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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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> 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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, 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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> 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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, 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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> 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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, 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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> 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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, 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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> 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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, 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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre cos $eq_no = 1
> array_tmp2_g[1] := sin(array_x[1]);
> array_tmp2[1] := cos(array_x[1]);
> #emit pre div $eq_no = 1 i = 1
> array_tmp3[1] := (array_tmp1[1] / (array_tmp2[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := -att(1,array_tmp1,array_x,1);
> #emit pre cos $eq_no = 1
> array_tmp2_g[2] := (att(1,array_tmp2,array_x,1));
> array_tmp2[2] := (-att(1,array_tmp2_g,array_x,1));
> #emit pre div $eq_no = 1 i = 2
> array_tmp3[2] := ((array_tmp1[2] - ats(2,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 2
> array_tmp4[2] := array_const_0D0[2] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := -att(2,array_tmp1,array_x,1);
> #emit pre cos $eq_no = 1
> array_tmp2_g[3] := (att(2,array_tmp2,array_x,1));
> array_tmp2[3] := (-att(2,array_tmp2_g,array_x,1));
> #emit pre div $eq_no = 1 i = 3
> array_tmp3[3] := ((array_tmp1[3] - ats(3,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 3
> array_tmp4[3] := array_const_0D0[3] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := -att(3,array_tmp1,array_x,1);
> #emit pre cos $eq_no = 1
> array_tmp2_g[4] := (att(3,array_tmp2,array_x,1));
> array_tmp2[4] := (-att(3,array_tmp2_g,array_x,1));
> #emit pre div $eq_no = 1 i = 4
> array_tmp3[4] := ((array_tmp1[4] - ats(4,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 4
> array_tmp4[4] := array_const_0D0[4] + array_tmp3[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_tmp4[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 sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := -att(4,array_tmp1,array_x,1);
> #emit pre cos $eq_no = 1
> array_tmp2_g[5] := (att(4,array_tmp2,array_x,1));
> array_tmp2[5] := (-att(4,array_tmp2_g,array_x,1));
> #emit pre div $eq_no = 1 i = 5
> array_tmp3[5] := ((array_tmp1[5] - ats(5,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit pre add $eq_no = 1 i = 5
> array_tmp4[5] := array_const_0D0[5] + array_tmp3[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_tmp4[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 sin $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1);
> #emit cos $eq_no = 1
> array_tmp2_g[kkk] := (att(kkk-1,array_tmp2,array_x,1));
> array_tmp2[kkk] := (-att(kkk-1,array_tmp2_g,array_x,1));
> #emit div $eq_no = 1
> array_tmp3[kkk] := ((array_tmp1[kkk] - ats(kkk,array_tmp2,array_tmp3,2))/array_tmp2[1]);
> #emit add $eq_no = 1
> array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[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_tmp4[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 INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2_g[1] := sin(array_x[1]);
array_tmp2[1] := cos(array_x[1]);
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[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[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1);
array_tmp2_g[2] := att(1, array_tmp2, array_x, 1);
array_tmp2[2] := -att(1, array_tmp2_g, array_x, 1);
array_tmp3[2] :=
(array_tmp1[2] - ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[2] := array_const_0D0[2] + array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[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[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1);
array_tmp2_g[3] := att(2, array_tmp2, array_x, 1);
array_tmp2[3] := -att(2, array_tmp2_g, array_x, 1);
array_tmp3[3] :=
(array_tmp1[3] - ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[3] := array_const_0D0[3] + array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[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[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1);
array_tmp2_g[4] := att(3, array_tmp2, array_x, 1);
array_tmp2[4] := -att(3, array_tmp2_g, array_x, 1);
array_tmp3[4] :=
(array_tmp1[4] - ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[4] := array_const_0D0[4] + array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[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[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1);
array_tmp2_g[5] := att(4, array_tmp2, array_x, 1);
array_tmp2[5] := -att(4, array_tmp2_g, array_x, 1);
array_tmp3[5] :=
(array_tmp1[5] - ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[5] := array_const_0D0[5] + array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[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[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2_g[kkk] := att(kkk - 1, array_tmp2, array_x, 1);
array_tmp2[kkk] := -att(kkk - 1, array_tmp2_g, array_x, 1);
array_tmp3[kkk] := (
array_tmp1[kkk] - ats(kkk, array_tmp2, array_tmp3, 2))/
array_tmp2[1];
array_tmp4[kkk] := array_const_0D0[kkk] + array_tmp3[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_tmp4[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)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! 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
> INFO,
> glob_max_terms,
> DEBUGMASSIVE,
> DEBUGL,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_hmin,
> glob_disp_incr,
> glob_clock_sec,
> min_in_hour,
> glob_html_log,
> glob_log10relerr,
> glob_max_sec,
> glob_warned2,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> djd_debug,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_start,
> glob_small_float,
> glob_max_iter,
> glob_iter,
> hours_in_day,
> glob_warned,
> glob_h,
> glob_initial_pass,
> sec_in_min,
> glob_display_flag,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_dump,
> glob_max_minutes,
> glob_current_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_almost_1,
> days_in_year,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_hmax,
> djd_debug2,
> glob_optimal_clock_start_sec,
> glob_large_float,
> glob_not_yet_start_msg,
> years_in_century,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_subiter_method,
> glob_percent_done,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_hmin_init,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_norms,
> array_m1,
> array_tmp1_g,
> array_tmp2_g,
> array_pole,
> array_1st_rel_error,
> array_y_init,
> array_y_higher_work,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_set_initial,
> array_y_higher_work2,
> array_complex_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> DEBUGL := 3;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_log10abserr := 0.0;
> glob_hmin := 0.00000000001;
> glob_disp_incr := 0.1;
> glob_clock_sec := 0.0;
> min_in_hour := 60.0;
> glob_html_log := true;
> glob_log10relerr := 0.0;
> glob_max_sec := 10000.0;
> glob_warned2 := false;
> glob_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> djd_debug := true;
> glob_log10normmin := 0.1;
> MAX_UNCHANGED := 10;
> glob_start := 0;
> glob_small_float := 0.1e-50;
> glob_max_iter := 1000;
> glob_iter := 0;
> hours_in_day := 24.0;
> glob_warned := false;
> glob_h := 0.1;
> glob_initial_pass := true;
> sec_in_min := 60.0;
> glob_display_flag := true;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_max_hours := 0.0;
> glob_optimal_done := false;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_dump := false;
> glob_max_minutes := 0.0;
> glob_current_iter := 0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_dump_analytic := false;
> glob_almost_1 := 0.9990;
> days_in_year := 365.0;
> glob_orig_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmax := 1.0;
> djd_debug2 := true;
> glob_optimal_clock_start_sec := 0.0;
> glob_large_float := 9.0e100;
> glob_not_yet_start_msg := true;
> years_in_century := 100.0;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_subiter_method := 3;
> glob_percent_done := 0.0;
> glob_normmax := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> glob_reached_optimal_h := false;
> #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/divpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) / cos ( 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 := 0.1;");
> omniout_str(ALWAYS,"x_end := 1.0 ;");
> 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 := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> 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,"");
> 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_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_tmp2_g:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> 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_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[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_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_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 <=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 <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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_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_complex_pole[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_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[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_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 1.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> 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)) / (convfp(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)) / (convfp(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)) / (convfp(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 ) = sin ( x ) / cos ( 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,"2012-06-13T13:26:46-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) / cos ( 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," 090 | ")
