115044247787610619469026517
absolute error = 3.2e-30
relative error = 1.8080000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.565
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.436
y[1] (analytic) = 1.7730496453900709219858156028369
y[1] (numeric) = 1.7730496453900709219858156028337
absolute error = 3.2e-30
relative error = 1.8048000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.564
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.437
y[1] (analytic) = 1.7761989342806394316163410301954
y[1] (numeric) = 1.7761989342806394316163410301922
absolute error = 3.2e-30
relative error = 1.8016000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.563
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.438
y[1] (analytic) = 1.7793594306049822064056939501779
y[1] (numeric) = 1.7793594306049822064056939501747
absolute error = 3.2e-30
relative error = 1.7984000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.562
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.439
y[1] (analytic) = 1.78253119429590017825311942959
y[1] (numeric) = 1.7825311942959001782531194295868
absolute error = 3.2e-30
relative error = 1.7952000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.561
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 1.7857142857142857142857142857143
y[1] (numeric) = 1.7857142857142857142857142857111
absolute error = 3.2e-30
relative error = 1.7920000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.56
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.441
y[1] (analytic) = 1.7889087656529516994633273703041
y[1] (numeric) = 1.7889087656529516994633273703009
absolute error = 3.2e-30
relative error = 1.7888000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.559
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.442
y[1] (analytic) = 1.7921146953405017921146953405018
y[1] (numeric) = 1.7921146953405017921146953404986
absolute error = 3.2e-30
relative error = 1.7856000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.558
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.443
y[1] (analytic) = 1.7953321364452423698384201077199
y[1] (numeric) = 1.7953321364452423698384201077167
absolute error = 3.2e-30
relative error = 1.7824000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.557
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.444
y[1] (analytic) = 1.7985611510791366906474820143885
y[1] (numeric) = 1.7985611510791366906474820143852
absolute error = 3.3e-30
relative error = 1.8348000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.556
Order of pole = 651
memory used=114.4MB, alloc=4.1MB, time=11.44
TOP MAIN SOLVE Loop
x[1] = 0.445
y[1] (analytic) = 1.8018018018018018018018018018018
y[1] (numeric) = 1.8018018018018018018018018017985
absolute error = 3.3e-30
relative error = 1.8315000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.555
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.446
y[1] (analytic) = 1.8050541516245487364620938628159
y[1] (numeric) = 1.8050541516245487364620938628126
absolute error = 3.3e-30
relative error = 1.8282000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.554
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.447
y[1] (analytic) = 1.8083182640144665461121157323689
y[1] (numeric) = 1.8083182640144665461121157323656
absolute error = 3.3e-30
relative error = 1.8249000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.553
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.448
y[1] (analytic) = 1.8115942028985507246376811594203
y[1] (numeric) = 1.811594202898550724637681159417
absolute error = 3.3e-30
relative error = 1.8216000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.552
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.449
y[1] (analytic) = 1.814882032667876588021778584392
y[1] (numeric) = 1.8148820326678765880217785843887
absolute error = 3.3e-30
relative error = 1.8183000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.551
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 1.8181818181818181818181818181818
y[1] (numeric) = 1.8181818181818181818181818181785
absolute error = 3.3e-30
relative error = 1.8150000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.55
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.451
y[1] (analytic) = 1.8214936247723132969034608378871
y[1] (numeric) = 1.8214936247723132969034608378837
absolute error = 3.4e-30
relative error = 1.8666000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.549
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.452
y[1] (analytic) = 1.8248175182481751824817518248175
y[1] (numeric) = 1.8248175182481751824817518248141
absolute error = 3.4e-30
relative error = 1.8632000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.548
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.453
y[1] (analytic) = 1.8281535648994515539305301645338
y[1] (numeric) = 1.8281535648994515539305301645304
absolute error = 3.4e-30
relative error = 1.8598000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.547
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.454
y[1] (analytic) = 1.8315018315018315018315018315018
y[1] (numeric) = 1.8315018315018315018315018314984
absolute error = 3.4e-30
relative error = 1.8564000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.546
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.455
y[1] (analytic) = 1.8348623853211009174311926605505
y[1] (numeric) = 1.834862385321100917431192660547
absolute error = 3.5e-30
relative error = 1.9075000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.545
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.456
y[1] (analytic) = 1.8382352941176470588235294117647
y[1] (numeric) = 1.8382352941176470588235294117612
absolute error = 3.5e-30
relative error = 1.9040000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.544
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.457
y[1] (analytic) = 1.8416206261510128913443830570902
