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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> 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 := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, glob_last;
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 := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
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_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(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 (abs(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");
> newline();
> 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
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(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 < abs(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");
newline();
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
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> 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));
> 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));
> 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 Function number 5
> 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_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, 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));
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))
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
> # Begin Function number 6
> check_for_pole := proc()
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #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 ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < 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-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> 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 (abs(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
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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 ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(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 (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * 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 := false;
> #TOP WHICH RADII EQ = 1
> if not found 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 := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found 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] > 0.0) 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 := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found 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 := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found 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] > 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 := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found 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 := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> 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
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < 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 - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
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 < abs(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
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := 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 abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(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 < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*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 := false;
if not found 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 := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found 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 0. < 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 := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found 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 := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < 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 := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found 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 := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") 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;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre tan $eq_no = 1
> array_tmp1_a1[1] := sin(array_x[1]);
> array_tmp1_a2[1] := cos(array_x[1]);
> array_tmp1[1] := (array_tmp1_a1[1] / array_tmp1_a2[1]);
> #emit pre add $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] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre tan $eq_no = 1
> array_tmp1_a1[2] := att(1,array_tmp1_a2,array_x,1);
> array_tmp1_a2[2] := -att(1,array_tmp1_a1,array_x,1);
> array_tmp1[2] := (array_tmp1_a1[2] - ats(2,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[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] * (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 tan $eq_no = 1
> array_tmp1_a1[3] := att(2,array_tmp1_a2,array_x,1);
> array_tmp1_a2[3] := -att(2,array_tmp1_a1,array_x,1);
> array_tmp1[3] := (array_tmp1_a1[3] - ats(3,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[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] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre tan $eq_no = 1
> array_tmp1_a1[4] := att(3,array_tmp1_a2,array_x,1);
> array_tmp1_a2[4] := -att(3,array_tmp1_a1,array_x,1);
> array_tmp1[4] := (array_tmp1_a1[4] - ats(4,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[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] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre tan $eq_no = 1
> array_tmp1_a1[5] := att(4,array_tmp1_a2,array_x,1);
> array_tmp1_a2[5] := -att(4,array_tmp1_a1,array_x,1);
> array_tmp1[5] := (array_tmp1_a1[5] - ats(5,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[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] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> 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 tan $eq_no = 1
> array_tmp1_a1[kkk] := att(kkk-1 ,array_tmp1_a2,array_x,1);
> array_tmp1_a2[kkk] := -att(kkk-1,array_tmp1_a1,array_x,1);
> array_tmp1[kkk] := (array_tmp1_a1[kkk] - ats(kkk ,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1];
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[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] * (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 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 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
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, glob_last;
array_tmp1_a1[1] := sin(array_x[1]);
array_tmp1_a2[1] := cos(array_x[1]);
array_tmp1[1] := array_tmp1_a1[1]/array_tmp1_a2[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]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1_a1[2] := att(1, array_tmp1_a2, array_x, 1);
array_tmp1_a2[2] := -att(1, array_tmp1_a1, array_x, 1);
array_tmp1[2] := (
array_tmp1_a1[2] - ats(2, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*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_a1[3] := att(2, array_tmp1_a2, array_x, 1);
array_tmp1_a2[3] := -att(2, array_tmp1_a1, array_x, 1);
array_tmp1[3] := (
array_tmp1_a1[3] - ats(3, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1_a1[4] := att(3, array_tmp1_a2, array_x, 1);
array_tmp1_a2[4] := -att(3, array_tmp1_a1, array_x, 1);
array_tmp1[4] := (
array_tmp1_a1[4] - ats(4, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1_a1[5] := att(4, array_tmp1_a2, array_x, 1);
array_tmp1_a2[5] := -att(4, array_tmp1_a1, array_x, 1);
array_tmp1[5] := (
array_tmp1_a1[5] - ats(5, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1_a1[kkk] := att(kkk - 1, array_tmp1_a2, array_x, 1);
array_tmp1_a2[kkk] := -att(kkk - 1, array_tmp1_a1, array_x, 1);
array_tmp1[kkk] := (
array_tmp1_a1[kkk] - ats(kkk, array_tmp1_a2, array_tmp1, 2))/
array_tmp1_a2[1];
array_tmp2[kkk] := array_const_0D0[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]*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 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= 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);
> fi;
> fi;
> # End Function number 1
> 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
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> 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
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> 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
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_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,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= 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)
> fi;
> # End Function number 1
> 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
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> 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 5
> 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 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> 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 10
> 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 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 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
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> 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 + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_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 + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_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 11
> 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 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_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
+ array_aa[iii_att]*array_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
> # Begin Function number 5
> 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 11
> 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 11
> # End Function number 5
> 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
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> 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
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> 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 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> 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
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> 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 (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> 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 < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_1 := proc(nnn)
> if (nnn <= glob_max_terms) then # if number 13
> ret := array_fact_1[nnn];
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_1`
factorial_1 := proc(nnn)
local ret;
if nnn <= glob_max_terms then ret := array_fact_1[nnn]
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> ret := array_fact_2[mmm,nnn];
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_3`
factorial_3 := proc(mmm, nnn)
local ret;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
ret := array_fact_2[mmm, nnn]
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - log(abs(cos((x))))
> end;
exact_soln_y := proc(x) 2.0 - log(abs(cos(x))) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_unchanged_h_cnt,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> sec_in_min,
> glob_start,
> glob_optimal_start,
> glob_hmin,
> glob_not_yet_start_msg,
> glob_not_yet_finished,
> djd_debug,
> glob_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_last_good_h,
> glob_h,
> glob_clock_sec,
> centuries_in_millinium,
> glob_dump,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_display_flag,
> days_in_year,
> glob_log10normmin,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_relerr,
> glob_dump_analytic,
> glob_hmax,
> glob_disp_incr,
> glob_html_log,
> glob_log10abserr,
> glob_normmax,
> glob_hmin_init,
> glob_optimal_done,
> years_in_century,
> hours_in_day,
> djd_debug2,
> MAX_UNCHANGED,
> glob_warned2,
> min_in_hour,
> glob_small_float,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_tmp1_a1,
> array_tmp1_a2,
> array_1st_rel_error,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_norms,
> array_complex_pole,
> array_fact_2,
> array_y_set_initial,
> array_y_higher_work2,
> array_real_pole,
> array_poles,
> array_y_higher_work,
> array_y_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_iolevel := 5;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> glob_max_minutes := 0.0;
> glob_warned := false;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_max_hours := 0.0;
> glob_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_reached_optimal_h := false;
> glob_initial_pass := true;
> glob_almost_1 := 0.9990;
> glob_max_opt_iter := 10;
> glob_unchanged_h_cnt := 0;
> glob_log10_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_clock_start_sec := 0.0;
> sec_in_min := 60.0;
> glob_start := 0;
> glob_optimal_start := 0.0;
> glob_hmin := 0.00000000001;
> glob_not_yet_start_msg := true;
> glob_not_yet_finished := true;
> djd_debug := true;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_last_good_h := 0.1;
> glob_h := 0.1;
> glob_clock_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> glob_subiter_method := 3;
> glob_log10relerr := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_log10_relerr := 0.1e-10;
> glob_display_flag := true;
> days_in_year := 365.0;
> glob_log10normmin := 0.1;
> glob_percent_done := 0.0;
> glob_max_sec := 10000.0;
> glob_no_eqs := 0;
> glob_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_hmax := 1.0;
> glob_disp_incr := 0.1;
> glob_html_log := true;
> glob_log10abserr := 0.0;
> glob_normmax := 0.0;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> years_in_century := 100.0;
> hours_in_day := 24.0;
> djd_debug2 := true;
> MAX_UNCHANGED := 10;
> glob_warned2 := false;
> min_in_hour := 60.0;
> glob_small_float := 0.1e-50;
> glob_current_iter := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> #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/tanpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( x ) ;");
> 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 := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> 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,"2.0 - log(abs(cos((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;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #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_tmp1_a1:= Array(0..(max_terms + 1),[]);
> array_tmp1_a2:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_init:= 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_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_a2[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_type_pole[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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_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_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_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_norms[term] := 0.0;
> term := term + 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
> ;
> 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 <=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 <=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_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 <=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[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_tmp1_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_a1[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_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_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_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_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_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_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_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
> temp1 := iiif !;
> temp2 := jjjf !;
> array_fact_1[iiif] := temp1;
> array_fact_2[iiif,jjjf] := temp1/temp2;
> 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 := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #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);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> 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;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> 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] * 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]* (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();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> 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 (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #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] / (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 * (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] / (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 * (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] / (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 * (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
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = tan ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-17T03:38:07-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tan")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( x ) ;")
> ;
> 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_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 3
> 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 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 091 | ")
> ;
> logitem_str(html_log_file,"tan diffeq.mxt")
> ;
> logitem_str(html_log_file,"tan maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly for speeding factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `iiif` is implicitly declared local to procedure `mainprog`
Warning, `jjjf` is implicitly declared local to procedure `mainprog`
Warning, `temp1` is implicitly declared local to procedure `mainprog`
Warning, `temp2` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, iiif,
jjjf, temp1, temp2;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_max_minutes, glob_warned, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_abserr, glob_look_poles, glob_reached_optimal_h,
glob_initial_pass, glob_almost_1, glob_max_opt_iter, glob_unchanged_h_cnt,
glob_log10_abserr, glob_large_float, glob_clock_start_sec, sec_in_min,
glob_start, glob_optimal_start, glob_hmin, glob_not_yet_start_msg,
glob_not_yet_finished, djd_debug, glob_iter, glob_orig_start_sec,
glob_smallish_float, glob_last_good_h, glob_h, glob_clock_sec,
centuries_in_millinium, glob_dump, glob_optimal_expect_sec,
glob_subiter_method, glob_log10relerr, glob_curr_iter_when_opt,
glob_log10_relerr, glob_display_flag, days_in_year, glob_log10normmin,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_relerr,
glob_dump_analytic, glob_hmax, glob_disp_incr, glob_html_log,
glob_log10abserr, glob_normmax, glob_hmin_init, glob_optimal_done,
years_in_century, hours_in_day, djd_debug2, MAX_UNCHANGED, glob_warned2,
min_in_hour, glob_small_float, glob_current_iter,
glob_optimal_clock_start_sec, glob_max_trunc_err, array_const_0D0,
array_const_1, array_tmp1_a1, array_tmp1_a2, array_1st_rel_error,
array_type_pole, array_fact_1, array_m1, array_y_init, array_tmp0,
array_tmp1, array_tmp2, array_last_rel_error, array_pole, array_y, array_x,
array_norms, array_complex_pole, array_fact_2, array_y_set_initial,
array_y_higher_work2, array_real_pole, array_poles, array_y_higher_work,
array_y_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_iolevel := 5;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
glob_max_minutes := 0.;
glob_warned := false;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_max_hours := 0.;
glob_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_reached_optimal_h := false;
glob_initial_pass := true;
glob_almost_1 := 0.9990;
glob_max_opt_iter := 10;
glob_unchanged_h_cnt := 0;
glob_log10_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_clock_start_sec := 0.;
sec_in_min := 60.0;
glob_start := 0;
glob_optimal_start := 0.;
glob_hmin := 0.1*10^(-10);
glob_not_yet_start_msg := true;
glob_not_yet_finished := true;
djd_debug := true;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_last_good_h := 0.1;
glob_h := 0.1;
glob_clock_sec := 0.;
centuries_in_millinium := 10.0;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
glob_subiter_method := 3;
glob_log10relerr := 0.;
glob_curr_iter_when_opt := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_display_flag := true;
days_in_year := 365.0;
glob_log10normmin := 0.1;
glob_percent_done := 0.;
glob_max_sec := 10000.0;
glob_no_eqs := 0;
glob_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_hmax := 1.0;
glob_disp_incr := 0.1;
glob_html_log := true;
glob_log10abserr := 0.;
glob_normmax := 0.;
glob_hmin_init := 0.001;
glob_optimal_done := false;
years_in_century := 100.0;
hours_in_day := 24.0;
djd_debug2 := true;
MAX_UNCHANGED := 10;
glob_warned2 := false;
min_in_hour := 60.0;
glob_small_float := 0.1*10^(-50);
glob_current_iter := 0;
glob_optimal_clock_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
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/tanpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( x ) ;");
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 := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
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, "2.0\t- log(abs(cos((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;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_tmp1_a1 := Array(0 .. max_terms + 1, []);
array_tmp1_a2 := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_init := 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_last_rel_error := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_tmp1_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_a2[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_type_pole[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_m1[term] := 0.; term := term + 1
end do;
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_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_last_rel_error[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_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_norms[term] := 0.; term := term + 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;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[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_poles[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[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp1_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_a2[term] := 0.; term := term + 1
end do;
array_tmp1_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_a1[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_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[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_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 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_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
temp1 := iiif!;
temp2 := jjjf!;
array_fact_1[iiif] := temp1;
array_fact_2[iiif, jjjf] := temp1/temp2;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
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);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
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;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*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]*
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();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
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 array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
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*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]/(
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*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]/(
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*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;
display_alot(current_iter)
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 ) = tan ( x ) ;");
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, "2012-06-17T03:38:07-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "tan");
logitem_str(html_log_file, "diff ( y , x , 1 ) = tan ( x ) ;");
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_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_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 091 | ");
logitem_str(html_log_file,
"tan diffeq.mxt");
logitem_str(html_log_file,
"tan maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly for speeding factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/tanpostode.ode#################
diff ( y , x , 1 ) = tan ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 - log(abs(cos((x))))
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 2
y[1] (numeric) = 2
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 2.0000005000000833333555555623016
y[1] (numeric) = 2.0000005000000833341333337650796
absolute error = 7.777782027780e-19
relative error = 3.8888900416673275460398341155912e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 2.0000020000013333347555572825419
y[1] (numeric) = 2.0000020000013333363111228897218
absolute error = 1.5555656071799e-18
relative error = 7.7778202580740567069070092666832e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 2.0000045000067500162000442608434
y[1] (numeric) = 2.0000045000067500185334196965844
absolute error = 2.3333754357410e-18
relative error = 1.1666850928251035718785034776957e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 2.0000080000213334243559976657853
y[1] (numeric) = 2.000008000021333427467218577436
absolute error = 3.1112209116507e-18
relative error = 1.5556042333918232500865325541196e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 2.0000125000520836805581907455634
y[1] (numeric) = 2.0000125000520836844473060047022
absolute error = 3.8891152591388e-18
relative error = 1.9445454761095347727033886322501e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 2.0000180001080010368113308750952
y[1] (numeric) = 2.0000180001080010414784025789558
absolute error = 4.6670717038606e-18
relative error = 2.3335148501706374526463930489112e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.17
NO POLE
x[1] = 0.007
y[1] (analytic) = 2.0000245002000859477944457038803
y[1] (numeric) = 2.000024500200085953239549177164
absolute error = 5.4451034732837e-18
relative error = 2.7225183855192585533055095227649e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 2.0000320003413391588687375355708
y[1] (numeric) = 2.0000320003413391650919613326443
absolute error = 6.2232237970735e-18
relative error = 3.1115621130118928125033443772702e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 2.0000405005467618100904021720563
y[1] (numeric) = 2.0000405005467618170918480795355
absolute error = 7.0014459074792e-18
relative error = 3.5006520645782808601498198261310e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 2.0000500008333555562301806003859
y[1] (numeric) = 2.0000500008333555640099636401063
absolute error = 7.7797830397204e-18
relative error = 3.8897942733825746004771347525727e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 2.0000605012201227028016840979645
y[1] (numeric) = 2.000060501220122711359932530338
absolute error = 8.5582484323735e-18
relative error = 4.2789947739843876378198997400085e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 2.0000720017280663581008055881231
y[1] (numeric) = 2.0000720017280663674376609158806
absolute error = 9.3368553277575e-18
relative error = 4.6682596024995288319818110847309e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 2.0000845023801906012588024023147
y[1] (numeric) = 2.0000845023801906113744193746364
absolute error = 1.01156169723217e-17
relative error = 5.0575947967616670194546566606891e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 2.000098003201500666311908004791
y[1] (numeric) = 2.0000980032015006772064546218228
absolute error = 1.08945466170318e-17
relative error = 5.4470063964831750205509381123829e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 2.0001125042190031422906027186064
y[1] (numeric) = 2.0001125042190031539642602363635
absolute error = 1.16736575177571e-17
relative error = 5.8365004434165009664432807214222e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 2.0001280054617061893319460661503
y[1] (numeric) = 2.0001280054617062017849090018085
absolute error = 1.24529629356582e-17
relative error = 6.2260829815157650133196724771829e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 2.0001445069606197708186460110779
y[1] (numeric) = 2.0001445069606197840511221486518
absolute error = 1.32324761375739e-17
relative error = 6.6157600570979295483760584190366e-16 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.35
NO POLE
x[1] = 0.018
y[1] (analytic) = 2.0001620087487559015488131694577
y[1] (numeric) = 2.000162008748755915561023565867
absolute error = 1.40122103964093e-17
relative error = 7.0055377190045409008551365282039e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 2.0001805108611289119406209541629
y[1] (numeric) = 2.000180510861128926732799945687
absolute error = 1.47921789915241e-17
relative error = 7.3954220187635406384598966859107e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 2.0002000133347557282763656359674
y[1] (numeric) = 2.0002000133347557438487608450876
absolute error = 1.55723952091202e-17
relative error = 7.7854190107506945552247074910310e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 2.0002205162086561689906934554522
y[1] (numeric) = 2.0002205162086561853435657980831
absolute error = 1.63528723426309e-17
relative error = 8.1755347523517873161960899998461e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 2.0002420195238532570080352096754
y[1] (numeric) = 2.0002420195238532741416589027855
absolute error = 1.71336236931101e-17
relative error = 8.5657753041247808663973677917849e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 2.0002645233233735481345621745959
y[1] (numeric) = 2.0002645233233735660492247442166
absolute error = 1.79146625696207e-17
relative error = 8.9561467299615347196349700165146e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 2.0002880276522474755102508164671
y[1] (numeric) = 2.0002880276522474942062531060922
absolute error = 1.86960022896251e-17
relative error = 9.3466550972505360141083922249527e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 2.0003125325575097101269175008517
y[1] (numeric) = 2.0003125325575097296045736802265
absolute error = 1.94776561793748e-17
relative error = 9.7373064770391375464166487383454e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 2.0003380380881995374183583345463
y[1] (numeric) = 2.0003380380881995576779959088471
absolute error = 2.02596375743008e-17
relative error = 1.0128106944196151736928694362178e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 2.0003645442953612499290033815852
y[1] (numeric) = 2.0003645442953612709709632009899
absolute error = 2.10419598194047e-17
relative error = 1.0519062577574748559933542877675e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 2.0003920512320445560677687876376
y[1] (numeric) = 2.0003920512320445778924050572873
absolute error = 2.18246362696497e-17
relative error = 1.0910179460175255540716974940100e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.0MB, time=0.54
NO POLE
x[1] = 0.029
y[1] (analytic) = 2.0004205589533050049540648355588
y[1] (numeric) = 2.0004205589533050275617451259114
absolute error = 2.26076802903526e-17
relative error = 1.1301463679308407762928376450706e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 2.000450067516204427363192646657
y[1] (numeric) = 2.0004500675162044507542979042327
absolute error = 2.33911052575757e-17
relative error = 1.1692921326758496013146309517125e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 2.0004805769798113927786371454431
y[1] (numeric) = 2.0004805769798114169535617039625
absolute error = 2.41749245585194e-17
relative error = 1.2084558498946811021689224552270e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 2.0005120874052016825590390283112
y[1] (numeric) = 2.0005120874052017075181906202267
absolute error = 2.49591515919155e-17
relative error = 1.2476381297095381811691510913776e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 2.0005445988554587792279038268238
y[1] (numeric) = 2.0005445988554588049717035952449
absolute error = 2.57437997684211e-17
relative error = 1.2868395827390956177463173564621e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 2.0005781113956743718943817421411
y[1] (numeric) = 2.0005781113956743984232642531532
absolute error = 2.65288825110121e-17
relative error = 1.3260608201148721445284768638503e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 2.0006126250929488778137277567206
y[1] (numeric) = 2.0006126250929489051281410120991
absolute error = 2.73144132553785e-17
relative error = 1.3653024534976863244932590742350e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 2.0006481400163919800963276108466
y[1] (numeric) = 2.0006481400163920081967330611665
absolute error = 2.81004054503199e-17
relative error = 1.4045650950941160482708472423992e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 2.0006846562371231815744515729312
y[1] (numeric) = 2.0006846562371232104613241310719
absolute error = 2.88868725581407e-17
relative error = 1.4438493576729364623039149323374e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 2.000722173828272374836174541998
y[1] (numeric) = 2.000722173828272404510002597045
absolute error = 2.96738280550470e-17
relative error = 1.4831558545816360970941727678045e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 2.0007606928649804284361779064556
y[1] (numeric) = 2.0007606928649804588974633379996
absolute error = 3.04612854315440e-17
relative error = 1.5224851997629510104456324101950e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 2.0008002134243997892934257533484
y[1] (numeric) = 2.0008002134243998205426839461815
absolute error = 3.12492581928331e-17
relative error = 1.5618380077713767609396810117089e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.74
NO POLE
x[1] = 0.041
y[1] (analytic) = 2.0008407355856951012859854848946
y[1] (numeric) = 2.0008407355856951333237453441055
absolute error = 3.20377598592109e-17
relative error = 1.6012148937897679700134520493034e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 2.0008822594300438400535406624792
y[1] (numeric) = 2.0008822594300438728803446289472
absolute error = 3.28268039664680e-17
relative error = 1.6406164736459203078066823609252e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 2.0009247850406369640184219705438
y[1] (numeric) = 2.0009247850406369976348260368329
absolute error = 3.36164040662891e-17
relative error = 1.6800433638292096713044032762471e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 2.0009683125026795816362605822236
y[1] (numeric) = 2.0009683125026796160428343088766
absolute error = 3.44065737266530e-17
relative error = 1.7194961815072183806051216838984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 2.0010128419033916348876469233352
y[1] (numeric) = 2.0010128419033916700849734555695
absolute error = 3.51973265322343e-17
relative error = 1.7589755445424381497451958566531e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 2.0010583733320085990224568796665
y[1] (numeric) = 2.0010583733320086350111329644716
absolute error = 3.59886760848051e-17
relative error = 1.7984820715089646648060588736434e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 2.0011049068797821985687868826991
y[1] (numeric) = 2.001104906879782235349422886337
absolute error = 3.67806360036379e-17
relative error = 1.8380163817092435366276569991709e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 2.0011524426399811396187190491822
y[1] (numeric) = 2.0011524426399811771919389750913
absolute error = 3.75732199259091e-17
relative error = 1.8775790951908374359295734666720e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 2.001200980707891858403417648649
y[1] (numeric) = 2.0012009807078918967698591557525
absolute error = 3.83664415071035e-17
relative error = 1.9171708327632341936582533170408e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 2.0012505211808192861703386383269
y[1] (numeric) = 2.001250521180819325330653059746
absolute error = 3.91603144214191e-17
relative error = 1.9567922160146606794145359119941e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 2.0013010641580876303756148452488
y[1] (numeric) = 2.0013010641580876703304672074221
absolute error = 3.99548523621733e-17
relative error = 1.9964438673289572187206096287002e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 2.0013526097410411722049605990636
y[1] (numeric) = 2.0013526097410412129550296412735
absolute error = 4.07500690422099e-17
relative error = 2.0361264099024823558457640987200e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=0.93
NO POLE
x[1] = 0.053
y[1] (analytic) = 2.0014051580330450804367212344132
y[1] (numeric) = 2.0014051580330451219826994287198
absolute error = 4.15459781943066e-17
relative error = 2.0758404677610327637463976396497e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 2.0014587091394862416609748971576
y[1] (numeric) = 2.0014587091394862840035684687412
absolute error = 4.23425935715836e-17
relative error = 2.1155866657768080725779889262446e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 2.0015132631677741068688765125758
y[1] (numeric) = 2.0015132631677741500088054604895
absolute error = 4.31399289479137e-17
relative error = 2.1553656296854403889621647767611e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 2.0015688202273415544267166143509
y[1] (numeric) = 2.0015688202273415983647147326827
absolute error = 4.39379981183318e-17
relative error = 2.1951779861029833710119637246700e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 2.0016253804296457694494509990761
y[1] (numeric) = 2.0016253804296458141862658985236
absolute error = 4.47368148994475e-17
relative error = 2.2350243625430455113518417132425e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 2.001682943888169139588740870654
y[1] (numeric) = 2.0016829438881691851251340005103
absolute error = 4.55363931298563e-17
relative error = 2.2749053874338425830294407594979e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 2.0017415107184201672508272807356
y[1] (numeric) = 2.0017415107184202135875739512895
absolute error = 4.63367466705539e-17