> ;
> logitem_str(html_log_file,"div diffeq.mxt")
> ;
> logitem_str(html_log_file,"div maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> 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;
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;
global INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_iolevel,
glob_log10abserr, glob_hmin, glob_disp_incr, glob_clock_sec, min_in_hour,
glob_html_log, glob_log10relerr, glob_max_sec, glob_warned2, glob_relerr,
glob_abserr, glob_log10_relerr, glob_log10_abserr, glob_last_good_h,
djd_debug, glob_log10normmin, MAX_UNCHANGED, glob_start, glob_small_float,
glob_max_iter, glob_iter, hours_in_day, glob_warned, glob_h,
glob_initial_pass, sec_in_min, glob_display_flag, glob_unchanged_h_cnt,
glob_no_eqs, glob_max_hours, glob_optimal_done, glob_not_yet_finished,
glob_clock_start_sec, centuries_in_millinium, glob_dump, glob_max_minutes,
glob_current_iter, glob_smallish_float, glob_optimal_start,
glob_max_rel_trunc_err, glob_dump_analytic, glob_almost_1, days_in_year,
glob_orig_start_sec, glob_max_trunc_err, glob_hmax, djd_debug2,
glob_optimal_clock_start_sec, glob_large_float, glob_not_yet_start_msg,
years_in_century, glob_max_opt_iter, glob_optimal_expect_sec,
glob_subiter_method, glob_percent_done, glob_normmax,
glob_curr_iter_when_opt, glob_look_poles, glob_hmin_init,
glob_reached_optimal_h, array_const_1, array_const_0D0, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_last_rel_error,
array_type_pole, array_y, array_x, array_norms, array_m1, array_tmp1_g,
array_tmp2_g, array_pole, array_1st_rel_error, array_y_init,
array_y_higher_work, array_real_pole, array_y_higher, array_poles,
array_y_set_initial, array_y_higher_work2, array_complex_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
DEBUGL := 3;
ALWAYS := 1;
glob_iolevel := 5;
glob_log10abserr := 0.;
glob_hmin := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_clock_sec := 0.;
min_in_hour := 60.0;
glob_html_log := true;
glob_log10relerr := 0.;
glob_max_sec := 10000.0;
glob_warned2 := false;
glob_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
djd_debug := true;
glob_log10normmin := 0.1;
MAX_UNCHANGED := 10;
glob_start := 0;
glob_small_float := 0.1*10^(-50);
glob_max_iter := 1000;
glob_iter := 0;
hours_in_day := 24.0;
glob_warned := false;
glob_h := 0.1;
glob_initial_pass := true;
sec_in_min := 60.0;
glob_display_flag := true;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_max_hours := 0.;
glob_optimal_done := false;
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
centuries_in_millinium := 10.0;
glob_dump := false;
glob_max_minutes := 0.;
glob_current_iter := 0;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_dump_analytic := false;
glob_almost_1 := 0.9990;
days_in_year := 365.0;
glob_orig_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmax := 1.0;
djd_debug2 := true;
glob_optimal_clock_start_sec := 0.;
glob_large_float := 0.90*10^101;
glob_not_yet_start_msg := true;
years_in_century := 100.0;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_subiter_method := 3;
glob_percent_done := 0.;
glob_normmax := 0.;
glob_curr_iter_when_opt := 0;
glob_look_poles := false;
glob_hmin_init := 0.001;
glob_reached_optimal_h := false;
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/divpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) / cos ( 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 := 0.1;");
omniout_str(ALWAYS, "x_end := 1.0 ;");
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 := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
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, "");
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_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_tmp2_g := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_norms[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_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 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 <= 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 <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_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_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[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_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp2_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp2_g[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.1;
x_end := 1.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.0001;
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)/convfp(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)/convfp(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)/convfp(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 ) = sin ( x ) / cos ( 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, "2012-06-13T13:26:46-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "div");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) / cos ( 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, " 090 | ");
logitem_str(html_log_file,
"div diffeq.mxt");
logitem_str(html_log_file,
"div maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/divpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 1.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
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] = 0.1
y[1] (analytic) = 2.0050083556232353090791329977213
y[1] (numeric) = 2.0050083556232353090791329977213
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1001
y[1] (analytic) = 2.0050183941408128764996479973735
y[1] (numeric) = 2.0050183941408128764996488429212
absolute error = 8.455477e-25
relative error = 4.2171568224556497595801630406164e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1002
y[1] (analytic) = 2.0050284427592637190410951908048
y[1] (numeric) = 2.005028442759263719041096882039
absolute error = 1.6912342e-24
relative error = 8.4349636340947417548906943320370e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1003
y[1] (analytic) = 2.0050385014787908383875034755221
y[1] (numeric) = 2.0050385014787908383875060125819
absolute error = 2.5370598e-24
relative error = 1.2653421857629285264440372393537e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1004
y[1] (analytic) = 2.0050485702995974443703038670178
y[1] (numeric) = 2.0050485702995974443703072500424
absolute error = 3.3830246e-24
relative error = 1.6872531918239283628545282485996e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1005
y[1] (analytic) = 2.0050586492218869549848330096909
y[1] (numeric) = 2.0050586492218869549848372388197
absolute error = 4.2291288e-24
relative error = 2.1092294739813316526353744856184e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.18
NO POLE
x[1] = 0.1006
y[1] (analytic) = 2.0050687382458629964068540899123
y[1] (numeric) = 2.0050687382458629964068591652848
absolute error = 5.0753725e-24
relative error = 2.5312710747463931128553927210262e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1007
y[1] (analytic) = 2.0050788373717294030090951541011
y[1] (numeric) = 2.0050788373717294030091010758569
absolute error = 5.9217558e-24
relative error = 2.9533780366273660618085390784161e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1008
y[1] (analytic) = 2.0050889465996902173778048346799
y[1] (numeric) = 2.0050889465996902173778116029589
absolute error = 6.7682790e-24
relative error = 3.3755505018756985286179938588279e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1009
y[1] (analytic) = 2.0050990659299496903293254867837
y[1] (numeric) = 2.0050990659299496903293331017259
absolute error = 7.6149422e-24
relative error = 3.7977885129921237823761615316473e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 2.0051091953627122809266837385959
y[1] (numeric) = 2.0051091953627122809266922003413
absolute error = 8.4617454e-24
relative error = 4.2200920626017680709170152108229e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1011
y[1] (analytic) = 2.0051193348981826564961984581912
y[1] (numeric) = 2.0051193348981826564962077668802
absolute error = 9.3086890e-24
relative error = 4.6424613428171261842850520940584e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1012
y[1] (analytic) = 2.0051294845365656926441061397678
y[1] (numeric) = 2.0051294845365656926441162955408
absolute error = 1.01557730e-23
relative error = 5.0648963462562851546002172858984e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1013
y[1] (analytic) = 2.0051396442780664732732037121527
y[1] (numeric) = 2.0051396442780664732732147151502
absolute error = 1.10029975e-23
relative error = 5.4873971154071595607378953802243e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1014
y[1] (analytic) = 2.0051498141228902905995087724693
y[1] (numeric) = 2.005149814122890290599520622832
absolute error = 1.18503627e-23
relative error = 5.9099637426262269489635762946320e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.39
NO POLE
x[1] = 0.1015
y[1] (analytic) = 2.0051599940712426451689372478581
y[1] (numeric) = 2.005159994071242645168949945727
absolute error = 1.26978689e-23
relative error = 6.3325963701372595227452015562111e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1016
y[1] (analytic) = 2.0051701841233292458739984881456
y[1] (numeric) = 2.0051701841233292458740120336618
absolute error = 1.35455162e-23
relative error = 6.7552950404168160905633294285734e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1017
y[1] (analytic) = 2.0051803842793560099705077923581
y[1] (numeric) = 2.0051803842793560099705221856626
absolute error = 1.43933045e-23
relative error = 7.1780596961967716336588471875686e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1018
y[1] (analytic) = 2.0051905945395290630943163719814
y[1] (numeric) = 2.0051905945395290630943316132156
absolute error = 1.52412342e-23