y[1] (numeric) = 1.8416206261510128913443830570867
absolute error = 3.5e-30
relative error = 1.9005000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.543
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.458
y[1] (analytic) = 1.8450184501845018450184501845018
y[1] (numeric) = 1.8450184501845018450184501844983
absolute error = 3.5e-30
relative error = 1.8970000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.542
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.459
y[1] (analytic) = 1.8484288354898336414048059149723
y[1] (numeric) = 1.8484288354898336414048059149687
absolute error = 3.6e-30
relative error = 1.9476000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.541
Order of pole = 651
memory used=118.2MB, alloc=4.1MB, time=11.83
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 1.8518518518518518518518518518519
y[1] (numeric) = 1.8518518518518518518518518518483
absolute error = 3.6e-30
relative error = 1.9439999999999999999999999999999e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.54
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.461
y[1] (analytic) = 1.8552875695732838589981447124304
y[1] (numeric) = 1.8552875695732838589981447124269
absolute error = 3.5e-30
relative error = 1.8865000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.539
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.462
y[1] (analytic) = 1.8587360594795539033457249070632
y[1] (numeric) = 1.8587360594795539033457249070597
absolute error = 3.5e-30
relative error = 1.8830000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.538
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.463
y[1] (analytic) = 1.8621973929236499068901303538175
y[1] (numeric) = 1.862197392923649906890130353814
absolute error = 3.5e-30
relative error = 1.8795000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.537
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.464
y[1] (analytic) = 1.8656716417910447761194029850746
y[1] (numeric) = 1.8656716417910447761194029850711
absolute error = 3.5e-30
relative error = 1.8760000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.536
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.465
y[1] (analytic) = 1.869158878504672897196261682243
y[1] (numeric) = 1.8691588785046728971962616822395
absolute error = 3.5e-30
relative error = 1.8725000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.535
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.466
y[1] (analytic) = 1.8726591760299625468164794007491
y[1] (numeric) = 1.8726591760299625468164794007456
absolute error = 3.5e-30
relative error = 1.8690000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.534
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.467
y[1] (analytic) = 1.8761726078799249530956848030019
y[1] (numeric) = 1.8761726078799249530956848029984
absolute error = 3.5e-30
relative error = 1.8655000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.533
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.468
y[1] (analytic) = 1.8796992481203007518796992481203
y[1] (numeric) = 1.8796992481203007518796992481168
absolute error = 3.5e-30
relative error = 1.8620000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.532
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.469
y[1] (analytic) = 1.8832391713747645951035781544256
y[1] (numeric) = 1.8832391713747645951035781544221
absolute error = 3.5e-30
relative error = 1.8585000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.531
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 1.8867924528301886792452830188679
y[1] (numeric) = 1.8867924528301886792452830188644
absolute error = 3.5e-30
relative error = 1.8550000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.53
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.471
y[1] (analytic) = 1.8903591682419659735349716446125
y[1] (numeric) = 1.8903591682419659735349716446089
absolute error = 3.6e-30
relative error = 1.9044000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.529
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.472
y[1] (analytic) = 1.8939393939393939393939393939394
y[1] (numeric) = 1.8939393939393939393939393939358
absolute error = 3.6e-30
relative error = 1.9008000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.528
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.473
y[1] (analytic) = 1.8975332068311195445920303605313
y[1] (numeric) = 1.8975332068311195445920303605277
absolute error = 3.6e-30
relative error = 1.8972000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.527
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.474
y[1] (analytic) = 1.9011406844106463878326996197719
y[1] (numeric) = 1.9011406844106463878326996197682
absolute error = 3.7e-30
relative error = 1.9462000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.526
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.1MB, time=12.21
x[1] = 0.475
y[1] (analytic) = 1.9047619047619047619047619047619
y[1] (numeric) = 1.9047619047619047619047619047582
absolute error = 3.7e-30
relative error = 1.9425000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.525
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.476
y[1] (analytic) = 1.9083969465648854961832061068702
y[1] (numeric) = 1.9083969465648854961832061068665
absolute error = 3.7e-30
relative error = 1.9388000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.524
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.477
y[1] (analytic) = 1.9120458891013384321223709369025
y[1] (numeric) = 1.9120458891013384321223709368987
absolute error = 3.8e-30
relative error = 1.9874000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.523
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.478
y[1] (analytic) = 1.9157088122605363984674329501916
y[1] (numeric) = 1.9157088122605363984674329501878
absolute error = 3.8e-30
relative error = 1.9836000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.522
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.479