relative error = 2.3148216901353938622260411929832e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 2.0018010810379343982598482637709
y[1] (numeric) = 2.0018010810379344453977376691214
absolute error = 4.71378894053505e-17
relative error = 2.3547739009567070310864777602629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 2.0018616549662753669824921167912
y[1] (numeric) = 2.0018616549662754149223273580767
absolute error = 4.79398352412855e-17
relative error = 2.3947626511729715366244140928918e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 2.0019232326250355579301657932514
y[1] (numeric) = 2.0019232326250356066727639022963
absolute error = 4.87425981090449e-17
relative error = 2.4347885730428750855348255140222e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 2.0019858141378373838551433756696
y[1] (numeric) = 2.0019858141378374334013353390478
absolute error = 4.95461919633782e-17
relative error = 2.4748522998258831985730121433759e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=1.13
NO POLE
x[1] = 0.064
y[1] (analytic) = 2.0020493996303341803574460719639
y[1] (numeric) = 2.0020493996303342307080768554815
absolute error = 5.03506307835176e-17
relative error = 2.5149544657996214798513555335202e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 2.0021139892302112170194921539039
y[1] (numeric) = 2.0021139892302112681754207275008
absolute error = 5.11559285735969e-17
relative error = 2.5550957062772305058084482057542e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 2.0021795830671867250858427315552
y[1] (numeric) = 2.0021795830671867770479420946285
absolute error = 5.19620993630733e-17
relative error = 2.5952766576248529554016804764750e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 2.0022461812730129417056572436521
y[1] (numeric) = 2.0022461812730129944748144508007
absolute error = 5.27691572071486e-17
relative error = 2.6354979572790779366326024974286e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 2.0023137839814771707557610491142
y[1] (numeric) = 2.0023137839814772243328772363072
absolute error = 5.35771161871930e-17
relative error = 2.6757602437645021226572013968851e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 2.0023823913284028602625165381279
y[1] (numeric) = 2.0023823913284029146485069492969
absolute error = 5.43859904111690e-17
relative error = 2.7160641567112826064996667452237e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 2.0024520034516506964409787510246
y[1] (numeric) = 2.0024520034516507516367727650816
absolute error = 5.51957940140570e-17
relative error = 2.7564103368727611653393045488977e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 2.0025226204911197143701066083408
y[1] (numeric) = 2.0025226204911197703766477666233
absolute error = 5.60065411582825e-17
relative error = 2.7967994261431547098739367977824e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 2.0025942425887484253230915246866
y[1] (numeric) = 2.0025942425887484821413375588299
absolute error = 5.68182460341433e-17
relative error = 2.8372320675752317917325276515026e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 2.0026668698885159607721564111478
y[1] (numeric) = 2.0026668698885160184030792713874
absolute error = 5.76309228602396e-17
relative error = 2.8777089053981197644197903064233e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 2.0027405025364432330874698747138
y[1] (numeric) = 2.0027405025364432915320557586179
absolute error = 5.84445858839041e-17
relative error = 2.9182305850350975475848411185945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 2.0028151406805941129501128074729
y[1] (numeric) = 2.0028151406805941722093621891067
absolute error = 5.92592493816338e-17
relative error = 2.9587977531214586623384093120039e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=1.33
NO POLE
x[1] = 0.076
y[1] (analytic) = 2.0028907844710766234993275319063
y[1] (numeric) = 2.0028907844710766835742551914298
absolute error = 6.00749276595235e-17
relative error = 2.9994110575224443024526791525593e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 2.0029674340600441512345732404228
y[1] (numeric) = 2.0029674340600442121262082941227
absolute error = 6.08916350536999e-17
relative error = 3.0400711473511912866500367075886e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 2.0030450896016966736932056462047
y[1] (numeric) = 2.0030450896016967354025915769626
absolute error = 6.17093859307579e-17
relative error = 3.0807786729867745478788319031788e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 2.0031237512522820039248935574283
y[1] (numeric) = 2.0031237512522820664530882456259
absolute error = 6.25281946881976e-17
relative error = 3.1215342860922690317520878795453e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 2.0032034191700970517841805069258
y[1] (numeric) = 2.0032034191700971151322562617889
absolute error = 6.33480757548631e-17
relative error = 3.1623386396328856908042498223570e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 2.0032840935154891020628956233724
y[1] (numeric) = 2.0032840935154891662319392147547
absolute error = 6.41690435913823e-17
relative error = 3.2031923878941413988603695248441e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 2.0033657744508571094844146271212
y[1] (numeric) = 2.00336577445085717447552731773
absolute error = 6.49911126906088e-17
relative error = 3.2440961865001174620572032236225e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 2.0034484621406530105820691829242
y[1] (numeric) = 2.003448462140653076396366760989
absolute error = 6.58142975780648e-17
relative error = 3.2850506924317515736497958135075e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 2.0035321567513830524843008520412
y[1] (numeric) = 2.0035321567513831191229136644264
absolute error = 6.66386128123852e-17
relative error = 3.3260565640451729621115661524508e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 2.0036168584516091386294545667602
y[1] (numeric) = 2.0036168584516092060935275525246
absolute error = 6.74640729857644e-17
relative error = 3.3671144610901553607113315788071e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 2.0037025674119501914334059102733
y[1] (numeric) = 2.003702567411950259724098634676
absolute error = 6.82906927244027e-17
relative error = 3.4082250447285328253891249726109e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 2.0037892838050835319335165333294
y[1] (numeric) = 2.0037892838050836010520032222859
absolute error = 6.91184866889565e-17
relative error = 3.4493889775527877892833606033815e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=1.53
NO POLE
x[1] = 0.088
y[1] (analytic) = 2.0038770078057462764327127853365
y[1] (numeric) = 2.0038770078057463463801823603246
absolute error = 6.99474695749881e-17
relative error = 3.4906069236046014818190613707323e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 2.003965739590736750167784090823
y[1] (numeric) = 2.0039657395907368209454402042414
absolute error = 7.07776561134184e-17
relative error = 3.5318795483935311698449872933574e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 2.0040554793389159180262997716708
y[1] (numeric) = 2.0040554793389159896353608426513
absolute error = 7.16090610709805e-17
relative error = 3.5732075189157141559493742090814e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 2.0041462272312088323368459105899
y[1] (numeric) = 2.0041462272312089047785451612652
absolute error = 7.24416992506753e-17
relative error = 3.6145915036726531826368384949370e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 2.0042379834506060977575874812476
y[1] (numeric) = 2.004237983450606171033172973476
absolute error = 7.32755854922284e-17
relative error = 3.6560321726900480607187171781829e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 2.0043307481821653532884653446555
y[1] (numeric) = 2.0043307481821654273992000172048
absolute error = 7.41107346725493e-17
relative error = 3.6975301975367231682417685340960e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 2.0044245216130127714326428392592
y[1] (numeric) = 2.0044245216130128463798045454508
absolute error = 7.49471617061916e-17
relative error = 3.7390862513435857006451864118635e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 2.0045193039323445745331225830883
y[1] (numeric) = 2.0045193039323446503180041289036
absolute error = 7.57848815458153e-17
relative error = 3.7807010088226693053163784161792e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 2.0046150953314285683107607697867
y[1] (numeric) = 2.0046150953314286449346699524376
absolute error = 7.66239091826509e-17
relative error = 3.8223751462862478732954538119884e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 2.0047118960036056926302136858497
y[1] (numeric) = 2.0047118960036057700944733328146
absolute error = 7.74642596469649e-17
relative error = 3.8641093416659992770474461478415e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 2.0048097061442915895206594134848
y[1] (numeric) = 2.0048097061442916678266074220122
absolute error = 7.83059480085274e-17
relative error = 3.9059042745322537179058345254173e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 2.0049085259509781884784467217598
y[1] (numeric) = 2.0049085259509782676274360988414
absolute error = 7.91489893770816e-17
relative error = 3.9477606261133164423210877998309e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.1MB, time=1.72
NO POLE
x[1] = 0.1
y[1] (analytic) = 2.0050083556232353090791329977213
y[1] (numeric) = 2.0050083556232353890725319005363
absolute error = 7.99933989028150e-17
relative error = 3.9896790793148545886616297051058e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 2.0051091953627122809266837385959
y[1] (numeric) = 2.005109195362712361765875515428
absolute error = 8.08391917768321e-17
relative error = 4.0316603187393379291088702813137e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 2.0052110453731395809679176257221
y[1] (numeric) = 2.0052110453731396626543008573516
absolute error = 8.16863832316295e-17
relative error = 4.0737050307055781312313799723971e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 2.0053139058603304882005935402182
y[1] (numeric) = 2.005313905860330570735582081791
absolute error = 8.25349885415728e-17
relative error = 4.1158139032683363432112448834593e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 2.0054177770321827558038490693382
y[1] (numeric) = 2.0054177770321828391888720927134
absolute error = 8.33850230233752e-17
relative error = 4.1579876262379938499913659579388e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 2.0055226590986803007200141007995
y[1] (numeric) = 2.0055226590986803849565161373777
absolute error = 8.42365020365782e-17
relative error = 4.2002268912003054797118918549945e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 2.0056285522718949107171380199288
y[1] (numeric) = 2.0056285522718949958065790039632
absolute error = 8.50894409840344e-17
relative error = 4.2425323915362354864345236006228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 2.0057354567659879689618848211429
y[1] (numeric) = 2.0057354567659880549057401335348
absolute error = 8.59438553123919e-17
relative error = 4.2849048224418507052920049050303e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 2.0058433727972121961327671309818
y[1] (numeric) = 2.0058433727972122829325276435629
absolute error = 8.67997605125811e-17
relative error = 4.3273448809483105962250125193130e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 2.0059523005839134101040077246038
y[1] (numeric) = 2.0059523005839134977611798449073
absolute error = 8.76571721203035e-17
relative error = 4.3698532659419339521830653644869e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 2.0060622403465323032306356113409
y[1] (numeric) = 2.0060622403465323917467413278633
absolute error = 8.85161057165224e-17
relative error = 4.4124306781843370095253207052034e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=38.1MB, alloc=4.2MB, time=1.92
x[1] = 0.111
y[1] (analytic) = 2.0061731923076062372657431776415
y[1] (numeric) = 2.0061731923076063266423201055971
absolute error = 8.93765769279556e-17
relative error = 4.4550778203326476685176469180060e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 2.0062851566917710559411512175826
y[1] (numeric) = 2.0062851566917711461797526451533
absolute error = 9.02386014275707e-17
relative error = 4.4977953969598254500756781462720e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 2.0063981337257629152430499622528
y[1] (numeric) = 2.0063981337257630063452448973347
absolute error = 9.11021949350819e-17
relative error = 4.5405841145750320712144232941847e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 2.0065121236384201314145064498531
y[1] (numeric) = 2.0065121236384202233818796673026
absolute error = 9.19673732174495e-17
relative error = 4.5834446816441121716629893638085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 2.0066271266606850467170517685652
y[1] (numeric) = 2.0066271266606851395512038579465
absolute error = 9.28341520893813e-17
relative error = 4.6263778086101440260245317785984e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 2.0067431430256059129838858643474
y[1] (numeric) = 2.0067431430256060066864332781837
absolute error = 9.37025474138363e-17
relative error = 4.6693842079140798909329180896462e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 2.0068601729683387929975627461547
y[1] (numeric) = 2.0068601729683388875701378486854
absolute error = 9.45725751025307e-17
relative error = 4.7124645940154756945305030026228e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 2.0069782167261494797253450519834
y[1] (numeric) = 2.0069782167261495751695961684291
absolute error = 9.54442511164457e-17
relative error = 4.7556196834132848610439691239756e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 2.0070972745384154334457440710196
y[1] (numeric) = 2.007097274538415529763335537358
absolute error = 9.63175914663384e-17
relative error = 4.7988501946667807553393607603066e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 2.0072173466466277368000894604662
y[1] (numeric) = 2.0072173466466278339927016737208
absolute error = 9.71926122132546e-17
relative error = 4.8421568484165476496820558803639e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 2.0073384332943930678033020608256
y[1] (numeric) = 2.007338433294393165872631529869
absolute error = 9.80693294690434e-17
relative error = 4.8855403674055349406856163604637e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 2.0074605347274356908483734110635
y[1] (numeric) = 2.0074605347274357897961328079388
absolute error = 9.89477593968753e-17
relative error = 4.9290014765002590111937819571889e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.2MB, time=2.12
NO POLE
x[1] = 0.123
y[1] (analytic) = 2.0075836511935994657393868057698
y[1] (numeric) = 2.0075836511935995655673050175314
absolute error = 9.98279182117616e-17
relative error = 4.9725409027120428257899278565374e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 2.0077077829428498747882470307837
y[1] (numeric) = 2.0077077829428499754980692118607
absolute error = 1.007098221810770e-16
relative error = 5.0161593752183876135204678818421e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 2.0078329302272760680106192724675
y[1] (numeric) = 2.0078329302272761696041068975517
absolute error = 1.015934876250842e-16
relative error = 5.0598576253844165481482967866714e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 2.0079590933010929264569121296132
y[1] (numeric) = 2.0079590933010930289358430470742
absolute error = 1.024789309174610e-16
relative error = 5.1036363867844150272891537327638e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 2.0080862724206431437144751766449
y[1] (numeric) = 2.008086272420643247080643662475
absolute error = 1.033661684858301e-16
relative error = 5.1474963952234771983214215049686e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 2.0082144678443993256175181431687
y[1] (numeric) = 2.0082144678443994298727349554602
absolute error = 1.042552168122915e-16
relative error = 5.1914383887592534336357768201123e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 2.0083436798329661082015964989065
y[1] (numeric) = 2.0083436798329662133476889328632
absolute error = 1.051460924339567e-16
relative error = 5.2354631077237586040303936564425e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 2.008473908649082293939847075567
y[1] (numeric) = 2.0084739086490823999786590190537
absolute error = 1.060388119434867e-16
relative error = 5.2795712947453404273886768076009e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 2.0086051545576230062984973292569
y[1] (numeric) = 2.0086051545576231132318893188881
absolute error = 1.069333919896312e-16
relative error = 5.3237636947706781019736339637189e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 2.0087374178256018626495129596427
y[1] (numeric) = 2.0087374178256019704793622374147
absolute error = 1.078298492777720e-16
relative error = 5.3680410550869602814498420758704e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 2.0088706987221731655785908663584
y[1] (numeric) = 2.0088706987221732743067914368258
absolute error = 1.087282005704674e-16
relative error = 5.4124041253440827376783408403045e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 2.0090049975186341126270478502428
y[1] (numeric) = 2.0090049975186342222555105382434
absolute error = 1.096284626880006e-16
relative error = 5.4568536575770147502360266793937e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.2MB, time=2.32
NO POLE
x[1] = 0.135
y[1] (analytic) = 2.0091403144884270245065000681108
y[1] (numeric) = 2.0091403144884271350371525770411
absolute error = 1.105306525089303e-16
relative error = 5.5013904062282442724591772686908e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 2.0092766499071415918255740361572
y[1] (numeric) = 2.0092766499071417032603610068007
absolute error = 1.114347869706435e-16
relative error = 5.5460151281703015542997422427768e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 2.0094140040525171403682369600856
y[1] (numeric) = 2.0094140040525172527091200299981
absolute error = 1.123408830699125e-16
relative error = 5.5907285827284604324177562383101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 2.0095523772044449149636823610216
y[1] (numeric) = 2.0095523772044450282126402244746
absolute error = 1.132489578634530e-16
relative error = 5.6355315317034626538752490411662e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 2.0096917696449703819880563766269
y[1] (numeric) = 2.0096917696449704961470848451132
absolute error = 1.141590284684863e-16
relative error = 5.6804247393944142117737752802891e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 2.0098321816582955505386607580818
y[1] (numeric) = 2.0098321816582956656097728213855
absolute error = 1.150711120633037e-16
relative error = 5.7254089726217587856948396731254e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 2.0099736135307813123216204672764
y[1] (numeric) = 2.0099736135307814283068463551106
absolute error = 1.159852258878342e-16
relative error = 5.7704850007503826860285676850101e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 2.0101160655509498002943569162601
y[1] (numeric) = 2.0101160655509499171957441604743
absolute error = 1.169013872442142e-16
relative error = 5.8156535957127862727970793502855e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 733.2
Order of pole = 1.413e+04
x[1] = 0.143
y[1] (analytic) = 2.0102595380094867661045622943983
y[1] (numeric) = 2.0102595380094868839241757917599
absolute error = 1.178196134973616e-16
relative error = 5.8609155320324409102189331104032e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 41.26
Order of pole = 771.5
x[1] = 0.144
y[1] (analytic) = 2.0104040311992439763677261095047
y[1] (numeric) = 2.0104040311992440951076481850567
absolute error = 1.187399220755520e-16
relative error = 5.9062715868472166645436063468147e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 21.56
Order of pole = 391.1
x[1] = 0.145
y[1] (analytic) = 2.0105495454152416278256220392318
y[1] (numeric) = 2.0105495454152417474879525102292
absolute error = 1.196623304709974e-16
relative error = 5.9517225399329003076876758613007e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 14.74
Order of pole = 259.5
x[1] = 0.146
y[1] (analytic) = 2.0106960809546707814285214600564
y[1] (numeric) = 2.0106960809546709020153777004853
absolute error = 1.205868562404289e-16
relative error = 5.9972691737268778837431156017167e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.2MB, time=2.52
Real estimate of pole used
Radius of convergence = 11.28
Order of pole = 192.8
x[1] = 0.147
y[1] (analytic) = 2.0108436381168958153842596052013
y[1] (numeric) = 2.0108436381168959368977766108835
absolute error = 1.215135170056822e-16
relative error = 6.0429122733519217780726207004623e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 9.192
Order of pole = 152.5
x[1] = 0.148
y[1] (analytic) = 2.0109922172034568972176412117464
y[1] (numeric) = 2.0109922172034570196599716660324
absolute error = 1.224423304542860e-16
relative error = 6.0886526266400869060885911159705e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.794
Order of pole = 125.6
x[1] = 0.149
y[1] (analytic) = 2.0111418185180724748840347630414
y[1] (numeric) = 2.0111418185180725982573491030945
absolute error = 1.233733143400531e-16
relative error = 6.1344910241567057171903718957353e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.793
Order of pole = 106.2
x[1] = 0.15
y[1] (analytic) = 2.0112924423666417869813680274198
y[1] (numeric) = 2.0112924423666419112878545110957
absolute error = 1.243064864836759e-16
relative error = 6.1804282592245661800820108641838e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.042
Order of pole = 91.75
x[1] = 0.151
y[1] (analytic) = 2.0114440890572473921051025503044
y[1] (numeric) = 2.0114440890572475173469673236281
absolute error = 1.252418647733237e-16
relative error = 6.2264651279481430862638335719307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.457
Order of pole = 80.46
x[1] = 0.152
y[1] (analytic) = 2.0115967589001577173911310862869
y[1] (numeric) = 2.011596758900157843570598251531
absolute error = 1.261794671652441e-16
relative error = 6.2726024292379966716943083601651e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.989
Order of pole = 71.44
x[1] = 0.153
y[1] (analytic) = 2.0117504522078296262919096729698
y[1] (numeric) = 2.0117504522078297534112213573372
absolute error = 1.271193116843674e-16
relative error = 6.3188409648352834786291242664720e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.606
Order of pole = 64.07
x[1] = 0.154
y[1] (analytic) = 2.0119051692949110056315051616113
y[1] (numeric) = 2.0119051692949111336929215865255
absolute error = 1.280614164249142e-16
relative error = 6.3651815393363890260014603514282e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.287
Order of pole = 57.92
x[1] = 0.155
y[1] (analytic) = 2.0120609104782433719856095433441
y[1] (numeric) = 2.0120609104782435009914090943502
absolute error = 1.290057995510061e-16
relative error = 6.4116249602176769385765754665809e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.018
Order of pole = 52.73
x[1] = 0.156
y[1] (analytic) = 2.0122176760768644974329443564304
y[1] (numeric) = 2.0122176760768646273854236537109
absolute error = 1.299524792972805e-16
relative error = 6.4581720378604038522392773002519e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.787
Order of pole = 48.29
x[1] = 0.157
y[1] (analytic) = 2.0123754664120110547248518422239
y[1] (numeric) = 2.0123754664120111856263258117316
absolute error = 1.309014739695077e-16
relative error = 6.5048235855757102405997326284368e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.588
Order of pole = 44.45
x[1] = 0.158
memory used=53.4MB, alloc=4.2MB, time=2.72
y[1] (analytic) = 2.0125342818071212819202443478551
y[1] (numeric) = 2.0125342818071214137730462930675
absolute error = 1.318528019452124e-16
relative error = 6.5515804196297911474457167632359e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.414
Order of pole = 41.1
x[1] = 0.159
y[1] (analytic) = 2.01269412258783766653345976484
y[1] (numeric) = 2.0126941225878377993399414391381
absolute error = 1.328064816742981e-16
relative error = 6.5984433592691718771432902784825e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.26
Order of pole = 38.15
x[1] = 0.16
y[1] (analytic) = 2.0128549890820096492429485575849
y[1] (numeric) = 2.0128549890820097830054802372597
absolute error = 1.337625316796748e-16
relative error = 6.6454132267461081331776457652650e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.124
Order of pole = 35.53
x[1] = 0.161
y[1] (analytic) = 2.0130168816196963472090971869651
y[1] (numeric) = 2.013016881619696481930067744856
absolute error = 1.347209705578909e-16
relative error = 6.6924908473441549187736352296713e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.002
Order of pole = 33.2
x[1] = 0.162
y[1] (analytic) = 2.0131798005331692970498734846944
y[1] (numeric) = 2.0131798005331694327316904644624
absolute error = 1.356818169797680e-16
relative error = 6.7396770494038392026515414087965e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.893
Order of pole = 31.11
x[1] = 0.163
y[1] (analytic) = 2.0133437461569152175233617970464
y[1] (numeric) = 2.0133437461569153541684514880858
absolute error = 1.366450896910394e-16
relative error = 6.7869726643484756964341292181691e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.795
Order of pole = 29.22
x[1] = 0.164
y[1] (analytic) = 2.0135087188276387919666395046947
y[1] (numeric) = 2.013508718827638929577447017687
absolute error = 1.376108075129923e-16
relative error = 6.8343785267101253307366560852683e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.706
Order of pole = 27.51
x[1] = 0.165
y[1] (analytic) = 2.0136747188842654705408318521251
y[1] (numeric) = 2.0136747188842656091198211952391
absolute error = 1.385789893431140e-16
relative error = 6.8818954741557109127557111044431e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.625
Order of pole = 25.95
x[1] = 0.166
y[1] (analytic) = 2.0138417466679442923325688984354
y[1] (numeric) = 2.0138417466679444318822230541763
absolute error = 1.395496541557409e-16
relative error = 6.9295243475132299514358013415227e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.55
Order of pole = 24.53
x[1] = 0.167
y[1] (analytic) = 2.0140098025220507273624568446486
y[1] (numeric) = 2.0140098025220508678852778473606
absolute error = 1.405228210027120e-16
relative error = 6.9772659907981486648705463271383e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.482
Order of pole = 23.23
x[1] = 0.168
y[1] (analytic) = 2.0141788867921895385515660142714
y[1] (numeric) = 2.014178886792189680050075028297
absolute error = 1.414985090140256e-16
relative error = 7.0251212512399121821156127008322e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.42
Order of pole = 22.04
x[1] = 0.169
y[1] (analytic) = 2.0143489998261976636973293771518
y[1] (numeric) = 2.0143489998261978061740667756523
absolute error = 1.424767373985005e-16
relative error = 7.0730909793086350662597123396476e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.2MB, time=2.92
Real estimate of pole used
Radius of convergence = 2.362
Order of pole = 20.93
x[1] = 0.17
y[1] (analytic) = 2.0145201419741471175106387252292
y[1] (numeric) = 2.0145201419741472609681641696693
absolute error = 1.434575254444401e-16
relative error = 7.1211760287418922848660802960538e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.309
Order of pole = 19.92
x[1] = 0.171
y[1] (analytic) = 2.0146923135883479137663204461019
y[1] (numeric) = 2.0146923135883480582072129664027
absolute error = 1.444408925203008e-16
relative error = 7.1693772565716797114182200829958e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.259
Order of pole = 18.97
x[1] = 0.172
y[1] (analytic) = 2.0148655150233510076195693101194
y[1] (numeric) = 2.014865515023351153046427385484
absolute error = 1.454268580753646e-16
relative error = 7.2176955231515387451768249260893e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.213
Order of pole = 18.1
x[1] = 0.173
y[1] (analytic) = 2.0150397466359512581413168026708
y[1] (numeric) = 2.0150397466359514045567584430858
absolute error = 1.464154416404150e-16
relative error = 7.2661316921837999360907976675207e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.17
Order of pole = 17.28
x[1] = 0.174
y[1] (analytic) = 2.0152150087851904111259103093034
y[1] (numeric) = 2.0152150087851905585325731377207
absolute error = 1.474066628284173e-16
relative error = 7.3146866307469997747985030655718e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.13
Order of pole = 16.52
x[1] = 0.175
y[1] (analytic) = 2.0153913018323601022248809111587
y[1] (numeric) = 2.0153913018323602506254222463614
absolute error = 1.484005413352027e-16
relative error = 7.3633612093234404166403705271679e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.093
Order of pole = 15.81
x[1] = 0.176
y[1] (analytic) = 2.0155686261410048804609806859361
y[1] (numeric) = 2.0155686261410050298580776260925
absolute error = 1.493970969401564e-16
relative error = 7.4121563018269018177815162281307e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.057
Order of pole = 15.15
x[1] = 0.177
y[1] (analytic) = 2.0157469820769252521770752492412
y[1] (numeric) = 2.0157469820769254025734247561514
absolute error = 1.503963495069102e-16
relative error = 7.4610727856305306349474460624001e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.025
Order of pole = 14.52
x[1] = 0.178
y[1] (analytic) = 2.0159263700081807454748838268924
y[1] (numeric) = 2.0159263700081808968732028109307
absolute error = 1.513983189840383e-16
relative error = 7.5101115415948409311150710349434e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.994
Order of pole = 13.94
x[1] = 0.179
y[1] (analytic) = 2.0161067903050929951989674347616
y[1] (numeric) = 2.01610679030509314760199284052
absolute error = 1.524030254057584e-16
relative error = 7.5592734540959304146591502351208e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.964
Order of pole = 13.39
x[1] = 0.18
y[1] (analytic) = 2.0162882433402488485217757733345
y[1] (numeric) = 2.0162882433402490019322646659701
absolute error = 1.534104888926356e-16
relative error = 7.6085594110537877205086833863943e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.937
Order of pole = 12.87
x[1] = 0.181
y[1] (analytic) = 2.0164707294885034911859752337688
y[1] (numeric) = 2.0164707294885036456067048860613
absolute error = 1.544207296522925e-16
relative error = 7.6579703039608589186303018601452e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.2MB, time=3.12
Real estimate of pole used
Radius of convergence = 1.911
Order of pole = 12.39
x[1] = 0.182
y[1] (analytic) = 2.0166542491269835944606939753071
y[1] (numeric) = 2.016654249126983749894461955428
absolute error = 1.554337679801209e-16
relative error = 7.7075070279106446140559248555923e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.887
Order of pole = 11.93
x[1] = 0.183
y[1] (analytic) = 2.0168388026350904828687353850041
y[1] (numeric) = 2.0168388026350906393183596450046
absolute error = 1.564496242600005e-16
relative error = 7.7571704816265949910699234743324e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.863
Order of pole = 11.49
x[1] = 0.184
y[1] (analytic) = 2.0170243903945033227422283845393
y[1] (numeric) = 2.0170243903945034802105473495597
absolute error = 1.574683189650204e-16
relative error = 7.8069615674910940075959556127082e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.841
Order of pole = 11.08
x[1] = 0.185
y[1] (analytic) = 2.017211012789182331664602020121
y[1] (numeric) = 2.0172110127891824901544746783255
absolute error = 1.584898726582045e-16
relative error = 7.8568811915745868343600986102125e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.821
Order of pole = 10.69
x[1] = 0.186
y[1] (analytic) = 2.0173986702053720088571925749931
y[1] (numeric) = 2.0173986702053721683714985682364
absolute error = 1.595143059932433e-16
relative error = 7.9069302636649739874456212167170e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.801
Order of pole = 10.33
x[1] = 0.187
y[1] (analytic) = 2.0175873630316043865692140947539
y[1] (numeric) = 2.0175873630316045471108538099819
absolute error = 1.605416397152280e-16
relative error = 7.9571096972970683843210517278151e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.782
Order of pole = 9.978
x[1] = 0.188
y[1] (analytic) = 2.0177770916587023025302477285834
y[1] (numeric) = 2.0177770916587024641021423899742
absolute error = 1.615718946613908e-16
relative error = 8.0074204097823081780388266882910e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.764
Order of pole = 9.648
x[1] = 0.189
y[1] (analytic) = 2.0179678564797826935248316796769
y[1] (numeric) = 2.0179678564797828561299234415251
absolute error = 1.626050917618482e-16
relative error = 8.0578633222385662376980062064978e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.747
Order of pole = 9.333
x[1] = 0.19
y[1] (analytic) = 2.0181596578902599101491618408727
y[1] (numeric) = 2.0181596578902600737904138812233
absolute error = 1.636412520403506e-16
relative error = 8.1084393596202193354292069067829e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.731
Order of pole = 9.035
x[1] = 0.191
y[1] (analytic) = 2.0183524962878490528103433819497
y[1] (numeric) = 2.0183524962878492174907399969846
absolute error = 1.646803966150349e-16
relative error = 8.1591494507483129740009817690844e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.715
Order of pole = 8.751
x[1] = 0.192
y[1] (analytic) = 2.0185463720725693290290656687196
y[1] (numeric) = 2.0185463720725694947516123679023
absolute error = 1.657225466991827e-16
relative error = 8.2099945283409502002493489307834e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.701
Order of pole = 8.48
x[1] = 0.193
y[1] (analytic) = 2.0187412856467474321070069463458
y[1] (numeric) = 2.018741285646747598874730548329
absolute error = 1.667677236019832e-16
relative error = 8.2609755290438592728795660582606e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.2MB, time=3.32
Real estimate of pole used
Radius of convergence = 1.687
Order of pole = 8.223
x[1] = 0.194
y[1] (analytic) = 2.0189372374150209412207112258461
y[1] (numeric) = 2.0189372374150211090366599551463
absolute error = 1.678159487293002e-16
relative error = 8.3120933934611099435238731901779e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.673
Order of pole = 7.978
x[1] = 0.195
y[1] (analytic) = 2.0191342277843417430041177891565
y[1] (numeric) = 2.0191342277843419118713613736013
absolute error = 1.688672435844448e-16
relative error = 8.3633490661860570877617870787501e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.66
Order of pole = 7.744
x[1] = 0.196
y[1] (analytic) = 2.0193322571639794746823636902184
y[1] (numeric) = 2.0193322571639796446039934591705
absolute error = 1.699216297689521e-16
relative error = 8.4147434958324269377362608111643e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.648
Order of pole = 7.521
x[1] = 0.197
y[1] (analytic) = 2.019531325965524988819921593161
y[1] (numeric) = 2.0195313259655251597990505765243
absolute error = 1.709791289833633e-16
relative error = 8.4662776350656147317036145058423e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.636
Order of pole = 7.308
x[1] = 0.198
y[1] (analytic) = 2.0197314346028938397465792697594
y[1] (numeric) = 2.0197314346028940117863422977719
absolute error = 1.720397630280125e-16
relative error = 8.5179524406341585642159817153745e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.625
Order of pole = 7.104
x[1] = 0.199
y[1] (analytic) = 2.0199325834923297917252130930153
y[1] (numeric) = 2.0199325834923299648287668968342
absolute error = 1.731035538038189e-16
relative error = 8.5697688734014235540578252513998e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.614
Order of pole = 6.91
x[1] = 0.2
y[1] (analytic) = 2.0201347730524083489257559281057
y[1] (numeric) = 2.0201347730524085230962792411887
absolute error = 1.741705233130830e-16
relative error = 8.6217278983774264629020924665558e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.604
Order of pole = 6.724
x[1] = 0.201
y[1] (analytic) = 2.0203380037040403072702099523364
y[1] (numeric) = 2.0203380037040404825109036126253
absolute error = 1.752406936602889e-16
relative error = 8.6738304847509041883355887528974e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.594
Order of pole = 6.547
x[1] = 0.202
y[1] (analytic) = 2.0205422758704753282140071485046
y[1] (numeric) = 2.0205422758704755045280942014162
absolute error = 1.763140870529116e-16
relative error = 8.7260776059215710950489876153117e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.584
Order of pole = 6.377
x[1] = 0.203
y[1] (analytic) = 2.020747589977305534529474527685
y[1] (numeric) = 2.0207475899773057119202003299134
absolute error = 1.773907258022284e-16
relative error = 8.7784702395325200856654770272942e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.575
Order of pole = 6.214
x[1] = 0.204
y[1] (analytic) = 2.0209539464524691281576175644916
y[1] (numeric) = 2.0209539464524693066282498886286
absolute error = 1.784706323241370e-16
relative error = 8.8310093675028955314621559084731e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.566
Order of pole = 6.058
memory used=68.6MB, alloc=4.2MB, time=3.51
x[1] = 0.205
y[1] (analytic) = 2.0211613457262540301948938870235
y[1] (numeric) = 2.0211613457262542097487230270015
absolute error = 1.795538291399780e-16
relative error = 8.8836959760607236402295918100776e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.557
Order of pole = 5.909
x[1] = 0.206
y[1] (analytic) = 2.0213697882313015430821099717627
y[1] (numeric) = 2.0213697882313017237224488491249
absolute error = 1.806403388773622e-16
relative error = 8.9365310557759195008794860075135e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.549
Order of pole = 5.766
x[1] = 0.207
y[1] (analytic) = 2.0215792744026100350630364675623
y[1] (numeric) = 2.0215792744026102167932207385668
absolute error = 1.817301842710045e-16
relative error = 8.9895156015935592780729625419873e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.541
Order of pole = 5.629
x[1] = 0.208
y[1] (analytic) = 2.0217898046775386469808028295565
y[1] (numeric) = 2.0217898046775388298041909931188
absolute error = 1.828233881635623e-16
relative error = 9.0426506128673130545858432015056e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.534