relative error = 7.6008905295608516373798487387212e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1019
y[1] (analytic) = 2.0052008149040547392780587538716
y[1] (numeric) = 2.0052008149040547392780748431771
absolute error = 1.60893055e-23
relative error = 8.0237876328460620520997061363609e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 2.0052110453731395809679176257221
y[1] (numeric) = 2.0052110453731395809679345632405
absolute error = 1.69375184e-23
relative error = 8.4467509986452238356911610953498e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1021
y[1] (analytic) = 2.0052212859469903390404061269981
y[1] (numeric) = 2.0052212859469903390404239128712
absolute error = 1.77858731e-23
relative error = 8.8697807192887459048823597493689e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1022
y[1] (analytic) = 2.0052315366258139728191675882519
y[1] (numeric) = 2.0052315366258139728191862226217
absolute error = 1.86343698e-23
relative error = 9.2928768871029703356723345556365e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1023
y[1] (analytic) = 2.0052417974098176500917927217353
y[1] (numeric) = 2.0052417974098176500918122047438
absolute error = 1.94830085e-23
relative error = 9.7160394946715722812627204659171e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=0.61
NO POLE
x[1] = 0.1024
y[1] (analytic) = 2.0052520682992087471266542662285
y[1] (numeric) = 2.005252068299208747126674598018
absolute error = 2.03317895e-23
relative error = 1.0139268684183320398513105211256e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1025
y[1] (analytic) = 2.0052623492941948486897590890093
y[1] (numeric) = 2.0052623492941948486897802697222
absolute error = 2.11807129e-23
relative error = 1.0562564498084309234547077953318e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1026
y[1] (analytic) = 2.005272640394983748061617747887
y[1] (numeric) = 2.0052726403949837480616397776659
absolute error = 2.20297789e-23
relative error = 1.0985927028686102936246181199963e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1027
y[1] (analytic) = 2.0052829416017834470541315162315
y[1] (numeric) = 2.0052829416017834470541543952192
absolute error = 2.28789877e-23
relative error = 1.1409356368296177609590366011963e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1028
y[1] (analytic) = 2.005293252914802156027496873929
y[1] (numeric) = 2.0052932529148021560275206022683
absolute error = 2.37283393e-23
relative error = 1.1832852509481880514686237426463e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1029
y[1] (analytic) = 2.0053035743342482939071274672
y[1] (numeric) = 2.0053035743342482939071520450339
absolute error = 2.45778339e-23
relative error = 1.2256415544544037208612364897635e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 2.0053139058603304882005935402182
y[1] (numeric) = 2.00531390586033048820061896769
absolute error = 2.54274718e-23
relative error = 1.2680045615646878070735127981650e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1031
y[1] (analytic) = 2.0053242474932575750145788414723
y[1] (numeric) = 2.0053242474932575750146051187252
absolute error = 2.62772529e-23
relative error = 1.3103742665480511526079407789594e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1032
y[1] (analytic) = 2.0053345992332385990718550078141
y[1] (numeric) = 2.0053345992332385990718821349917
absolute error = 2.71271776e-23
relative error = 1.3527506886068973293049137152377e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1033
y[1] (analytic) = 2.0053449610804828137282734291436
y[1] (numeric) = 2.0053449610804828137283014063895
absolute error = 2.79772459e-23
relative error = 1.3951338269963198137638733889834e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.0MB, time=0.82
NO POLE
x[1] = 0.1034
y[1] (analytic) = 2.0053553330351996809897745966794
y[1] (numeric) = 2.0053553330351996809898034241374
absolute error = 2.88274580e-23
relative error = 1.4375236909445013676603667638772e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1035
y[1] (analytic) = 2.005365715097598871529414937771
y[1] (numeric) = 2.005365715097598871529444615585
absolute error = 2.96778140e-23
relative error = 1.4799202846925910719783661125790e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1036
y[1] (analytic) = 2.0053761072678902647044111402085
y[1] (numeric) = 2.0053761072678902647044416685227
absolute error = 3.05283142e-23
relative error = 1.5223236224546203401110202368679e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1037
y[1] (analytic) = 2.0053865095462839485732019689931
y[1] (numeric) = 2.0053865095462839485732333479517
absolute error = 3.13789586e-23
relative error = 1.5647337034843945357343456412184e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1038
y[1] (analytic) = 2.0053969219329902199125275785286
y[1] (numeric) = 2.0053969219329902199125598082761
absolute error = 3.22297475e-23
relative error = 1.6071505419951446421869778620905e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1039
y[1] (analytic) = 2.0054073444282195842345263232045
y[1] (numeric) = 2.0054073444282195842345594038854
absolute error = 3.30806809e-23
relative error = 1.6495741372400299980087471390276e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 2.0054177770321827558038490693382
y[1] (numeric) = 2.0054177770321827558038830010972
absolute error = 3.39317590e-23
relative error = 1.6920044984449874218939522482512e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1041
y[1] (analytic) = 2.0054282197450906576547910114508
y[1] (numeric) = 2.0054282197450906576548257944328
absolute error = 3.47829820e-23
relative error = 1.7344416348355392029299739378821e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1042
y[1] (analytic) = 2.0054386725671544216084409958533
y[1] (numeric) = 2.0054386725671544216084766302033
absolute error = 3.56343500e-23
relative error = 1.7768855506503524248666244843780e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.04
NO POLE
x[1] = 0.1043
y[1] (analytic) = 2.0054491354985853882898483545216
y[1] (numeric) = 2.0054491354985853882898848403848
absolute error = 3.64858632e-23
relative error = 1.8193362551141969137073573933375e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1044
y[1] (analytic) = 2.0054596085395951071452072522444
y[1] (numeric) = 2.0054596085395951071452445897661
absolute error = 3.73375217e-23
relative error = 1.8617937524650385282934853637427e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1045
y[1] (analytic) = 2.005470091690395336459058550029
y[1] (numeric) = 2.0054700916903953364590967393547
absolute error = 3.81893257e-23
relative error = 1.9042580519268931453413838118852e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1046
y[1] (analytic) = 2.0054805849511980433715091877551
y[1] (numeric) = 2.0054805849511980433715482290305
absolute error = 3.90412754e-23
relative error = 1.9467291627233599931193767439325e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1047
y[1] (analytic) = 2.0054910883222154038954690890679
y[1] (numeric) = 2.0054910883222154038955089824387
absolute error = 3.98933708e-23
relative error = 1.9892070841050014359193096610952e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1048
y[1] (analytic) = 2.0055016018036598029339055915065
y[1] (numeric) = 2.0055016018036598029339463371187
absolute error = 4.07456122e-23
relative error = 2.0316918302810225201380567118235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1049
y[1] (analytic) = 2.0055121253957438342971154048667
y[1] (numeric) = 2.0055121253957438342971570028665
absolute error = 4.15979998e-23
relative error = 2.0741834104738482715997599288970e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 2.0055226590986803007200141007995
y[1] (numeric) = 2.005522659098680300720056551333
absolute error = 4.24505335e-23
relative error = 2.1166818189467911674079690400622e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1051
y[1] (analytic) = 2.0055332029126822138794431366493
y[1] (numeric) = 2.005533202912682213879486439863
absolute error = 4.33032137e-23
relative error = 2.1591870748940851293399765863293e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=1.26
NO POLE
x[1] = 0.1052
y[1] (analytic) = 2.0055437568379627944114944165428
y[1] (numeric) = 2.0055437568379627944115385725833
absolute error = 4.41560405e-23
relative error = 2.2016991825507984581395639998991e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1053
y[1] (analytic) = 2.005554320874735471928852392737
y[1] (numeric) = 2.005554320874735471928897401751
absolute error = 4.50090140e-23
relative error = 2.2442181461516847775106444306250e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1054
y[1] (analytic) = 2.0055648950232138850381537102422
y[1] (numeric) = 2.0055648950232138850381995723766
absolute error = 4.58621344e-23
relative error = 2.2867439749173091645357000195837e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1055
y[1] (analytic) = 2.0055754792836118813573643977379
y[1] (numeric) = 2.0055754792836118813574111131397
absolute error = 4.67154018e-23
relative error = 2.3292766730817162431738485740254e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1056
y[1] (analytic) = 2.0055860736561435175331746078019
y[1] (numeric) = 2.0055860736561435175332221766183
absolute error = 4.75688164e-23
relative error = 2.3718162498647088196405854190933e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1057
y[1] (analytic) = 2.005596678141023059258410909477
y[1] (numeric) = 2.0055966781410230592584593318553
absolute error = 4.84223783e-23
relative error = 2.4143627094996211319746399206285e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1058
y[1] (analytic) = 2.0056072927384649812894661362023
y[1] (numeric) = 2.00560729273846498128951541229
absolute error = 4.92760877e-23
relative error = 2.4569160612054922299475252127801e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1059
y[1] (analytic) = 2.0056179174486839674637467921395
y[1] (numeric) = 2.0056179174486839674637969220843
absolute error = 5.01299448e-23
relative error = 2.4994763142009391267133659510289e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 2.0056285522718949107171380199288
y[1] (numeric) = 2.0056285522718949107171890038784
absolute error = 5.09839496e-23