y[1] (analytic) = 1.9193857965451055662188099808061
y[1] (numeric) = 1.9193857965451055662188099808024
absolute error = 3.7e-30
relative error = 1.9277000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.521
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 1.9230769230769230769230769230769
y[1] (numeric) = 1.9230769230769230769230769230732
absolute error = 3.7e-30
relative error = 1.9240000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.52
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.481
y[1] (analytic) = 1.9267822736030828516377649325626
y[1] (numeric) = 1.9267822736030828516377649325589
absolute error = 3.7e-30
relative error = 1.9203000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.519
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.482
y[1] (analytic) = 1.9305019305019305019305019305019
y[1] (numeric) = 1.9305019305019305019305019304982
absolute error = 3.7e-30
relative error = 1.9166000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.518
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.483
y[1] (analytic) = 1.9342359767891682785299806576402
y[1] (numeric) = 1.9342359767891682785299806576365
absolute error = 3.7e-30
relative error = 1.9129000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.517
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.484
y[1] (analytic) = 1.9379844961240310077519379844961
y[1] (numeric) = 1.9379844961240310077519379844924
absolute error = 3.7e-30
relative error = 1.9092000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.516
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.485
y[1] (analytic) = 1.9417475728155339805825242718447
y[1] (numeric) = 1.9417475728155339805825242718409
absolute error = 3.8e-30
relative error = 1.9570000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.515
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.486
y[1] (analytic) = 1.9455252918287937743190661478599
y[1] (numeric) = 1.9455252918287937743190661478561
absolute error = 3.8e-30
relative error = 1.9532000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.514
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.487
y[1] (analytic) = 1.9493177387914230019493177387914
y[1] (numeric) = 1.9493177387914230019493177387876
absolute error = 3.8e-30
relative error = 1.9494000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.513
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.488
y[1] (analytic) = 1.953125
y[1] (numeric) = 1.9531249999999999999999999999962
absolute error = 3.8e-30
relative error = 1.9456000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.512
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.489
y[1] (analytic) = 1.9569471624266144814090019569472
y[1] (numeric) = 1.9569471624266144814090019569433
absolute error = 3.9e-30
relative error = 1.9929000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.511
Order of pole = 651
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.1MB, time=12.59
x[1] = 0.49
y[1] (analytic) = 1.960784313725490196078431372549
y[1] (numeric) = 1.9607843137254901960784313725451
absolute error = 3.9e-30
relative error = 1.9890000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.51
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.491
y[1] (analytic) = 1.9646365422396856581532416502947
y[1] (numeric) = 1.9646365422396856581532416502908
absolute error = 3.9e-30
relative error = 1.9851000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.509
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.492
y[1] (analytic) = 1.968503937007874015748031496063
y[1] (numeric) = 1.9685039370078740157480314960591
absolute error = 3.9e-30
relative error = 1.9812000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.508
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.493
y[1] (analytic) = 1.972386587771203155818540433925
y[1] (numeric) = 1.9723865877712031558185404339211
absolute error = 3.9e-30
relative error = 1.9773000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.507
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.494
y[1] (analytic) = 1.9762845849802371541501976284585
y[1] (numeric) = 1.9762845849802371541501976284545
absolute error = 4.0e-30
relative error = 2.0240000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.506
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.495
y[1] (analytic) = 1.980198019801980198019801980198
y[1] (numeric) = 1.980198019801980198019801980194
absolute error = 4.0e-30
relative error = 2.0200000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.505
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.496
y[1] (analytic) = 1.984126984126984126984126984127
y[1] (numeric) = 1.9841269841269841269841269841229
absolute error = 4.1e-30
relative error = 2.0664000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.504
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.497
y[1] (analytic) = 1.9880715705765407554671968190855
y[1] (numeric) = 1.9880715705765407554671968190814
absolute error = 4.1e-30
relative error = 2.0623000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.503
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.498
y[1] (analytic) = 1.9920318725099601593625498007968
y[1] (numeric) = 1.9920318725099601593625498007927
absolute error = 4.1e-30
relative error = 2.0582000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.502
Order of pole = 651
TOP MAIN SOLVE Loop
x[1] = 0.499
y[1] (analytic) = 1.9960079840319361277445109780439
y[1] (numeric) = 1.9960079840319361277445109780398
absolute error = 4.1e-30
relative error = 2.0541000000000000000000000000000e-28 %
Correct digits = 29
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 0.501
Order of pole = 651
Finished!
diff ( y , x , 1 ) = y * y;
Iterations = 500
Total Elapsed Time = 12 Seconds
Elapsed Time(since restart) = 12 Seconds
Time to Timeout = 2 Minutes 47 Seconds
Percent Done = 100.2 %
> quit
memory used=128.3MB, alloc=4.1MB, time=12.83