Order of pole = 5.498
x[1] = 0.209
y[1] (analytic) = 2.0220013794958110214805992004502
y[1] (numeric) = 2.0220013794958112054005727069297
absolute error = 1.839199735064795e-16
relative error = 9.0959370933930921608938717380222e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.526
Order of pole = 5.371
x[1] = 0.21
y[1] (analytic) = 2.0222139992995190546876829504448
y[1] (numeric) = 2.0222139992995192397076463112808
absolute error = 1.850199633608360e-16
relative error = 9.1493760514429054420217648336085e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.519
Order of pole = 5.251
x[1] = 0.211
y[1] (analytic) = 2.0224276645331266704301589953657
y[1] (numeric) = 2.0224276645331268565535398935687
absolute error = 1.861233808982030e-16
relative error = 9.2029684997989386905600379792431e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.512
Order of pole = 5.134
x[1] = 0.212
y[1] (analytic) = 2.0226423756434736170764769728296
y[1] (numeric) = 2.0226423756434738043067263743328
absolute error = 1.872302494015032e-16
relative error = 9.2567154557878121303656002794629e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.506
Order of pole = 5.023
x[1] = 0.213
y[1] (analytic) = 2.0228581330797792870580645860946
y[1] (numeric) = 2.0228581330797794753986568519724
absolute error = 1.883405922658778e-16
relative error = 9.3106179413151092877811098390291e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.499
Order of pole = 4.916
x[1] = 0.214
y[1] (analytic) = 2.0230749372936465591479949422592
y[1] (numeric) = 2.0230749372936467486024279418168
absolute error = 1.894544329995576e-16
relative error = 9.3646769829000431269931627181473e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.493
Order of pole = 4.813
x[1] = 0.215
y[1] (analytic) = 2.0232927887390656635670665335059
y[1] (numeric) = 2.0232927887390658541388617582472
absolute error = 1.905717952247413e-16
relative error = 9.4188936117104120981988299207974e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.487
Order of pole = 4.714
x[1] = 0.216
y[1] (analytic) = 2.0235116878724180699891576550507
y[1] (numeric) = 2.0235116878724182616818603335295
absolute error = 1.916927026784788e-16
relative error = 9.4732688635977366912690738258392e-15 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.2MB, time=3.71
Real estimate of pole used
Radius of convergence = 1.481
Order of pole = 4.62
x[1] = 0.217
y[1] (analytic) = 2.0237316351524803985182025393771
y[1] (numeric) = 2.0237316351524805913353817529375
absolute error = 1.928171792135604e-16
relative error = 9.5278037791326203598900710171029e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.476
Order of pole = 4.528
x[1] = 0.218
y[1] (analytic) = 2.0239526310404283537096243313672
y[1] (numeric) = 2.0239526310404285476548731307793
absolute error = 1.939452487994121e-16
relative error = 9.5824994036403440534312405819499e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.471
Order of pole = 4.441
x[1] = 0.219
y[1] (analytic) = 2.0241746759998406817095502513561
y[1] (numeric) = 2.0241746759998408767864857743526
absolute error = 1.950769355229965e-16
relative error = 9.6373567872366689994138612709707e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.465
Order of pole = 4.356
x[1] = 0.22
y[1] (analytic) = 2.0243977704967031505856269113214
y[1] (numeric) = 2.0243977704967033467978905010417
absolute error = 1.962122635897203e-16
relative error = 9.6923769848638964935011183564955e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.46
Order of pole = 4.275
x[1] = 0.221
y[1] (analytic) = 2.0246219149994125539237487818968
y[1] (numeric) = 2.0246219149994127512750061062438
absolute error = 1.973512573243470e-16
relative error = 9.7475610563271148660344114384437e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.455
Order of pole = 4.197
x[1] = 0.222
y[1] (analytic) = 2.0248471099787807377655102732928
y[1] (numeric) = 2.0248471099787809362594514452096
absolute error = 1.984939411719168e-16
relative error = 9.8029100663307317654015817907214e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.451
Order of pole = 4.122
x[1] = 0.223
y[1] (analytic) = 2.0250733559080386509616918102938
y[1] (numeric) = 2.025073355908038850602031508965
absolute error = 1.996403396986712e-16
relative error = 9.8584250845151675928548991492148e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.446
Order of pole = 4.05
x[1] = 0.224
y[1] (analytic) = 2.0253006532628404190175926691481
y[1] (numeric) = 2.0253006532628406198080702621331
absolute error = 2.007904775929850e-16
relative error = 9.9141071854938427816620429607567e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.442
Order of pole = 3.98
x[1] = 0.225
y[1] (analytic) = 2.0255290025212674415065282214064
y[1] (numeric) = 2.0255290025212676434509078877108
absolute error = 2.019443796663044e-16
relative error = 9.9699574488903940110989095629196e-15 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.437
Order of pole = 3.913
x[1] = 0.226
y[1] (analytic) = 2.0257584041638325131283166157178
y[1] (numeric) = 2.0257584041638327162303874698084
absolute error = 2.031020708540906e-16
relative error = 1.0025976959376089054190500095513e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.433
Order of pole = 3.849
x[1] = 0.227
y[1] (analytic) = 2.0259888586734839684900898425384
y[1] (numeric) = 2.0259888586734841727536660593093
absolute error = 2.042635762167709e-16
relative error = 1.0082166806707538313638421074808e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.429
Order of pole = 3.787
x[1] = 0.228
y[1] (analytic) = 2.0262203665356098506872765880431
y[1] (numeric) = 2.0262203665356100561161975287385
absolute error = 2.054289209406954e-16
relative error = 1.0138528085764608530143881644953e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=3.91
Real estimate of pole used
Radius of convergence = 1.425
Order of pole = 3.727
x[1] = 0.229
y[1] (analytic) = 2.0264529282380421037631193117791
y[1] (numeric) = 2.0264529282380423103612496508796
absolute error = 2.065981303391005e-16
relative error = 1.0195061896588597205323702035360e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.421
Order of pole = 3.67
x[1] = 0.23
y[1] (analytic) = 2.0266865442710607891256055974283
y[1] (numeric) = 2.026686544271060996896835450507
absolute error = 2.077712298530787e-16
relative error = 1.0251769344420642342591903213192e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.417
Order of pole = 3.614
x[1] = 0.231
y[1] (analytic) = 2.0269212151273983260012140472416
y[1] (numeric) = 2.0269212151273985349494590997972
absolute error = 2.089482450525556e-16
relative error = 1.0308651539740411198225696181698e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.414
Order of pole = 3.561
x[1] = 0.232
y[1] (analytic) = 2.0271569413022437560053978382063
y[1] (numeric) = 2.0271569413022439661345994754792
absolute error = 2.101292016372729e-16
relative error = 1.0365709598305008096236536377811e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.41
Order of pole = 3.509
x[1] = 0.233
y[1] (analytic) = 2.0273937232932470319102545518643
y[1] (numeric) = 2.0273937232932472432243799896428
absolute error = 2.113141254377785e-16
relative error = 1.0422944641188154857578534819295e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.407
Order of pole = 3.46
x[1] = 0.234
y[1] (analytic) = 2.0276315616005233306903590501213
y[1] (numeric) = 2.0276315616005235431934014665444
absolute error = 2.125030424164231e-16
relative error = 1.0480357794819613497931865690044e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.403
Order of pole = 3.412
x[1] = 0.235
y[1] (analytic) = 2.027870456726657390928267016708
y[1] (numeric) = 2.0278704567266576046242456850715
absolute error = 2.136959786683635e-16
relative error = 1.0537950191024860321974059070408e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.4
Order of pole = 3.366
x[1] = 0.236
y[1] (analytic) = 2.0281104091767078746617303386537
y[1] (numeric) = 2.0281104091767080895546907612276
absolute error = 2.148929604225739e-16
relative error = 1.0595722967065074766343969427905e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.397
Order of pole = 3.321
x[1] = 0.237
y[1] (analytic) = 2.0283514194582117537552017848307
y[1] (numeric) = 2.0283514194582119698492158276932
absolute error = 2.160940140428625e-16
relative error = 1.0653677265677309073902680268677e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.394
Order of pole = 3.279
x[1] = 0.238
y[1] (analytic) = 2.0285934880811887208787454700745
y[1] (numeric) = 2.0285934880811889381779114989712
absolute error = 2.172991660288967e-16
relative error = 1.0711814235115000775335366648315e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.391
Order of pole = 3.237
x[1] = 0.239
y[1] (analytic) = 2.0288366155581456251780113944973
y[1] (numeric) = 2.0288366155581458436864544117308
absolute error = 2.185084430172335e-16
relative error = 1.0770135029188659556443334207810e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.388
Order of pole = 3.197
x[1] = 0.24
y[1] (analytic) = 2.0290808024040809327194769394176
y[1] (numeric) = 2.0290808024040811524413487217773
absolute error = 2.197218717823597e-16
relative error = 1.0828640807306954512548394839327e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=4.11
Real estimate of pole used
Radius of convergence = 1.385
Order of pole = 3.159
x[1] = 0.241
y[1] (analytic) = 2.0293260491364892117957056050425
y[1] (numeric) = 2.0293260491364894327351848427787
absolute error = 2.209394792377362e-16
relative error = 1.0887332734517920011437287252532e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.382
Order of pole = 3.122
x[1] = 0.242
y[1] (analytic) = 2.0295723562753656431759235119699
y[1] (numeric) = 2.0295723562753658653372159488223
absolute error = 2.221612924368524e-16
relative error = 1.0946211981550575128823012845604e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.379
Order of pole = 3.086
x[1] = 0.243
y[1] (analytic) = 2.0298197243432105553877672802453
y[1] (numeric) = 2.0298197243432107787751058545313
absolute error = 2.233873385742860e-16
relative error = 1.1005279724856724189282825694065e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.376
Order of pole = 3.052
x[1] = 0.244
y[1] (analytic) = 2.0300681538650339851166128677155
y[1] (numeric) = 2.0300681538650342097342578544864
absolute error = 2.246176449867709e-16
relative error = 1.1064537146653070685632246084353e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.374
Order of pole = 3.019
x[1] = 0.245
y[1] (analytic) = 2.0303176453683602628094538155793
y[1] (numeric) = 2.030317645368360488661692969852
absolute error = 2.258522391542727e-16
relative error = 1.1123985434963619104875712613570e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.371
Order of pole = 2.986
x[1] = 0.246
y[1] (analytic) = 2.030568199383232623570859135269
y[1] (numeric) = 2.0305681993832328506620078363406
absolute error = 2.270911487010716e-16
relative error = 1.1183625783662353982276844764564e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.369
Order of pole = 2.955
x[1] = 0.247
y[1] (analytic) = 2.0308198164422178434391057991997
y[1] (numeric) = 2.0308198164422180717735071960522
absolute error = 2.283344013968525e-16
relative error = 1.1243459392516185510101568695159e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.366
Order of pole = 2.926
x[1] = 0.248
y[1] (analytic) = 2.0310724970804109011311484907425
y[1] (numeric) = 2.0310724970804111307131736485462
absolute error = 2.295820251578037e-16
relative error = 1.1303487467228229808891718131014e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.364
Order of pole = 2.897
x[1] = 0.249
y[1] (analytic) = 2.0313262418354396653456599484168
y[1] (numeric) = 2.0313262418354398961797079961388
absolute error = 2.308340480477220e-16
relative error = 1.1363711219481314671655348916946e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.362
Order of pole = 2.869
x[1] = 0.25
y[1] (analytic) = 2.0315810512474696077139489283075
y[1] (numeric) = 2.0315810512474698398044472074344
absolute error = 2.320904982791269e-16
relative error = 1.1424131866981842886073256824038e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.359
Order of pole = 2.842
x[1] = 0.251
y[1] (analytic) = 2.0318369258592085414891395298224
y[1] (numeric) = 2.0318369258592087748405437442045
absolute error = 2.333514042143821e-16
relative error = 1.1484750633503923627542413393833e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.357
Order of pole = 2.816
memory used=83.9MB, alloc=4.3MB, time=4.30
x[1] = 0.252
y[1] (analytic) = 2.0320938662159113860645754059848
y[1] (numeric) = 2.0320938662159116206813697728092
absolute error = 2.346167943668244e-16
relative error = 1.1545568748933775999358221876783e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.355
Order of pole = 2.791
x[1] = 0.253
y[1] (analytic) = 2.0323518728653849574129952335437
y[1] (numeric) = 2.0323518728653851932996926354452
absolute error = 2.358866974019015e-16
relative error = 1.1606587449314477672528148592965e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.353
Order of pole = 2.767
x[1] = 0.254
y[1] (analytic) = 2.0326109463579927845386117734909
y[1] (numeric) = 2.0326109463579930216997539118085
absolute error = 2.371611421383176e-16
relative error = 1.1667807976891003583570666855682e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.35
Order of pole = 2.744
x[1] = 0.255
y[1] (analytic) = 2.0328710872466599520348159324566
y[1] (numeric) = 2.0328710872466601904749734816436
absolute error = 2.384401575491870e-16
relative error = 1.1729231580155563647422558075731e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.348
Order of pole = 2.721
x[1] = 0.256
y[1] (analytic) = 2.0331322960868779688408194634497
y[1] (numeric) = 2.0331322960868782085645922266453
absolute error = 2.397237727631956e-16
relative error = 1.1790859513893233672062776538345e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.346
Order of pole = 2.699
x[1] = 0.257
y[1] (analytic) = 2.0333945734367096632911453442167
y[1] (numeric) = 2.0333945734367099043031624099883
absolute error = 2.410120170657716e-16
relative error = 1.1852693039227942511945251980676e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.344
Order of pole = 2.678
x[1] = 0.258
y[1] (analytic) = 2.0336579198567941045524734669816
y[1] (numeric) = 2.0336579198567943468573933672451
absolute error = 2.423049199002635e-16
relative error = 1.1914733423668721074267521219045e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.342
Order of pole = 2.658
x[1] = 0.259
y[1] (analytic) = 2.033922335910351550542951088533
y[1] (numeric) = 2.0339223359103517941454619576605
absolute error = 2.436025108691275e-16
relative error = 1.1976981941156315547832077848956e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.34
Order of pole = 2.639
x[1] = 0.26
y[1] (analytic) = 2.0341878221631884224296825487606
y[1] (numeric) = 2.0341878221631886673345022838833
absolute error = 2.449048197351227e-16
relative error = 1.2039439872110085221193176611481e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.338
Order of pole = 2.62
x[1] = 0.261
y[1] (analytic) = 2.0344543791837023058007210931906
y[1] (numeric) = 2.0344543791837025520125975157055
absolute error = 2.462118764225149e-16
relative error = 1.2102108503475223301068225830386e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.336
Order of pole = 2.602
x[1] = 0.262
y[1] (analytic) = 2.0347220075428869786084972553844
y[1] (numeric) = 2.0347220075428872261322082736746
absolute error = 2.475237110182902e-16
relative error = 1.2164989128770358754505103548110e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.335
Order of pole = 2.584
x[1] = 0.263
y[1] (analytic) = 2.0349907078143374659822331929929
y[1] (numeric) = 2.0349907078143377148225869663682
absolute error = 2.488403537733753e-16
relative error = 1.2228083048135385827470084791846e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=4.51
Real estimate of pole used
Radius of convergence = 1.333
Order of pole = 2.567
x[1] = 0.264
y[1] (analytic) = 2.0352604805742551220075106516918
y[1] (numeric) = 2.0352604805742553721693457555603
absolute error = 2.501618351038685e-16
relative error = 1.2291391568379716897592399558493e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.331
Order of pole = 2.551
x[1] = 0.265
y[1] (analytic) = 2.0355313264014527385717818792799
y[1] (numeric) = 2.0355313264014529900599674715585
absolute error = 2.514881855922786e-16
relative error = 1.2354916003030820040427589030299e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.329
Order of pole = 2.535
x[1] = 0.266
y[1] (analytic) = 2.0358032458773596813752378531476
y[1] (numeric) = 2.0358032458773599341946738419207
absolute error = 2.528194359887731e-16
relative error = 1.2418657672383109135603034376261e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.327
Order of pole = 2.519
x[1] = 0.267
y[1] (analytic) = 2.0360762395860270532070766435962
y[1] (numeric) = 2.0360762395860273073626938560314
absolute error = 2.541556172124352e-16
relative error = 1.2482617903547160943846347006459e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.326
Order of pole = 2.505
x[1] = 0.268
y[1] (analytic) = 2.0363503081141328845878466387303
y[1] (numeric) = 2.0363503081141331400846069912606
absolute error = 2.554967603525303e-16
relative error = 1.2546798030499292535495323397917e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.324
Order of pole = 2.49
x[1] = 0.269
y[1] (analytic) = 2.0366254520509873518791747296974
y[1] (numeric) = 2.0366254520509876087220713994786
absolute error = 2.568428966697812e-16
relative error = 1.2611199394131458757234947957288e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.322
Order of pole = 2.476
x[1] = 0.27
y[1] (analytic) = 2.0369016719885380229628284239075
y[1] (numeric) = 2.0369016719885382811568860215607
absolute error = 2.581940575976532e-16
relative error = 1.2675823342301527648840136829580e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.321
Order of pole = 2.463
x[1] = 0.271
y[1] (analytic) = 2.0371789685213751305917032447482
y[1] (numeric) = 2.0371789685213753901419779883964
absolute error = 2.595502747436482e-16
relative error = 1.2740671229883888568445760238051e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.319
Order of pole = 2.45
x[1] = 0.272
y[1] (analytic) = 2.0374573422467368735159727156
y[1] (numeric) = 2.037457342246737134427552606208
absolute error = 2.609115798906080e-16
relative error = 1.2805744418820401815831311271841e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.318
Order of pole = 2.438
x[1] = 0.273
y[1] (analytic) = 2.0377367937645147454882877402373
y[1] (numeric) = 2.0377367937645150077662927382651
absolute error = 2.622780049980278e-16
relative error = 1.2871044278171737786110167023501e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.316
Order of pole = 2.426
x[1] = 0.274
y[1] (analytic) = 2.0380173236772588922525653077633
y[1] (numeric) = 2.0380173236772591559021475111421
absolute error = 2.636495822033788e-16
relative error = 1.2936572184169050585152616744912e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.314
Order of pole = 2.414
x[1] = 0.275
y[1] (analytic) = 2.0382989325901834966215631950301
y[1] (numeric) = 2.0382989325901837616479070184708
absolute error = 2.650263438234407e-16
relative error = 1.3002329520266024306342336564307e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=4.70
Real estimate of pole used
Radius of convergence = 1.313
Order of pole = 2.403
x[1] = 0.276
y[1] (analytic) = 2.0385816211111721917490977402253
y[1] (numeric) = 2.0385816211111724581574200958694
absolute error = 2.664083223556441e-16
relative error = 1.3068317677191290876134689839162e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.311
Order of pole = 2.392
x[1] = 0.277
y[1] (analytic) = 2.0388653898507835027034258453294
y[1] (numeric) = 2.0388653898507837704989763247518
absolute error = 2.677955504794224e-16
relative error = 1.3134538053001198750976592787462e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.31
Order of pole = 2.382
x[1] = 0.278
y[1] (analytic) = 2.0391502394222563164489801600361
y[1] (numeric) = 2.0391502394222565856370412176101
absolute error = 2.691880610575740e-16
relative error = 1.3200992053132970611966670321737e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.308
Order of pole = 2.372
x[1] = 0.279
y[1] (analytic) = 2.0394361704415153803443179332608
y[1] (numeric) = 2.0394361704415156509302050708953
absolute error = 2.705858871376345e-16
relative error = 1.3267681090458234217283308167079e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.307
Order of pole = 2.362
x[1] = 0.28
y[1] (analytic) = 2.0397231835271768292648193185168
y[1] (numeric) = 2.0397231835271771012538812717758
absolute error = 2.719890619532590e-16
relative error = 1.3334606585336930193065466479824e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.305
Order of pole = 2.352
x[1] = 0.281
y[1] (analytic) = 2.0400112793005537414593500144062
y[1] (numeric) = 2.0400112793005540148569689400208
absolute error = 2.733976189256146e-16
relative error = 1.3401769965671600531694832681335e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.304
Order of pole = 2.343
x[1] = 0.282
y[1] (analytic) = 2.0403004583856617232507860396412
y[1] (numeric) = 2.0403004583856619980623777044244
absolute error = 2.748115916647832e-16
relative error = 1.3469172666962061554611005088950e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.303
Order of pole = 2.334
x[1] = 0.283
y[1] (analytic) = 2.0405907214092245226909852119978
y[1] (numeric) = 2.0405907214092247989219991831728
absolute error = 2.762310139711750e-16
relative error = 1.3536816132360479786519206740369e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.301
Order of pole = 2.326
x[1] = 0.284
y[1] (analytic) = 2.0408820690006796722814805512123
y[1] (numeric) = 2.0408820690006799499374003881644
absolute error = 2.776559198369521e-16
relative error = 1.3604701812726820160660680179342e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.3
Order of pole = 2.318
x[1] = 0.285
y[1] (analytic) = 2.0411745017921841608718653861046
y[1] (numeric) = 2.0411745017921844399582088335672
absolute error = 2.790863434474626e-16
relative error = 1.3672831166684684993268591007868e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.298
Order of pole = 2.31
x[1] = 0.286
y[1] (analytic) = 2.0414680204186201348485384453887
y[1] (numeric) = 2.041468020418620415370857628075
absolute error = 2.805223191826863e-16
relative error = 1.3741205660677596425608295722622e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.297
Order of pole = 2.302
x[1] = 0.287
y[1] (analytic) = 2.0417626255176006287271796791835
y[1] (numeric) = 2.0417626255176009106910612978736
absolute error = 2.819638816186901e-16
relative error = 1.3809826769025628031436268740277e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.3MB, time=4.91
Real estimate of pole used
Radius of convergence = 1.296
Order of pole = 2.295
x[1] = 0.288
y[1] (analytic) = 2.0420583177294753252630340238399
y[1] (numeric) = 2.0420583177294756086740995529346
absolute error = 2.834110655290947e-16
relative error = 1.3878695973982462783971698967241e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.294
Order of pole = 2.287
x[1] = 0.289
y[1] (analytic) = 2.0423550976973363451937908162702
y[1] (numeric) = 2.0423550976973366300576967028227
absolute error = 2.848639058865525e-16
relative error = 1.3947814765792871242204954201584e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.293
Order of pole = 2.28
x[1] = 0.29
y[1] (analytic) = 2.0426529660670240667305611156225
y[1] (numeric) = 2.042652966067024353052998979859
absolute error = 2.863224378642365e-16
relative error = 1.4017184642750598919468970328261e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.292
Order of pole = 2.274
x[1] = 0.291
y[1] (analytic) = 2.0429519234871329749131738302496
y[1] (numeric) = 2.0429519234871332626998706675893
absolute error = 2.877866968373397e-16
relative error = 1.4086807111256637117086725431542e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.29
Order of pole = 2.267
x[1] = 0.292
y[1] (analytic) = 2.0432519706090175409467343070484
y[1] (numeric) = 2.0432519706090178302034526916357
absolute error = 2.892567183845873e-16
relative error = 1.4156683685877988564310957960296e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.289
Order of pole = 2.261
x[1] = 0.293
y[1] (analytic) = 2.0435531080867981316371159492246
y[1] (numeric) = 2.0435531080867984223696542389827
absolute error = 2.907325382897581e-16
relative error = 1.4226815889406750353783445720308e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.288
Order of pole = 2.255
x[1] = 0.294
y[1] (analytic) = 2.0438553365773669490437865183829
y[1] (numeric) = 2.0438553365773672412579790616024
absolute error = 2.922141925432195e-16
relative error = 1.4297205252919728279276287439188e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.287
Order of pole = 2.249
x[1] = 0.295
y[1] (analytic) = 2.0441586567403940004691060788612
y[1] (numeric) = 2.0441586567403942941708234223343
absolute error = 2.937017173434731e-16
relative error = 1.4367853315838434414228300907220e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.285
Order of pole = 2.244
x[1] = 0.296
y[1] (analytic) = 2.0444630692383330989039730879105
y[1] (numeric) = 2.0444630692383333940991221866218
absolute error = 2.951951490987113e-16
relative error = 1.4438761625989486238717749367498e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.284
Order of pole = 2.238
x[1] = 0.297
y[1] (analytic) = 2.0447685747364278940504389564239
y[1] (numeric) = 2.0447685747364281907449633848113
absolute error = 2.966945244283874e-16
relative error = 1.4509931739665528293737603637249e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.283
Order of pole = 2.233
x[1] = 0.298
y[1] (analytic) = 2.0450751739027179340426595334412
y[1] (numeric) = 2.0450751739027182322425396982368
absolute error = 2.981998801647956e-16
relative error = 1.4581365221686498910696852643445e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.281
Order of pole = 2.228
memory used=99.1MB, alloc=4.3MB, time=5.10
x[1] = 0.299
y[1] (analytic) = 2.0453828674080447579883044358079
y[1] (numeric) = 2.0453828674080450576995577904729
absolute error = 2.997112533546650e-16
relative error = 1.4653063645461441225126124156314e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.28
Order of pole = 2.223
x[1] = 0.3
y[1] (analytic) = 2.0456916559260580194533019846541
y[1] (numeric) = 2.045691655926058320681983245418
absolute error = 3.012286812607639e-16
relative error = 1.4725028593050676146364907078808e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.279
Order of pole = 2.218
x[1] = 0.301
y[1] (analytic) = 2.0460015401332216410135587554711
y[1] (numeric) = 2.0460015401332219437657601189885
absolute error = 3.027522013635174e-16
relative error = 1.4797261655228482633392080858949e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.278
Order of pole = 2.213
x[1] = 0.302
y[1] (analytic) = 2.0463125207088199999980584315
y[1] (numeric) = 2.0463125207088203042799097941371
absolute error = 3.042818513626371e-16
relative error = 1.4869764431546225195191727275053e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.277
Order of pole = 2.209
x[1] = 0.303
y[1] (analytic) = 2.0466245983349641455485148041096
y[1] (numeric) = 2.0466245983349644513661839828726
absolute error = 3.058176691787630e-16
relative error = 1.4942538530395932116535700159803e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.275
Order of pole = 2.205
x[1] = 0.304
y[1] (analytic) = 2.0469377736965980471215284223117
y[1] (numeric) = 2.0469377736965983544812213774299
absolute error = 3.073596929551182e-16
relative error = 1.5015585569074352323360345820078e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.274
Order of pole = 2.201
x[1] = 0.305
y[1] (analytic) = 2.0472520474815048745599755902724
y[1] (numeric) = 2.0472520474815051834679366494485
absolute error = 3.089079610591761e-16
relative error = 1.5088907173847474797034336950596e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.273
Order of pole = 2.197
x[1] = 0.306
y[1] (analytic) = 2.0475674203803133098611421806083
y[1] (numeric) = 2.0475674203803136203236542649483
absolute error = 3.104625120843400e-16
relative error = 1.5162504980015504224649292434554e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.272
Order of pole = 2.193
x[1] = 0.307
y[1] (analytic) = 2.047883893086503890769903106658
y[1] (numeric) = 2.0478838930865042027932879582944
absolute error = 3.120233848516364e-16
relative error = 1.5236380631978354934052248595726e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.271
Order of pole = 2.189
x[1] = 0.308
y[1] (analytic) = 2.0482014662964153863260413133014
y[1] (numeric) = 2.0482014662964156999166597247226
absolute error = 3.135906184114212e-16
relative error = 1.5310535783301622546995076706078e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.269
Order of pole = 2.185
x[1] = 0.309
y[1] (analytic) = 2.0485201407092512044955978380302
y[1] (numeric) = 2.0485201407092515196598498831276
absolute error = 3.151642520450974e-16
relative error = 1.5384972096782963534459329102411e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.268
Order of pole = 2.182
x[1] = 0.31
y[1] (analytic) = 2.0488399170270858320169468968932
y[1] (numeric) = 2.0488399170270861487612721637418
absolute error = 3.167443252668486e-16
relative error = 1.5459691244519091141817641179342e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.3MB, time=5.31
Real estimate of pole used
Radius of convergence = 1.267
Order of pole = 2.178
x[1] = 0.311
y[1] (analytic) = 2.0491607959548713065930970989676
y[1] (numeric) = 2.0491607959548716249239749243513
absolute error = 3.183308778253837e-16
relative error = 1.5534694907973161557435776984713e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.266
Order of pole = 2.175
x[1] = 0.312
y[1] (analytic) = 2.0494827782004437215625318237054
y[1] (numeric) = 2.0494827782004440414864815294016
absolute error = 3.199239497056962e-16
relative error = 1.5609984778042714812973483761931e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.265
Order of pole = 2.172
x[1] = 0.313
y[1] (analytic) = 2.0498058644745297631817185437439
y[1] (numeric) = 2.0498058644745300847052996745806
absolute error = 3.215235811308367e-16
relative error = 1.5685562555128100519153861899911e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.264
Order of pole = 2.169
x[1] = 0.314
y[1] (analytic) = 2.0501300554907532806532384776702
y[1] (numeric) = 2.0501300554907536037830510413691
absolute error = 3.231298125636989e-16
relative error = 1.5761429949201401539690713088872e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.263
Order of pole = 2.166
x[1] = 0.315
y[1] (analytic) = 2.0504553519656418890343144492054
y[1] (numeric) = 2.0504553519656422137769991580254
absolute error = 3.247426847088200e-16
relative error = 1.5837588679875897941176951525934e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.261
Order of pole = 2.163
x[1] = 0.316
y[1] (analytic) = 2.0507817546186336051613462480171
y[1] (numeric) = 2.0507817546186339315235847622118
absolute error = 3.263622385141947e-16
relative error = 1.5914040476476030597331930803696e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.26
Order of pole = 2.16
x[1] = 0.317
y[1] (analytic) = 2.0511092641720835167268991698492
y[1] (numeric) = 2.0511092641720838447154143429522
absolute error = 3.279885151731030e-16
relative error = 1.5990787078107872621050255662917e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.259
Order of pole = 2.158
x[1] = 0.318
y[1] (analytic) = 2.0514378813512704846464327971406
y[1] (numeric) = 2.0514378813512708142679889230934
absolute error = 3.296215561259528e-16
relative error = 1.6067830233730155773886190909205e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.258
Order of pole = 2.155
x[1] = 0.319
y[1] (analytic) = 2.051767606884403878852903503338
y[1] (numeric) = 2.0517676068844042101143065654742
absolute error = 3.312614030621362e-16
relative error = 1.6145171702225796580690031015909e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.257
Order of pole = 2.153
x[1] = 0.32
y[1] (analytic) = 2.0520984415026303476582256625338
y[1] (numeric) = 2.0520984415026306805663235844348
absolute error = 3.329080979219010e-16
relative error = 1.6222813252473993636699286381183e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.256
Order of pole = 2.15
x[1] = 0.321
y[1] (analytic) = 2.052430385940040620821433159017
y[1] (numeric) = 2.0524303859400409553831160572528
absolute error = 3.345616828982358e-16
relative error = 1.6300756663422816450974000884750e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.255
Order of pole = 2.148
x[1] = 0.322
y[1] (analytic) = 2.0527634409336763464642445572365
y[1] (numeric) = 2.0527634409336766826864449960074
absolute error = 3.362222004387709e-16
relative error = 1.6379003724162391378180333909055e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.3MB, time=5.51
Real estimate of pole used
Radius of convergence = 1.254
Order of pole = 2.146
x[1] = 0.323
y[1] (analytic) = 2.0530976072235369619756022502914
y[1] (numeric) = 2.0530976072235372998652954979846
absolute error = 3.378896932476932e-16
relative error = 1.6457556233998595215307423156095e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.253
Order of pole = 2.144
x[1] = 0.324
y[1] (analytic) = 2.0534328855525865990476280933954
y[1] (numeric) = 2.0534328855525869386118323810716
absolute error = 3.395642042876762e-16
relative error = 1.6536416002527308371574394697850e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.251
Order of pole = 2.142
x[1] = 0.325
y[1] (analytic) = 2.0537692766667610229863154871676
y[1] (numeric) = 2.0537692766667613642320922689935
absolute error = 3.412457767818259e-16
relative error = 1.6615584849709264833744608764402e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.25
Order of pole = 2.139
x[1] = 0.326
y[1] (analytic) = 2.0541067813149746064411606437227
y[1] (numeric) = 2.0541067813149749493756148593635
absolute error = 3.429344542156408e-16
relative error = 1.6695064605945409512881888457492e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.249
Order of pole = 2.138
x[1] = 0.327
y[1] (analytic) = 2.0544454002491273376988238863168
y[1] (numeric) = 2.0544454002491276823291042253052
absolute error = 3.446302803389884e-16
relative error = 1.6774857112152878099058350396059e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.248
Order of pole = 2.136
x[1] = 0.328
y[1] (analytic) = 2.0547851342241118636868053410416
y[1] (numeric) = 2.0547851342241122100201045091376
absolute error = 3.463332991680960e-16
relative error = 1.6854964219841490519717232169579e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.247
Order of pole = 2.134
x[1] = 0.329
y[1] (analytic) = 2.055125983997820567834018317313
y[1] (numeric) = 2.0551259839978209158775733048712
absolute error = 3.480435549875582e-16
relative error = 1.6935387791190873059826727814558e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.246
Order of pole = 2.132
x[1] = 0.33
y[1] (analytic) = 2.0554679503311526829360480835943
y[1] (numeric) = 2.0554679503311530326971404359542
absolute error = 3.497610923523599e-16
relative error = 1.7016129699128148895216753361001e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.245
Order of pole = 2.13
x[1] = 0.331
y[1] (analytic) = 2.0558110339880214391737936671464
y[1] (numeric) = 2.0558110339880217906597497570617
absolute error = 3.514859560899153e-16
relative error = 1.7097191827406219550557146784472e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.244
Order of pole = 2.129
x[1] = 0.332
y[1] (analytic) = 2.0561552357353612474351057831601
y[1] (numeric) = 2.0561552357353616006532970852826
absolute error = 3.532181913021225e-16
relative error = 1.7178576070682615980356159041004e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.243
Order of pole = 2.127
x[1] = 0.333
y[1] (analytic) = 2.0565005563431349180899550712814
y[1] (numeric) = 2.0565005563431352730477984387165
absolute error = 3.549578433674351e-16
relative error = 1.7260284334598985515002234910541e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.242
Order of pole = 2.126
x[1] = 0.334
y[1] (analytic) = 2.0568469965843409153705915284993
y[1] (numeric) = 2.0568469965843412720755494714489
absolute error = 3.567049579429496e-16
relative error = 1.7342318535861154405529985463143e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.3MB, time=5.71
Real estimate of pole used
Radius of convergence = 1.241
Order of pole = 2.124
x[1] = 0.335
y[1] (analytic) = 2.0571945572350206475090884191635
y[1] (numeric) = 2.0571945572350210059686693856732
absolute error = 3.584595809665097e-16
relative error = 1.7424680602319817571928246002578e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.24
Order of pole = 2.123
x[1] = 0.336
y[1] (analytic) = 2.0575432390742657927856020584289
y[1] (numeric) = 2.057543239074266153007360717256
absolute error = 3.602217586588271e-16
relative error = 1.7507372473051834175182541097216e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.238
Order of pole = 2.121
x[1] = 0.337
y[1] (analytic) = 2.0578930428842256616416227478907
y[1] (numeric) = 2.0578930428842260236331602735101
absolute error = 3.619915375256194e-16
relative error = 1.7590396098442156242693960692672e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.237
Order of pole = 2.12
x[1] = 0.338
y[1] (analytic) = 2.0582439694501145950134418351513
y[1] (numeric) = 2.0582439694501149587824061949154
absolute error = 3.637689643597641e-16
relative error = 1.7673753440266339790677696912391e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.236
Order of pole = 2.119
x[1] = 0.339
y[1] (analytic) = 2.0585960195602193990420154164483
y[1] (numeric) = 2.0585960195602197645961016599195
absolute error = 3.655540862434712e-16
relative error = 1.7757446471773757961912267907692e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.235
Order of pole = 2.117
x[1] = 0.34
y[1] (analytic) = 2.0589491940059068163163666475347
y[1] (numeric) = 2.0589491940059071836633171980068
absolute error = 3.673469505504721e-16
relative error = 1.7841477177771402392116654003367e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.234
Order of pole = 2.116
x[1] = 0.341
y[1] (analytic) = 2.059303493581631033808636017342
y[1] (numeric) = 2.0593034935816314029562409655678
absolute error = 3.691476049482258e-16