relative error = 2.5420434677322200977032481403428e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1061
y[1] (analytic) = 2.0056391972083129131014861329089
y[1] (numeric) = 2.0056391972083129131015379710114
absolute error = 5.18381025e-23
relative error = 2.5846175409891487031918785804247e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=1.48
NO POLE
x[1] = 0.1062
y[1] (analytic) = 2.0056498522581532858020987148442
y[1] (numeric) = 2.0056498522581532858021514072476
absolute error = 5.26924034e-23
relative error = 2.6271985282313276223264941916942e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1063
y[1] (analytic) = 2.005660517421631549155262290199
y[1] (numeric) = 2.0056605174216315491553158370516
absolute error = 5.35468526e-23
relative error = 2.6697864436618082988593594462356e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1064
y[1] (analytic) = 2.0056711926989634326657775680081
y[1] (numeric) = 2.0056711926989634326658319694584
absolute error = 5.44014503e-23
relative error = 2.7123812964972499132858014340745e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1065
y[1] (analytic) = 2.0056818780903648750245122623911
y[1] (numeric) = 2.0056818780903648750245675185877
absolute error = 5.52561966e-23
relative error = 2.7549830909680514634883825440335e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1066
y[1] (analytic) = 2.0056925735960520241259714927643
y[1] (numeric) = 2.0056925735960520241260276038558
absolute error = 5.61110915e-23
relative error = 2.7975918263184842182913114843393e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1067
y[1] (analytic) = 2.0057032792162412370858857668053
y[1] (numeric) = 2.0057032792162412370859427329407
absolute error = 5.69661354e-23
relative error = 2.8402075217357362718452366854708e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1068
y[1] (analytic) = 2.0057139949511490802588165492306
y[1] (numeric) = 2.005713994951149080258874370559
absolute error = 5.78213284e-23
relative error = 2.8828301814490898568125266599077e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1069
y[1] (analytic) = 2.005724720800992329255779419447
y[1] (numeric) = 2.0057247208009923292558380961175
absolute error = 5.86766705e-23
relative error = 2.9254598047017783860627519062753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 2.0057354567659879689618848211429
y[1] (numeric) = 2.0057354567659879689619443533049
absolute error = 5.95321620e-23
relative error = 2.9680964056939290913743695345216e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=1.70
NO POLE
x[1] = 0.1071
y[1] (analytic) = 2.0057462028463531935539964068893
y[1] (numeric) = 2.0057462028463531935540567946922
absolute error = 6.03878029e-23
relative error = 3.0107399836681084738066922227149e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1072
y[1] (analytic) = 2.0057569590423054065184069808196
y[1] (numeric) = 2.0057569590423054065184682244131
absolute error = 6.12435935e-23
relative error = 3.0533905528236160896716766655805e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1073
y[1] (analytic) = 2.0057677253540622206685320424664
y[1] (numeric) = 2.0057677253540622206685941420004
absolute error = 6.20995340e-23
relative error = 3.0960481223735945429552497520204e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1074
y[1] (analytic) = 2.0057785017818414581626209348313
y[1] (numeric) = 2.0057785017818414581626838904558
absolute error = 6.29556245e-23
relative error = 3.1387126965451626847303604890140e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1075
y[1] (analytic) = 2.00578928832586115052148559977
y[1] (numeric) = 2.0057892883258611505215494116351
absolute error = 6.38118651e-23
relative error = 3.1813842795651177385338310495096e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1076
y[1] (analytic) = 2.0058000849863395386462469437773
y[1] (numeric) = 2.0058000849863395386463116120333
absolute error = 6.46682560e-23
relative error = 3.2240628806454767830878456104484e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1077
y[1] (analytic) = 2.0058108917634950728360988172598
y[1] (numeric) = 2.0058108917634950728361643420571
absolute error = 6.55247973e-23
relative error = 3.2667485040123125011947612450789e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1078
y[1] (analytic) = 2.0058217086575464128060896103868
y[1] (numeric) = 2.005821708657546412806155991876
absolute error = 6.63814892e-23
relative error = 3.3094411588768630664294767950018e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1079
y[1] (analytic) = 2.0058325356687124277049214686148
y[1] (numeric) = 2.0058325356687124277049887069467
absolute error = 6.72383319e-23
relative error = 3.3521408544499362960088456713451e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.1MB, time=1.91
x[1] = 0.108
y[1] (analytic) = 2.0058433727972121961327671309818
y[1] (numeric) = 2.0058433727972121961328352263073
absolute error = 6.80953255e-23
relative error = 3.3948475949564750429021562862716e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1081
y[1] (analytic) = 2.0058542200432650061591043942728
y[1] (numeric) = 2.005854220043265006159173346743
absolute error = 6.89524702e-23
relative error = 3.4375613896065058433341058376517e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1082
y[1] (analytic) = 2.0058650774070903553405682061597
y[1] (numeric) = 2.0058650774070903553406380159257
absolute error = 6.98097660e-23
relative error = 3.4802822376388632181137113102745e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1083
y[1] (analytic) = 2.005875944888907950738820390423
y[1] (numeric) = 2.0058759448889079507388910576363
absolute error = 7.06672133e-23
relative error = 3.5230101582335783073793832511571e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1084
y[1] (analytic) = 2.0058868224889377089384370073665
y[1] (numeric) = 2.0058868224889377089385085321786
absolute error = 7.15248121e-23
relative error = 3.5657451506287291095196432882547e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1085
y[1] (analytic) = 2.0058977102073997560648133525357
y[1] (numeric) = 2.0058977102073997560648857350982
absolute error = 7.23825625e-23
relative error = 3.6084872190474760704555352208478e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1086
y[1] (analytic) = 2.0059086080445144278020865968595
y[1] (numeric) = 2.0059086080445144278021598373244
absolute error = 7.32404649e-23
relative error = 3.6512363826684706572909589573984e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1087
y[1] (analytic) = 2.005919516000502269411076071334
y[1] (numeric) = 2.0059195160005022694111501698532
absolute error = 7.40985192e-23
relative error = 3.6939926357434894314544999785867e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1088
y[1] (analytic) = 2.0059304340755840357472411993701
y[1] (numeric) = 2.0059304340755840357473161560957
absolute error = 7.49567256e-23
relative error = 3.7367559874798534024653046232187e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1089
y[1] (analytic) = 2.0059413622699806912786570799332
y[1] (numeric) = 2.0059413622699806912787328950176
absolute error = 7.58150844e-23
relative error = 3.7795264520696397284639412512021e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=2.14
NO POLE
x[1] = 0.109
y[1] (analytic) = 2.0059523005839134101040077246038
y[1] (numeric) = 2.0059523005839134101040843981995
absolute error = 7.66735957e-23
relative error = 3.8223040337340551005166193173371e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1091
y[1] (analytic) = 2.0059632490176035759705969516906
y[1] (numeric) = 2.0059632490176035759706744839502
absolute error = 7.75322596e-23
relative error = 3.8650887366939794901449408030246e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1092
y[1] (analytic) = 2.0059742075712727822923769405337
y[1] (numeric) = 2.00597420757127278229245533161
absolute error = 7.83910763e-23
relative error = 3.9078805701550748772021424293465e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1093
y[1] (analytic) = 2.0059851762451428321679944491357
y[1] (numeric) = 2.0059851762451428321680736991816
absolute error = 7.92500459e-23
relative error = 3.9506795383374853159851087778558e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1094
y[1] (analytic) = 2.0059961550394357383988546982636
y[1] (numeric) = 2.0059961550394357383989348074322
absolute error = 8.01091686e-23
relative error = 3.9934856504460817097575285354616e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1095
y[1] (analytic) = 2.006007143954373723507202925167
y[1] (numeric) = 2.0060071439543737235072838936116
absolute error = 8.09684446e-23
relative error = 4.0362989156852979235125966385899e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1096
y[1] (analytic) = 2.0060181429901792197542236100613
y[1] (numeric) = 2.0060181429901792197543054379352
absolute error = 8.18278739e-23
relative error = 4.0791193332891307427066129248265e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1097
y[1] (analytic) = 2.0060291521470748691581573785274
y[1] (numeric) = 2.0060291521470748691582400659842
absolute error = 8.26874568e-23
relative error = 4.1219469174462750760860921724802e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1098
y[1] (analytic) = 2.006040171425283523512435582984
y[1] (numeric) = 2.0060401714252835235125191301775
absolute error = 8.35471935e-23
relative error = 4.1647816773599330746364879231201e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=2.35
NO POLE
x[1] = 0.1099
y[1] (analytic) = 2.0060512008250282444038325663905
y[1] (numeric) = 2.0060512008250282444039169734745
absolute error = 8.44070840e-23
relative error = 4.2076236122630328069704889563164e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 2.0060622403465323032306356113409
y[1] (numeric) = 2.0060622403465323032307208784695
absolute error = 8.52671286e-23
relative error = 4.2504727363429530944443948500456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1101
y[1] (analytic) = 2.0060732899900191812208325777162
y[1] (numeric) = 2.0060732899900191812209187050435
absolute error = 8.61273273e-23
relative error = 4.2933290488319352176787752285910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1102
y[1] (analytic) = 2.0060843497557125694503172320603