relative error = 1.7925847554708319408876460442347e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.233
Order of pole = 2.115
x[1] = 0.342
y[1] (analytic) = 2.059658919084941227659862316538
y[1] (numeric) = 2.0596589190849415986159597166814
absolute error = 3.709560974001434e-16
relative error = 1.8010559610760727590071845195736e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.232
Order of pole = 2.114
x[1] = 0.343
y[1] (analytic) = 2.0600154713164891449765564442427
y[1] (numeric) = 2.0600154713164895177490326120729
absolute error = 3.727724761678302e-16
relative error = 1.8095615365917780607297218227102e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.231
Order of pole = 2.113
x[1] = 0.344
y[1] (analytic) = 2.0603731510800367227991156865652
y[1] (numeric) = 2.0603731510800370973959054999104
absolute error = 3.745967898133452e-16
relative error = 1.8181016852067963583167943110803e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.23
Order of pole = 2.112
x[1] = 0.345
y[1] (analytic) = 2.0607319591824637444041177163211
y[1] (numeric) = 2.0607319591824641208332049178007
absolute error = 3.764290872014796e-16
relative error = 1.8266766113086198541773593667622e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.3MB, time=5.91
Real estimate of pole used
Radius of convergence = 1.229
Order of pole = 2.111
x[1] = 0.346
y[1] (analytic) = 2.0610918964337755331035313507095
y[1] (numeric) = 2.0610918964337759113729488527621
absolute error = 3.782694175020526e-16
relative error = 1.8352865204921574303137181884976e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.228
Order of pole = 2.11
x[1] = 0.347
y[1] (analytic) = 2.0614529636471106837048851096489
y[1] (numeric) = 2.0614529636471110638227153018751
absolute error = 3.801178301922262e-16
relative error = 1.8439316195685781208658707120949e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.227
Order of pole = 2.109
x[1] = 0.348
y[1] (analytic) = 2.0618151616387488317974448890659
y[1] (numeric) = 2.0618151616387492137718199479046
absolute error = 3.819743750588387e-16
relative error = 1.8526121165742233936189506071875e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.226
Order of pole = 2.108
x[1] = 0.349
y[1] (analytic) = 2.0621784912281184610304686482384
y[1] (numeric) = 2.0621784912281188448695708489952
absolute error = 3.838391022007568e-16
relative error = 1.8613282207795875370727936256091e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.225
Order of pole = 2.107
x[1] = 0.35
y[1] (analytic) = 2.0625429532378047485506289562402
y[1] (numeric) = 2.0625429532378051342626909874864
absolute error = 3.857120620312462e-16
relative error = 1.8700801426983654492145215883308e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.224
Order of pole = 2.106
x[1] = 0.351
y[1] (analytic) = 2.0629085484935574487667235979281
y[1] (numeric) = 2.0629085484935578363600288782901
absolute error = 3.875933052803620e-16
relative error = 1.8788680940965739102209094196792e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.223
Order of pole = 2.105
x[1] = 0.352
y[1] (analytic) = 2.0632752778242988156108302534566
y[1] (numeric) = 2.0632752778242992050937132508149
absolute error = 3.894828829973583e-16
relative error = 1.8876922880017432025685367631438e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.222
Order of pole = 2.104
x[1] = 0.353
y[1] (analytic) = 2.0636431420621315634661035860873
y[1] (numeric) = 2.0636431420621319548469501392037
absolute error = 3.913808465531164e-16
relative error = 1.8965529387121759449636371168045e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.221
Order of pole = 2.104
x[1] = 0.354
y[1] (analytic) = 2.0640121420423468669324619505675
y[1] (numeric) = 2.0640121420423472602197095931618
absolute error = 3.932872476425943e-16
relative error = 1.9054502618062859977675772902801e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.22
Order of pole = 2.103
x[1] = 0.355
y[1] (analytic) = 2.0643822786034323996024664184822
y[1] (numeric) = 2.0643822786034327948046047057763
absolute error = 3.952021382872941e-16
relative error = 1.9143844741520007289079975098319e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.219
Order of pole = 2.102
x[1] = 0.356
y[1] (analytic) = 2.0647535525870804120207569580081
y[1] (numeric) = 2.0647535525870808091463277957591
absolute error = 3.971255708377510e-16
relative error = 1.9233557939162443383195309136428e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.218
Order of pole = 2.102
x[1] = 0.357
y[1] (analytic) = 2.0651259648381958490014794541382
y[1] (numeric) = 2.0651259648381962480590774301795
absolute error = 3.990575979760413e-16
relative error = 1.9323644405744894054086847752808e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=6.12
Real estimate of pole used
Radius of convergence = 1.217
Order of pole = 2.101
x[1] = 0.358
y[1] (analytic) = 2.0654995162049045064792128627881
y[1] (numeric) = 2.0654995162049049074774855811
absolute error = 4.009982727183119e-16
relative error = 1.9414106349203885322905795782600e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.215
Order of pole = 2.1
x[1] = 0.359
y[1] (analytic) = 2.0658742075385612280699882097805
y[1] (numeric) = 2.0658742075385616310176366271098
absolute error = 4.029476484173293e-16
relative error = 1.9504945990754761542835953866423e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.214
Order of pole = 2.1
x[1] = 0.36
y[1] (analytic) = 2.0662500396937581415200804254628
y[1] (numeric) = 2.0662500396937585464258591905126
absolute error = 4.049057787650498e-16
relative error = 1.9596165564989485087536929027322e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.213
Order of pole = 2.099
x[1] = 0.361
y[1] (analytic) = 2.0666270135283329352213502000148
y[1] (numeric) = 2.0666270135283333420940679952258
absolute error = 4.068727177952110e-16
relative error = 1.9687767319975219981256732303204e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.212
Order of pole = 2.098
x[1] = 0.362
y[1] (analytic) = 2.0670051299033771749730162061359
y[1] (numeric) = 2.0670051299033775838215360920798
absolute error = 4.088485198859439e-16
relative error = 1.9779753517353663105414803805997e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.211
Order of pole = 2.098
x[1] = 0.363
y[1] (analytic) = 2.067384389683244661170848217986
y[1] (numeric) = 2.0673843896832450720040879803924
absolute error = 4.108332397624064e-16
relative error = 1.9872126432441159208599636661713e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.21
Order of pole = 2.097
x[1] = 0.364
y[1] (analytic) = 2.0677647937355598266058889116417
y[1] (numeric) = 2.0677647937355602394328214110804
absolute error = 4.128269324994387e-16
relative error = 1.9964888354329621369021622994189e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.209
Order of pole = 2.097
x[1] = 0.365
y[1] (analytic) = 2.0681463429312261750559365170184
y[1] (numeric) = 2.0681463429312265898855900412583
absolute error = 4.148296535242399e-16
relative error = 2.0058041585988220486752807774245e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.208
Order of pole = 2.096
x[1] = 0.366
y[1] (analytic) = 2.068529038144434760854152058724
y[1] (numeric) = 2.068529038144435177695610677791
absolute error = 4.168414586190670e-16
relative error = 2.0151588444365899272527745501281e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.207
Order of pole = 2.096
x[1] = 0.367
y[1] (analytic) = 2.0689128802526727096202937286401
y[1] (numeric) = 2.0689128802526731284826976525956
absolute error = 4.188624039239555e-16
relative error = 2.0245531260494669431758987899358e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.206
Order of pole = 2.095
x[1] = 0.368
y[1] (analytic) = 2.0692978701367317803412270315954
y[1] (numeric) = 2.0692978701367322012337729710587
absolute error = 4.208925459394633e-16
relative error = 2.0339872379593771600231142004253e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.205
Order of pole = 2.095
x[1] = 0.369
y[1] (analytic) = 2.0696840086807169689885127931935
y[1] (numeric) = 2.069684008680717391920454322629
absolute error = 4.229319415294355e-16
relative error = 2.0434614161174579354316342333627e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.3MB, time=6.32
Real estimate of pole used
Radius of convergence = 1.204
Order of pole = 2.094
x[1] = 0.37
y[1] (analytic) = 2.0700712967720551538620359720183
y[1] (numeric) = 2.0700712967720555788426838958121
absolute error = 4.249806479237938e-16
relative error = 2.0529758979146423453718858528700e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.203
Order of pole = 2.094
x[1] = 0.371
y[1] (analytic) = 2.0704597353015037828498065338844
y[1] (numeric) = 2.070459735301504209888529255232
absolute error = 4.270387227213476e-16
relative error = 2.0625309221923193424064900894559e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.202
Order of pole = 2.093
x[1] = 0.372
y[1] (analytic) = 2.0708493251631596027952394807824
y[1] (numeric) = 2.0708493251631600319014633734111
absolute error = 4.291062238926287e-16
relative error = 2.0721267292530805571350144630814e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.201
Order of pole = 2.093
x[1] = 0.373
y[1] (analytic) = 2.0712400672544674311644045394511
y[1] (numeric) = 2.0712400672544678623476143222003
absolute error = 4.311832097827492e-16
relative error = 2.0817635608715515324054190291470e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.2
Order of pole = 2.093
x[1] = 0.374
y[1] (analytic) = 2.071631962476228970206927062298
y[1] (numeric) = 2.0716319624762294034766661765814
absolute error = 4.332697391142834e-16
relative error = 2.0914416603053109738924446999041e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.199
Order of pole = 2.092
x[1] = 0.375
y[1] (analytic) = 2.0720250117326116638054204353949
y[1] (numeric) = 2.0720250117326120991712914255678
absolute error = 4.353658709901729e-16
relative error = 2.1011612723058938714579372513927e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.198
Order of pole = 2.092
x[1] = 0.376
y[1] (analytic) = 2.0724192159311575972095367836735
y[1] (numeric) = 2.0724192159311580346812016803301
absolute error = 4.374716648966566e-16
relative error = 2.1109226431298864133181521708998e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.197
Order of pole = 2.092
x[1] = 0.377
y[1] (analytic) = 2.0728145759827924398519370719223
y[1] (numeric) = 2.0728145759827928794391177781462
absolute error = 4.395871807062239e-16
relative error = 2.1207260205501041983005517302247e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.196
Order of pole = 2.091
x[1] = 0.378
y[1] (analytic) = 2.0732110928018344314447038818929
y[1] (numeric) = 2.0732110928018348731571825624863
absolute error = 4.417124786805934e-16
relative error = 2.1305716538668645562453223763012e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.195
Order of pole = 2.091
x[1] = 0.379
y[1] (analytic) = 2.0736087673060034115559502614436
y[1] (numeric) = 2.0736087673060038554035697351592
absolute error = 4.438476194737156e-16
relative error = 2.1404597939193454426412222309173e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.194
Order of pole = 2.091
x[1] = 0.38
y[1] (analytic) = 2.0740076004164298928676161523367
y[1] (numeric) = 2.0740076004164303388602802871376
absolute error = 4.459926641348009e-16
relative error = 2.1503906930970368835919801286554e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.193
Order of pole = 2.09
x[1] = 0.381
y[1] (analytic) = 2.074407593057664178316690070747
y[1] (numeric) = 2.0744075930576646264643641821195
absolute error = 4.481476741113725e-16
relative error = 2.1603646053512827409747906084665e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.3MB, time=6.52
Real estimate of pole used
Radius of convergence = 1.192
Order of pole = 2.09
x[1] = 0.382
y[1] (analytic) = 2.0748087461576855223233480009184
y[1] (numeric) = 2.0748087461576859726360592532639
absolute error = 4.503127112523455e-16
relative error = 2.1703817862069187626226060853054e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.191
Order of pole = 2.09
x[1] = 0.383
y[1] (analytic) = 2.0752110606479113363107639304316
y[1] (numeric) = 2.075211060647911788798601741562
absolute error = 4.524878378111304e-16
relative error = 2.1804424927739979328936430081011e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.19
Order of pole = 2.089
x[1] = 0.384
y[1] (analytic) = 2.0756145374632064387226171684409
y[1] (numeric) = 2.0756145374632068933957336172045
absolute error = 4.546731164487636e-16
relative error = 2.1905469837596153494265770152490e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.189
Order of pole = 2.089
x[1] = 0.385
y[1] (analytic) = 2.0760191775418923497456006097662
y[1] (numeric) = 2.0760191775418928066142108468294
absolute error = 4.568686102370632e-16
relative error = 2.2006955194798241181538290430122e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.188
Order of pole = 2.089
x[1] = 0.386
y[1] (analytic) = 2.0764249818257566309455215021616
y[1] (numeric) = 2.0764249818257570900199041639737
absolute error = 4.590743826618121e-16
relative error = 2.2108883618716515888922461419730e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.187
Order of pole = 2.089
x[1] = 0.387
y[1] (analytic) = 2.0768319512600622700268821062616
y[1] (numeric) = 2.0768319512600627313173797322284
absolute error = 4.612904976259668e-16
relative error = 2.2211257745052079031053769486262e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.186
Order of pole = 2.088
x[1] = 0.388
y[1] (analytic) = 2.0772400867935571109271319729777
y[1] (numeric) = 2.0772400867935575744441514258713
absolute error = 4.635170194528936e-16
relative error = 2.2314080225958947223441832634481e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.185
Order of pole = 2.088
x[1] = 0.389
y[1] (analytic) = 2.0776493893784833294580964674126
y[1] (numeric) = 2.0776493893784837952121093570444
absolute error = 4.657540128896318e-16
relative error = 2.2417353730167118838435771601289e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.184
Order of pole = 2.088
x[1] = 0.39
y[1] (analytic) = 2.0780598599705869547084077081218
y[1] (numeric) = 2.0780598599705874227099508183063
absolute error = 4.680015431101845e-16
relative error = 2.2521080943106645433108559158492e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.183
Order of pole = 2.088
x[1] = 0.391
y[1] (analytic) = 2.078471499529127436422094332818
y[1] (numeric) = 2.0784714995291279066817700516546
absolute error = 4.702596757188366e-16
relative error = 2.2625264567032685475026736969537e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.182
Order of pole = 2.088
x[1] = 0.392
y[1] (analytic) = 2.0788843090168872585698255139545
y[1] (numeric) = 2.0788843090168877310983022674554
absolute error = 4.725284767535009e-16
relative error = 2.2729907321151580339240293570512e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.3MB, time=6.72
Real estimate of pole used
Radius of convergence = 1.181
Order of pole = 2.087
x[1] = 0.393
y[1] (analytic) = 2.0792982894001815993306524981965
y[1] (numeric) = 2.0792982894001820741386651872893
absolute error = 4.748080126890928e-16
relative error = 2.2835011941747973227143240088564e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.18
Order of pole = 2.087
x[1] = 0.394
y[1] (analytic) = 2.0797134416488680377034477013184
y[1] (numeric) = 2.0797134416488685148017981422509
absolute error = 4.770983504409325e-16
relative error = 2.2940581182312914668735836111540e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.179
Order of pole = 2.087
x[1] = 0.395
y[1] (analytic) = 2.0801297667363563069686071238421
y[1] (numeric) = 2.0801297667363567863681644920189
absolute error = 4.793995573681768e-16
relative error = 2.3046617813673052173710780318131e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.178
Order of pole = 2.087
x[1] = 0.396
y[1] (analytic) = 2.0805472656396180952219566326578
y[1] (numeric) = 2.0805472656396185769336579099374
absolute error = 4.817117012772796e-16
relative error = 2.3153124624120857225266274676404e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.177
Order of pole = 2.087
x[1] = 0.397
y[1] (analytic) = 2.0809659393391968932041865504051
y[1] (numeric) = 2.0809659393391973772390369758862
absolute error = 4.840348504254811e-16
relative error = 2.3260104419545886111346422415715e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.176
Order of pole = 2.086
x[1] = 0.398
y[1] (analytic) = 2.0813857888192178896505320786134
y[1] (numeric) = 2.0813857888192183760196056029408
absolute error = 4.863690735243274e-16
relative error = 2.3367560023567152746990496642430e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.175
Order of pole = 2.086
x[1] = 0.399
y[1] (analytic) = 2.0818068150673979143868194241832
y[1] (numeric) = 2.0818068150673984031012591674024
absolute error = 4.887144397432192e-16
relative error = 2.3475494277666547386379634240785e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.174
Order of pole = 2.086
x[1] = 0.4
y[1] (analytic) = 2.0822290190750554293994091739943
y[1] (numeric) = 2.0822290190750559204704278869853
absolute error = 4.910710187129910e-16
relative error = 2.3583910041323364874750810056039e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.173
Order of pole = 2.086
x[1] = 0.401
y[1] (analytic) = 2.082652401837120568107989542161
y[1] (numeric) = 2.0826524018371210615468700716812
absolute error = 4.934388805295202e-16
relative error = 2.3692810192149909932028404067508e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.172
Order of pole = 2.086
x[1] = 0.402
y[1] (analytic) = 2.0830769643521452230716026722043
y[1] (numeric) = 2.0830769643521457188896984295721
absolute error = 4.958180957573678e-16
relative error = 2.3802197626028257402105238651411e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.171
Order of pole = 2.086
x[1] = 0.403
y[1] (analytic) = 2.0835027076223131823597272863241
y[1] (numeric) = 2.083502707622313680568462719773
absolute error = 4.982087354334489e-16
relative error = 2.3912075257248077263878810276903e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.17
Order of pole = 2.086
x[1] = 0.404
y[1] (analytic) = 2.0839296326534503148216907107722
y[1] (numeric) = 2.0839296326534508154325617815069
absolute error = 5.006108710707347e-16
relative error = 2.4022446018645602274505668431062e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.3MB, time=6.92
Real estimate of pole used
Radius of convergence = 1.169
Order of pole = 2.085
x[1] = 0.405
y[1] (analytic) = 2.0843577404550348044891427454574
y[1] (numeric) = 2.0843577404550353075137174074443
absolute error = 5.030245746619869e-16
relative error = 2.4133312861743777582192347729854e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.168
Order of pole = 2.085
x[1] = 0.406
y[1] (analytic) = 2.084787032040207434347793063385
y[1] (numeric) = 2.0847870320402079397977117469078
absolute error = 5.054499186835228e-16
relative error = 2.4244678756893506842668652585397e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.167
Order of pole = 2.085
x[1] = 0.407
y[1] (analytic) = 2.0852175084257819197160928980269
y[1] (numeric) = 2.0852175084257824276030689970405
absolute error = 5.078869760990136e-16
relative error = 2.4356546693416110906365281451087e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.166
Order of pole = 2.085
x[1] = 0.408
y[1] (analytic) = 2.0856491706322552914700307815789
y[1] (numeric) = 2.0856491706322558018058511448926
absolute error = 5.103358203633137e-16
relative error = 2.4468919679746889576795342853763e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.165
Order of pole = 2.085
x[1] = 0.409
y[1] (analytic) = 2.0860820196838183293547111122715
y[1] (numeric) = 2.0860820196838188421512365385961
absolute error = 5.127965254263246e-16
relative error = 2.4581800743579955128789574079803e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.164
Order of pole = 2.085
x[1] = 0.41
y[1] (analytic) = 2.0865160566083660456248934331431
y[1] (numeric) = 2.0865160566083665608940591700332
absolute error = 5.152691657368901e-16
relative error = 2.4695192932014175274578725029878e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.163
Order of pole = 2.085
x[1] = 0.411
y[1] (analytic) = 2.086951282437508219258189577267
y[1] (numeric) = 2.086951282437508737012005823993
absolute error = 5.177538162467260e-16
relative error = 2.4809099311700374967707747488560e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.162
Order of pole = 2.085
x[1] = 0.412
y[1] (analytic) = 2.0873876982065799809861453553894
y[1] (numeric) = 2.0873876982065805012366977697729
absolute error = 5.202505524143835e-16
relative error = 2.4923522968989754532393694059551e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.161
Order of pole = 2.084
x[1] = 0.413
y[1] (analytic) = 2.0878253049546524493899733119598
y[1] (numeric) = 2.0878253049546529721494235212052
absolute error = 5.227594502092454e-16
relative error = 2.5038467010083476859639482181116e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.16
Order of pole = 2.084
x[1] = 0.414
y[1] (analytic) = 2.088264103724543418309253336022
y[1] (numeric) = 2.0882641037245439435898394515804
absolute error = 5.252805861155584e-16
relative error = 2.5153934561183577587510147605191e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.159
Order of pole = 2.084
x[1] = 0.415
y[1] (analytic) = 2.0887040955628280958134786664709
y[1] (numeric) = 2.0887040955628286236275158029698
absolute error = 5.278140371364989e-16
relative error = 2.5269928768645069425117037407727e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.158
Order of pole = 2.084
x[1] = 0.416
y[1] (analytic) = 2.0891452815198498949878961595599
y[1] (numeric) = 2.0891452815198504253477769578336
absolute error = 5.303598807982737e-16
relative error = 2.5386452799129303434143242378153e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.3MB, time=7.12
Real estimate of pole used
Radius of convergence = 1.157
Order of pole = 2.084
x[1] = 0.417
y[1] (analytic) = 2.0895876626497312767866716737703
y[1] (numeric) = 2.0895876626497318097048668280276
absolute error = 5.329181951542573e-16
relative error = 2.5503509839758664304973369782662e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.156
Order of pole = 2.084
x[1] = 0.418
y[1] (analytic) = 2.0900312400103846452080041574658
y[1] (numeric) = 2.090031240010385180697062946629
absolute error = 5.354890587891632e-16
relative error = 2.5621103098272470766746407252034e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.155
Order of pole = 2.084
x[1] = 0.419
y[1] (analytic) = 2.0904760146635232950474155830821
y[1] (numeric) = 2.0904760146635238331199664063344
absolute error = 5.380725508232523e-16
relative error = 2.5739235803184225125421023165618e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.154
Order of pole = 2.084
x[1] = 0.42
y[1] (analytic) = 2.0909219876746724124870583436505
y[1] (numeric) = 2.0909219876746729531558092602283
absolute error = 5.406687509165778e-16
relative error = 2.5857911203940178695036862862572e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.153
Order of pole = 2.084
x[1] = 0.421
y[1] (analytic) = 2.0913691601131801287805071996326
y[1] (numeric) = 2.0913691601131806720582464728983
absolute error = 5.432777392732657e-16
relative error = 2.5977132571079165569342598484713e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.152
Order of pole = 2.084
x[1] = 0.422
y[1] (analytic) = 2.0918175330522286272941394235245
y[1] (numeric) = 2.0918175330522291731937360693585
absolute error = 5.458995966458340e-16
relative error = 2.6096903196393848454001035415377e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.151
Order of pole = 2.084
x[1] = 0.423
y[1] (analytic) = 2.0922671075688453041678545244069
y[1] (numeric) = 2.0922671075688458527022588639545
absolute error = 5.485344043395476e-16
relative error = 2.6217226393093228453638055923645e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.15
Order of pole = 2.084
x[1] = 0.424
y[1] (analytic) = 2.0927178847439139828595439332407
y[1] (numeric) = 2.0927178847439145340417881500531
absolute error = 5.511822442168124e-16
relative error = 2.6338105495966581532554369187528e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.149
Order of pole = 2.084
x[1] = 0.425
y[1] (analytic) = 2.0931698656621861828393913817083
y[1] (numeric) = 2.0931698656621867366825900833149
absolute error = 5.538431987016066e-16
relative error = 2.6459543861548721298187427590954e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.148
Order of pole = 2.083
x[1] = 0.426
y[1] (analytic) = 2.0936230514122924427017665029932
y[1] (numeric) = 2.0936230514122929992191172869443
absolute error = 5.565173507839511e-16
relative error = 2.6581544868286674178133836834921e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.147
Order of pole = 2.083
x[1] = 0.427
y[1] (analytic) = 2.0940774430867536979641675131001
y[1] (numeric) = 2.0940774430867542571689515375189
absolute error = 5.592047840244188e-16
relative error = 2.6704111916707752598802340099135e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.146
Order of pole = 2.083
memory used=141.1MB, alloc=4.3MB, time=7.33
x[1] = 0.428
y[1] (analytic) = 2.0945330417819927138243737879406
y[1] (numeric) = 2.0945330417819932757299563466231
absolute error = 5.619055825586825e-16
relative error = 2.6827248429589006992468362087328e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.145
Order of pole = 2.083
x[1] = 0.429
y[1] (analytic) = 2.0949898485983455731486858270537
y[1] (numeric) = 2.0949898485983461377685169291568
absolute error = 5.646198311021031e-16
relative error = 2.6950957852128132926905867076210e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.144
Order of pole = 2.083
x[1] = 0.43
y[1] (analytic) = 2.0954478646400732199658585829015
y[1] (numeric) = 2.0954478646400737873134735372594
absolute error = 5.673476149543579e-16
relative error = 2.7075243652115818813915408026306e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.143
Order of pole = 2.083
x[1] = 0.431
y[1] (analytic) = 2.0959070910153730587430745294087
y[1] (numeric) = 2.0959070910153736288320945335175
absolute error = 5.700890200041088e-16
relative error = 2.7200109320109519645498402178569e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.142
Order of pole = 2.083
x[1] = 0.432
y[1] (analytic) = 2.0963675288363906097220552398346
y[1] (numeric) = 2.0963675288363911825661879735465
absolute error = 5.728441327337119e-16
relative error = 2.7325558369608723291695324443207e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.141
Order of pole = 2.083
x[1] = 0.433
y[1] (analytic) = 2.0968291792192312205951747380674
y[1] (numeric) = 2.096829179219231796208214962035
absolute error = 5.756130402239676e-16
relative error = 2.7451594337231661285540092154808e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.14
Order of pole = 2.083
x[1] = 0.434
y[1] (analytic) = 2.0972920432839718348032145757135
y[1] (numeric) = 2.0972920432839724131990447346266
absolute error = 5.783958301589131e-16
relative error = 2.7578220782893549576907241427421e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.139
Order of pole = 2.083
x[1] = 0.435
y[1] (analytic) = 2.0977561221546728167381895674904
y[1] (numeric) = 2.0977561221546733979307803981467
absolute error = 5.811925908306563e-16
relative error = 2.7705441289986306309396282471534e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.138
Order of pole = 2.083
x[1] = 0.436
y[1] (analytic) = 2.098221416959389834136474487828
y[1] (numeric) = 2.0982214169593904181398856320805
absolute error = 5.840034111442525e-16
relative error = 2.7833259465559808116008247408130e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.137
Order of pole = 2.083
x[1] = 0.437
y[1] (analytic) = 2.0986879288301857979492758915178
y[1] (numeric) = 2.0986879288301863847776565141417
absolute error = 5.868283806226239e-16
relative error = 2.7961678940504679577484880495369e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.136
Order of pole = 2.083
x[1] = 0.438
y[1] (analytic) = 2.0991556589031428599793196708782
y[1] (numeric) = 2.0991556589031434496469090824003
absolute error = 5.896675894115221e-16
relative error = 2.8090703369736619989057217674564e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.135
Order of pole = 2.083
x[1] = 0.439
y[1] (analytic) = 2.0996246083183744685744641022415
y[1] (numeric) = 2.099624608318375061095592386776
absolute error = 5.925211282845345e-16
relative error = 2.8220336432382304877876386309867e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.3MB, time=7.53
Real estimate of pole used
Radius of convergence = 1.134
Order of pole = 2.083
x[1] = 0.44
y[1] (analytic) = 2.1000947782200374826708000675464
y[1] (numeric) = 2.1000947782200380780598887156814
absolute error = 5.953890886481350e-16
relative error = 2.8350581831966875802326998278544e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.133
Order of pole = 2.083
x[1] = 0.441
y[1] (analytic) = 2.1005661697563443444796649652401
y[1] (numeric) = 2.1005661697563449427512275120188
absolute error = 5.982715625467787e-16
relative error = 2.8481443296602998579473007356676e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.132
Order of pole = 2.083
x[1] = 0.442
y[1] (analytic) = 2.1010387840795753111148746522805
y[1] (numeric) = 2.1010387840795759122835173203224
absolute error = 6.011686426680419e-16
relative error = 2.8612924579181546238751004689130e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.131
Order of pole = 2.083
x[1] = 0.443
y[1] (analytic) = 2.1015126223460907454583686904158
y[1] (numeric) = 2.1015126223460913495387910382237
absolute error = 6.040804223478079e-16
relative error = 2.8745029457563924794170916892278e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.13
Order of pole = 2.083
x[1] = 0.444
y[1] (analytic) = 2.1019876857163434665643683106615
y[1] (numeric) = 2.1019876857163440735713638861593
absolute error = 6.070069955754978e-16
relative error = 2.8877761734775998010802187571043e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.129
Order of pole = 2.083
x[1] = 0.445
y[1] (analytic) = 2.1024639753548911599040639664818
y[1] (numeric) = 2.1024639753548917698525209658302
absolute error = 6.099484569993484e-16
relative error = 2.9011125239203705316157406134581e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.128
Order of pole = 2.083
x[1] = 0.446
y[1] (analytic) = 2.1029414924304088477547802260496
y[1] (numeric) = 2.1029414924304094606596821577859
absolute error = 6.129049019317363e-16
relative error = 2.9145123824790324141315484311563e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.127
Order of pole = 2.083
x[1] = 0.447
y[1] (analytic) = 2.103420238115701420039510165481
y[1] (numeric) = 2.1034202381157020359159365200306
absolute error = 6.158764263545496e-16
relative error = 2.9279761371235437371944723356191e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.126
Order of pole = 2.082
x[1] = 0.448
y[1] (analytic) = 2.1039002135877162259246694774701
y[1] (numeric) = 2.1039002135877168447877964020774
absolute error = 6.188631269246073e-16
relative error = 2.9415041784195604650179339687652e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.125
Order of pole = 2.082
x[1] = 0.449
y[1] (analytic) = 2.1043814200275557264858923135875
y[1] (numeric) = 2.104381420027556348350993292714
absolute error = 6.218651009791265e-16
relative error = 2.9550968995486736231004778385572e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.124
Order of pole = 2.082
x[1] = 0.45
y[1] (analytic) = 2.1048638586204902087536765449528
y[1] (numeric) = 2.1048638586204908336361230861913
absolute error = 6.248824465412385e-16
relative error = 2.9687546963288215568460161633201e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.123
Order of pole = 2.082
x[1] = 0.451
y[1] (analytic) = 2.1053475305559705614526857673214
y[1] (numeric) = 2.1053475305559711893679480928755
absolute error = 6.279152623255541e-16
relative error = 2.9824779672348778683755645822692e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.3MB, time=7.73
Real estimate of pole used
Radius of convergence = 1.122
Order of pole = 2.082
x[1] = 0.452
y[1] (analytic) = 2.1058324370276411127505291061225
y[1] (numeric) = 2.1058324370276417437141768499007
absolute error = 6.309636477437782e-16
relative error = 2.9962671134194148814354461251700e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.121
Order of pole = 2.082
x[1] = 0.453
y[1] (analytic) = 2.1063185792333525303338678089308
y[1] (numeric) = 2.1063185792333531643615707193059
absolute error = 6.340277029103751e-16
relative error = 3.0101225387336486523824642550500e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.12
Order of pole = 2.082
x[1] = 0.454
y[1] (analytic) = 2.1068059583751747841317398625602
y[1] (numeric) = 2.1068059583751754212392685108433
absolute error = 6.371075286482831e-16
relative error = 3.0240446497485582397075420562165e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.119
Order of pole = 2.082
x[1] = 0.455
y[1] (analytic) = 2.1072945756594101720080505557603
y[1] (numeric) = 2.1072945756594108122112770504424
absolute error = 6.402032264946821e-16
relative error = 3.0380338557761961554882935332599e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.118
Order of pole = 2.082
x[1] = 0.456
y[1] (analytic) = 2.1077844322966064087472481437615
y[1] (numeric) = 2.1077844322966070520621468505724
absolute error = 6.433148987068109e-16
relative error = 3.0520905688911736763362921644170e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.117
Order of pole = 2.082
x[1] = 0.457
y[1] (analytic) = 2.1082755295015697786592896760549
y[1] (numeric) = 2.1082755295015704251019379438926
absolute error = 6.464426482678377e-16
relative error = 3.0662152039523369712421860559501e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.116
Order of pole = 2.082
x[1] = 0.458
y[1] (analytic) = 2.1087678684933783521321027433093
y[1] (numeric) = 2.1087678684933790017186816360925
absolute error = 6.495865788927832e-16
relative error = 3.0804081786246305271073713994101e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.115
Order of pole = 2.082
x[1] = 0.459
y[1] (analytic) = 2.1092614504953952664618645037582
y[1] (numeric) = 2.1092614504953959192086595382545
absolute error = 6.527467950344963e-16
relative error = 3.0946699134011471994802368073241e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.114
Order of pole = 2.082
x[1] = 0.46
y[1] (analytic) = 2.109756276735282071293549985367
y[1] (numeric) = 2.1097562767352827272169518750507
absolute error = 6.559234018896837e-16
relative error = 3.1090008316253703747101109351607e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.113
Order of pole = 2.082
x[1] = 0.461
y[1] (analytic) = 2.1102523484450121390063474503436
y[1] (numeric) = 2.1102523484450127981228528553378
absolute error = 6.591165054049942e-16
relative error = 3.1234013595136113456074278849441e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.112
Order of pole = 2.082
x[1] = 0.462
y[1] (analytic) = 2.1107496668608841403806996769025
y[1] (numeric) = 2.1107496668608848027069119600595
absolute error = 6.623262122831570e-16
relative error = 3.1378719261776378858409985852671e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.111
Order of pole = 2.082
x[1] = 0.463
y[1] (analytic) = 2.1112482332235355858859064845699
y[1] (numeric) = 2.1112482332235362514385364737453
absolute error = 6.655526299891754e-16
relative error = 3.1524129636474999580102569949960e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.3MB, time=7.93
Real estimate of pole used
Radius of convergence = 1.11
Order of pole = 2.082
x[1] = 0.464
y[1] (analytic) = 2.1117480487779564329294158297936
y[1] (numeric) = 2.1117480487779571017252825863708
absolute error = 6.687958667565772e-16
relative error = 3.1670249068945580009996033274453e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.109
Order of pole = 2.082
x[1] = 0.465
y[1] (analytic) = 2.1122491147735027594111384553856
y[1] (numeric) = 2.1122491147735034314671700491057
absolute error = 6.720560315937201e-16
relative error = 3.1817081938547050243489207240476e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.108
Order of pole = 2.082
x[1] = 0.466
y[1] (analytic) = 2.1127514324639105039283445187234
y[1] (numeric) = 2.112751432463911179261578808879
absolute error = 6.753332342901556e-16
relative error = 3.1964632654517983617373378488232e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.107
Order of pole = 2.082
x[1] = 0.467
y[1] (analytic) = 2.1132550031073092729789399791717
y[1] (numeric) = 2.1132550031073099516065254022206
absolute error = 6.786275854230489e-16
relative error = 3.2112905656212885085875509852125e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.106
Order of pole = 2.082
x[1] = 0.468
y[1] (analytic) = 2.1137598279662362155131759255234
y[1] (numeric) = 2.1137598279662368974523722891814
absolute error = 6.819391963636580e-16
relative error = 3.2261905413340594540578209340537e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.105
Order of pole = 2.082
x[1] = 0.469
y[1] (analytic) = 2.1142659083076499651861156012579
y[1] (numeric) = 2.1142659083076506504542948851294
absolute error = 6.852681792838715e-16
relative error = 3.2411636426204773851867390107122e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.104
Order of pole = 2.082
x[1] = 0.47
y[1] (analytic) = 2.1147732454029446506654717721142
y[1] (numeric) = 2.1147732454029453392801189349186
absolute error = 6.886146471628044e-16
relative error = 3.2562103225946436962175574290469e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.103
Order of pole = 2.082
x[1] = 0.471
y[1] (analytic) = 2.1152818405279639743517314111258
y[1] (numeric) = 2.1152818405279646663304452045815
absolute error = 6.919787137934557e-16
relative error = 3.2713310374788695127418496766149e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.102
Order of pole = 2.082
x[1] = 0.472
y[1] (analytic) = 2.1157916949630153598698055863413
y[1] (numeric) = 2.115791694963016055230299375766
absolute error = 6.953604937894247e-16
relative error = 3.2865262466283562902963319972962e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.101
Order of pole = 2.082
x[1] = 0.473
y[1] (analytic) = 2.1163028099928841686937800626363
y[1] (numeric) = 2.1163028099928848674538826543262
absolute error = 6.987601025916899e-16
relative error = 3.3017964125561001482010182547148e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.1
Order of pole = 2.082
x[1] = 0.474
y[1] (analytic) = 2.1168151869068479862686966092692
y[1] (numeric) = 2.1168151869068486884463530847174
absolute error = 7.021776564754482e-16
relative error = 3.3171420009580082709515838293851e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.3MB, time=8.14
Real estimate of pole used
Radius of convergence = 1.098
Order of pole = 2.082
x[1] = 0.475
y[1] (analytic) = 2.117328826998690977995666478318
y[1] (numeric) = 2.1173288269986916836089390353352
absolute error = 7.056132725570172e-16
relative error = 3.3325634807382398137665957675349e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.097
Order of pole = 2.082
x[1] = 0.476
y[1] (analytic) = 2.1178437315667183154490061263295
y[1] (numeric) = 2.1178437315667190245160749271302
absolute error = 7.090670688008007e-16
relative error = 3.3480613240347709707497042652328e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.096
Order of pole = 2.082
x[1] = 0.477
y[1] (analytic) = 2.1183599019137706731964911341508
y[1] (numeric) = 2.1183599019137713857356551604678
absolute error = 7.125391640263170e-16
relative error = 3.3636360062451814991117430733560e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.095
Order of pole = 2.082
x[1] = 0.478
y[1] (analytic) = 2.1188773393472387965962475810212
y[1] (numeric) = 2.1188773393472395126259254963131
absolute error = 7.160296779152919e-16
relative error = 3.3792880060526708476097103434588e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.094
Order of pole = 2.082
x[1] = 0.479
y[1] (analytic) = 2.1193960451790781409462409929272
y[1] (numeric) = 2.119396045179078860484972011744
absolute error = 7.195387310188168e-16
relative error = 3.3950178054523049385610297077123e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.093
Order of pole = 2.082
x[1] = 0.48
y[1] (analytic) = 2.1199160207258235823647815576117
y[1] (numeric) = 2.1199160207258243054312263221833
absolute error = 7.230664447645716e-16
relative error = 3.4108258897774913431991318549920e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.092
Order of pole = 2.082
x[1] = 0.481
y[1] (analytic) = 2.1204372673086042007829407264671
y[1] (numeric) = 2.1204372673086049273958821905817
absolute error = 7.266129414641146e-16
relative error = 3.4267127477266923790465003705385e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.091
Order of pole = 2.082
x[1] = 0.482
y[1] (analytic) = 2.12095978625315813543226875517
y[1] (numeric) = 2.1209597862531588656106130754087
absolute error = 7.301783443202387e-16
relative error = 3.4426788713903719606057377965349e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.09
Order of pole = 2.082
x[1] = 0.483
y[1] (analytic) = 2.1214835788898475132137153200166
y[1] (numeric) = 2.121483578889848246976492754412
absolute error = 7.337627774343954e-16
relative error = 3.4587247562781824072809984205229e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.089
Order of pole = 2.082
x[1] = 0.484
y[1] (analytic) = 2.1220086465536734503361862365609
y[1] (numeric) = 2.1220086465536741877025520507474
absolute error = 7.373663658141865e-16
relative error = 3.4748509013463898544585560737169e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.088
Order of pole = 2.082
x[1] = 0.485
y[1] (analytic) = 2.1225349905842911276157186537912
y[1] (numeric) = 2.1225349905842918686049540347176
absolute error = 7.409892353809264e-16
relative error = 3.4910578090255510445991755329671e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.087
Order of pole = 2.082
x[1] = 0.486
y[1] (analytic) = 2.1230626123260249398288250545615
y[1] (numeric) = 2.1230626123260256844603380318328
absolute error = 7.446315129772713e-16
relative error = 3.5073459852484231568204507163455e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.3MB, time=8.34
Real estimate of pole used
Radius of convergence = 1.086
Order of pole = 2.082
x[1] = 0.487
y[1] (analytic) = 2.1235915131278837195161431165762
y[1] (numeric) = 2.1235915131278844678094694914974
absolute error = 7.482933263749212e-16
relative error = 3.5237159394781335703808756147113e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.085
Order of pole = 2.082
x[1] = 0.488
y[1] (analytic) = 2.1241216943435760356351341346258
y[1] (numeric) = 2.1241216943435767876099384170176
absolute error = 7.519748042823918e-16
relative error = 3.5401681847365949691235400209914e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.084
Order of pole = 2.082
x[1] = 0.489
y[1] (analytic) = 2.124653157331525567463197432109
y[1] (numeric) = 2.1246531573315263231392737849672
absolute error = 7.556760763528582e-16
relative error = 3.5567032376331738088229854585037e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.083
Order of pole = 2.082
x[1] = 0.49
y[1] (analytic) = 2.1251859034548865541552121577616
y[1] (numeric) = 2.125185903454887313552485349833
absolute error = 7.593972731920714e-16
relative error = 3.5733216183936159123490111364930e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.082
Order of pole = 2.082
x[1] = 0.491
y[1] (analytic) = 2.1257199340815593203621812330174
y[1] (numeric) = 2.1257199340815600835007075993652
absolute error = 7.631385263663478e-16
relative error = 3.5900238508892291803843308211865e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.081
Order of pole = 2.082
x[1] = 0.492
y[1] (analytic) = 2.1262552505842058783203351491064
y[1] (numeric) = 2.1262552505842066452203035597393
absolute error = 7.668999684106329e-16
relative error = 3.6068104626663281022930071084396e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.08
Order of pole = 2.082
x[1] = 0.493
y[1] (analytic) = 2.1267918543402656068227559749231
y[1] (numeric) = 2.1267918543402663775044888115625
absolute error = 7.706817328366394e-16
relative error = 3.6236819849759400340685491757238e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.079
Order of pole = 2.082
x[1] = 0.494
y[1] (analytic) = 2.1273297467319710074883044924483
y[1] (numeric) = 2.1273297467319717819722586335099
absolute error = 7.744839541410616e-16
relative error = 3.6406389528037811951956085933039e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.078
Order of pole = 2.082
x[1] = 0.495
y[1] (analytic) = 2.1278689291463635387453759932105
y[1] (numeric) = 2.1278689291463643170521438070756
absolute error = 7.783067678138651e-16
relative error = 3.6576819049004966850539671959771e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.077
Order of pole = 2.082
x[1] = 0.496
y[1] (analytic) = 2.1284094029753095279507731155848
y[1] (numeric) = 2.1284094029753103101010834622389
absolute error = 7.821503103466541e-16
relative error = 3.6748113838121743290185019252935e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.076
Order of pole = 2.082
x[1] = 0.497
y[1] (analytic) = 2.128951169615516162066767348895
y[1] (numeric) = 2.1289511696155169480814865900118
absolute error = 7.860147192411168e-16
relative error = 3.6920279359111336830500550127991e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.075
Order of pole = 2.082
x[1] = 0.498
y[1] (analytic) = 2.129494230468547557322224648122
y[1] (numeric) = 2.1294942304685483472223576656705
absolute error = 7.899001330175485e-16
relative error = 3.7093321114269872897913393675295e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.3MB, time=8.54
Real estimate of pole used
Radius of convergence = 1.074
Order of pole = 2.082
x[1] = 0.499
y[1] (analytic) = 2.1300385869408409082864951659371
y[1] (numeric) = 2.1300385869408417020931863893931
absolute error = 7.938066912234560e-16
relative error = 3.7267244644779900573627568756932e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.073
Order of pole = 2.082
x[1] = 0.5
y[1] (analytic) = 2.130584240443722716787612591826
y[1] (numeric) = 2.1305842404437235145221470340657
absolute error = 7.977345344422397e-16
relative error = 3.7442055531026587992437335267109e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.072
Order of pole = 2.082
x[1] = 0.501
y[1] (analytic) = 2.1311311923934251011092151678795
y[1] (numeric) = 2.1311311923934259027930194698391
absolute error = 8.016838043019596e-16
relative error = 3.7617759392916899884284336480713e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.071
Order of pole = 2.082
x[1] = 0.502
y[1] (analytic) = 2.1316794442111021859034883057481
y[1] (numeric) = 2.1316794442111029915581317899292
absolute error = 8.056546434841811e-16
relative error = 3.7794361890201553958481084775127e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.07
Order of pole = 2.082
x[1] = 0.503
y[1] (analytic) = 2.1322289973228465732603380392364
y[1] (numeric) = 2.1322289973228473829075337721409
absolute error = 8.096471957329045e-16
relative error = 3.7971868722799928371179840169523e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.069
Order of pole = 2.082
x[1] = 0.504
y[1] (analytic) = 2.1327798531597058953759354937272
y[1] (numeric) = 2.1327798531597067090375413573061
absolute error = 8.136616058635789e-16
relative error = 3.8150285631127942052270045374656e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.068
Order of pole = 2.082
x[1] = 0.505
y[1] (analytic) = 2.1333320131576994492667253204352
y[1] (numeric) = 2.1333320131577002669647450926337
absolute error = 8.176980197721985e-16
relative error = 3.8329618396428802987394833816808e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.067
Order of pole = 2.082
x[1] = 0.506
y[1] (analytic) = 2.1338854787578349139779658154572
y[1] (numeric) = 2.133885478757835735734550259944
absolute error = 8.217565844444868e-16
relative error = 3.8509872841106871166474741935352e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.066
Order of pole = 2.082
x[1] = 0.507
y[1] (analytic) = 2.1344402514061251507388654075507
y[1] (numeric) = 2.134440251406125976576313372716
absolute error = 8.258374479651653e-16
relative error = 3.8691054829064465353966231802292e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.065
Order of pole = 2.082
x[1] = 0.508
y[1] (analytic) = 2.1349963325536050865193995430729
y[1] (numeric) = 2.1349963325536059164601590703832
absolute error = 8.299407595273103e-16
relative error = 3.8873170266041770984918298969857e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.064
Order of pole = 2.082
x[1] = 0.509
y[1] (analytic) = 2.1355537236563486814469339119095
y[1] (numeric) = 2.1355537236563495155136033537068
absolute error = 8.340666694417973e-16
relative error = 3.9056225099959814100797843236273e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.063
Order of pole = 2.082
memory used=167.8MB, alloc=4.3MB, time=8.73
x[1] = 0.51
y[1] (analytic) = 2.1361124261754859805438446366325
y[1] (numeric) = 2.1361124261754868187591737834673
absolute error = 8.382153291468348e-16
relative error = 3.9240225321266573907723775562803e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.062
Order of pole = 2.082
x[1] = 0.511
y[1] (analytic) = 2.1366724415772202502504136824883
y[1] (numeric) = 2.1366724415772210926373049000758
absolute error = 8.423868912175875e-16
relative error = 3.9425176963286222067711445869859e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.061
Order of pole = 2.082
x[1] = 0.512
y[1] (analytic) = 2.137233771332845200200388533899
y[1] (numeric) = 2.1372337713328460467818979097903
absolute error = 8.465815093758913e-16
relative error = 3.9611086102571589074911137294490e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.06
Order of pole = 2.082
x[1] = 0.513
y[1] (analytic) = 2.137796416918762290719729321568
y[1] (numeric) = 2.137796416918763141519067821627
absolute error = 8.507993385000590e-16
relative error = 3.9797958859259794059125659033635e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.059
Order of pole = 2.082
x[1] = 0.514
y[1] (analytic) = 2.1383603798164981265222242724934
y[1] (numeric) = 2.1383603798164989815627589072728
absolute error = 8.550405346347794e-16
relative error = 3.9985801397431152118960826965457e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.058
Order of pole = 2.082
x[1] = 0.515
y[1] (analytic) = 2.1389256615127219370788357945697
y[1] (numeric) = 2.13892566151272279638409079568
absolute error = 8.593052550011103e-16
relative error = 4.0174619925471370110607282763104e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.057
Order of pole = 2.082
x[1] = 0.516
y[1] (analytic) = 2.1394922634992631441408449012686
y[1] (numeric) = 2.1394922634992640077345029078344
absolute error = 8.635936580065658e-16
relative error = 4.0364420696437037039041188830927e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.056
Order of pole = 2.082
x[1] = 0.517
y[1] (analytic) = 2.1400601872731290169000912353196
y[1] (numeric) = 2.140060187273129884805994490619
absolute error = 8.679059032552994e-16
relative error = 4.0555210008424466503204138472450e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.055
Order of pole = 2.082
x[1] = 0.518
y[1] (analytic) = 2.1406294343365224152728598704981
y[1] (numeric) = 2.1406294343365232875150114288823
absolute error = 8.722421515583842e-16
relative error = 4.0746994204941939098387504540816e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.054
Order of pole = 2.082
x[1] = 0.519
y[1] (analytic) = 2.1412000061968596217972445666753
y[1] (numeric) = 2.1412000061968604983998095108654
absolute error = 8.766025649441901e-16
relative error = 4.0939779675285327108606784924291e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.053
Order of pole = 2.082
x[1] = 0.52
y[1] (analytic) = 2.1417719043667882626371204362693
y[1] (numeric) = 2.14177190436678914362442710513
absolute error = 8.809873066688607e-16
relative error = 4.1133572854917214506744924063842e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.052
Order of pole = 2.082
x[1] = 0.521
y[1] (analytic) = 2.1423451303642053181891872632637
y[1] (numeric) = 2.1423451303642062035857284901528
absolute error = 8.853965412268891e-16
relative error = 4.1328380225849461580264045445834e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.3MB, time=8.94
Real estimate of pole used
Radius of convergence = 1.051
Order of pole = 2.082
x[1] = 0.522
y[1] (analytic) = 2.1429196857122752237928982141354
y[1] (numeric) = 2.1429196857122761136233325759305
absolute error = 8.898304343617951e-16
relative error = 4.1524208317029317516472866574305e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.05
Order of pole = 2.082
x[1] = 0.523
y[1] (analytic) = 2.1434955719394480610464676105372
y[1] (numeric) = 2.1434955719394489553356206874415
absolute error = 8.942891530769043e-16
relative error = 4.1721063704729090666171523945707e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.049
Order of pole = 2.082
x[1] = 0.524
y[1] (analytic) = 2.1440727905794778402355560156469
y[1] (numeric) = 2.1440727905794787390084216618765
absolute error = 8.987728656462296e-16
relative error = 4.1918953012939386093849048354181e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.048
Order of pole = 2.082
x[1] = 0.525
y[1] (analytic) = 2.1446513431714408743846613410521
y[1] (numeric) = 2.1446513431714417776664029665096
absolute error = 9.032817416254575e-16
relative error = 4.2117882913766008504083998117117e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.047
Order of pole = 2.082
x[1] = 0.526
y[1] (analytic) = 2.14523123125975424544470123234
y[1] (numeric) = 2.1452312312597551532606530953793
absolute error = 9.078159518630393e-16
relative error = 4.2317860127830521116285657390117e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.046
Order of pole = 2.082
x[1] = 0.527
y[1] (analytic) = 2.1458124563941943631337548647797
y[1] (numeric) = 2.1458124563941952755094233761682
absolute error = 9.123756685113885e-16
relative error = 4.2518891424674506910261481720600e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.045
Order of pole = 2.082
x[1] = 0.528
y[1] (analytic) = 2.1463950201299156169514417033653
y[1] (numeric) = 2.1463950201299165339125067415506
absolute error = 9.169610650381853e-16
relative error = 4.2720983623167559835199277141877e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.044
Order of pole = 2.082
x[1] = 0.529
y[1] (analytic) = 2.146978924027469121890950983952
y[1] (numeric) = 2.1469789240274700434632672217424
absolute error = 9.215723162377904e-16
relative error = 4.2924143591919093970392832704398e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.043
Order of pole = 2.082
x[1] = 0.53
y[1] (analytic) = 2.1475641696528215583762988863935
y[1] (numeric) = 2.1475641696528224845858971291611
absolute error = 9.262095982427676e-16
relative error = 4.3128378249693932615054881361161e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.042
Order of pole = 2.082
x[1] = 0.531
y[1] (analytic) = 2.1481507585773741069559808308282
y[1] (numeric) = 2.1481507585773750378290693663464
absolute error = 9.308730885355182e-16
relative error = 4.3333694565831802201170102291224e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.041
Order of pole = 2.082
x[1] = 0.532
y[1] (analytic) = 2.14873869237798147828780427118
y[1] (numeric) = 2.1487386923779824138507702312064
absolute error = 9.355629659600264e-16
relative error = 4.3540099560670678704965359078046e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.04
Order of pole = 2.082
x[1] = 0.533
y[1] (analytic) = 2.1493279726369710389533330244065
y[1] (numeric) = 2.1493279726369719792327437581254
absolute error = 9.402794107337189e-16
relative error = 4.3747600305974120352344493122248e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.3MB, time=9.14
Real estimate of pole used
Radius of convergence = 1.039
Order of pole = 2.082
x[1] = 0.534
y[1] (analytic) = 2.1499186009421620336440478012406
y[1] (numeric) = 2.1499186009421629786666522606788
absolute error = 9.450226044594382e-16
relative error = 4.3956203925362547920841256547958e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.038
Order of pole = 2.082
x[1] = 0.535
y[1] (analytic) = 2.1505105788868849042650294376249
y[1] (numeric) = 2.1505105788868858540577595751562
absolute error = 9.497927301375313e-16
relative error = 4.4165917594748536225151395299713e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.037
Order of pole = 2.082
x[1] = 0.536
y[1] (analytic) = 2.1511039080700007065057016115941
y[1] (numeric) = 2.1511039080700016610956737896511
absolute error = 9.545899721780570e-16
relative error = 4.4376748542776249862858692762962e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.036
Order of pole = 2.082
x[1] = 0.537
y[1] (analytic) = 2.1516985900959206244309288162523
y[1] (numeric) = 2.151698590095921583845445229361
absolute error = 9.594145164131087e-16
relative error = 4.4588704051264863107447028111137e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.035
Order of pole = 2.082
x[1] = 0.538
y[1] (analytic) = 2.1522946265746255836495532963326
y[1] (numeric) = 2.1522946265746265479161034055915
absolute error = 9.642665501092589e-16
relative error = 4.4801791455656236181229941571739e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.034
Order of pole = 2.082
x[1] = 0.539
y[1] (analytic) = 2.1528920191216859636212717966934
y[1] (numeric) = 2.1528920191216869327675337768162
absolute error = 9.691462619801228e-16
relative error = 4.5016018145466710680196091503659e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.033
Order of pole = 2.082
x[1] = 0.54
y[1] (analytic) = 2.1534907693582814096665995714796
y[1] (numeric) = 2.153490769358282383720441770524
absolute error = 9.740538421990444e-16
relative error = 4.5231391564743165736319846571112e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.032
Order of pole = 2.082
x[1] = 0.541
y[1] (analytic) = 2.1540908789112207452485454205553
y[1] (numeric) = 2.1540908789112217242380278324621
absolute error = 9.789894824119068e-16
relative error = 4.5447919212523397160576409309398e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.031
Order of pole = 2.082
x[1] = 0.542
y[1] (analytic) = 2.1546923494129619850985278156771
y[1] (numeric) = 2.1546923494129629690519035657419
absolute error = 9.839533757500648e-16
relative error = 4.5665608643300714483545997556130e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.03
Order of pole = 2.082
x[1] = 0.543
y[1] (analytic) = 2.1552951825016324497629987157303
y[1] (numeric) = 2.155295182501633438708715559136
absolute error = 9.889457168434057e-16
relative error = 4.5884467467493012833269935984292e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.029
Order of pole = 2.082
x[1] = 0.544
y[1] (analytic) = 2.1558993798210489821512087137848
y[1] (numeric) = 2.1558993798210499761179105473207
absolute error = 9.939667018335359e-16
relative error = 4.6104503351916190913436049117984e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.028
Order of pole = 2.082
x[1] = 0.545
memory used=179.2MB, alloc=4.3MB, time=9.34
y[1] (analytic) = 2.1565049430207382666685449768764
y[1] (numeric) = 2.1565049430207392656850733639735
absolute error = 9.990165283870971e-16
relative error = 4.6325724020262074020970322267113e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.027
Order of pole = 2.082
x[1] = 0.546
y[1] (analytic) = 2.157111873755957251523902303074
y[1] (numeric) = 2.1571118737559582556192980122855
absolute error = 1.0040953957092115e-15
relative error = 4.6548137253580796594236582179006e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.026
Order of pole = 2.082
x[1] = 0.547
y[1] (analytic) = 2.1577201736877136748036078029445
y[1] (numeric) = 2.1577201736877146840071123600034
absolute error = 1.0092035045570589e-15
relative error = 4.6771750890767760976905500917621e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.025
Order of pole = 2.082
x[1] = 0.548
y[1] (analytic) = 2.1583298444827866949085114900662
y[1] (numeric) = 2.1583298444827877092495687436537
absolute error = 1.0143410572535875e-15
relative error = 4.6996572829055237736792036046526e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.024
Order of pole = 2.082
x[1] = 0.549
y[1] (analytic) = 2.1589408878137476259549787165413
y[1] (numeric) = 2.1589408878137486454632364178984
absolute error = 1.0195082577013571e-15
relative error = 4.7222611024508529022735942675947e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.023
Order of pole = 2.082
x[1] = 0.55
y[1] (analytic) = 2.159553305358980778744676196012
y[1] (numeric) = 2.1595533053589818034499875925316
absolute error = 1.0247053113965196e-15
relative error = 4.7449873492526903596073227591613e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.022
Order of pole = 2.082
x[1] = 0.551
y[1] (analytic) = 2.1601670988027044079122316027689
y[1] (numeric) = 2.1601670988027054378446570457046
absolute error = 1.0299324254429357e-15
relative error = 4.7678368308349233822477755735308e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.021
Order of pole = 2.082
x[1] = 0.552
y[1] (analytic) = 2.1607822698349917658640677081811
y[1] (numeric) = 2.1607822698349928010538762746121
absolute error = 1.0351898085664310e-15
relative error = 4.7908103607564463946238090687869e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.02
Order of pole = 2.082
x[1] = 0.553
y[1] (analytic) = 2.1613988201517922641259660047505
y[1] (numeric) = 2.1613988201517933046036371339424
absolute error = 1.0404776711291919e-15
relative error = 4.8139087586626909004358444511080e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.019
Order of pole = 2.082
x[1] = 0.554
y[1] (analytic) = 2.1620167514549527427212020662941
y[1] (numeric) = 2.1620167514549537885174272105968
absolute error = 1.0457962251443027e-15
relative error = 4.8371328503376429865746509615448e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.018
Order of pole = 2.082
x[1] = 0.555
y[1] (analytic) = 2.1626360654522388482054157956763
y[1] (numeric) = 2.1626360654522398993511000861031
absolute error = 1.0511456842904268e-15
relative error = 4.8604834677563599009065811426020e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.017
Order of pole = 2.082
x[1] = 0.556
y[1] (analytic) = 2.1632567638573565209887345176453
y[1] (numeric) = 2.1632567638573575775149984442777
absolute error = 1.0565262639266324e-15
relative error = 4.8839614491379855694568599043130e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.3MB, time=9.54
Real estimate of pole used
Radius of convergence = 1.016
Order of pole = 2.082
x[1] = 0.557
y[1] (analytic) = 2.1638788483899735925800558850976
y[1] (numeric) = 2.1638788483899746545182369924615
absolute error = 1.0619381811073639e-15
relative error = 4.9075676389992686027632136857468e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.015
Order of pole = 2.082
x[1] = 0.558
y[1] (analytic) = 2.1645023207757414933928210869112
y[1] (numeric) = 2.1645023207757425607744756844734
absolute error = 1.0673816545975622e-15
relative error = 4.9313028882085955597999692717230e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.014
Order of pole = 2.082
x[1] = 0.559
y[1] (analytic) = 2.1651271827463170717560671817652
y[1] (numeric) = 2.1651271827463181446129720696989
absolute error = 1.0728569048879337e-15
relative error = 4.9551680540405364916107072108806e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.013
Order of pole = 2.082
x[1] = 0.56
y[1] (analytic) = 2.1657534360393845247790408455362
y[1] (numeric) = 2.1657534360393856031431950559076
absolute error = 1.0783641542103714e-15
relative error = 4.9791640002309164024588426577484e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.012
Order of pole = 2.082
x[1] = 0.561
y[1] (analytic) = 2.166381082398677441722184723456
y[1] (numeric) = 2.1663810823986785256258112769836
absolute error = 1.0839036265535276e-15
relative error = 5.0032915970324082187055469952292e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.011
Order of pole = 2.082
x[1] = 0.562
y[1] (analytic) = 2.1670101235740009605318722388431
y[1] (numeric) = 2.1670101235740020500074199173857
absolute error = 1.0894755476785426e-15
relative error = 5.0275517212706654637381084417222e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.01
Order of pole = 2.082
x[1] = 0.563
y[1] (analytic) = 2.1676405613212540382008674476446
y[1] (numeric) = 2.1676405613212551332810125825727
absolute error = 1.0950801451349281e-15
relative error = 5.0519452564009864851442343882079e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.009
Order of pole = 2.082
x[1] = 0.564
y[1] (analytic) = 2.1682723974024518356211236651662
y[1] (numeric) = 2.1682723974024529363387719417757
absolute error = 1.1007176482766095e-15
relative error = 5.0764730925655274508462790001990e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.008
Order of pole = 2.082
x[1] = 0.565
y[1] (analytic) = 2.1689056335857482176002084543699
y[1] (numeric) = 2.1689056335857493239884967324977
absolute error = 1.1063882882781278e-15
relative error = 5.1011361266510651393001879779785e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.007
Order of pole = 2.082
x[1] = 0.566
y[1] (analytic) = 2.1695402716454583687173534833506
y[1] (numeric) = 2.1695402716454594808096516343526
absolute error = 1.1120922981510020e-15
relative error = 5.1259352623473114537151382446142e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.006
Order of pole = 2.082
x[1] = 0.567
y[1] (analytic) = 2.1701763133620815256998760657177
y[1] (numeric) = 2.1701763133620826435297888259732
absolute error = 1.1178299127602555e-15
relative error = 5.1508714102057935516268876027490e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.005
Order of pole = 2.082
x[1] = 0.568
y[1] (analytic) = 2.1708137605223238270055052275761
y[1] (numeric) = 2.1708137605223249506068740686837
absolute error = 1.1236013688411076e-15
relative error = 5.1759454876993023779677093067986e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.3MB, time=9.74
Real estimate of pole used
Radius of convergence = 1.004
Order of pole = 2.082
x[1] = 0.569
y[1] (analytic) = 2.1714526149191212803009692379352
y[1] (numeric) = 2.1714526149191224097078742537661
absolute error = 1.1294069050158309e-15
relative error = 5.2011584192819109865325592628293e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.003
Order of pole = 2.082
x[1] = 0.57
y[1] (analytic) = 2.1720928783516628485320640383724
y[1] (numeric) = 2.1720928783516639837788258491505
absolute error = 1.1352467618107781e-15
relative error = 5.2265111364495764466438192135732e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.002
Order of pole = 2.082
x[1] = 0.571
y[1] (analytic) = 2.1727345526254136552853232587698
y[1] (numeric) = 2.1727345526254147964065049323481
absolute error = 1.1411211816735783e-15
relative error = 5.2520045778013234354005078597456e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.001
Order of pole = 2.082
x[1] = 0.572
y[1] (analytic) = 2.1733776395521383101463508585089
y[1] (numeric) = 2.1733776395521394571767598490162
absolute error = 1.1470304089905073e-15
relative error = 5.2776396891010278497203430390092e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1
Order of pole = 2.082
x[1] = 0.573
y[1] (analytic) = 2.1740221409499243547648572397406
y[1] (numeric) = 2.1740221409499255077395473437708
absolute error = 1.1529746901040302e-15
relative error = 5.3034174233397901946321706113171e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9993
Order of pole = 2.082
x[1] = 0.574
y[1] (analytic) = 2.1746680586432058303414592978551
y[1] (numeric) = 2.1746680586432069892957326283766
absolute error = 1.1589542733305215e-15
relative error = 5.3293387407989202414879647708077e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9983
Order of pole = 2.082
x[1] = 0.575
y[1] (analytic) = 2.1753153944627869672563646642743
y[1] (numeric) = 2.1753153944627881322257736424371
absolute error = 1.1649694089781628e-15
relative error = 5.3554046091135309377200095123326e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9973
Order of pole = 2.082
x[1] = 0.576
y[1] (analytic) = 2.1759641502458659975651607219814
y[1] (numeric) = 2.1759641502458671685855100870023
absolute error = 1.1710203493650209e-15
relative error = 5.3816160033367519464082053787891e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9963
Order of pole = 2.082
x[1] = 0.577
y[1] (analytic) = 2.1766143278360590910920702022652
y[1] (numeric) = 2.1766143278360602681994190395726
absolute error = 1.1771073488373074e-15
relative error = 5.4079739060045653423176196922465e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9953
Order of pole = 2.082
x[1] = 0.578
y[1] (analytic) = 2.1772659290834244158562176731574
y[1] (numeric) = 2.1772659290834255990868814609805
absolute error = 1.1832306637878231e-15
relative error = 5.4344793072012760726547110861217e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9943
Order of pole = 2.082
x[1] = 0.579
y[1] (analytic) = 2.1779189558444863235716753808886
y[1] (numeric) = 2.1779189558444875129622280554767
absolute error = 1.1893905526745881e-15
relative error = 5.4611332046256187239485728464010e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9933
Order of pole = 2.082
x[1] = 0.58
y[1] (analytic) = 2.1785734099822596609673230840681
y[1] (numeric) = 2.1785734099822608565545991237285
absolute error = 1.1955872760396604e-15
relative error = 5.4879366036575108368456226247520e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.3MB, time=9.94
Real estimate of pole used
Radius of convergence = 0.9923
Order of pole = 2.082
x[1] = 0.581
y[1] (analytic) = 2.1792292933662742076778651087088
y[1] (numeric) = 2.1792292933662754094989616368536
absolute error = 1.2018210965281448e-15
relative error = 5.5148905174254583798400780262460e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9913
Order of pole = 2.082
x[1] = 0.582
y[1] (analytic) = 2.1798866078725992414626992370468
y[1] (numeric) = 2.1798866078726004495549781444407
absolute error = 1.2080922789073939e-15
relative error = 5.5419959668746189618274346534190e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9903
Order of pole = 2.082
x[1] = 0.583
y[1] (analytic) = 2.1805453553838682315147266146227
y[1] (numeric) = 2.1805453553838694459158167010267
absolute error = 1.2144010900864040e-15
relative error = 5.5692539808355329181035598451268e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9893
Order of pole = 2.082
x[1] = 0.584
y[1] (analytic) = 2.1812055377893036606266300125238
y[1] (numeric) = 2.1812055377893048813744291479317
absolute error = 1.2207477991354079e-15
relative error = 5.5966655960935286942196394519632e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9883
Order of pole = 2.082
x[1] = 0.585
y[1] (analytic) = 2.1818671569847419769876299132626
y[1] (numeric) = 2.181867156984743204120307218929
absolute error = 1.2271326773056664e-15
relative error = 5.6242318574588080016220765038764e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9873
Order of pole = 2.082
x[1] = 0.586
y[1] (analytic) = 2.1825302148726586763892544017433
y[1] (numeric) = 2.1825302148726599099452524512044
absolute error = 1.2335559980494611e-15
relative error = 5.6519538178372198527158527747947e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9863
Order of pole = 2.082
x[1] = 0.587
y[1] (analytic) = 2.1831947133621935156242301434955
y[1] (numeric) = 2.183194713362194755642267183786
absolute error = 1.2400180370402905e-15
relative error = 5.6798325383017297938993321824488e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9853
Order of pole = 2.082
x[1] = 0.588
y[1] (analytic) = 2.1838606543691758578682182313069
y[1] (numeric) = 2.1838606543691771043872904245792
absolute error = 1.2465190721932723e-15
relative error = 5.7078690881645947419396801746807e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9843
Order of pole = 2.082
x[1] = 0.589
y[1] (analytic) = 2.1845280398161501508397807932199
y[1] (numeric) = 2.1845280398161514038991644789731
absolute error = 1.2530593836857532e-15
relative error = 5.7360645450502464602746729772266e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9833
Order of pole = 2.082
x[1] = 0.59
y[1] (analytic) = 2.1851968716324015385396723984441
y[1] (numeric) = 2.1851968716324027981789263765729
absolute error = 1.2596392539781288e-15
relative error = 5.7644199949688926341103211618628e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9823
Order of pole = 2.082
x[1] = 0.591
y[1] (analytic) = 2.1858671517539816073763048962235
y[1] (numeric) = 2.1858671517539828736352727311013
absolute error = 1.2662589678348778e-15
relative error = 5.7929365323908517814031725851706e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.3MB, time=10.14
Real estimate of pole used
Radius of convergence = 0.9813
Order of pole = 2.082
x[1] = 0.592
y[1] (analytic) = 2.186538882123734267490035803556
y[1] (numeric) = 2.1865388821237355404088481493653
absolute error = 1.2729188123458093e-15
relative error = 5.8216152603216134805305012909639e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9803
Order of pole = 2.082
x[1] = 0.593
y[1] (analytic) = 2.187212064691321770094779152712
y[1] (numeric) = 2.1872120646913230497138561002413
absolute error = 1.2796190769475293e-15
relative error = 5.8504572903776487720361341686153e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9793
Order of pole = 2.082
x[1] = 0.594
y[1] (analytic) = 2.187886701413250861661334255001
y[1] (numeric) = 2.1878867014132521480213877001269
absolute error = 1.2863600534451259e-15
relative error = 5.8794637428629653442714107855784e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9783
Order of pole = 2.082
x[1] = 0.595
y[1] (analytic) = 2.1885627942528990757727725738929
y[1] (numeric) = 2.1885627942529003689148086079714
absolute error = 1.2931420360340785e-15
relative error = 5.9086357468464286067656564502528e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9773
Order of pole = 2.082
x[1] = 0.596
y[1] (analytic) = 2.1892403451805411634882162736533
y[1] (numeric) = 2.1892403451805424634535375960435
absolute error = 1.2999653213223902e-15
relative error = 5.9379744402398418186450009009236e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9763
Order of pole = 2.082
x[1] = 0.597
y[1] (analytic) = 2.1899193561733756630573844688876
y[1] (numeric) = 2.1899193561733769698875928218373
absolute error = 1.3068302083529497e-15
relative error = 5.9674809698768108564383519533521e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9753
Order of pole = 2.082
x[1] = 0.598
y[1] (analytic) = 2.190599829215551609834375200237
y[1] (numeric) = 2.1905998292155529235713738263587
absolute error = 1.3137369986261217e-15
relative error = 5.9971564915923857966340540697914e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9743
Order of pole = 2.082
x[1] = 0.599
y[1] (analytic) = 2.1912817662981953872452931610007
y[1] (numeric) = 2.1912817662981967079312892835718
absolute error = 1.3206859961225711e-15
relative error = 6.0270021703035002363535048125135e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9733
Order of pole = 2.082
x[1] = 0.6
y[1] (analytic) = 2.1919651694194377196705256625065
y[1] (numeric) = 2.1919651694194390473480329888287
absolute error = 1.3276775073263222e-15
relative error = 6.0570191800902104969088243283131e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9723
Order of pole = 2.082
x[1] = 0.601
y[1] (analytic) = 2.1926500405844408081087127211842
y[1] (numeric) = 2.1926500405844421428205539692402
absolute error = 1.3347118412480560e-15
relative error = 6.0872087042777454927305792698008e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9713
Order of pole = 2.082
x[1] = 0.602
y[1] (analytic) = 2.1933363818054256094957519509524
y[1] (numeric) = 2.1933363818054269512850613996008
absolute error = 1.3417893094486484e-15
relative error = 6.1175719355193766309939301205418e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9703
Order of pole = 2.082
x[1] = 0.603
y[1] (analytic) = 2.1940241951016992605585256290076
y[1] (numeric) = 2.1940241951017006094687516919591
absolute error = 1.3489102260629515e-15
relative error = 6.1481100758801143263830650130786e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.3MB, time=10.35
Real estimate of pole used
Radius of convergence = 0.9693
Order of pole = 2.082
x[1] = 0.604
y[1] (analytic) = 2.1947134824996826470894363546594
y[1] (numeric) = 2.1947134824996840031643441784815
absolute error = 1.3560749078238221e-15
relative error = 6.1788243369212463330676164666576e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9683
Order of pole = 2.082
x[1] = 0.605
y[1] (analytic) = 2.195404246032938119534289627739
y[1] (numeric) = 2.1954042460329394828179637141373
absolute error = 1.3632836740863983e-15
relative error = 6.2097159397857184585682696876219e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9673
Order of pole = 2.082
x[1] = 0.606
y[1] (analytic) = 2.1960964877421973557925669286194
y[1] (numeric) = 2.1960964877421987263294137812479