y[1] (numeric) = 2.0060843497557125694504042197408
absolute error = 8.69876805e-23
relative error = 4.3361925689013412327480332055301e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1103
y[1] (analytic) = 2.0060954196438363688611122718535
y[1] (numeric) = 2.0060954196438363688612001200416
absolute error = 8.78481881e-23
relative error = 4.3790632907978340744317952845702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1104
y[1] (analytic) = 2.0061064996546146902796100478556
y[1] (numeric) = 2.0061064996546146902796987567059
absolute error = 8.87088503e-23
relative error = 4.4219412237223066368214693659055e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1105
y[1] (analytic) = 2.0061175897882718544348309876978
y[1] (numeric) = 2.0061175897882718544349205573652
absolute error = 8.95696674e-23
relative error = 4.4648263818599633584298780850553e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1106
y[1] (analytic) = 2.0061286900450323919766997239048
y[1] (numeric) = 2.0061286900450323919767901545442
absolute error = 9.04306394e-23
relative error = 4.5077187644412815020750017997037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1107
y[1] (analytic) = 2.006139800425121043494338929529
y[1] (numeric) = 2.0061398004251210434944302212956
absolute error = 9.12917666e-23
relative error = 4.5506183856506093759506136546679e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1108
y[1] (analytic) = 2.006150920928762759534380864587
y[1] (numeric) = 2.0061509209287627595344730176361
absolute error = 9.21530491e-23
relative error = 4.5935252497024026552775703367907e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=2.57
NO POLE
x[1] = 0.1109
y[1] (analytic) = 2.006162051556182700619296636487
y[1] (numeric) = 2.006162051556182700619389650974
absolute error = 9.30144870e-23
relative error = 4.6364393608107845895279834183504e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 2.0061731923076062372657431776415
y[1] (numeric) = 2.006173192307606237265837053722
absolute error = 9.38760805e-23
relative error = 4.6793607281741602763861767760628e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1111
y[1] (analytic) = 2.0061843431832589500029279434632
y[1] (numeric) = 2.006184343183258950003022681293
absolute error = 9.47378298e-23
relative error = 4.7222893609904910967072007726098e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1112
y[1] (analytic) = 2.0061955041833666293909913339431
y[1] (numeric) = 2.0061955041833666293910869336781
absolute error = 9.55997350e-23
relative error = 4.7652252634727351602858571344620e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1113
y[1] (analytic) = 2.0062066753081552760394068420149
y[1] (numeric) = 2.0062066753081552760395033038112
absolute error = 9.64617963e-23
relative error = 4.8081684448180482330630909911977e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1114
y[1] (analytic) = 2.0062178565578511006253989319133
y[1] (numeric) = 2.0062178565578511006254962559271
absolute error = 9.73240138e-23
relative error = 4.8511189092386375297103034592508e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1115
y[1] (analytic) = 2.0062290479326805239123786507344
y[1] (numeric) = 2.006229047932680523912476837122
absolute error = 9.81863876e-23
relative error = 4.8940766609463759876472316415333e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1116
y[1] (analytic) = 2.006240249432870176768396976413
y[1] (numeric) = 2.0062402494328701767684960253311
absolute error = 9.90489181e-23
relative error = 4.9370417191061457357580768001503e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1117
y[1] (analytic) = 2.0062514610586469001846159053331
y[1] (numeric) = 2.0062514610586469001847158169383
absolute error = 9.99116052e-23
relative error = 4.9800140779600596694353731209562e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=2.79
NO POLE
x[1] = 0.1118
y[1] (analytic) = 2.0062626828102377452937972827898
y[1] (numeric) = 2.006262682810237745293898057239
absolute error = 1.007744492e-22
relative error = 5.0229937516876869606288857129020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1119
y[1] (analytic) = 2.0062739146878699733888093795282
y[1] (numeric) = 2.0062739146878699733889110169784
absolute error = 1.016374502e-22
relative error = 5.0659807444993096591161874301749e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 2.0062851566917710559411512175826
y[1] (numeric) = 2.0062851566917710559412537181909
absolute error = 1.025006083e-22
relative error = 5.1089750606048739202994727889643e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1121
y[1] (analytic) = 2.0062964088221686746194946486475
y[1] (numeric) = 2.0062964088221686746195980125713
absolute error = 1.033639238e-22
relative error = 5.1519767141826065280130768158197e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1122
y[1] (analytic) = 2.0063076710792907213082441882121
y[1] (numeric) = 2.006307671079290721308348415609
absolute error = 1.042273969e-22
relative error = 5.1949857144258936721760391631116e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1123
y[1] (analytic) = 2.006318943463365298126114608695
y[1] (numeric) = 2.0063189434633652981262196997225
absolute error = 1.050910275e-22
relative error = 5.2380020555749154464985421628579e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1124
y[1] (analytic) = 2.0063302259746207174447262948164
y[1] (numeric) = 2.0063302259746207174448322496324
absolute error = 1.059548160e-22
relative error = 5.2810257567908607308512299752664e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1125
y[1] (analytic) = 2.0063415186132855019072183644532
y[1] (numeric) = 2.0063415186132855019073251832155
absolute error = 1.068187623e-22
relative error = 5.3240568123132629834149279807451e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1126
y[1] (analytic) = 2.0063528213795883844468795582191
y[1] (numeric) = 2.0063528213795883844469872410859
absolute error = 1.076828668e-22
relative error = 5.3670952413023835692463648771417e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1127
y[1] (analytic) = 2.006364134273758308305796901022
y[1] (numeric) = 2.0063641342737583083059054481516
absolute error = 1.085471296e-22
relative error = 5.4101410479653883899687194394592e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.1MB, time=3.00
NO POLE
x[1] = 0.1128
y[1] (analytic) = 2.006375457296024427053522138848
y[1] (numeric) = 2.0063754572960244270536315503988
absolute error = 1.094115508e-22
relative error = 5.4531942365091048362668558806387e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1129
y[1] (analytic) = 2.0063867904466161046057559540291
y[1] (numeric) = 2.0063867904466161046058662301598
absolute error = 1.102761307e-22
relative error = 5.4962548211081892549123364541933e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 2.0063981337257629152430499622528
y[1] (numeric) = 2.0063981337257629152431611031221
absolute error = 1.111408693e-22
relative error = 5.5393228009845665737993107949640e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1131
y[1] (analytic) = 2.0064094871336946436295264945746
y[1] (numeric) = 2.0064094871336946436296385003414
absolute error = 1.120057668e-22
relative error = 5.5823981853279899608122511750028e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1132
y[1] (analytic) = 2.0064208506706412848316161677002
y[1] (numeric) = 2.0064208506706412848317290385235
absolute error = 1.128708233e-22
relative error = 5.6254809783437608360617480160426e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1133
y[1] (analytic) = 2.0064322243368330443368132458039
y[1] (numeric) = 2.006432224336833044336926981843
absolute error = 1.137360391e-22
relative error = 5.6685711942047826219601415487914e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1134
y[1] (analytic) = 2.0064436081325003380724487971565
y[1] (numeric) = 2.0064436081325003380725633985708
absolute error = 1.146014143e-22
relative error = 5.7116688371155068855163782184017e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1135
y[1] (analytic) = 2.0064550020578737924244816488361
y[1] (numeric) = 2.0064550020578737924245971157851
absolute error = 1.154669490e-22
relative error = 5.7547739112800444498624028126691e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1136
y[1] (analytic) = 2.006466406113184244256307142801
y[1] (numeric) = 2.0064664061131842442564234754444
absolute error = 1.163326434e-22
relative error = 5.7978864258860512447583862291753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.1MB, time=3.22
NO POLE
x[1] = 0.1137
y[1] (analytic) = 2.0064778202986627409275836966056
y[1] (numeric) = 2.0064778202986627409277008951032
absolute error = 1.171984976e-22
relative error = 5.8410063851368708492573840574587e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1138
y[1] (analytic) = 2.0064892446145405403130771720435
y[1] (numeric) = 2.0064892446145405403131952365554
absolute error = 1.180645119e-22
relative error = 5.8841338032031639603970316219829e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1139
y[1] (analytic) = 2.0065006790610491108215230550071
y[1] (numeric) = 2.0065006790610491108216419856935
absolute error = 1.189306864e-22
relative error = 5.9272686842874203269701430923258e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 2.0065121236384201314145064498531
y[1] (numeric) = 2.0065121236384201314146262468744
absolute error = 1.197970213e-22
relative error = 5.9704110375755598665736998710545e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1141
y[1] (analytic) = 2.0065235783468854916253598915696
y[1] (numeric) = 2.0065235783468854916254805550861
absolute error = 1.206635165e-22
relative error = 6.0135608573018138666476410555330e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1142
y[1] (analytic) = 2.0065350431866772915780789790412
y[1] (numeric) = 2.0065350431866772915782005092136
absolute error = 1.215301724e-22
relative error = 6.0567181626188764536571062648421e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1143
y[1] (analytic) = 2.006546518158027842006255832715
y[1] (numeric) = 2.0065465181580278420063782297042
absolute error = 1.223969892e-22
relative error = 6.0998829627113826318538376823497e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1144