absolute error = 1.3705368468526285e-15
relative error = 6.2407861152843736811500906050387e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9663
Order of pole = 2.082
x[1] = 0.607
y[1] (analytic) = 2.1967902096753893721356919844515
y[1] (numeric) = 2.1967902096753907499704427805074
absolute error = 1.3778347507960559e-15
relative error = 6.2720361039830601656320880254773e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9653
Order of pole = 2.082
x[1] = 0.608
y[1] (analytic) = 2.1974854138876686831555063594275
y[1] (numeric) = 2.1974854138876700683332196462865
absolute error = 1.3851777132868590e-15
relative error = 6.3034671562906067900535969001022e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9643
Order of pole = 2.082
x[1] = 0.609
y[1] (analytic) = 2.1981821024414436116618388195463
y[1] (numeric) = 2.1981821024414450042279032367012
absolute error = 1.3925660644171549e-15
relative error = 6.3350805325476934347014080815550e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9633
Order of pole = 2.082
x[1] = 0.61
y[1] (analytic) = 2.1988802774064047494547766086059
y[1] (numeric) = 2.1988802774064061494549136351709
absolute error = 1.4000001370265650e-15
relative error = 6.3668775031166104472438452160352e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9623
Order of pole = 2.082
x[1] = 0.611
y[1] (analytic) = 2.1995799408595535699040263514274
y[1] (numeric) = 2.1995799408595549773842930794748
absolute error = 1.4074802667280474e-15
relative error = 6.3988593484719230544115647700401e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9613
Order of pole = 2.082
x[1] = 0.612
y[1] (analytic) = 2.2002810948852311932745882975126
y[1] (numeric) = 2.2002810948852326082813802315127
absolute error = 1.4150067919340001e-15
relative error = 6.4310273592920555162268595151158e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9603
Order of pole = 2.082
x[1] = 0.613
y[1] (analytic) = 2.2009837415751473057448605638081
y[1] (numeric) = 2.2009837415751487283249144464439
absolute error = 1.4225800538826358e-15
relative error = 6.4633828365517947620130378627697e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9593
Order of pole = 2.082
x[1] = 0.614
y[1] (analytic) = 2.2016878830284092330702404648652
y[1] (numeric) = 2.2016878830284106632706371294988
absolute error = 1.4302003966646336e-15
relative error = 6.4959270916157336608492382465991e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9583
Order of pole = 2.082
x[1] = 0.615
y[1] (analytic) = 2.2023935213515511698522984739584
y[1] (numeric) = 2.2023935213515526077204657240286
absolute error = 1.4378681672500702e-15
relative error = 6.5286614463326617418668631354300e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.3MB, time=10.55
Real estimate of pole used
Radius of convergence = 0.9573
Order of pole = 2.082
x[1] = 0.616
y[1] (analytic) = 2.2031006586585635653806673867987
y[1] (numeric) = 2.2031006586585650109643829024309
absolute error = 1.4455837155156322e-15
relative error = 6.5615872331309065939160741590324e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9563
Order of pole = 2.082
x[1] = 0.617
y[1] (analytic) = 2.2038092970709226670219154132421
y[1] (numeric) = 2.2038092970709241203693096853577
absolute error = 1.4533473942721156e-15
relative error = 6.5947057951146495579855917904621e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9553
Order of pole = 2.082
x[1] = 0.618
y[1] (analytic) = 2.2045194387176202221368577605403
y[1] (numeric) = 2.2045194387176216832964170527538
absolute error = 1.4611595592922135e-15
relative error = 6.6280184861612161033863328563049e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9543
Order of pole = 2.082
x[1] = 0.619
y[1] (analytic) = 2.2052310857351933395150073587541
y[1] (numeric) = 2.2052310857351948085355766973503
absolute error = 1.4690205693385962e-15
relative error = 6.6615266710193557608340125717264e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9533
Order of pole = 2.082
x[1] = 0.62
y[1] (analytic) = 2.2059442402677545113221722854327
y[1] (numeric) = 2.2059442402677559882529584777202
absolute error = 1.4769307861922875e-15
relative error = 6.6952317254085246058506610812849e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9523
Order of pole = 2.082
x[1] = 0.621
y[1] (analytic) = 2.2066589044670217965645757490443
y[1] (numeric) = 2.2066589044670232814551504303842
absolute error = 1.4848905746813399e-15
relative error = 6.7291350361191782389336553554504e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9513
Order of pole = 2.082
x[1] = 0.622
y[1] (analytic) = 2.2073750804923491670803047714707
y[1] (numeric) = 2.2073750804923506599806074812827
absolute error = 1.4929003027098120e-15
relative error = 6.7632380011140858776867293727322e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9503
Order of pole = 2.082
x[1] = 0.623
y[1] (analytic) = 2.2080927705107570170763865578527
y[1] (numeric) = 2.2080927705107585180367278449057
absolute error = 1.5009603412870530e-15
relative error = 6.7975420296306833654885187251752e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9493
Order of pole = 2.082
x[1] = 0.624
y[1] (analytic) = 2.208811976696962837237347552099
y[1] (numeric) = 2.2088119766969643463084121093955
absolute error = 1.5090710645572965e-15
relative error = 6.8320485422844706016869816677743e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9483
Order of pole = 2.082
x[1] = 0.625
y[1] (analytic) = 2.2095327012334120544387299496412
y[1] (numeric) = 2.2095327012334135716715797792084
absolute error = 1.5172328498295672e-15
relative error = 6.8667589711734651901867560918438e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9473
Order of pole = 2.082
x[1] = 0.626
y[1] (analytic) = 2.2102549463103090381067245830799
y[1] (numeric) = 2.2102549463103105635528021909855
absolute error = 1.5254460776079056e-15
relative error = 6.9016747599837308288072887450286e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=206.0MB, alloc=4.3MB, time=10.75
Real estimate of pole used
Radius of convergence = 0.9463
Order of pole = 2.082
x[1] = 0.627
y[1] (analytic) = 2.2109787141256482742728282252082
y[1] (numeric) = 2.2109787141256498079839598471205
absolute error = 1.5337111316219123e-15
relative error = 6.9367973640959830526080026501926e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9453
Order of pole = 2.082
x[1] = 0.628
y[1] (analytic) = 2.2117040068852457083802480879995
y[1] (numeric) = 2.2117040068852472504086469456174
absolute error = 1.5420283988576179e-15
relative error = 6.9721282506932948005869255168263e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9442
Order of pole = 2.082
x[1] = 0.629
y[1] (analytic) = 2.2124308268027702579066572625857
y[1] (numeric) = 2.2124308268027718083049268512657
absolute error = 1.5503982695886800e-15
relative error = 7.0076688988699038451789074736405e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9432
Order of pole = 2.082
x[1] = 0.63
y[1] (analytic) = 2.213159176099775495875852677753
y[1] (numeric) = 2.2131591760997770546969900856661
absolute error = 1.5588211374079131e-15
relative error = 7.0434207997411435159436234630040e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9422
Order of pole = 2.082
x[1] = 0.631
y[1] (analytic) = 2.2138890570057315063388824935197
y[1] (numeric) = 2.2138890570057330736362817526745
absolute error = 1.5672973992591548e-15
relative error = 7.0793854565545072195459906943475e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9412
Order of pole = 2.082
x[1] = 0.632
y[1] (analytic) = 2.2146204717580569129132933392159
y[1] (numeric) = 2.2146204717580584887407488086863
absolute error = 1.5758274554694704e-15
relative error = 7.1155643848018513276089604489654e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9402
Order of pole = 2.082
x[1] = 0.633
y[1] (analytic) = 2.2153534226021510814773001063353
y[1] (numeric) = 2.2153534226021526658890098880388
absolute error = 1.5844117097817035e-15
relative error = 7.1519591123327657855882255728251e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9392
Order of pole = 2.082
x[1] = 0.634
y[1] (analytic) = 2.2160879117914264981239027764462
y[1] (numeric) = 2.2160879117914280911744721638187
absolute error = 1.5930505693873725e-15
relative error = 7.1885711794691069387447018425003e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9382
Order of pole = 2.082
x[1] = 0.635
y[1] (analytic) = 2.2168239415873413234882666718305
y[1] (numeric) = 2.2168239415873429252327116317518
absolute error = 1.6017444449599213e-15
relative error = 7.2254021391207249438821719670501e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9372
Order of pole = 2.082
x[1] = 0.636
y[1] (analytic) = 2.2175615142594321245700452366493
y[1] (numeric) = 2.2175615142594337350637959249735
absolute error = 1.6104937506883242e-15
relative error = 7.2624535569023805867427826794554e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9362
Order of pole = 2.082
x[1] = 0.637
y[1] (analytic) = 2.2183006320853467851807586718735
y[1] (numeric) = 2.2183006320853484044796629829264
absolute error = 1.6192989043110529e-15
relative error = 7.2997270112518819166492957540758e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9352
Order of pole = 2.082
x[1] = 0.638
y[1] (analytic) = 2.2190412973508775961548481478901
y[1] (numeric) = 2.2190412973508792243151752982972
absolute error = 1.6281603271504071e-15
relative error = 7.3372240935494421524530722011459e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.3MB, time=10.95
Real estimate of pole used
Radius of convergence = 0.9342
Order of pole = 2.082
x[1] = 0.639
y[1] (analytic) = 2.2197835123499945264716046018773
y[1] (numeric) = 2.219783512349996163550048749092
absolute error = 1.6370784441472147e-15
relative error = 7.3749464082382805463847331434676e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9332
Order of pole = 2.082
x[1] = 0.64
y[1] (analytic) = 2.2205272793848786764438239975253
y[1] (numeric) = 2.22052727938488032249750789343
absolute error = 1.6460536838959047e-15
relative error = 7.4128955729464747382948401227162e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9322
Order of pole = 2.082
x[1] = 0.641
y[1] (analytic) = 2.221272600765955914137768094818
y[1] (numeric) = 2.2212726007659575692242467747774
absolute error = 1.6550864786799594e-15
relative error = 7.4510732186100888299491325103266e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9312
Order of pole = 2.082
x[1] = 0.642
y[1] (analytic) = 2.2220194788119306961978119674057
y[1] (numeric) = 2.2220194788119323603750764751523
absolute error = 1.6641772645077466e-15
relative error = 7.4894809895975747544530585794914e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9302
Order of pole = 2.082
x[1] = 0.643
y[1] (analytic) = 2.2227679158498200742580374423526
y[1] (numeric) = 2.2227679158498217475845185910937
absolute error = 1.6733264811487411e-15
relative error = 7.5281205438354831752258186043460e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9292
Order of pole = 2.082
x[1] = 0.644
y[1] (analytic) = 2.2235179142149878881319860573754
y[1] (numeric) = 2.2235179142149895706665582275108
absolute error = 1.6825345721701354e-15
relative error = 7.5669935529354777379796940082596e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9282
Order of pole = 2.082
x[1] = 0.645
y[1] (analytic) = 2.2242694762511791469808167776354
y[1] (numeric) = 2.2242694762511808387828017514836
absolute error = 1.6918019849738482e-15
relative error = 7.6061017023226855910696539427624e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9272
Order of pole = 2.082
x[1] = 0.646
y[1] (analytic) = 2.2250226043105545996692233393221
y[1] (numeric) = 2.225022604310556300798394173255
absolute error = 1.7011291708339329e-15
relative error = 7.6454466913653881978587907147077e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9262
Order of pole = 2.082
x[1] = 0.647
y[1] (analytic) = 2.2257773007537254955276544503777
y[1] (numeric) = 2.2257773007537272060442393847693
absolute error = 1.7105165849343916e-15
relative error = 7.6850302335060712404181813089809e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9252
Order of pole = 2.082
x[1] = 0.648
y[1] (analytic) = 2.2265335679497885367486479477148
y[1] (numeric) = 2.2265335679497902567133343551147
absolute error = 1.7199646864073999e-15
relative error = 7.7248540563938514245542592712933e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9242
Order of pole = 2.082
x[1] = 0.649
y[1] (analytic) = 2.2272914082763610236544381614512
y[1] (numeric) = 2.2272914082763627531283765333981
absolute error = 1.7294739383719469e-15
relative error = 7.7649199020182938663244305200926e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9232
Order of pole = 2.082
x[1] = 0.65
y[1] (analytic) = 2.2280508241196161940824249547138
y[1] (numeric) = 2.2280508241196179331272329276095
absolute error = 1.7390448079728957e-15
relative error = 7.8052295268446377011636238683023e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.3MB, time=11.15
Real estimate of pole used
Radius of convergence = 0.9222
Order of pole = 2.082
x[1] = 0.651
y[1] (analytic) = 2.2288118178743187581446039856814
y[1] (numeric) = 2.2288118178743205068223704061498
absolute error = 1.7486777664204684e-15
relative error = 7.8457847019504416342210904358805e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9212
Order of pole = 2.082
x[1] = 0.652
y[1] (analytic) = 2.2295743919438606296266514785814
y[1] (numeric) = 2.2295743919438623879999405087447
absolute error = 1.7583732890301633e-15
relative error = 7.8865872131636776713308744561617e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9202
Order of pole = 2.082
x[1] = 0.653
y[1] (analytic) = 2.2303385487402968553020340029206
y[1] (numeric) = 2.2303385487402986234338892660261
absolute error = 1.7681318552631055e-15
relative error = 7.9276388612022720064118983320558e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9192
Order of pole = 2.082
x[1] = 0.654
y[1] (analytic) = 2.2311042906843817434462752647102
y[1] (numeric) = 2.2311042906843835214002240315506
absolute error = 1.7779539487668404e-15
relative error = 7.9689414618151292017558051814783e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9182
Order of pole = 2.082
x[1] = 0.655
y[1] (analytic) = 2.2318716202056051928463585382168
y[1] (numeric) = 2.2318716202056069806864159547885
absolute error = 1.7878400574165717e-15
relative error = 8.0104968459246402582951959939592e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9172
Order of pole = 2.082
x[1] = 0.656
y[1] (analytic) = 2.2326405397422292236101759492136
y[1] (numeric) = 2.232640539742231021400849306066
absolute error = 1.7977906733568524e-15
relative error = 8.0523068597707060317789450128548e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9162
Order of pole = 2.082
x[1] = 0.657
y[1] (analytic) = 2.2334110517413247110909552073995
y[1] (numeric) = 2.2334110517413265188972482511311
absolute error = 1.8078062930437316e-15
relative error = 8.0943733650562817975809008341323e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9152
Order of pole = 2.082
x[1] = 0.658
y[1] (analytic) = 2.2341831586588083242517014324096
y[1] (numeric) = 2.2341831586588101421391187197743
absolute error = 1.8178874172873647e-15
relative error = 8.1366982390944701894312651581487e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9142
Order of pole = 2.082
x[1] = 0.659
y[1] (analytic) = 2.234956862959479669804887289874
y[1] (numeric) = 2.2349568629594814978394385849646
absolute error = 1.8280345512950906e-15
relative error = 8.1792833749571717184022716773450e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9132
Order of pole = 2.082
x[1] = 0.66
y[1] (analytic) = 2.2357321671170586434729096259867
y[1] (numeric) = 2.2357321671170604817211143409709
absolute error = 1.8382482047149842e-15
relative error = 8.2221306816253230282176057747882e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9122
Order of pole = 2.082
x[1] = 0.661
y[1] (analytic) = 2.2365090736142229897252060453324
y[1] (numeric) = 2.2365090736142248382540977252194
absolute error = 1.8485288916798870e-15
relative error = 8.2652420841407283198964643007114e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.3MB, time=11.35
Real estimate of pole used
Radius of convergence = 0.9112
Order of pole = 2.082
x[1] = 0.662
y[1] (analytic) = 2.2372875849426460713583913113087
y[1] (numeric) = 2.2372875849426479302355221632324
absolute error = 1.8588771308519237e-15
relative error = 8.3086195237595121108563161424755e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9102
Order of pole = 2.082
x[1] = 0.663
y[1] (analytic) = 2.2380677036030348502963319652502
y[1] (numeric) = 2.2380677036030367195897774327599
absolute error = 1.8692934454675097e-15
relative error = 8.3522649581072079620428356958263e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9092
Order of pole = 2.082
x[1] = 0.664
y[1] (analytic) = 2.2388494321051680809977290731372
y[1] (numeric) = 2.2388494321051699607760924559934
absolute error = 1.8797783633828562e-15
relative error = 8.3961803613355057561939365710700e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9082
Order of pole = 2.082
x[1] = 0.665
y[1] (analytic) = 2.2396327729679347178695244414661
y[1] (numeric) = 2.239632772967936608201941561444
absolute error = 1.8903324171199779e-15
relative error = 8.4403677242806724066294147325934e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9072
Order of pole = 2.082
x[1] = 0.666
y[1] (analytic) = 2.2404177287193725380952859305868
y[1] (numeric) = 2.2404177287193744390514298437979
absolute error = 1.9009561439132111e-15
relative error = 8.4848290546236732811956854344636e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9062
Order of pole = 2.082
x[1] = 0.667
y[1] (analytic) = 2.2412043018967069812986635790197
y[1] (numeric) = 2.2412043018967088929487493352655
absolute error = 1.9116500857562458e-15
relative error = 8.5295663770520027581577981743630e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9052
Order of pole = 2.082
x[1] = 0.668
y[1] (analytic) = 2.2419924950463902074730410908424
y[1] (numeric) = 2.2419924950463921298878305405234
absolute error = 1.9224147894496810e-15
relative error = 8.5745817334232572327999460059122e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9042
Order of pole = 2.082
x[1] = 0.669
y[1] (analytic) = 2.2427823107241403746196377956708
y[1] (numeric) = 2.2427823107241423078704444447785
absolute error = 1.9332508066491077e-15
relative error = 8.6198771829304627909150338188683e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9032
Order of pole = 2.082
x[1] = 0.67
y[1] (analytic) = 2.243573751494981137547545443231
y[1] (numeric) = 2.2435737514949830817062393569579
absolute error = 1.9441586939137269e-15
relative error = 8.6654548022691821574114858438445e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9022
Order of pole = 2.082
x[1] = 0.671
y[1] (analytic) = 2.2443668199332813693005131290614
y[1] (numeric) = 2.2443668199332833244395258845694
absolute error = 1.9551390127555080e-15
relative error = 8.7113166858064169389505572149233e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9012
Order of pole = 2.082
x[1] = 0.672
y[1] (analytic) = 2.2451615186227951066867232624988
y[1] (numeric) = 2.2451615186227970728790529513953
absolute error = 1.9661923296888965e-15
relative error = 8.7574649457513366683338802581588e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.9002
Order of pole = 2.082
x[1] = 0.673
y[1] (analytic) = 2.2459578501567017213993327919074
y[1] (numeric) = 2.2459578501567036987185490729822
absolute error = 1.9773192162810748e-15
relative error = 8.8039017123278433059853253200061e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.3MB, time=11.55
Real estimate of pole used
Radius of convergence = 0.8992
Order of pole = 2.082
x[1] = 0.674
y[1] (analytic) = 2.2467558171376463182271879154443
y[1] (numeric) = 2.2467558171376483067474371182301
absolute error = 1.9885202492027858e-15
relative error = 8.8506291339490060328694965326102e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8982
Order of pole = 2.082
x[1] = 0.675
y[1] (analytic) = 2.2475554221777803618668582602831
y[1] (numeric) = 2.2475554221777823616628685400068
absolute error = 1.9997960102797237e-15
relative error = 8.8976493773933774318836704802976e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8972
Order of pole = 2.082
x[1] = 0.676
y[1] (analytic) = 2.2483566678988025338589790523688
y[1] (numeric) = 2.2483566678988045450060655968694
absolute error = 2.0111470865445006e-15
relative error = 8.9449646279832207454164305297493e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8962
Order of pole = 2.082
x[1] = 0.677
y[1] (analytic) = 2.2491595569319998211838381774053
y[1] (numeric) = 2.2491595569320018437579084666013
absolute error = 2.0225740702891960e-15
relative error = 8.9925770897646710842587490644830e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8952
Order of pole = 2.082
x[1] = 0.678
y[1] (analytic) = 2.2499640919182888380632003185928
y[1] (numeric) = 2.249964091918290872140759437088
absolute error = 2.0340775591184952e-15
relative error = 9.0404889856898484491447417749515e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8942
Order of pole = 2.082
x[1] = 0.679
y[1] (analytic) = 2.2507702755082573825275236263311
y[1] (numeric) = 2.2507702755082594281856796297558
absolute error = 2.0456581560034247e-15
relative error = 9.0887025578009496448503081126121e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8932
Order of pole = 2.082
x[1] = 0.68
y[1] (analytic) = 2.2515781103622062293199967204696
y[1] (numeric) = 2.2515781103622082866364660561621
absolute error = 2.0573164693356925e-15
relative error = 9.1372200674163451397713754634871e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8922
Order of pole = 2.082
x[1] = 0.681
y[1] (analytic) = 2.2523875991501911607212063497531
y[1] (numeric) = 2.2523875991501932297743193323924
absolute error = 2.0690531129826393e-15
relative error = 9.1860437953186983515909727802540e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8912
Order of pole = 2.082
x[1] = 0.682
y[1] (analytic) = 2.2531987445520652368907398513178
y[1] (numeric) = 2.2531987445520673177594461941278
absolute error = 2.0808687063428100e-15
relative error = 9.2351760419451398161598971465798e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8902
Order of pole = 2.082
x[1] = 0.683
y[1] (analytic) = 2.2540115492575213073346327934349
y[1] (numeric) = 2.2540115492575234000985071955862
absolute error = 2.0927638744021513e-15
relative error = 9.2846191275795125680438943227497e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8892
Order of pole = 2.082
x[1] = 0.684
y[1] (analytic) = 2.2548260159661347651202919878734
y[1] (numeric) = 2.2548260159661368698595397787183
absolute error = 2.1047392477908449e-15
relative error = 9.3343753925467213587107917224627e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8882
Order of pole = 2.082
memory used=225.0MB, alloc=4.3MB, time=11.75
x[1] = 0.685
y[1] (analytic) = 2.2556421473874065454733585778446
y[1] (numeric) = 2.2556421473874086622688214186279
absolute error = 2.1167954628407833e-15
relative error = 9.3844471974092070953285647879792e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8872
Order of pole = 2.082
x[1] = 0.686
y[1] (analytic) = 2.2564599462408063704039263100876
y[1] (numeric) = 2.2564599462408084993370879537834
absolute error = 2.1289331616436958e-15
relative error = 9.4348369231655704138873959941321e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8862
Order of pole = 2.082
x[1] = 0.687
y[1] (analytic) = 2.2572794152558162410225975650574
y[1] (numeric) = 2.2572794152558183821755896749915
absolute error = 2.1411529921099341e-15
relative error = 9.4855469714513761379957582155634e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8852
Order of pole = 2.082
x[1] = 0.688
y[1] (analytic) = 2.2581005571719741792200454405323
y[1] (numeric) = 2.2581005571719763326756534684571
absolute error = 2.1534556080279248e-15
relative error = 9.5365797647421609144893244160963e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8842
Order of pole = 2.082
x[1] = 0.689
y[1] (analytic) = 2.2589233747389182203970553679296
y[1] (numeric) = 2.2589233747389203862387244922263
absolute error = 2.1658416691242967e-15
relative error = 9.5879377465586688391295184969718e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8832
Order of pole = 2.082
x[1] = 0.69
y[1] (analytic) = 2.259747870716430658945445607569
y[1] (numeric) = 2.2597478707164328372572867322622
absolute error = 2.1783118411246932e-15
relative error = 9.6396233816743503639992900810540e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8822
Order of pole = 2.082
x[1] = 0.691
y[1] (analytic) = 2.2605740478744825481938137532761
y[1] (numeric) = 2.260574047874484739060609568552
absolute error = 2.1908667958152759e-15
relative error = 9.6916391563251410248548462610217e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8812
Order of pole = 2.082
x[1] = 0.692
y[1] (analytic) = 2.2614019089932784565457273263219
y[1] (numeric) = 2.261401908993280660052938431252
absolute error = 2.2035072111049301e-15
relative error = 9.7439875784215567476671187577662e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8802
Order of pole = 2.082
x[1] = 0.693
y[1] (analytic) = 2.2622314568633014815517719162198
y[1] (numeric) = 2.2622314568633036977855430043999
absolute error = 2.2162337710881801e-15
relative error = 9.7966711777631299358793584164671e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8791
Order of pole = 2.082
x[1] = 0.694
y[1] (analytic) = 2.2630626942853585236707914082017
y[1] (numeric) = 2.263062694285360752717957517025
absolute error = 2.2290471661088233e-15
relative error = 9.8496925062552152555627583541443e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8781
Order of pole = 2.082
x[1] = 0.695
y[1] (analytic) = 2.2638956240706258214897029156932
y[1] (numeric) = 2.2638956240706280634377957399851
absolute error = 2.2419480928242919e-15
relative error = 9.9030541381281929922744947542534e-14 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8771
Order of pole = 2.082
x[1] = 0.696
y[1] (analytic) = 2.2647302490406947501854454169814
y[1] (numeric) = 2.2647302490406970051226996877339
absolute error = 2.2549372542707525e-15
relative error = 9.9567586701591043186799893032897e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.3MB, time=11.95
Real estimate of pole used
Radius of convergence = 0.8761
Order of pole = 2.082
x[1] = 0.697
y[1] (analytic) = 2.2655665720276178850269270996325
y[1] (numeric) = 2.2655665720276201530422870285835
absolute error = 2.2680153599289510e-15
relative error = 1.0010808721895739833370089303840e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8751
Order of pole = 2.082
x[1] = 0.698
y[1] (analytic) = 2.2664045958739553317292733803101
y[1] (numeric) = 2.2664045958739576129123991711247
absolute error = 2.2811831257908146e-15
relative error = 1.0065206935883222004068693414573e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8741
Order of pole = 2.082
x[1] = 0.699
y[1] (analytic) = 2.2672443234328213254872468430288
y[1] (numeric) = 2.2672443234328236199285212698464
absolute error = 2.2944412744268176e-15
relative error = 1.0119955977893099454802657977059e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8731
Order of pole = 2.082
x[1] = 0.7
y[1] (analytic) = 2.2680857575679311005294132926142
y[1] (numeric) = 2.268085757567933408319948346738
absolute error = 2.3077905350541238e-15
relative error = 1.0175058537154997798014195627868e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8721
Order of pole = 2.082
x[1] = 0.701
y[1] (analytic) = 2.2689289011536480320494661350163
y[1] (numeric) = 2.2689289011536503532811097405288
absolute error = 2.3212316436055125e-15
relative error = 1.0230517326590845935864497633888e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8711
Order of pole = 2.082
x[1] = 0.702
y[1] (analytic) = 2.2697737570750310523860957708006
y[1] (numeric) = 2.269773757075033387151438569901
absolute error = 2.3347653427991004e-15
relative error = 1.0286335083051719966433029654552e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8701
Order of pole = 2.082
x[1] = 0.703
y[1] (analytic) = 2.2706203282278823433379030374283
y[1] (numeric) = 2.2706203282278846917302852462958
absolute error = 2.3483923822088675e-15
relative error = 1.0342514567557328124272230682327e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8691
Order of pole = 2.082
x[1] = 0.704
y[1] (analytic) = 2.2714686175187953065151073909101
y[1] (numeric) = 2.2714686175187976686286257269089
absolute error = 2.3621135183359988e-15
relative error = 1.0399058565538176319000875210545e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8681
Order of pole = 2.082
x[1] = 0.705
y[1] (analytic) = 2.2723186278652028136451929257121
y[1] (numeric) = 2.2723186278652051895747076067631
absolute error = 2.3759295146810510e-15
relative error = 1.0455969887080442189372851212326e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8671
Order of pole = 2.082
x[1] = 0.706
y[1] (analytic) = 2.2731703621954257387651699577365
y[1] (numeric) = 2.2731703621954281286063117746924
absolute error = 2.3898411418169559e-15
relative error = 1.0513251367173596417295786844216e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8661
Order of pole = 2.082
x[1] = 0.707
y[1] (analytic) = 2.2740238234487217742488082200897
y[1] (numeric) = 2.2740238234487241780979856829596
absolute error = 2.4038491774628699e-15
relative error = 1.0570905865960799727474506523049e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8651
Order of pole = 2.082
x[1] = 0.708
y[1] (analytic) = 2.2748790145753345326330212436224
y[1] (numeric) = 2.2748790145753369505874278025041
absolute error = 2.4179544065588817e-15
relative error = 1.0628936268992115692044997937304e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.3MB, time=12.15
Real estimate of pole used
Radius of convergence = 0.8641
Order of pole = 2.082
x[1] = 0.709
y[1] (analytic) = 2.2757359385365429362235517297003
y[1] (numeric) = 2.2757359385365453683811730712879
absolute error = 2.4321576213415876e-15
relative error = 1.0687345487480567383697770019297e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8631
Order of pole = 2.082
x[1] = 0.71
y[1] (analytic) = 2.2765945983047108964762262047543
y[1] (numeric) = 2.2765945983047133429358476253013
absolute error = 2.4464596214205470e-15
relative error = 1.0746136458561079800144546737582e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8621
Order of pole = 2.082
x[1] = 0.711
y[1] (analytic) = 2.2774549968633372851663155261067
y[1] (numeric) = 2.277454996863339746027529381736
absolute error = 2.4608612138556293e-15
relative error = 1.0805312145552343615611987119712e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8611
Order of pole = 2.082
x[1] = 0.712
y[1] (analytic) = 2.2783171372071061993749574556623
y[1] (numeric) = 2.2783171372071086747381706909244
absolute error = 2.4753632132352621e-15
relative error = 1.0864875538221629906739788931558e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8601
Order of pole = 2.082
x[1] = 0.713
y[1] (analytic) = 2.2791810223419375223381701198588
y[1] (numeric) = 2.2791810223419400123046118754527
absolute error = 2.4899664417555939e-15
relative error = 1.0924829653052599793220208437590e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8591
Order of pole = 2.082
x[1] = 0.714
y[1] (analytic) = 2.2800466552850377822207123368858
y[1] (numeric) = 2.2800466552850402868924416374683
absolute error = 2.5046717293005825e-15
relative error = 1.0985177533516143931074850513603e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8581
Order of pole = 2.082
x[1] = 0.715
y[1] (analytic) = 2.2809140390649513108939301404405
y[1] (numeric) = 2.2809140390649538303738436634612
absolute error = 2.5194799135230207e-15
relative error = 1.1045922250344288345102210005917e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8571
Order of pole = 2.082
x[1] = 0.716
y[1] (analytic) = 2.2817831767216117048137700070342
y[1] (numeric) = 2.2817831767216142392056099335467
absolute error = 2.5343918399265125e-15
relative error = 1.1107066901807209887810260847746e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8561
Order of pole = 2.082
x[1] = 0.717
y[1] (analytic) = 2.2826540713063935901123399641789
y[1] (numeric) = 2.2826540713063961395207019125889
absolute error = 2.5494083619484100e-15
relative error = 1.1168614613993391235950188291706e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8551
Order of pole = 2.082
x[1] = 0.718
y[1] (analytic) = 2.2835267258821646940337616022256
y[1] (numeric) = 2.2835267258821672585641026459513
absolute error = 2.5645303410437257e-15
relative error = 1.1230568541092964847661914818079e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8541
Order of pole = 2.082
x[1] = 0.719
y[1] (analytic) = 2.2844011435233382248625807355185
y[1] (numeric) = 2.2844011435233408046212275055499
absolute error = 2.5797586467700314e-15
relative error = 1.1292931865684279726311937425103e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8531
memory used=236.5MB, alloc=4.3MB, time=12.35
Order of pole = 2.082
x[1] = 0.72
y[1] (analytic) = 2.2852773273159255625106937811594
y[1] (numeric) = 2.2852773273159281576048506545168
absolute error = 2.5950941568733574e-15
relative error = 1.1355707799023735566902753390010e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8521
Order of pole = 2.082
x[1] = 0.721
y[1] (analytic) = 2.286155280357589261946602588617
y[1] (numeric) = 2.2861552803575918724843599637204
absolute error = 2.6105377573751034e-15
relative error = 1.1418899581338918556077541163407e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8511
Order of pole = 2.082
x[1] = 0.722
y[1] (analytic) = 2.2870350057576963716688342237229
y[1] (numeric) = 2.287035005757698997759176883699
absolute error = 2.6260903426599761e-15
relative error = 1.1482510482125088623225714027681e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8501
Order of pole = 2.082
x[1] = 0.723
y[1] (analytic) = 2.2879165066373720694435558701423
y[1] (numeric) = 2.2879165066373747111963714351087
absolute error = 2.6417528155649664e-15
relative error = 1.1546543800445058497685261536359e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8491
Order of pole = 2.082
x[1] = 0.724
y[1] (analytic) = 2.2887997861295536175447803650893
y[1] (numeric) = 2.2887997861295562750708678344676
absolute error = 2.6575260874693783e-15
relative error = 1.1611002865232501195054865119709e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8481
Order of pole = 2.082
x[1] = 0.725
y[1] (analytic) = 2.2896848473790446397540967601086
y[1] (numeric) = 2.2896848473790473131651751460336
absolute error = 2.6734110783859250e-15
relative error = 1.1675891035598737177913196416509e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8471
Order of pole = 2.082
x[1] = 0.726
y[1] (analytic) = 2.2905716935425697223955745400089
y[1] (numeric) = 2.2905716935425724118042915929143
absolute error = 2.6894087170529054e-15
relative error = 1.1741211701143042121198145853556e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8461
Order of pole = 2.082
x[1] = 0.727
y[1] (analytic) = 2.2914603277888293417003816132254
y[1] (numeric) = 2.2914603277888320472203226407005
absolute error = 2.7055199410274751e-15
relative error = 1.1806968282266519896166814862385e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8451
Order of pole = 2.082
x[1] = 0.728
y[1] (analytic) = 2.2923507532985551198147267969008
y[1] (numeric) = 2.2923507532985578415604235769266
absolute error = 2.7217456967800258e-15
relative error = 1.1873164230489584257172468440852e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8441
Order of pole = 2.082
x[1] = 0.729
y[1] (analytic) = 2.293242973264565411783989174158
y[1] (numeric) = 2.2932429732645681498709289638466
absolute error = 2.7380869397896886e-15
relative error = 1.1939803028773099436887677669382e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8431
Order of pole = 2.082
x[1] = 0.73
y[1] (analytic) = 2.2941369908918212258653313364992
y[1] (numeric) = 2.2941369908918239804099659774744
absolute error = 2.7545446346409752e-15
relative error = 1.2006888191843223038708950512770e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8421
Order of pole = 2.082
x[1] = 0.731
y[1] (analytic) = 2.295032809397482479540713101157
y[1] (numeric) = 2.295032809397485250660468222729
absolute error = 2.7711197551215720e-15
relative error = 1.2074423266519998713011668479095e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.3MB, time=12.55
Real estimate of pole used
Radius of convergence = 0.8411
Order of pole = 2.082
x[1] = 0.732
y[1] (analytic) = 2.2959304320109645936220287950544
y[1] (numeric) = 2.2959304320109673814353131163571
absolute error = 2.7878132843213027e-15
relative error = 1.2142411832049748443192489706772e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8401
Order of pole = 2.082
x[1] = 0.733
y[1] (analytic) = 2.2968298619739954268600866309728
y[1] (numeric) = 2.2968298619739982314863013632466
absolute error = 2.8046262147322738e-15
relative error = 1.2210857500441308759408356106373e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8391
Order of pole = 2.082
x[1] = 0.734
y[1] (analytic) = 2.2977311025406725534893350987139
y[1] (numeric) = 2.2977311025406753750488834489339
absolute error = 2.8215595483502200e-15
relative error = 1.2279763916806166245145865202151e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8381
Order of pole = 2.082
x[1] = 0.735
y[1] (analytic) = 2.2986341569775208861606207099052
y[1] (numeric) = 2.2986341569775237247749174869692
absolute error = 2.8386142967770640e-15
relative error = 1.2349134759702536520726203205341e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8371
Order of pole = 2.082
x[1] = 0.736
y[1] (analytic) = 2.2995390285635506467348359496629
y[1] (numeric) = 2.2995390285635535025263172743704
absolute error = 2.8557914813247075e-15
relative error = 1.2418973741483440617735869833826e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8361
Order of pole = 2.082
x[1] = 0.737
y[1] (analytic) = 2.3004457205903156874310880065578
y[1] (numeric) = 2.3004457205903185605232211266275
absolute error = 2.8730921331200697e-15
relative error = 1.2489284608648830180058740471058e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8351
Order of pole = 2.082
x[1] = 0.738
y[1] (analytic) = 2.3013542363619721648439899044454
y[1] (numeric) = 2.3013542363619750553612831158343
absolute error = 2.8905172932113889e-15
relative error = 1.2560071142201809586198222295854e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8341
Order of pole = 2.082
x[1] = 0.739
y[1] (analytic) = 2.3022645791953375693658482015365
y[1] (numeric) = 2.3022645791953404774338608773417
absolute error = 2.9080680126758052e-15
relative error = 1.2631337158009013221114235148488e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8331
Order of pole = 2.082
x[1] = 0.74
y[1] (analytic) = 2.3031767524199501125708976353428
y[1] (numeric) = 2.3031767524199530383162503635834
absolute error = 2.9257453527282406e-15
relative error = 1.2703086507165188419424497678442e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8321
Order of pole = 2.082
x[1] = 0.741
y[1] (analytic) = 2.3040907593781284751403151848554
y[1] (numeric) = 2.3040907593781314186907000164492
absolute error = 2.9435503848315938e-15
relative error = 1.2775323076362038638648236496239e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8311
Order of pole = 2.082
x[1] = 0.742
y[1] (analytic) = 2.305006603425031917928536228146
y[1] (numeric) = 2.3050066034250348794127270364129
absolute error = 2.9614841908082669e-15
relative error = 1.2848050788261380668948141689662e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8301
Order of pole = 2.082
x[1] = 0.743
y[1] (analytic) = 2.3059242879287207587933960561425
y[1] (numeric) = 2.3059242879287237383412590091852
absolute error = 2.9795478629530427e-15
relative error = 1.2921273601872675872419800194513e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.3MB, time=12.75
Real estimate of pole used
Radius of convergence = 0.8291
Order of pole = 2.082
x[1] = 0.744
y[1] (analytic) = 2.306843816270217217834833250583
y[1] (numeric) = 2.3068438162702202155773373979123
absolute error = 2.9977425041473293e-15
relative error = 1.2994995512934986434607658812708e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8281
Order of pole = 2.082
x[1] = 0.745
y[1] (analytic) = 2.307765191843566633709319662748
y[1] (numeric) = 2.3077651918435696497785476375397
absolute error = 3.0160692279747917e-15
relative error = 1.3069220554303420296194949828584e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8271
Order of pole = 2.082
x[1] = 0.746
y[1] (analytic) = 2.3086884180558990537098272842455
y[1] (numeric) = 2.3086884180559020882389861226328
absolute error = 3.0345291588383873e-15
relative error = 1.3143952796340115947459978696419e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8261
Order of pole = 2.082
x[1] = 0.747
y[1] (analytic) = 2.3096134983274912003240075550376
y[1] (numeric) = 2.3096134983274942534474396338631
absolute error = 3.0531234320788255e-15
relative error = 1.3219196347309832236224992300035e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8251
Order of pole = 2.082
x[1] = 0.748
y[1] (analytic) = 2.3105404360918288170063460090569
y[1] (numeric) = 2.3105404360918318888595401035266
absolute error = 3.0718531940944697e-15
relative error = 1.3294955353780199749644276674273e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8241
Order of pole = 2.082
x[1] = 0.749
y[1] (analytic) = 2.3114692347956693959233670453628
y[1] (numeric) = 2.3114692347956724866429695080641
absolute error = 3.0907196024627013e-15
relative error = 1.3371234001026695611927449470533e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8231
Order of pole = 2.082
x[1] = 0.75
y[1] (analytic) = 2.3123998978991052904545024936409
y[1] (numeric) = 2.3123998978991084001783285564063
absolute error = 3.1097238260627654e-15
relative error = 1.3448036513442403610580429235108e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8221
Order of pole = 2.082
x[1] = 0.751
y[1] (analytic) = 2.313332428875627215255006007754
y[1] (numeric) = 2.3133324288756303441220512078722
absolute error = 3.1288670452001182e-15
relative error = 1.3525367154952622495640437123378e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8211
Order of pole = 2.082
x[1] = 0.752
y[1] (analytic) = 2.314266831212188136711295691219
y[1] (numeric) = 2.3142668312121912848617474235142
absolute error = 3.1481504517322952e-15
relative error = 1.3603230229434381036748111827664e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8201
Order of pole = 2.082
x[1] = 0.753
y[1] (analytic) = 2.3152031084092675566433422859122
y[1] (numeric) = 2.3152031084092707242185914822352
absolute error = 3.1675752491963230e-15
relative error = 1.3681630081140934044475806336320e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8191
Order of pole = 2.082
x[1] = 0.754
y[1] (analytic) = 2.3161412639809361921331923232472
y[1] (numeric) = 2.3161412639809393792758452609402
absolute error = 3.1871426529376930e-15
relative error = 1.3760571095131293720388175030117e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.3MB, time=12.96
Real estimate of pole used
Radius of convergence = 0.8181
Order of pole = 2.082
x[1] = 0.755
y[1] (analytic) = 2.3170813014549210543834274603922
y[1] (numeric) = 2.3170813014549242612373177013124
absolute error = 3.2068538902409202e-15
relative error = 1.3840057697704871495759668341263e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8171
Order of pole = 2.082
x[1] = 0.756
y[1] (analytic) = 2.3180232243726709295343154497572
y[1] (numeric) = 2.3180232243726741562445159114642
absolute error = 3.2267102004617070e-15
relative error = 1.3920094356841290860522705941842e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8161
Order of pole = 2.082
x[1] = 0.757
y[1] (analytic) = 2.3189670362894222643936074974408
y[1] (numeric) = 2.318967036289425511106442658175
absolute error = 3.2467128351607342e-15
relative error = 1.4000685582645441224636632772233e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8151
Order of pole = 2.082
x[1] = 0.758
y[1] (analytic) = 2.319912740774265460058383867981
y[1] (numeric) = 2.3199127407742687269214421070833
absolute error = 3.2668630582391023e-15
relative error = 1.4081835927797846321968524419920e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.814
Order of pole = 2.082
x[1] = 0.759
y[1] (analytic) = 2.3208603414102115764340472344018
y[1] (numeric) = 2.3208603414102148635961933098458
absolute error = 3.2871621460754440e-15
relative error = 1.4163549988010410761513296329581e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.813
Order of pole = 2.082
x[1] = 0.76
y[1] (analytic) = 2.3218098417942594506815142338154
y[1] (numeric) = 2.3218098417942627582929018985461
absolute error = 3.3076113876647307e-15
relative error = 1.4245832402487616117180231141984e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.812
Order of pole = 2.082
x[1] = 0.761
y[1] (analytic) = 2.3227612455374632326498627836701
y[1] (numeric) = 2.3227612455374665608619475424683
absolute error = 3.3282120847587982e-15
relative error = 1.4328687854393247854515059568139e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.811
Order of pole = 2.082
x[1] = 0.762
y[1] (analytic) = 2.3237145562650003403781587908365
y[1] (numeric) = 2.3237145562650036893437107994486
absolute error = 3.3489655520086121e-15
relative error = 1.4412121071322713705343870273815e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.81
Order of pole = 2.082
x[1] = 0.763
y[1] (analytic) = 2.3246697776162398387769138290406
y[1] (numeric) = 2.3246697776162432086500309373386
absolute error = 3.3698731171082980e-15
relative error = 1.4496136825781033492393794101260e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.809
Order of pole = 2.082
x[1] = 0.764
y[1] (analytic) = 2.3256269132448112446266180893575
y[1] (numeric) = 2.3256269132448146355627390303193
absolute error = 3.3909361209409618e-15
relative error = 1.4580739935666580802409397033250e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.808
Order of pole = 2.082
x[1] = 0.765
y[1] (analytic) = 2.3265859668186737610580533794586
y[1] (numeric) = 2.3265859668186771732139711057804
absolute error = 3.4121559177263218e-15
relative error = 1.4665935264760640964583411482554e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.807
Order of pole = 2.082
x[1] = 0.766
y[1] (analytic) = 2.3275469420201859447066221526308
y[1] (numeric) = 2.3275469420201893782404973228111
absolute error = 3.4335338751701803e-15
relative error = 1.4751727723222875150009274418275e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.3MB, time=13.16
Real estimate of pole used
Radius of convergence = 0.806
Order of pole = 2.082
x[1] = 0.767
y[1] (analytic) = 2.3285098425461758087607335170664
y[1] (numeric) = 2.3285098425461792638321081328243
absolute error = 3.4550713746157579e-15
relative error = 1.4838122268092760575814558628731e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.805
Order of pole = 2.082
x[1] = 0.768
y[1] (analytic) = 2.3294746721080113651523689770483
y[1] (numeric) = 2.3294746721080148419221801739653
absolute error = 3.4767698111969170e-15
relative error = 1.4925123903797090519335177261132e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.804
Order of pole = 2.082
x[1] = 0.769
y[1] (analytic) = 2.3304414344316716091663123961783
y[1] (numeric) = 2.3304414344316751077969063894787
absolute error = 3.4986305939933004e-15
relative error = 1.5012737682663614779573500161663e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.803
Order of pole = 2.082
x[1] = 0.77
y[1] (analytic) = 2.3314101332578179497731734932087
y[1] (numeric) = 2.3314101332578214704283196806197
absolute error = 3.5206551461874110e-15
relative error = 1.5100968705440901165017958252180e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.802
Order of pole = 2.082
x[1] = 0.771
y[1] (analytic) = 2.3323807723418660890202652671271
y[1] (numeric) = 2.3323807723418696318651704907868
absolute error = 3.5428449052236597e-15
relative error = 1.5189822121824502812484320152942e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.801
Order of pole = 2.082
x[1] = 0.772
y[1] (analytic) = 2.3333533554540583538436163235351
y[1] (numeric) = 2.333353355454061919044939292944
absolute error = 3.5652013229694089e-15
relative error = 1.5279303130989516918866018539232e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.8
Order of pole = 2.082
x[1] = 0.773
y[1] (analytic) = 2.3343278863795364836939124030474
y[1] (numeric) = 2.3343278863795400714197782810856
absolute error = 3.5877258658780382e-15
relative error = 1.5369416982129616525592507282514e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.799
Order of pole = 2.082
x[1] = 0.774
y[1] (analytic) = 2.3353043689184148773989707993568
y[1] (numeric) = 2.3353043689184184878189859534181
absolute error = 3.6104200151540613e-15
relative error = 1.5460168975002646766879841728953e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.798
Order of pole = 2.082
x[1] = 0.775
y[1] (analytic) = 2.3362828068858543027154601462071
y[1] (numeric) = 2.3362828068858579360007270665291
absolute error = 3.6332852669203220e-15
relative error = 1.5551564460482871742165453614712e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.797
Order of pole = 2.082
x[1] = 0.776
y[1] (analytic) = 2.3372632041121360720529896372955
y[1] (numeric) = 2.337263204112139728376122024594
absolute error = 3.6563231323872985e-15
relative error = 1.5643608841119963206259155264048e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.796
Order of pole = 2.082
x[1] = 0.777
y[1] (analytic) = 2.338245564442736687884409552275
y[1] (numeric) = 2.3382455644427403674195475768197
absolute error = 3.6795351380245447e-15
relative error = 1.5736307571704819582488066040511e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.795
Order of pole = 2.082
memory used=255.5MB, alloc=4.3MB, time=13.35
x[1] = 0.778
y[1] (analytic) = 2.3392298917384029613871924699645
y[1] (numeric) = 2.3392298917384066643100182042631
absolute error = 3.7029228257342986e-15
relative error = 1.5829666159842309243902275367292e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.794
Order of pole = 2.082
x[1] = 0.779
y[1] (analytic) = 2.34021618987522760789210527488
y[1] (numeric) = 2.3402161898752313343798583021681
absolute error = 3.7264877530272881e-15
relative error = 1.5923690166531032294611651847021e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.793
Order of pole = 2.082
x[1] = 0.78
y[1] (analytic) = 2.3412044627447253227470395680139
y[1] (numeric) = 2.3412044627447290729785327687785
absolute error = 3.7502314932007646e-15
relative error = 1.6018385206750194937487931772311e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.792
Order of pole = 2.082
x[1] = 0.781
y[1] (analytic) = 2.3421947142539093412358459852287
y[1] (numeric) = 2.3421947142539131153914815040242
absolute error = 3.7741556355187955e-15
relative error = 1.6113756950053692926222414841837e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.791
Order of pole = 2.082
x[1] = 0.782
y[1] (analytic) = 2.3431869483253684862243198602231
y[1] (numeric) = 2.3431869483253722844861052550703
absolute error = 3.7982617853948472e-15
relative error = 1.6209811121171502144062934254658e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.79
Order of pole = 2.082
x[1] = 0.783
y[1] (analytic) = 2.3441811688973447072381153436455
y[1] (numeric) = 2.3441811688973485297896799203361
absolute error = 3.8225515645766906e-15
relative error = 1.6306553500618475458601947624869e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.789
Order of pole = 2.082
x[1] = 0.784
y[1] (analytic) = 2.34517737992381111471032625244
y[1] (numeric) = 2.3451773799238149617369375861019
absolute error = 3.8470266113336619e-15
relative error = 1.6403989925310647805545718154391e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.788
Order of pole = 2.082
x[1] = 0.785
y[1] (analytic) = 2.3461755853745505131697683684272
y[1] (numeric) = 2.3461755853745543848583490147388
absolute error = 3.8716885806463116e-15
relative error = 1.6502126289189151258682064064839e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.787
Order of pole = 2.082
x[1] = 0.786
y[1] (analytic) = 2.3471757892352344371746334752872
y[1] (numeric) = 2.347175789235238333713777873762
absolute error = 3.8965391443984748e-15
relative error = 1.6600968543851842069266170881365e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.786
Order of pole = 2.082
x[1] = 0.787
y[1] (analytic) = 2.3481779955075026938301640103494
y[1] (numeric) = 2.3481779955075066154101555821468
absolute error = 3.9215799915717974e-15
relative error = 1.6700522699192747414272519346343e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.785
Order of pole = 2.082
x[1] = 0.788
y[1] (analytic) = 2.3491822082090434157633227534292
y[1] (numeric) = 2.3491822082090473625761511961824
absolute error = 3.9468128284427532e-15
relative error = 1.6800794824049440639404822120552e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.784
Order of pole = 2.082
x[1] = 0.789
y[1] (analytic) = 2.3501884313736736284621084712748
y[1] (numeric) = 2.3501884313736776007014872534604
absolute error = 3.9722393787821856e-15
relative error = 1.6901791046858447586329738453852e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.3MB, time=13.55
Real estimate of pole used
Radius of convergence = 0.783
Order of pole = 2.082
x[1] = 0.79
y[1] (analytic) = 2.3511966690514203359221999259937
y[1] (numeric) = 2.3511966690514243337835839834047
absolute error = 3.9978613840574110e-15
relative error = 1.7003517556318800405460706819453e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.782
Order of pole = 2.082
x[1] = 0.791
y[1] (analytic) = 2.3522069253086021285790012339232
y[1] (numeric) = 2.3522069253086061522596048708422
absolute error = 4.0236806036369190e-15
relative error = 1.7105980602063846051627448567495e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.781
Order of pole = 2.082
x[1] = 0.792
y[1] (analytic) = 2.3532192042279113175389153751331
y[1] (numeric) = 2.3532192042279153672377303728407
absolute error = 4.0496988149977076e-15
relative error = 1.7209186495341429158281603637636e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.78
Order of pole = 2.082
x[1] = 0.793
y[1] (analytic) = 2.3542335099084965991597939037462
y[1] (numeric) = 2.3542335099085006750776078390347
absolute error = 4.0759178139352885e-15
relative error = 1.7313141609702555094679568937759e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.779
Order of pole = 2.082
x[1] = 0.794
y[1] (analytic) = 2.3552498464660462540670038501903
y[1] (numeric) = 2.3552498464660503564064186265935
absolute error = 4.1023394147764032e-15
relative error = 1.7417852381698662106023250833091e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.778
Order of pole = 2.082
x[1] = 0.795
y[1] (analytic) = 2.3562682180328718847284217478593
y[1] (numeric) = 2.3562682180328760136938723423447
absolute error = 4.1289654505944854e-15
relative error = 1.7523325311587608601483439871462e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.777
Order of pole = 2.082
x[1] = 0.796
y[1] (analytic) = 2.3572886287579926957489140234955
y[1] (numeric) = 2.3572886287579968515466874514073
absolute error = 4.1557977734279118e-15
relative error = 1.7629566964048508960114863225422e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.776
Order of pole = 2.082
x[1] = 0.797
y[1] (analytic) = 2.3583110828072203210824970843758
y[1] (numeric) = 2.3583110828072245039207515854542
absolute error = 4.1828382545010784e-15
relative error = 1.7736583968905529229800484909999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.775
Order of pole = 2.082
x[1] = 0.798
y[1] (analytic) = 2.3593355843632442023983937946845
y[1] (numeric) = 2.3593355843632484124871782430288
absolute error = 4.2100887844483443e-15
relative error = 1.7844383021860774139849002114905e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.774
Order of pole = 2.082
x[1] = 0.799
y[1] (analytic) = 2.3603621376257175228756201948992
y[1] (numeric) = 2.3603621376257217604268937357825
absolute error = 4.2375512735408833e-15
relative error = 1.7952970885236388847154158752200e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.773
Order of pole = 2.082
x[1] = 0.8
y[1] (analytic) = 2.3613907468113437007395518770172
y[1] (numeric) = 2.3613907468113479659672037935022
absolute error = 4.2652276519164850e-15
relative error = 1.8062354388726003987728745654553e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.772
Order of pole = 2.082
x[1] = 0.801
y[1] (analytic) = 2.362421416153963446893138040091
y[1] (numeric) = 2.3624214161539677400130078524387
absolute error = 4.2931198698123477e-15
relative error = 1.8172540430155654344342570080010e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.3MB, time=13.75
Real estimate of pole used
Radius of convergence = 0.771
Order of pole = 2.082
x[1] = 0.802
y[1] (analytic) = 2.3634541499046423910350576304017
y[1] (numeric) = 2.3634541499046467122649554313073
absolute error = 4.3212298978009056e-15
relative error = 1.8283535976254301474018488371283e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.77
Order of pole = 2.082
x[1] = 0.803
y[1] (analytic) = 2.364488952331759280697150895648
y[1] (numeric) = 2.3644889523317636302568779243825
absolute error = 4.3495597270287345e-15
relative error = 1.8395348063434097009179587095235e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.769
Order of pole = 2.082
x[1] = 0.804
y[1] (analytic) = 2.3655258277210947576739159919797
y[1] (numeric) = 2.3655258277210991357852854505601
absolute error = 4.3781113694585804e-15
relative error = 1.8507983798580523343290394061579e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.768
Order of pole = 2.082
x[1] = 0.805
y[1] (analytic) = 2.3665647803759207163577388789325
y[1] (numeric) = 2.3665647803759251232445969934868
absolute error = 4.4068868581145543e-15
relative error = 1.8621450359852542908672948998895e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.767
Order of pole = 2.082
x[1] = 0.806
y[1] (analytic) = 2.3676058146170902485348305867392
y[1] (numeric) = 2.3676058146170946844230779172806
absolute error = 4.4358882473305414e-15
relative error = 1.8735754997492907107766296326689e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.766
Order of pole = 2.082
x[1] = 0.807
y[1] (analytic) = 2.3686489347831281792385840745257
y[1] (numeric) = 2.3686489347831326443561970763943
absolute error = 4.4651176130018686e-15
relative error = 1.8850905034648756886323814073215e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.765
Order of pole = 2.082
x[1] = 0.808
y[1] (analytic) = 2.3696941452303221982992384138469
y[1] (numeric) = 2.3696941452303266928762912541269
absolute error = 4.4945770528402800e-15
relative error = 1.8966907868202670553864426745462e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.764
Order of pole = 2.082
x[1] = 0.809
y[1] (analytic) = 2.3707414503328145922713560940867
y[1] (numeric) = 2.3707414503328191165400427263514
absolute error = 4.5242686866322647e-15
relative error = 1.9083770969614290729909783237896e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.763
Order of pole = 2.082
x[1] = 0.81
y[1] (analytic) = 2.3717908544826945814636850864397
y[1] (numeric) = 2.3717908544826991356583415872296
absolute error = 4.5541946565007899e-15
relative error = 1.9201501885772698103073462465684e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.762
Order of pole = 2.082
x[1] = 0.811
y[1] (analytic) = 2.3728423620900912668394962223641
y[1] (numeric) = 2.3728423620900958511966233928488
absolute error = 4.5843571271704847e-15
relative error = 1.9320108239859666654583627618885e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.761
Order of pole = 2.082
x[1] = 0.812
y[1] (analytic) = 2.373895977583267191599463811175
y[1] (numeric) = 2.3738959775832718063577500475025
absolute error = 4.6147582862363275e-15
relative error = 1.9439597732223965694391680584698e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.3MB, time=13.96
Real estimate of pole used
Radius of convergence = 0.76
Order of pole = 2.082
x[1] = 0.813
y[1] (analytic) = 2.374951705408712522303598681322
y[1] (numeric) = 2.3749517054087171677039431172078
absolute error = 4.6454003444358858e-15
relative error = 1.9559978141266855781254536090980e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.759
Order of pole = 2.082
x[1] = 0.814
y[1] (analytic) = 2.3760095500312398544336534941734
y[1] (numeric) = 2.3760095500312445307191894193364
absolute error = 4.6762855359251630e-15
relative error = 1.9681257324338949052673788527767e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.758
Order of pole = 2.082
x[1] = 0.815
y[1] (analytic) = 2.3770695159340796473428058340519
y[1] (numeric) = 2.3770695159340843547589243921531
absolute error = 4.7074161185581012e-15
relative error = 1.9803443218648579884779454930878e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.757
Order of pole = 2.082
x[1] = 0.816
y[1] (analytic) = 2.3781316076189762935852908839943
y[1] (numeric) = 2.3781316076189810323796650537905
absolute error = 4.7387943741697962e-15
relative error = 1.9926543842181861110347485540877e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.756
Order of pole = 2.082
x[1] = 0.817
y[1] (analytic) = 2.3791958296062848276650081884792
y[1] (numeric) = 2.3791958296062895980876170519576
absolute error = 4.7704226088634784e-15
relative error = 2.0050567294634589435129183088998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.755
Order of pole = 2.082
x[1] = 0.818
y[1] (analytic) = 2.3802621864350682792889718935272
y[1] (numeric) = 2.3802621864350730815921251948409
absolute error = 4.8023031533013137e-15
relative error = 2.0175521758356164325854971588536e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.754
Order of pole = 2.082
x[1] = 0.819
y[1] (analytic) = 2.3813306826631956762588168297264
y[1] (numeric) = 2.3813306826632005106971798288079
absolute error = 4.8344383629990815e-15
relative error = 2.0301415499305696183410924233203e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.753
Order of pole = 2.082
x[1] = 0.82
y[1] (analytic) = 2.3824013228674407021814198318618
y[1] (numeric) = 2.3824013228674455690120384566481
absolute error = 4.8668306186247863e-15
relative error = 2.0428256868020475988495907169388e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.752
Order of pole = 2.082
x[1] = 0.821
y[1] (analytic) = 2.3834741116435810142280528164267
y[1] (numeric) = 2.3834741116435859137103791176879
absolute error = 4.8994823263012612e-15
relative error = 2.0556054300596985055607707196404e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.751
Order of pole = 2.082
x[1] = 0.822
y[1] (analytic) = 2.3845490536064982262203574925795
y[1] (numeric) = 2.3845490536065031586162754054003
absolute error = 4.9323959179128208e-15
relative error = 2.0684816319684619040805018580422e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.75
Order of pole = 2.082
x[1] = 0.823
y[1] (analytic) = 2.3856261533902785623708273721521
y[1] (numeric) = 2.3856261533902835279446787881771
absolute error = 4.9655738514160250e-15
relative error = 2.0814551535492315987506095011323e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7489
Order of pole = 2.082
x[1] = 0.824
y[1] (analytic) = 2.3867054156483141870554072622996
y[1] (numeric) = 2.3867054156483191860740184169126
absolute error = 4.9990186111546130e-15
relative error = 2.0945268646808267783054989102416e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.3MB, time=14.15
Real estimate of pole used
Radius of convergence = 0.7479
Order of pole = 2.082
x[1] = 0.825
y[1] (analytic) = 2.3877868450534052160462800467722
y[1] (numeric) = 2.3877868450534102487789882254419
absolute error = 5.0327327081786697e-15
relative error = 2.1076976442032905378331991670558e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7469
Order of pole = 2.082
x[1] = 0.826
y[1] (analytic) = 2.3888704462978624146839117506346
y[1] (numeric) = 2.3888704462978674814025923187218
absolute error = 5.0667186805680872e-15
relative error = 2.1209683800225349001024324206631e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7459
Order of pole = 2.082
x[1] = 0.827
y[1] (analytic) = 2.389956224093610588518975187407
y[1] (numeric) = 2.3899562240936156894980689477919
absolute error = 5.1009790937603849e-15
relative error = 2.1343399692163516712940788723505e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7449
Order of pole = 2.082
x[1] = 0.828
y[1] (analytic) = 2.3910441831722926720068765440173
y[1] (numeric) = 2.3910441831722978075234174269702
absolute error = 5.1355165408829529e-15
relative error = 2.1478133181418088435404675860020e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7439
Order of pole = 2.082
x[1] = 0.829
y[1] (analytic) = 2.3921343282853745208902747940046
y[1] (numeric) = 2.392134328285379691223917883789
absolute error = 5.1703336430897844e-15
relative error = 2.1613893425440525478359110666169e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7429
Order of pole = 2.082
x[1] = 0.83
y[1] (analytic) = 2.3932266642042504139582176602109
y[1] (numeric) = 2.3932266642042556193912675629748
absolute error = 5.2054330499027639e-15
relative error = 2.1750689676665348915594553584354e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7419
Order of pole = 2.082
x[1] = 0.831
y[1] (analytic) = 2.3943211957203492699243268839312
y[1] (numeric) = 2.3943211957203545107417664415113
absolute error = 5.2408174395575801e-15
relative error = 2.1888531283626887607334396055449e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7409
Order of pole = 2.082
x[1] = 0.832
y[1] (analytic) = 2.3954179276452415852208568008132
y[1] (numeric) = 2.395417927645246861710376155143
absolute error = 5.2764895193543298e-15
relative error = 2.2027427692090694467620389119574e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7399
Order of pole = 2.082
x[1] = 0.833
y[1] (analytic) = 2.3965168648107470985604307721968
y[1] (numeric) = 2.3965168648107524110124567850838
absolute error = 5.3124520260128870e-15
relative error = 2.2167388446199861222667134447183e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7389
Order of pole = 2.082
x[1] = 0.834
y[1] (analytic) = 2.3976180120690431881728370678336
y[1] (numeric) = 2.3976180120690485368805631009372
absolute error = 5.3487077260331036e-15
relative error = 2.2308423189636427931489300974850e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7379
Order of pole = 2.082
x[1] = 0.835
y[1] (analytic) = 2.3987213742927740076804466334668
y[1] (numeric) = 2.398721374292779392939862693386
absolute error = 5.3852594160599192e-15
relative error = 2.2450541666798128485603204353858e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7369
Order of pole = 2.082
memory used=274.6MB, alloc=4.3MB, time=14.35
x[1] = 0.836
y[1] (analytic) = 2.399826956375160366632607195231
y[1] (numeric) = 2.3998269563751657887425304486806
absolute error = 5.4221099232534496e-15
relative error = 2.2593753723990678880140399072034e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7359
Order of pole = 2.082
x[1] = 0.837
y[1] (analytic) = 2.4009347632301103617767788434971
y[1] (numeric) = 2.4009347632301158210388845076278
absolute error = 5.4592621056641307e-15
relative error = 2.2738069310635843230041196164031e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7349
Order of pole = 2.082
x[1] = 0.838
y[1] (analytic) = 2.4020447997923307652022131950863
y[1] (numeric) = 2.4020447997923362619210658080804
absolute error = 5.4967188526129941e-15
relative error = 2.2883498480495509333939491678848e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7339
Order of pole = 2.082
x[1] = 0.839
y[1] (analytic) = 2.4031570710174391755506491518225
y[1] (numeric) = 2.4031570710174447100337342289725
absolute error = 5.5344830850771500e-15
relative error = 2.3030051392912001169322875103103e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7329
Order of pole = 2.082
x[1] = 0.84
y[1] (analytic) = 2.4042715818820769385478109575598
y[1] (numeric) = 2.4042715818820825111055670381185
absolute error = 5.5725577560805587e-15
relative error = 2.3177738314064877908427663247953e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7319
Order of pole = 2.082
x[1] = 0.841
y[1] (analytic) = 2.4053883373840228431694566143278
y[1] (numeric) = 2.405388337384028454115307704495
absolute error = 5.6109458510901672e-15
relative error = 2.3326569618244447492642640635503e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7309
Order of pole = 2.082
x[1] = 0.842
y[1] (analytic) = 2.4065073425423075998163447687345
y[1] (numeric) = 2.40650734254231324946673318623
absolute error = 5.6496503884174955e-15
relative error = 2.3476555789142254932723886928253e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7299
Order of pole = 2.082
x[1] = 0.843
y[1] (analytic) = 2.4076286023973291069337740500129
y[1] (numeric) = 2.4076286023973347956081936757654
absolute error = 5.6886744196257525e-15
relative error = 2.3627707421158784319616782277728e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7289
Order of pole = 2.082
x[1] = 0.844
y[1] (analytic) = 2.4087521220109685125733087705853
y[1] (numeric) = 2.4087521220109742405943387131519
absolute error = 5.7280210299425666e-15
relative error = 2.3780035220728633523000467782292e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7279
Order of pole = 2.082
x[1] = 0.845
y[1] (analytic) = 2.4098779064667070774569472416969
y[1] (numeric) = 2.4098779064667128451502859201137
absolute error = 5.7676933386784168e-15
relative error = 2.3933550007663421776170973851407e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7269
Order of pole = 2.082
x[1] = 0.846
y[1] (analytic) = 2.4110059608697438461673221786496
y[1] (numeric) = 2.4110059608697496538618218294989
absolute error = 5.8076944996508493e-15
relative error = 2.4088262716512685326357031800475e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7259
Order of pole = 2.082
x[1] = 0.847
y[1] (analytic) = 2.4121362903471141331515553574677
y[1] (numeric) = 2.4121362903471199811792569720372
absolute error = 5.8480277016145695e-15
relative error = 2.4244184397943034947142866627984e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.3MB, time=14.55
Real estimate of pole used
Radius of convergence = 0.7249
Order of pole = 2.082
x[1] = 0.848
y[1] (analytic) = 2.4132689000478088302911295411691
y[1] (numeric) = 2.4132689000478147189872982386668
absolute error = 5.8886961686974977e-15
relative error = 2.4401326220135840699668004717045e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7239
Order of pole = 2.082
x[1] = 0.849
y[1] (analytic) = 2.4144037951428945428555985434151
y[1] (numeric) = 2.4144037951429004725587593862964
absolute error = 5.9297031608428813e-15
relative error = 2.4559699470203726204602968164189e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7229
Order of pole = 2.082
x[1] = 0.85
y[1] (analytic) = 2.4155409808256345607241400867236
y[1] (numeric) = 2.415540980825640531776114344277
absolute error = 5.9710519742575534e-15
relative error = 2.4719315555626140840644818359628e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7219
Order of pole = 2.082
x[1] = 0.851
y[1] (analytic) = 2.4166804623116106718258749124078
y[1] (numeric) = 2.4166804623116166845718167788427
absolute error = 6.0127459418664349e-15
relative error = 2.4880186005704306274815139319798e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7209
Order of pole = 2.082
x[1] = 0.852
y[1] (analytic) = 2.4178222448388458248175386068221
y[1] (numeric) = 2.4178222448388518796059723801962
absolute error = 6.0547884337733741e-15
relative error = 2.5042322473035818984614935661143e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7199
Order of pole = 2.082
x[1] = 0.853
y[1] (analytic) = 2.41896633366792764808550914825
y[1] (numeric) = 2.4189663336679337452683668766714
absolute error = 6.0971828577284214e-15
relative error = 2.5205736735009203430828725971718e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7189
Order of pole = 2.082
x[1] = 0.854
y[1] (analytic) = 2.4201127340821328322283727057604
y[1] (numeric) = 2.4201127340821389721610323073993
absolute error = 6.1399326596016389e-15
relative error = 2.5370440695318717682021629487547e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7179
Order of pole = 2.082
x[1] = 0.855
y[1] (analytic) = 2.4212614513875523832461623224899
y[1] (numeric) = 2.4212614513875585662874861860339
absolute error = 6.1830413238635440e-15
relative error = 2.5536446385499708409499532568117e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7169
Order of pole = 2.082
x[1] = 0.856
y[1] (analytic) = 2.4224124909132177537331385119972
y[1] (numeric) = 2.4224124909132239802455125842884
absolute error = 6.2265123740722912e-15
relative error = 2.5703765966484831235990047416199e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7159
Order of pole = 2.082
x[1] = 0.857
y[1] (analytic) = 2.4235658580112278594425073446017
y[1] (numeric) = 2.4235658580112341297918807122967
absolute error = 6.2703493733676950e-15
relative error = 2.5872411730181444979596194855369e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7149
Order of pole = 2.082
x[1] = 0.858
y[1] (analytic) = 2.4247215580568769886638002961625
y[1] (numeric) = 2.424721558056883303219725268362
absolute error = 6.3145559249721995e-15
relative error = 2.6042396101070497403554332685713e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7139
Order of pole = 2.082
x[1] = 0.859
y[1] (analytic) = 2.4258795964487836119267811100983
y[1] (numeric) = 2.4258795964487899710624538090021
absolute error = 6.3591356726989038e-15
relative error = 2.6213731637827232392244647555768e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.3MB, time=14.76
Real estimate of pole used
Radius of convergence = 0.7129
Order of pole = 2.082
x[1] = 0.86
y[1] (analytic) = 2.4270399786090200996197084626248
y[1] (numeric) = 2.4270399786090265037120099293754
absolute error = 6.4040923014667506e-15
relative error = 2.6386431034964039287233213313397e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7119
Order of pole = 2.082
x[1] = 0.861
y[1] (analytic) = 2.4282027099832433551845797438952
y[1] (numeric) = 2.4282027099832498046141175668862
absolute error = 6.4494295378229910e-15
relative error = 2.6560507124495786014505607354122e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7109
Order of pole = 2.082
x[1] = 0.862
y[1] (analytic) = 2.4293677960408263716276213436504
y[1] (numeric) = 2.429367796040832866778771816688
absolute error = 6.4951511504730376e-15
relative error = 2.6735972877627971666531449982021e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7099
Order of pole = 2.082
x[1] = 0.863
y[1] (analytic) = 2.4305352422749907191597851779972
y[1] (numeric) = 2.4305352422749972604207359958195
absolute error = 6.5412609508178223e-15
relative error = 2.6912841406468049635876090960857e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7089
Order of pole = 2.082
x[1] = 0.864
y[1] (analytic) = 2.4317050542029399718593706844765
y[1] (numeric) = 2.4317050542029465596221641832499
absolute error = 6.5877627934987734e-15
relative error = 2.7091125965760262658429275871675e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7079
Order of pole = 2.082
x[1] = 0.865
y[1] (analytic) = 2.4328772373659940813271271699924
y[1] (numeric) = 2.4328772373660007159877041205269
absolute error = 6.6346605769505345e-15
relative error = 2.7270839954644361278053596509740e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7069
Order of pole = 2.082
x[1] = 0.866
y[1] (analytic) = 2.4340517973297247053833144011125
y[1] (numeric) = 2.4340517973297313873415583626558
absolute error = 6.6819582439615433e-15
relative error = 2.7451996918438556714035363672544e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7059
Order of pole = 2.082
x[1] = 0.867
y[1] (analytic) = 2.4352287396840914999362210181004
y[1] (numeric) = 2.4352287396840982295960032606948
absolute error = 6.7296597822425944e-15
relative error = 2.7634610550447081356652525021883e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7049
Order of pole = 2.082
x[1] = 0.868
y[1] (analytic) = 2.4364080700435793822325722334435
y[1] (numeric) = 2.4364080700435861600017972369561
absolute error = 6.7777692250035126e-15
relative error = 2.7818694693792737466481949925861e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7039
Order of pole = 2.082
x[1] = 0.869
y[1] (analytic) = 2.4375897940473367737821120069795
y[1] (numeric) = 2.4375897940473436000727635450418
absolute error = 6.8262906515380623e-15
relative error = 2.8004263343274808411502853835060e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7029
Order of pole = 2.082
x[1] = 0.87
y[1] (analytic) = 2.4387739173593148313314323037092
y[1] (numeric) = 2.4387739173593217065596201209324
absolute error = 6.8752281878172232e-15