y[1] (analytic) = 2.0065580032611696642720303799694
y[1] (numeric) = 2.0065580032611696642721536439364
absolute error = 1.232639670e-22
relative error = 6.1430552617798511352958016534296e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1145
y[1] (analytic) = 2.0065694984963354903850594714949
y[1] (numeric) = 2.0065694984963354903851836026007
absolute error = 1.241311058e-22
relative error = 6.1862350590408266977123779385828e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.1MB, time=3.45
x[1] = 0.1146
y[1] (analytic) = 2.0065810038637582630215038319959
y[1] (numeric) = 2.0065810038637582630216288304019
absolute error = 1.249984060e-22
relative error = 6.2294223736450299439583977287705e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1147
y[1] (analytic) = 2.0065925193636711355430328485301
y[1] (numeric) = 2.0065925193636711355431587143977
absolute error = 1.258658676e-22
relative error = 6.2726172048082026056335737353725e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1148
y[1] (analytic) = 2.0066040449963074720158471997996
y[1] (numeric) = 2.0066040449963074720159739332904
absolute error = 1.267334908e-22
relative error = 6.3158195617129443893224508677931e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1149
y[1] (analytic) = 2.0066155807619008472297193297164
y[1] (numeric) = 2.0066155807619008472298469309921
absolute error = 1.276012757e-22
relative error = 6.3590294485578797686724910673497e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 2.0066271266606850467170517685652
y[1] (numeric) = 2.0066271266606850467171802377878
absolute error = 1.284692226e-22
relative error = 6.4022468795082615769034437417154e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1151
y[1] (analytic) = 2.006638682692894066771953305091
y[1] (numeric) = 2.0066386826928940667720826424226
absolute error = 1.293373316e-22
relative error = 6.4454718587618509745833356003713e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1152
y[1] (analytic) = 2.0066502488587621144693330128412
y[1] (numeric) = 2.006650248858762114469463218444
absolute error = 1.302056028e-22
relative error = 6.4887043905160629155310482779582e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1153
y[1] (analytic) = 2.0066618251585236076840121340961
y[1] (numeric) = 2.0066618251585236076841432081325
absolute error = 1.310740364e-22
relative error = 6.5319444839513666410693523116250e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1154
y[1] (analytic) = 2.006673411592413175109853824725
y[1] (numeric) = 2.0066734115924131751099857673575
absolute error = 1.319426325e-22
relative error = 6.5751921432643976690691165525015e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1155
y[1] (analytic) = 2.0066850081606656562789107633069
y[1] (numeric) = 2.0066850081606656562790435746983
absolute error = 1.328113914e-22
relative error = 6.6184473826181307712865609901167e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.1MB, time=3.67
NO POLE
x[1] = 0.1156
y[1] (analytic) = 2.0066966148635161015805906278612
y[1] (numeric) = 2.0066966148635161015807243081743
absolute error = 1.336803131e-22
relative error = 6.6617102012250198460635459718382e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1157
y[1] (analytic) = 2.0067082317011997722808394435325
y[1] (numeric) = 2.0067082317011997722809739929303
absolute error = 1.345493978e-22
relative error = 6.7049806082638573302079304130271e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1158
y[1] (analytic) = 2.0067198586739521405413428045815
y[1] (numeric) = 2.0067198586739521405414782232272
absolute error = 1.354186457e-22
relative error = 6.7482586129129722614728565002640e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1159
y[1] (analytic) = 2.0067314957820088894387449740344
y[1] (numeric) = 2.0067314957820088894388812620914
absolute error = 1.362880570e-22
relative error = 6.7915442243502297967081810092463e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 2.0067431430256059129838858643474
y[1] (numeric) = 2.0067431430256059129840230219792
absolute error = 1.371576318e-22
relative error = 6.8348374467698319411070772250159e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1161
y[1] (analytic) = 2.0067548004049793161410559024457
y[1] (numeric) = 2.006754800404979316141193929816
absolute error = 1.380273703e-22
relative error = 6.8781382893488014874841262543030e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1162
y[1] (analytic) = 2.0067664679203654148472687825009
y[1] (numeric) = 2.0067664679203654148474076797735
absolute error = 1.388972726e-22
relative error = 6.9214467562805551827135269560857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1163
y[1] (analytic) = 2.0067781455720007360315521098124
y[1] (numeric) = 2.0067781455720007360316918771513
absolute error = 1.397673389e-22
relative error = 6.9647628567412719753626661635998e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1164
y[1] (analytic) = 2.0067898333601220176342559391624
y[1] (numeric) = 2.0067898333601220176343965767318
absolute error = 1.406375694e-22
relative error = 7.0080865999066648220785655656523e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.1MB, time=3.88
NO POLE
x[1] = 0.1165
y[1] (analytic) = 2.0068015312849662086263792110185
y[1] (numeric) = 2.0068015312849662086265207189826
absolute error = 1.415079641e-22
relative error = 7.0514179849858726021565474463430e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1166
y[1] (analytic) = 2.0068132393467704690289140889579
y[1] (numeric) = 2.0068132393467704690290564674812
absolute error = 1.423785233e-22
relative error = 7.0947570261368740045472325626116e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1167
y[1] (analytic) = 2.0068249575457721699322082016954
y[1] (numeric) = 2.0068249575457721699323514509426
absolute error = 1.432492472e-22
relative error = 7.1381037325340685588721660950566e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1168
y[1] (analytic) = 2.0068366858822088935153447930956
y[1] (numeric) = 2.0068366858822088935154889132315
absolute error = 1.441201359e-22
relative error = 7.1814581083684215132779944062223e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1169
y[1] (analytic) = 2.0068484243563184330655407835567
y[1] (numeric) = 2.0068484243563184330656857747462
absolute error = 1.449911895e-22
relative error = 7.2248201578305464499701979660884e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 2.0068601729683387929975627461547
y[1] (numeric) = 2.006860172968338792997708608563
absolute error = 1.458624083e-22
relative error = 7.2681898950765214397430968649323e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1171
y[1] (analytic) = 2.0068719317185081888731608009409
y[1] (numeric) = 2.0068719317185081888733075347331
absolute error = 1.467337922e-22
relative error = 7.3115673143303228606251901958776e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1172
y[1] (analytic) = 2.0068837006070650474205204307878
y[1] (numeric) = 2.0068837006070650474206680361295
absolute error = 1.476053417e-22
relative error = 7.3549524397129068557435648935409e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1173
y[1] (analytic) = 2.0068954796342480065537322221844
y[1] (numeric) = 2.0068954796342480065538806992411
absolute error = 1.484770567e-22
relative error = 7.3983452654474858496572901183051e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1174
y[1] (analytic) = 2.006907268800295915392279534381
y[1] (numeric) = 2.0069072688002959153924288833185
absolute error = 1.493489375e-22
relative error = 7.4417458056883180455550628487157e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.1MB, time=4.10
NO POLE
x[1] = 0.1175
y[1] (analytic) = 2.0069190681054478342805441002912
y[1] (numeric) = 2.0069190681054478342806943212754
absolute error = 1.502209842e-22
relative error = 7.4851540646235499889272240527021e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1176
y[1] (analytic) = 2.0069308775499430348073295625594
y[1] (numeric) = 2.0069308775499430348074806557563
absolute error = 1.510931969e-22
relative error = 7.5285700464409743300295501471506e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1177
y[1] (analytic) = 2.0069426971340209998254029482057
y[1] (numeric) = 2.0069426971340209998255549137816
absolute error = 1.519655759e-22
relative error = 7.5719937652934361906714948802124e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1178
y[1] (analytic) = 2.0069545268579214234710540852655
y[1] (numeric) = 2.0069545268579214234712069233867
absolute error = 1.528381212e-22
relative error = 7.6154252203851695813609030140856e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1179
y[1] (analytic) = 2.00696636672188421118367296484
y[1] (numeric) = 2.0069663667218842111838266756732
absolute error = 1.537108332e-22
relative error = 7.6588644308507493402470982996209e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 2.0069782167261494797253450519834
y[1] (numeric) = 2.0069782167261494797254996356953
absolute error = 1.545837119e-22
relative error = 7.7023113958935818300826436846561e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1181
y[1] (analytic) = 2.006990076870957557200464548849
y[1] (numeric) = 2.0069900768709575572006200056063
absolute error = 1.554567573e-22
relative error = 7.7457661147168355336103274619278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1182
y[1] (analytic) = 2.0070019471565489830753656135249
y[1] (numeric) = 2.0070019471565489830755219434948
absolute error = 1.563299699e-22
relative error = 7.7892286114362220805250256544694e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1183
y[1] (analytic) = 2.0070138275831645081979715379917
y[1] (numeric) = 2.0070138275831645081981287413414
absolute error = 1.572033497e-22
relative error = 7.8326988852539918284868178715168e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.1MB, time=4.33
NO POLE
x[1] = 0.1184
y[1] (analytic) = 2.0070257181510450948174618886362
y[1] (numeric) = 2.007025718151045094817619965533
absolute error = 1.580768968e-22
relative error = 7.8761769403546537450224264913233e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1185
y[1] (analytic) = 2.0070376188604319166039576127611
y[1] (numeric) = 2.0070376188604319166041165633725
absolute error = 1.589506114e-22