relative error = 2.8191330647252723091787006973692e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.3MB, time=14.96
Real estimate of pole used
Radius of convergence = 0.7019
Order of pole = 2.082
x[1] = 0.871
y[1] (analytic) = 2.4399604456684076743458551366661
y[1] (numeric) = 2.4399604456684145989318622276316
absolute error = 6.9245860070909655e-15
relative error = 2.8379910909555873866144250551528e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.7009
Order of pole = 2.082
x[1] = 0.872
y[1] (analytic) = 2.4411493846885936175428640470432
y[1] (numeric) = 2.4411493846886005919111945456993
absolute error = 6.9743683304986561e-15
relative error = 2.8570018591419978641039706165260e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6999
Order of pole = 2.082
x[1] = 0.873
y[1] (analytic) = 2.4423407401590774171062428226879
y[1] (numeric) = 2.4423407401590844416856705109222
absolute error = 7.0245794276882343e-15
relative error = 2.8761668313450403768406959703780e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6989
Order of pole = 2.082
x[1] = 0.874
y[1] (analytic) = 2.4435345178444335392967231266724
y[1] (numeric) = 2.4435345178444406145203405709677
absolute error = 7.0752236174442953e-15
relative error = 2.8954874857612860782065338787980e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6979
Order of pole = 2.082
x[1] = 0.875
y[1] (analytic) = 2.4447307235347504602625820023596
y[1] (numeric) = 2.4447307235347575865678503275818
absolute error = 7.1263052683252222e-15
relative error = 2.9149653169251897011991662167079e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6969
Order of pole = 2.082
x[1] = 0.876
y[1] (analytic) = 2.4459293630457760059422778253392
y[1] (numeric) = 2.4459293630457831837710771348493
absolute error = 7.1778287993095101e-15
relative error = 2.9346018359137609113861364870374e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6959
Order of pole = 2.082
x[1] = 0.877
y[1] (analytic) = 2.4471304422190637410408822565258
y[1] (numeric) = 2.4471304422190709708395627079548
absolute error = 7.2297986804514290e-15
relative error = 2.9543985705541018301829386216039e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6949
Order of pole = 2.082
x[1] = 0.878
y[1] (analytic) = 2.448333966922120416152769373826
y[1] (numeric) = 2.4483339669221276983722029199999
absolute error = 7.2822194335461739e-15
relative error = 2.9743570656338550036072896004328e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6939
Order of pole = 2.082
x[1] = 0.879
y[1] (analytic) = 2.4495399430485544821947748728641
y[1] (numeric) = 2.4495399430485618172904076775172
absolute error = 7.3350956328046531e-15
relative error = 2.9944788831146068510494921429255e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6929
Order of pole = 2.082
x[1] = 0.88
y[1] (analytic) = 2.4507483765182256814068516756497
y[1] (numeric) = 2.4507483765182330698387572137178
absolute error = 7.3884319055380681e-15
relative error = 3.0147656023482923003439005793962e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6919
Order of pole = 2.082
x[1] = 0.881
y[1] (analytic) = 2.4519592732773957242711373127776
y[1] (numeric) = 2.4519592732774031665040701652211
absolute error = 7.4422329328524435e-15
relative error = 3.0352188202966480418463395688839e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6909
Order of pole = 2.082
x[1] = 0.882
y[1] (analytic) = 2.4531726392988800617953270936281
y[1] (numeric) = 2.4531726392988875582987774468919
absolute error = 7.4965034503532638e-15
relative error = 3.0558401517537609005622022260677e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.3MB, time=15.16
Real estimate of pole used
Radius of convergence = 0.6899
Order of pole = 2.082
x[1] = 0.883
y[1] (analytic) = 2.4543884805822007627023295979441
y[1] (numeric) = 2.4543884805822083139505784583243
absolute error = 7.5512482488603802e-15
relative error = 3.0766312295717600302579301554639e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6889
Order of pole = 2.082
x[1] = 0.884
y[1] (analytic) = 2.4556068031537405051653818662942
y[1] (numeric) = 2.4556068031537481116375569996474
absolute error = 7.6064721751333532e-15
relative error = 3.0975937048897024003777979253832e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6879
Order of pole = 2.082
x[1] = 0.885
y[1] (analytic) = 2.4568276130668976928261355020896
y[1] (numeric) = 2.4568276130669053550062681094871
absolute error = 7.6621801326073975e-15
relative error = 3.1187292473657009930398582551870e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6869
Order of pole = 2.082
x[1] = 0.886
y[1] (analytic) = 2.4580509164022427049327066038183
y[1] (numeric) = 2.4580509164022504233097887439178
absolute error = 7.7183770821400995e-15
relative error = 3.1400395454123463322342633670982e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6859
Order of pole = 2.082
x[1] = 0.887
y[1] (analytic) = 2.4592767192676752905353271202512
y[1] (numeric) = 2.4592767192676830656033698893351
absolute error = 7.7750680427690839e-15
relative error = 3.1615263064354741396589477575406e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6848
Order of pole = 2.082
x[1] = 0.888
y[1] (analytic) = 2.4605050277985831167790581817777
y[1] (numeric) = 2.46050502779859094903715066258
absolute error = 7.8322580924808023e-15
relative error = 3.1831912570763300881563840330114e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6838
Order of pole = 2.082
x[1] = 0.889
y[1] (analytic) = 2.461735848158001481436042750437
y[1] (numeric) = 2.4617358481580093713884117410637
absolute error = 7.8899523689906267e-15
relative error = 3.2050361434571863297973566027203e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6828
Order of pole = 2.082
x[1] = 0.89
y[1] (analytic) = 2.462969186536774199924001320499
y[1] (numeric) = 2.4629691865367821480800718549293
absolute error = 7.9481560705344303e-15
relative error = 3.2270627314304638987196205999922e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6818
Order of pole = 2.082
x[1] = 0.891
y[1] (analytic) = 2.4642050491537156771631263932715
y[1] (numeric) = 2.4642050491537236840375830651123
absolute error = 8.0068744566718408e-15
relative error = 3.2492728068314158503333934748236e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6808
Order of pole = 2.082
x[1] = 0.892
y[1] (analytic) = 2.4654434422557741747302252824181
y[1] (numeric) = 2.4654434422557822408430743837756
absolute error = 8.0661128491013575e-15
relative error = 3.2716681757344280917235435790107e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6798
Order of pole = 2.082
x[1] = 0.893
y[1] (analytic) = 2.4666843721181962838769129571229
y[1] (numeric) = 2.4666843721182044097535454446465
absolute error = 8.1258766324875236e-15
relative error = 3.2942506647129945059999243777160e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6788
Order of pole = 2.082
memory used=293.7MB, alloc=4.3MB, time=15.36
x[1] = 0.894
y[1] (analytic) = 2.467927845044692615087883820843
y[1] (numeric) = 2.4679278450447008012591391211947
absolute error = 8.1861712553003517e-15
relative error = 3.3170221211034252531412759606660e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6778
Order of pole = 2.082
x[1] = 0.895
y[1] (analytic) = 2.4691738673676047149658105213453
y[1] (numeric) = 2.4691738673676129619680411885466
absolute error = 8.2470022306672013e-15
relative error = 3.3399844132723470468225107666249e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6768
Order of pole = 2.082
x[1] = 0.896
y[1] (analytic) = 2.4704224454480732213412463126546
y[1] (numeric) = 2.4704224454480815297163835499664
absolute error = 8.3083751372373118e-15
relative error = 3.3631394308880556990657616303994e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6758
Order of pole = 2.082
x[1] = 0.897
y[1] (analytic) = 2.4716735856762072676190626162668
y[1] (numeric) = 2.4716735856762156379146826754663
absolute error = 8.3702956200591995e-15
relative error = 3.3864890851957828278032840412644e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6748
Order of pole = 2.082
x[1] = 0.898
y[1] (analytic) = 2.4729272944712551474874529918576
y[1] (numeric) = 2.4729272944712635802568444629848
absolute error = 8.4327693914711272e-15
relative error = 3.4100353092969382331463922903476e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6738
Order of pole = 2.082
x[1] = 0.899
y[1] (analytic) = 2.4741835782817762512313967248747
y[1] (numeric) = 2.474183578281784747033628729738
absolute error = 8.4958022320048633e-15
relative error = 3.4337800584323923710004488928336e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6728
Order of pole = 2.082
x[1] = 0.9
y[1] (analytic) = 2.4754424435858142850097179361052
y[1] (numeric) = 2.4754424435858228444097092390523
absolute error = 8.5593999913029471e-15
relative error = 3.4577253102698628245198327961170e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6718
Order of pole = 2.082
x[1] = 0.901
y[1] (analytic) = 2.4767038968910717845735180553032
y[1] (numeric) = 2.4767038968910804081421071049869
absolute error = 8.6235685890496837e-15
relative error = 3.4818730651954709301017735954781e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6708
Order of pole = 2.082
x[1] = 0.902
y[1] (analytic) = 2.4779679447350859350238194930062
y[1] (numeric) = 2.4779679447350946233378354091007
absolute error = 8.6883140159160945e-15
relative error = 3.5062253466095353018349272691856e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6698
Order of pole = 2.082
x[1] = 0.903
y[1] (analytic) = 2.4792345936854057083277554890539
y[1] (numeric) = 2.4792345936854144619700900081079
absolute error = 8.7536423345190540e-15
relative error = 3.5307842012266704257001247746681e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6688
Order of pole = 2.082
x[1] = 0.904
y[1] (analytic) = 2.480503850339770330435594796536
y[1] (numeric) = 2.480503850339779149995275191383
absolute error = 8.8195596803948470e-15
relative error = 3.5555516993802593873098518486167e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6678
Order of pole = 2.082
x[1] = 0.905
y[1] (analytic) = 2.4817757213262890899653197503312
y[1] (numeric) = 2.4817757213262979760375827377167
absolute error = 8.8860722629873855e-15
relative error = 3.5805299353313714063073234680451e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.3MB, time=15.56
Real estimate of pole used
Radius of convergence = 0.6668
Order of pole = 2.082
x[1] = 0.906
y[1] (analytic) = 2.4830502133036225005474023401894
y[1] (numeric) = 2.4830502133036314537337689915182
absolute error = 8.9531863666513288e-15
relative error = 3.6057210275821960453157958560633e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6658
Order of pole = 2.082
x[1] = 0.907
y[1] (analytic) = 2.4843273329611648290498654301863
y[1] (numeric) = 2.4843273329611738499582171005398
absolute error = 9.0209083516703535e-15
relative error = 3.6311271191940667435451716492109e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6648
Order of pole = 2.082
x[1] = 0.908
y[1] (analytic) = 2.4856070870192280020326958156971
y[1] (numeric) = 2.4856070870192370912773511065233
absolute error = 9.0892446552908262e-15
relative error = 3.6567503781101482658818299694164e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6638
Order of pole = 2.082
x[1] = 0.909
y[1] (analytic) = 2.4868894822292269029112132728282
y[1] (numeric) = 2.4868894822292360611130060439632
absolute error = 9.1582017927711350e-15
relative error = 3.6825929974828634594323648329197e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6628
Order of pole = 2.082
x[1] = 0.91
y[1] (analytic) = 2.4881745253738660724401163363826
y[1] (numeric) = 2.4881745253738753002264747833249
absolute error = 9.2277863584469423e-15
relative error = 3.7086571960061367480251052518576e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6618
Order of pole = 2.082
x[1] = 0.911
y[1] (analytic) = 2.4894622232673278252636427649233
y[1] (numeric) = 2.4894622232673371232686695775464
absolute error = 9.2980050268126231e-15
relative error = 3.7349452182525319314016797007882e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6608
Order of pole = 2.082
x[1] = 0.912
y[1] (analytic) = 2.4907525827554617954126223657806
y[1] (numeric) = 2.4907525827554711642771759849422
absolute error = 9.3688645536191616e-15
relative error = 3.7614593350153647566901223185120e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6598
Order of pole = 2.082
x[1] = 0.913
y[1] (analytic) = 2.4920456107159759237661842413299
y[1] (numeric) = 2.4920456107159853641379612301106
absolute error = 9.4403717769887807e-15
relative error = 3.7882018436558708833486099776238e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6588
Order of pole = 2.082
x[1] = 0.914
y[1] (analytic) = 2.4933413140586289006345321003904
y[1] (numeric) = 2.4933413140586384131681506469774
absolute error = 9.5125336185465870e-15
relative error = 3.8151750684555124970781186653918e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6578
Order of pole = 2.082
x[1] = 0.915
y[1] (analytic) = 2.4946396997254240767595429181799
y[1] (numeric) = 2.4946396997254336621166274876945
absolute error = 9.5853570845695146e-15
relative error = 3.8423813609735065186492560589829e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6568
Order of pole = 2.082
x[1] = 0.916
y[1] (analytic) = 2.495940774690804856171999136785
y[1] (numeric) = 2.4959407746908145150212662896478
absolute error = 9.6588492671528628e-15
relative error = 3.8698231004096614873083619180741e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6558
Order of pole = 2.082
x[1] = 0.917
y[1] (analytic) = 2.4972445459618515844880563422414
y[1] (numeric) = 2.4972445459618613175054017369623
absolute error = 9.7330173453947209e-15
relative error = 3.8975026939726088212382011806470e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.3MB, time=15.77
Real estimate of pole used
Radius of convergence = 0.6548
Order of pole = 2.082
x[1] = 0.918
y[1] (analytic) = 2.4985510205784799463731008614433
y[1] (numeric) = 2.4985510205784897542416874600281
absolute error = 9.8078685865985848e-15
relative error = 3.9254225772535181442957388360537e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6538
Order of pole = 2.082
x[1] = 0.919
y[1] (analytic) = 2.4998602056136408860484892864313
y[1] (numeric) = 2.4998602056136507694588367809033
absolute error = 9.8834103474944720e-15
relative error = 3.9535852146053864903383043244191e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6528
Order of pole = 2.082
x[1] = 0.92
y[1] (analytic) = 2.5011721081735220648658092223645
y[1] (numeric) = 2.5011721081735320245158847012137
absolute error = 9.9596500754788492e-15
relative error = 3.9819930995279935910306012325572e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6518
Order of pole = 2.082
x[1] = 0.921
y[1] (analytic) = 2.5024867353977508701242826152063
y[1] (numeric) = 2.5024867353977609067195924888967
absolute error = 1.00365953098736904e-14
relative error = 4.0106487550586162719110535308786e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6508
Order of pole = 2.082
x[1] = 0.922
y[1] (analytic) = 2.5038040944595989894597752781418
y[1] (numeric) = 2.5038040944596091037134584831346
absolute error = 1.01142536832049928e-14
relative error = 4.0395547341685980669654824725292e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6498
Order of pole = 2.082
x[1] = 0.923
y[1] (analytic) = 2.5051241925661885652886045265855
y[1] (numeric) = 2.505124192566198757921527027666
absolute error = 1.01926329225010805e-14
relative error = 4.0687136201658705521087720676029e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6488
Order of pole = 2.082
x[1] = 0.924
y[1] (analytic) = 2.5064470369586999439459773738799
y[1] (numeric) = 2.5064470369587102156868279849122
absolute error = 1.02717408506110323e-14
relative error = 4.0981280271035247162240104125440e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6478
Order of pole = 2.082
x[1] = 0.925
y[1] (analytic) = 2.5077726349125810343174711627231
y[1] (numeric) = 2.5077726349125913859028587063034
absolute error = 1.03515853875435803e-14
relative error = 4.1278006001945341265009568605320e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6468
Order of pole = 2.082
x[1] = 0.926
y[1] (analytic) = 2.5091009937377582909225138529795
y[1] (numeric) = 2.509100993737768723097065679806
absolute error = 1.04321745518268265e-14
relative error = 4.1577340162327311143325273173177e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6458
Order of pole = 2.082
x[1] = 0.927
y[1] (analytic) = 2.5104321207788493365713599164856
y[1] (numeric) = 2.5104321207788598500878218056215
absolute error = 1.05135164618891359e-14
relative error = 4.1879309840201409753669303328671e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6448
Order of pole = 2.082
x[1] = 0.928
y[1] (analytic) = 2.5117660234153772398816177923474
y[1] (numeric) = 2.5117660234153878355009552539155
absolute error = 1.05956193374615681e-14
relative error = 4.2183942448007798144589164841453e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.3MB, time=15.97
Real estimate of pole used
Radius of convergence = 0.6438
Order of pole = 2.082
x[1] = 0.929
y[1] (analytic) = 2.5131027090619864631069944548048
y[1] (numeric) = 2.5131027090619971415984954570237
absolute error = 1.06784915010022189e-14
relative error = 4.2491265727010246808278452030896e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6428
Order of pole = 2.082
x[1] = 0.93
y[1] (analytic) = 2.5144421851686604958996106044357
y[1] (numeric) = 2.514442185168671258040989747283
absolute error = 1.07621413791428473e-14
relative error = 4.2801307751766654045949037665748e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6418
Order of pole = 2.082
x[1] = 0.931
y[1] (analytic) = 2.5157844592209411907980355259412
y[1] (numeric) = 2.5157844592209520373755396841157
absolute error = 1.08465775041581745e-14
relative error = 4.3114096934667512024356863481309e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6408
Order of pole = 2.082
x[1] = 0.932
y[1] (analytic) = 2.5171295387401498164061234326298
y[1] (numeric) = 2.5171295387401607482146388908734
absolute error = 1.09318085154582436e-14
relative error = 4.3429662030543451364287027277704e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6398
Order of pole = 2.082
x[1] = 0.933
y[1] (analytic) = 2.5184774312836098444028332744498
y[1] (numeric) = 2.5184774312836208622459943786906
absolute error = 1.10178431611042408e-14
relative error = 4.3748032141343034894746115707710e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6388
Order of pole = 2.082
x[1] = 0.934
y[1] (analytic) = 2.519828144444871486700512131357
y[1] (numeric) = 2.5198281444448825913908114795403
absolute error = 1.11046902993481833e-14
relative error = 4.4069236720881980172940092103051e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6378
Order of pole = 2.082
x[1] = 0.935
y[1] (analytic) = 2.5211816858539379992486495362969
y[1] (numeric) = 2.5211816858539491916075497331858
absolute error = 1.11923589001968889e-14
relative error = 4.4393305579665020632286142576790e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6368
Order of pole = 2.082
x[1] = 0.936
y[1] (analytic) = 2.5225380631774937691618979508853
y[1] (numeric) = 2.5225380631775050500199449515333
absolute error = 1.12808580470006480e-14
relative error = 4.4720268889781629002447719729453e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6358
Order of pole = 2.082
x[1] = 0.937
y[1] (analytic) = 2.5238972841191342020352352285622
y[1] (numeric) = 2.5238972841191455722321732955913
absolute error = 1.13701969380670291e-14
relative error = 4.5050157189876858899786392951861e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6348
Order of pole = 2.082
x[1] = 0.938
y[1] (analytic) = 2.5252593564195974264955508276819
y[1] (numeric) = 2.5252593564196088868804391279368
absolute error = 1.14603848883002549e-14
relative error = 4.5383001390198575076590537881921e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6338
Order of pole = 2.082
x[1] = 0.939
y[1] (analytic) = 2.5266242878569978332277018790857
y[1] (numeric) = 2.5266242878570093846590327456817
absolute error = 1.15514313308665960e-14
relative error = 4.5718832777722372686031372657094e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6328
Order of pole = 2.082
x[1] = 0.94
y[1] (analytic) = 2.5279920862470614659042415918926
y[1] (numeric) = 2.5279920862470731092500604781292
absolute error = 1.16433458188862366e-14
relative error = 4.6057683021355505666164102805734e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=309.0MB, alloc=4.3MB, time=16.17
Real estimate of pole used
Radius of convergence = 0.6318
Order of pole = 2.082
x[1] = 0.941
y[1] (analytic) = 2.5293627594433632816416050536771
y[1] (numeric) = 2.5293627594433750177796322057536
absolute error = 1.17361380271520765e-14
relative error = 4.6399584177221173790667535968445e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6308
Order of pole = 2.082
x[1] = 0.942
y[1] (analytic) = 2.5307363153375662988015809458018
y[1] (numeric) = 2.5307363153375781286193348217431
absolute error = 1.18298177538759413e-14
relative error = 4.6744568694024538054997597164824e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6298
Order of pole = 2.082
x[1] = 0.943
y[1] (analytic) = 2.5321127618596626501554373026144
y[1] (numeric) = 2.5321127618596745745503597652969
absolute error = 1.19243949224626825e-14
relative error = 4.7092669418501862684146384343303e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6288
Order of pole = 2.082
x[1] = 0.944
y[1] (analytic) = 2.5334921069782165596291410076466
y[1] (numeric) = 2.5334921069782285795087243203049
absolute error = 1.20198795833126583e-14
relative error = 4.7443919600954207667317281340942e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6278
Order of pole = 2.082
x[1] = 0.945
y[1] (analytic) = 2.5348743587006092610517506258265
y[1] (numeric) = 2.5348743587006213773336662789218
absolute error = 1.21162819156530953e-14
relative error = 4.7798352900867122304383925803645e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6268
Order of pole = 2.082
x[1] = 0.946
y[1] (analytic) = 2.5362595250732858775353073848877
y[1] (numeric) = 2.5362595250732980911475367837286
absolute error = 1.22136122293988409e-14
relative error = 4.8156003392617817387114106031485e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6258
Order of pole = 2.082
x[1] = 0.947
y[1] (analytic) = 2.5376476141820042803234372006093
y[1] (numeric) = 2.5376476141820165922044042436358
absolute error = 1.23118809670430265e-14
relative error = 4.8516905571271323299650462027468e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6248
Order of pole = 2.082
x[1] = 0.948
y[1] (analytic) = 2.5390386341520859461574457508242
y[1] (numeric) = 2.5390386341520983572561513289946
absolute error = 1.24110987055781704e-14
relative error = 4.8881094358467164826638529016186e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6238
Order of pole = 2.082
x[1] = 0.949
y[1] (analytic) = 2.5404325931486688324229775170978
y[1] (numeric) = 2.5404325931486813436991359653587
absolute error = 1.25112761584482609e-14
relative error = 4.9248605108398117761069902055135e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6228
Order of pole = 2.082
x[1] = 0.95
y[1] (analytic) = 2.541829499376962289557357829513
y[1] (numeric) = 2.5418294993769749019815353618834
absolute error = 1.26124241775323704e-14
relative error = 4.9619473613882641315541635091125e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6218
Order of pole = 2.082
x[1] = 0.951
y[1] (analytic) = 2.5432293610825040304175843031698
y[1] (numeric) = 2.5432293610825167449713394635307
absolute error = 1.27145537551603609e-14
relative error = 4.9993736112532606246158750217764e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.3MB, time=16.37
Real estimate of pole used
Radius of convergence = 0.6208
Order of pole = 2.082
x[1] = 0.952
y[1] (analytic) = 2.5446321865514191765316213253329
y[1] (numeric) = 2.5446321865514319942076474865857
absolute error = 1.28176760261612528e-14
relative error = 5.0371429293017971729185398850502e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6197
Order of pole = 2.082
x[1] = 0.953
y[1] (analytic) = 2.5460379841106814013812197780979
y[1] (numeric) = 2.5460379841106943231834897229396
absolute error = 1.29218022699448417e-14
relative error = 5.0752590301430101987712848197563e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6187
Order of pole = 2.082
x[1] = 0.954
y[1] (analytic) = 2.5474467621283761910929759711351
y[1] (numeric) = 2.5474467621283892180368885882906
absolute error = 1.30269439126171555e-14
relative error = 5.1137256747745430903643299626149e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6177
Order of pole = 2.082
x[1] = 0.955
y[1] (analytic) = 2.5488585290139662431458015022537
y[1] (numeric) = 2.5488585290139793762583306326137
absolute error = 1.31331125291303600e-14
relative error = 5.1525466712391232445562631885721e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6167
Order of pole = 2.082
x[1] = 0.956
y[1] (analytic) = 2.55027329321855902393744284378
y[1] (numeric) = 2.55027329321857226425728831151
absolute error = 1.32403198454677300e-14
relative error = 5.1917258752915276128194617046892e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6157
Order of pole = 2.082
x[1] = 0.957
y[1] (analytic) = 2.5516910632351765062902099598567
y[1] (numeric) = 2.5516910632351898548679508241724
absolute error = 1.33485777408643157e-14
relative error = 5.2312671910761183547446230420751e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6147
Order of pole = 2.082
x[1] = 0.958
y[1] (analytic) = 2.5531118475990271082166920024384
y[1] (numeric) = 2.5531118475990405661149420663866
absolute error = 1.34578982500639482e-14
relative error = 5.2711745718151343251121659150045e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6137
Order of pole = 2.082
x[1] = 0.959
y[1] (analytic) = 2.5545356548877798545100006524987
y[1] (numeric) = 2.5545356548877934228035662657372
absolute error = 1.35682935656132385e-14
relative error = 5.3114520205079268774209184221259e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6127
Order of pole = 2.082
x[1] = 0.96
y[1] (analytic) = 2.5559624937218407829700342532686
y[1] (numeric) = 2.5559624937218544627460744465056
absolute error = 1.36797760401932370e-14
relative error = 5.3521035906413319788862524724361e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6117
Order of pole = 2.082
x[1] = 0.961
y[1] (analytic) = 2.5573923727646316173274455680977
y[1] (numeric) = 2.5573923727646454096856345575354
absolute error = 1.37923581889894377e-14
relative error = 5.3931333869113759114251828915083e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6107
Order of pole = 2.082
x[1] = 0.962
y[1] (analytic) = 2.5588253007228707291804706027897
y[1] (numeric) = 2.558825300722884635233162703608
absolute error = 1.39060526921008183e-14
relative error = 5.4345455659565130858962986215291e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6097
Order of pole = 2.082
x[1] = 0.963
y[1] (analytic) = 2.5602612863468564115165840630706
y[1] (numeric) = 2.5602612863468704323889810516981
absolute error = 1.40208723969886275e-14
relative error = 5.4763443371026008456401842118397e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.3MB, time=16.57
Real estimate of pole used
Radius of convergence = 0.6087
Order of pole = 2.082
x[1] = 0.964
y[1] (analytic) = 2.5617003384307524866511380745996
y[1] (numeric) = 2.5617003384307666234814590402397
absolute error = 1.41368303209656401e-14
relative error = 5.5185339631198182215789590944062e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6077
Order of pole = 2.082
x[1] = 0.965
y[1] (analytic) = 2.5631424658128762716787649928161
y[1] (numeric) = 2.5631424658128905256184187194345
absolute error = 1.42539396537266184e-14
relative error = 5.5611187609917410170964494415533e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6067
Order of pole = 2.082
x[1] = 0.966
y[1] (analytic) = 2.5645876773759889248004335197777
y[1] (numeric) = 2.5645876773760032970141934405074
absolute error = 1.43722137599207297e-14
relative error = 5.6041031026967884007134535799578e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6057
Order of pole = 2.082
x[1] = 0.967
y[1] (analytic) = 2.566035982047588196159691816542
y[1] (numeric) = 2.5660359820476026878258735832303
absolute error = 1.44916661817666883e-14
relative error = 5.6474914160022617994158386926000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6047
Order of pole = 2.082
x[1] = 0.968
y[1] (analytic) = 2.5674873888002036070958646042911
y[1] (numeric) = 2.5674873888002182194065063156928
absolute error = 1.46123106417114017e-14
relative error = 5.6912881852711996126556664148834e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6037
Order of pole = 2.082
x[1] = 0.969
y[1] (analytic) = 2.56894190665169408199984701283
y[1] (numeric) = 2.5689419066517088161608921457509
absolute error = 1.47341610451329209e-14
relative error = 5.7354979522822774284937056353849e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6027
Order of pole = 2.082
x[1] = 0.97
y[1] (analytic) = 2.5703995446655480572397106807342
y[1] (numeric) = 2.5703995446655629144711937692399
absolute error = 1.48572314830885057e-14
relative error = 5.7801253170629859575740194633477e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6017
Order of pole = 2.082
x[1] = 0.971
y[1] (analytic) = 2.5718603119511860919086627648908
y[1] (numeric) = 2.571860311951201073444897873528
absolute error = 1.49815362351086372e-14
relative error = 5.8251749387363254097586603287269e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.6007
Order of pole = 2.082
x[1] = 0.972
y[1] (analytic) = 2.5733242176642660054370324309878
y[1] (numeric) = 2.5733242176642811125268044688092
absolute error = 1.51070897720378214e-14
relative error = 5.8706515363812577661741426165428e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5997
Order of pole = 2.082
x[1] = 0.973
y[1] (analytic) = 2.574791271006990567402959365034
y[1] (numeric) = 2.5747912710070058013097182880841
absolute error = 1.52339067589230501e-14
relative error = 5.9165598899071652124208083511791e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5987
Order of pole = 2.082
x[1] = 0.974
y[1] (analytic) = 2.5762614812284177651733831228739
y[1] (numeric) = 2.5762614812284331271754410736708
absolute error = 1.53620020579507969e-14
relative error = 5.9629048409425656053157251736069e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5977
Order of pole = 2.082
memory used=320.4MB, alloc=4.3MB, time=16.77
x[1] = 0.975
y[1] (analytic) = 2.577734857624773675307839950423
y[1] (numeric) = 2.5777348576247891666985713838735
absolute error = 1.54913907314334505e-14
relative error = 6.0096912937383433857742055759212e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5967
Order of pole = 2.082
x[1] = 0.976
y[1] (analytic) = 2.5792114095397679649625252875358
y[1] (numeric) = 2.5792114095397835870505701336343
absolute error = 1.56220880448460985e-14
relative error = 6.0569242160857566375440735993126e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5957
Order of pole = 2.082
x[1] = 0.977
y[1] (analytic) = 2.5806911463649120498411367519265
y[1] (numeric) = 2.5806911463649278039506066665263
absolute error = 1.57541094699145998e-14
relative error = 6.1046086402494886335416770357262e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5947
Order of pole = 2.082
x[1] = 0.978
y[1] (analytic) = 2.5821740775398399355522362575089
y[1] (numeric) = 2.582174077539855823022924013408
absolute error = 1.58874706877558991e-14
relative error = 6.1527496639160161152692629123176e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5937
Order of pole = 2.082
x[1] = 0.979
y[1] (analytic) = 2.5836602125526317695503243763516
y[1] (numeric) = 2.5836602125526477917379164479087
absolute error = 1.60221875920715571e-14
relative error = 6.2013524511575722331522862569159e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5927
Order of pole = 2.082
x[1] = 0.98
y[1] (analytic) = 2.5851495609401401311595694985215
y[1] (numeric) = 2.5851495609401562894358618940115
absolute error = 1.61582762923954900e-14
relative error = 6.2504222334119876691688834414687e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5917
Order of pole = 2.082
x[1] = 0.981
y[1] (analytic) = 2.5866421322883190875052442636482
y[1] (numeric) = 2.5866421322883353832583616605818
absolute error = 1.62957531173969336e-14
relative error = 6.2999643104786996636947905211646e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5907
Order of pole = 2.082
x[1] = 0.982
y[1] (analytic) = 2.5881379362325560435084587275423
y[1] (numeric) = 2.5881379362325724781430769672064
absolute error = 1.64346346182396641e-14
relative error = 6.3499840515312229218968821975404e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5897
Order of pole = 2.082
x[1] = 0.983
y[1] (analytic) = 2.5896369824580064144348115141095
y[1] (numeric) = 2.5896369824580229893723835126436
absolute error = 1.65749375719985341e-14
relative error = 6.4004868961463842911936753895852e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5887
Order of pole = 2.082
x[1] = 0.984
y[1] (analytic) = 2.5911392806999311498271756678028
y[1] (numeric) = 2.5911392806999478665061608022026
absolute error = 1.67166789851343998e-14
relative error = 6.4514783553506275188164717513685e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5877
Order of pole = 2.082
x[1] = 0.985
y[1] (analytic) = 2.5926448407440371379970651204698
y[1] (numeric) = 2.5926448407440539978731621490088
absolute error = 1.68598760970285390e-14
relative error = 6.5029640126837011225590423459197e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5867
Order of pole = 2.082
x[1] = 0.986
y[1] (analytic) = 2.5941536724268205205979618711298
y[1] (numeric) = 2.5941536724268375251443454488129
absolute error = 1.70045463835776831e-14
relative error = 6.5549495252800490730244628413549e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.3MB, time=16.96
Real estimate of pole used
Radius of convergence = 0.5857
Order of pole = 2.082
x[1] = 0.987
y[1] (analytic) = 2.5956657856359129471576956198785
y[1] (numeric) = 2.5956657856359300978652564706861
absolute error = 1.71507075608508076e-14
relative error = 6.6074406249682297056618045382660e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5847
Order of pole = 2.082
x[1] = 0.988
y[1] (analytic) = 2.597181190310430799805530412123
y[1] (numeric) = 2.5971811903104480981831192209734
absolute error = 1.72983775888088504e-14
relative error = 6.6604431193886952936806559258702e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5837
Order of pole = 2.082
x[1] = 0.989
y[1] (analytic) = 2.5986998964413274187931018170024
y[1] (numeric) = 2.5986998964413448663677769055543
absolute error = 1.74475746750885519e-14
relative error = 6.7139628931302716250626852359885e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5827
Order of pole = 2.082
x[1] = 0.99
y[1] (analytic) = 2.60022191407174835977683955433
y[1] (numeric) = 2.6002219140717659580941184059633
absolute error = 1.75983172788516333e-14
relative error = 6.7680059088856828921708310931229e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5817
Order of pole = 2.082
x[1] = 0.991
y[1] (analytic) = 2.6017472532973897142030818822118
y[1] (numeric) = 2.6017472532974074648271965827695
absolute error = 1.77506241147005577e-14
relative error = 6.8225782086264753390357084550945e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5807
Order of pole = 2.082
x[1] = 0.992
y[1] (analytic) = 2.6032759242668595245158183864662
y[1] (numeric) = 2.6032759242668774290299750486088
absolute error = 1.79045141566621426e-14
relative error = 6.8776859147976995645613878026684e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5797
Order of pole = 2.082
x[1] = 0.993
y[1] (analytic) = 2.6048079371820423262909673616633
y[1] (numeric) = 2.604807937182060386297609601983
absolute error = 1.80600066422403197e-14
relative error = 6.9333352315327190380473188113459e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5787
Order of pole = 2.082
x[1] = 0.994
y[1] (analytic) = 2.6063433022984668497903844213653
y[1] (numeric) = 2.6063433022984850669114609607284
absolute error = 1.82171210765393631e-14
relative error = 6.9895324458885191669074963330059e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5777
Order of pole = 2.082
x[1] = 0.995
y[1] (analytic) = 2.6078820299256769138234934186464
y[1] (numeric) = 2.6078820299256952897007298775855
absolute error = 1.83758772364589391e-14
relative error = 7.0462839291019006207450165796693e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5767
Order of pole = 2.082
x[1] = 0.996
y[1] (analytic) = 2.6094241304276055452046137382894
y[1] (numeric) = 2.6094241304276240814997887006415
absolute error = 1.85362951749623521e-14
relative error = 7.1035961378669457619195144634927e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5757
Order of pole = 2.082
x[1] = 0.997
y[1] (analytic) = 2.6109696142229523574998155523541
y[1] (numeric) = 2.6109696142229710558950409717518
absolute error = 1.86983952254193977e-14
relative error = 7.1614756156341579807894775208878e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5747
Order of pole = 2.082
x[1] = 0.998
y[1] (analytic) = 2.6125184917855642231685542246011
y[1] (numeric) = 2.6125184917855830853665602498587
absolute error = 1.88621980060252576e-14
relative error = 7.2199289939316795781293242849911e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.3MB, time=17.16
Real estimate of pole used
Radius of convergence = 0.5737
Order of pole = 2.082
x[1] = 0.999
y[1] (analytic) = 2.6140707736448192736225057491873
y[1] (numeric) = 2.6140707736448383013469300460921
absolute error = 1.90277244242969048e-14
relative error = 7.2789629937090035969242139625007e-13 %
h = 0.001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 0.5727
Order of pole = 2.082
x[1] = 1
y[1] (analytic) = 2.6156264703860142621470375164089
y[1] (numeric) = 2.6156264703860334571427191649247
absolute error = 1.91949956816485158e-14
relative error = 7.3385844267036025015155426835761e-13 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = tan ( x ) ;
Iterations = 1000
Total Elapsed Time = 17 Seconds
Elapsed Time(since restart) = 17 Seconds
Expected Time Remaining = 1 Minutes 8 Seconds
Optimized Time Remaining = 1 Minutes 8 Seconds
Time to Timeout = 14 Minutes 42 Seconds
Percent Done = 20.02 %
> quit
memory used=328.8MB, alloc=4.3MB, time=17.20