relative error = 7.9196627859048277042642210579244e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1186
y[1] (analytic) = 2.0070495297115663586682241145325
y[1] (numeric) = 2.0070495297115663586683839390261
absolute error = 1.598244936e-22
relative error = 7.9631564260882202565629538949106e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1187
y[1] (analytic) = 2.0070614507046900175813923038097
y[1] (numeric) = 2.0070614507046900175815530023535
absolute error = 1.606985438e-22
relative error = 8.0066578800354060498494734575465e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1188
y[1] (analytic) = 2.007073381840044701394697621308
y[1] (numeric) = 2.0070733818400447013948591940699
absolute error = 1.615727619e-22
relative error = 8.0501671419643523970642253343125e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1189
y[1] (analytic) = 2.0070853231178724296592370435438
y[1] (numeric) = 2.007085323117872429659399490692
absolute error = 1.624471482e-22
relative error = 8.0936842260223023789129216555409e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 2.0070972745384154334457440710196
y[1] (numeric) = 2.0070972745384154334459073927224
absolute error = 1.633217028e-22
relative error = 8.1372091363912644204962577127331e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1191
y[1] (analytic) = 2.0071092361019161553643817031061
y[1] (numeric) = 2.0071092361019161553645458995321
absolute error = 1.641964260e-22
relative error = 8.1807418872174679379665010705929e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1192
y[1] (analytic) = 2.0071212078086172495845534030846
y[1] (numeric) = 2.0071212078086172495847184744022
absolute error = 1.650713176e-22
relative error = 8.2242824677352449154474320153432e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1193
y[1] (analytic) = 2.0071331896587615818547320568124
y[1] (numeric) = 2.0071331896587615818548980031905
absolute error = 1.659463781e-22
relative error = 8.2678309020545375658451715097467e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.1MB, time=4.55
NO POLE
x[1] = 0.1194
y[1] (analytic) = 2.0071451816525922295223069284837
y[1] (numeric) = 2.0071451816525922295224737500913
absolute error = 1.668216076e-22
relative error = 8.3113871943556500013898571246035e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1195
y[1] (analytic) = 2.0071571837903524815534486169537
y[1] (numeric) = 2.0071571837903524815536163139599
absolute error = 1.676970062e-22
relative error = 8.3549513488185262211240309791184e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1196
y[1] (analytic) = 2.0071691960722858385529920161042
y[1] (numeric) = 2.0071691960722858385531605886783
absolute error = 1.685725741e-22
relative error = 8.3985233746048909049019608254388e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1197
y[1] (analytic) = 2.0071812184986360127843372827272
y[1] (numeric) = 2.0071812184986360127845067310386
absolute error = 1.694483114e-22
relative error = 8.4421032758938776015363675018390e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1198
y[1] (analytic) = 2.0071932510696469281893688154094
y[1] (numeric) = 2.0071932510696469281895391396277
absolute error = 1.703242183e-22
relative error = 8.4856910618463402176806238830282e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1199
y[1] (analytic) = 2.0072052937855627204083922479023
y[1] (numeric) = 2.0072052937855627204085634481973
absolute error = 1.712002950e-22
relative error = 8.5292867416226519008624783323201e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 2.0072173466466277368000894604662
y[1] (numeric) = 2.0072173466466277368002615370079
absolute error = 1.720765417e-22
relative error = 8.5728903243827045582481863225547e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1201
y[1] (analytic) = 2.0072294096530865364614916126805
y[1] (numeric) = 2.0072294096530865364616645656389
absolute error = 1.729529584e-22
relative error = 8.6165018093219252333781285409782e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1202
y[1] (analytic) = 2.0072414828051838902479702012141
y[1] (numeric) = 2.0072414828051838902481440307595
absolute error = 1.738295454e-22
relative error = 8.6601212105813833084409724385130e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.1MB, time=4.77
NO POLE
x[1] = 0.1203
y[1] (analytic) = 2.0072535661031647807932461460562
y[1] (numeric) = 2.007253566103164780793420852359
absolute error = 1.747063028e-22
relative error = 8.7037485323376825878220136690983e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1204
y[1] (analytic) = 2.0072656595472744025294169087069
y[1] (numeric) = 2.0072656595472744025295924919377
absolute error = 1.755832308e-22
relative error = 8.7473837837489655204893208879385e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1205
y[1] (analytic) = 2.007277763137758161707001645835
y[1] (numeric) = 2.0072777631377581617071781061645
absolute error = 1.764603295e-22
relative error = 8.7910269689910196475559334795367e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1206
y[1] (analytic) = 2.0072898768748616764150044019092
y[1] (numeric) = 2.0072898768748616764151817395083
absolute error = 1.773375991e-22
relative error = 8.8346780972211104348130623873185e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1207
y[1] (analytic) = 2.0073020007588307766009953443162
y[1] (numeric) = 2.007302000758830776601173559356
absolute error = 1.782150398e-22
relative error = 8.8783371775960191862506606566336e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1208
y[1] (analytic) = 2.0073141347899115040912100444795
y[1] (numeric) = 2.0073141347899115040913891371313
absolute error = 1.790926518e-22
relative error = 8.9220042192720425629438120980555e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1209
y[1] (analytic) = 2.0073262789683501126106668084981
y[1] (numeric) = 2.0073262789683501126108467789332
absolute error = 1.799704351e-22
relative error = 8.9656792214414898006361962417012e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 2.0073384332943930678033020608256
y[1] (numeric) = 2.0073384332943930678034829092155
absolute error = 1.808483899e-22
relative error = 9.0093621932598678167066916158902e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1211
y[1] (analytic) = 2.0073505977682870472521237845162
y[1] (numeric) = 2.0073505977682870472523055110327
absolute error = 1.817265165e-22
relative error = 9.0530531488638885375750938884003e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1212
y[1] (analytic) = 2.007362772390278940499383021565
y[1] (numeric) = 2.0073627723902789404995656263799
absolute error = 1.826048149e-22
relative error = 9.0967520874446750142911096006528e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.1MB, time=4.99
NO POLE
x[1] = 0.1213
y[1] (analytic) = 2.0073749571606158490667634368742
y[1] (numeric) = 2.0073749571606158490669469201596
absolute error = 1.834832854e-22
relative error = 9.1404590231379963425232327506287e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1214
y[1] (analytic) = 2.007387152079545086475588949381
y[1] (numeric) = 2.0073871520795450864757733113091
absolute error = 1.843619281e-22
relative error = 9.1841739601158133187731667891907e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1215
y[1] (analytic) = 2.0073993571473141782670494338844
y[1] (numeric) = 2.0073993571473141782672346746275
absolute error = 1.852407431e-22
relative error = 9.2278969025497201804014711676151e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1216
y[1] (analytic) = 2.0074115723641708620224444971134
y[1] (numeric) = 2.0074115723641708620226306168441
absolute error = 1.861197307e-22
relative error = 9.2716278645740233324742244912006e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1217
y[1] (analytic) = 2.0074237977303630873834453315821
y[1] (numeric) = 2.007423797730363087383632330473
absolute error = 1.869988909e-22
relative error = 9.3153668453778920260057160065135e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1218
y[1] (analytic) = 2.007436033246139016072374650778
y[1] (numeric) = 2.0074360332461390160725625290019
absolute error = 1.878782239e-22
relative error = 9.3591138541132069659522969656753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1219
y[1] (analytic) = 2.0074482789117470219125047092377
y[1] (numeric) = 2.0074482789117470219126934669677
absolute error = 1.887577300e-22
relative error = 9.4028689049128080591633817582399e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 2.0074605347274356908483734110635
y[1] (numeric) = 2.0074605347274356908485630484727
absolute error = 1.896374092e-22
relative error = 9.4466319969646699550496149356925e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1221
y[1] (analytic) = 2.0074728006934538209661185104394
y[1] (numeric) = 2.0074728006934538209663090277011
absolute error = 1.905172617e-22
relative error = 9.4904031394192955842095806981273e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.1MB, time=5.21
NO POLE
x[1] = 0.1222
y[1] (analytic) = 2.0074850768100504225138299077085
y[1] (numeric) = 2.0074850768100504225140213049963
absolute error = 1.913972878e-22
relative error = 9.5341823464080544736105710677382e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1223
y[1] (analytic) = 2.0074973630774747179219200445774
y[1] (numeric) = 2.007497363077474717922112322065
absolute error = 1.922774876e-22
relative error = 9.5779696220990500525320774581982e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1224
y[1] (analytic) = 2.0075096594959761418235124020146
y[1] (numeric) = 2.0075096594959761418237055598757
absolute error = 1.931578611e-22
relative error = 9.6217649656787201215603357501870e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1225
y[1] (analytic) = 2.0075219660658043410748481044157
y[1] (numeric) = 2.0075219660658043410750421428244
absolute error = 1.940384087e-22
relative error = 9.6655683962583170263404953994672e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1226
y[1] (analytic) = 2.0075342827872091747757106336107
y[1] (numeric) = 2.007534282787209174775905552741
absolute error = 1.949191303e-22
relative error = 9.7093799080421815954853263266094e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1227
y[1] (analytic) = 2.0075466096604407142898686562905
y[1] (numeric) = 2.0075466096604407142900644563168
absolute error = 1.958000263e-22
relative error = 9.7531995201405507902241538524174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1228
y[1] (analytic) = 2.0075589466857492432655369684361
y[1] (numeric) = 2.0075589466857492432657336495329
absolute error = 1.966810968e-22
relative error = 9.7970272367194024031251608820856e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1229
y[1] (analytic) = 2.0075712938633852576558555603345
y[1] (numeric) = 2.0075712938633852576560531226764
absolute error = 1.975623419e-22
relative error = 9.8408630619443430693184312641662e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 2.0075836511935994657393868057698
y[1] (numeric) = 2.0075836511935994657395852495315
absolute error = 1.984437617e-22
relative error = 9.8847069999806080338583995270762e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.1MB, time=5.42
x[1] = 0.1231
y[1] (analytic) = 2.0075960186766427881406307789818
y[1] (numeric) = 2.0075960186766427881408301043383
absolute error = 1.993253565e-22
relative error = 9.9285590649552245286779418110392e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1232
y[1] (analytic) = 2.0076083963127663578505587029874
y[1] (numeric) = 2.0076083963127663578507589101139
absolute error = 2.002071265e-22
relative error = 9.9724192660135511543308965601077e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1233
y[1] (analytic) = 2.0076207841022215202471645328628
y[1] (numeric) = 2.0076207841022215202473656219346
absolute error = 2.010890718e-22
relative error = 1.0016287607319430826109127194580e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1234
y[1] (analytic) = 2.0076331820452598331160346775888
y[1] (numeric) = 2.0076331820452598331162366487812
absolute error = 2.019711924e-22
relative error = 1.0060164088055344092362530963176e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1235
y[1] (analytic) = 2.0076455901421330666709358640636
y[1] (numeric) = 2.0076455901421330666711387175524
absolute error = 2.028534888e-22
relative error = 1.0104048732308315716164045250244e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1236
y[1] (analytic) = 2.007658008393093203574421146894
y[1] (numeric) = 2.0076580083930932035746248828549
absolute error = 2.037359609e-22
relative error = 1.0147941534278936391742455761720e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1237
y[1] (analytic) = 2.0076704367983924389584540675737
y[1] (numeric) = 2.0076704367983924389586586861827
absolute error = 2.046186090e-22
relative error = 1.0191842508091258261913546791816e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1238
y[1] (analytic) = 2.0076828753582831804450509666669
y[1] (numeric) = 2.0076828753582831804452564681001
absolute error = 2.055014332e-22
relative error = 1.0235751657906980125912257854158e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1239
y[1] (analytic) = 2.0076953240730180481669414526143
y[1] (numeric) = 2.0076953240730180481671478370478
absolute error = 2.063844335e-22
relative error = 1.0279668982906590977877832865870e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 2.0077077829428498747882470307837
y[1] (numeric) = 2.0077077829428498747884542983941
absolute error = 2.072676104e-22
relative error = 1.0323594507174351437337820675927e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.1MB, time=5.65
NO POLE
x[1] = 0.1241
y[1] (analytic) = 2.0077202519680317055251778963918
y[1] (numeric) = 2.0077202519680317055253860473557
absolute error = 2.081509639e-22
relative error = 1.0367528229889784563187813968341e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1242
y[1] (analytic) = 2.0077327311488167981667478949241
y[1] (numeric) = 2.0077327311488167981669569294183
absolute error = 2.090344942e-22
relative error = 1.0411470160193646983260414687004e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1243
y[1] (analytic) = 2.0077452204854586230955076536869
y[1] (numeric) = 2.0077452204854586230957175718881
absolute error = 2.099182012e-22
relative error = 1.0455420292284060853609179372237e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1244
y[1] (analytic) = 2.0077577199782108633082958881249
y[1] (numeric) = 2.0077577199782108633085066902103
absolute error = 2.108020854e-22
relative error = 1.0499378650243104231016532620110e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1245
y[1] (analytic) = 2.0077702296273274144370088865459
y[1] (numeric) = 2.0077702296273274144372205726928
absolute error = 2.116861469e-22
relative error = 1.0543345238229384310780519516548e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1246
y[1] (analytic) = 2.0077827494330623847693881768925
y[1] (numeric) = 2.0077827494330623847696007472783
absolute error = 2.125703858e-22
relative error = 1.0587320060401131540116596100652e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1247
y[1] (analytic) = 2.007795279395670095269826379207
y[1] (numeric) = 2.0077952793956700952700398340093
absolute error = 2.134548023e-22
relative error = 1.0631303125896786850316134924047e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1248
y[1] (analytic) = 2.0078078195154050796001912474399
y[1] (numeric) = 2.0078078195154050796004055868363
absolute error = 2.143393964e-22
relative error = 1.0675294433893176816313518222413e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1249
y[1] (analytic) = 2.0078203697925220841406679042518
y[1] (numeric) = 2.0078203697925220841408831284204
absolute error = 2.152241686e-22
relative error = 1.0719294008469501074122819965806e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.1MB, time=5.87
NO POLE
x[1] = 0.125
y[1] (analytic) = 2.0078329302272760680106192724675
y[1] (numeric) = 2.0078329302272760680108353815863
absolute error = 2.161091188e-22
relative error = 1.0763301843821118661563583191311e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1251
y[1] (analytic) = 2.0078455008199222030894647068384
y[1] (numeric) = 2.0078455008199222030896817010856
absolute error = 2.169942472e-22
relative error = 1.0807317949084648225024385522608e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1252
y[1] (analytic) = 2.0078580815707158740375768297778
y[1] (numeric) = 2.0078580815707158740377947093318
absolute error = 2.178795540e-22
relative error = 1.0851342333396205145295239792646e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1253
y[1] (analytic) = 2.007870672479912678317196574734
y[1] (numeric) = 2.0078706724799126783174153397733
absolute error = 2.187650393e-22
relative error = 1.0895375000911000607534434681980e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1254
y[1] (analytic) = 2.0078832735477684262133664408707
y[1] (numeric) = 2.0078832735477684262135860915742
absolute error = 2.196507035e-22
relative error = 1.0939415970724974175340228837200e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1255
y[1] (analytic) = 2.0078958847745391408548819627277
y[1] (numeric) = 2.0078958847745391408551024992741
absolute error = 2.205365464e-22
relative error = 1.0983465232051283130952188561152e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1256
y[1] (analytic) = 2.0079085061604810582352613985364
y[1] (numeric) = 2.0079085061604810582354828211048
absolute error = 2.214225684e-22
relative error = 1.1027522803984919953669952226664e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1257
y[1] (analytic) = 2.0079211377058506272337336408716
y[1] (numeric) = 2.0079211377058506272339559496413
absolute error = 2.223087697e-22
relative error = 1.1071588695659570704890078112332e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1258
y[1] (analytic) = 2.0079337794109045096362443533212
y[1] (numeric) = 2.0079337794109045096364675484715
absolute error = 2.231951503e-22
relative error = 1.1115662906247927603705303529440e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1259
y[1] (analytic) = 2.0079464312758995801564803368592
y[1] (numeric) = 2.0079464312758995801567044185697
absolute error = 2.240817105e-22
relative error = 1.1159745449863065054911113097608e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.2MB, time=6.09
NO POLE
x[1] = 0.126
y[1] (analytic) = 2.0079590933010929264569121296132
y[1] (numeric) = 2.0079590933010929264571370980636
absolute error = 2.249684504e-22
relative error = 1.1203836330657062908431567688643e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1261
y[1] (analytic) = 2.0079717654867418491698548437183
y[1] (numeric) = 2.0079717654867418491700806990885
absolute error = 2.258553702e-22
relative error = 1.1247935557761769148816529223795e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1262
y[1] (analytic) = 2.0079844478331038619185472429535
y[1] (numeric) = 2.0079844478331038619187739854235
absolute error = 2.267424700e-22
relative error = 1.1292043135328405885310666684016e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1263
y[1] (analytic) = 2.0079971403404366913382490648612
y[1] (numeric) = 2.0079971403404366913384766946112
absolute error = 2.276297500e-22
relative error = 1.1336159072487899814876302584822e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1264
y[1] (analytic) = 2.0080098430089982770973565910516
y[1] (numeric) = 2.008009843008998277097585108262
absolute error = 2.285172104e-22
relative error = 1.1380283378370669200307789185942e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1265
y[1] (analytic) = 2.0080225558390467719185364694001
y[1] (numeric) = 2.0080225558390467719187658742515
absolute error = 2.294048514e-22
relative error = 1.1424416062106623390012249833644e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1266
y[1] (analytic) = 2.0080352788308405415998777918457
y[1] (numeric) = 2.0080352788308405416001080845187
absolute error = 2.302926730e-22
relative error = 1.1468557122865177963606254604923e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1267
y[1] (analytic) = 2.0080480119846381650360624315051
y[1] (numeric) = 2.0080480119846381650362936121806
absolute error = 2.311806755e-22
relative error = 1.1512706574755373079391107215378e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1268
y[1] (analytic) = 2.0080607553006984342395536428183
y[1] (numeric) = 2.0080607553006984342397857116774
absolute error = 2.320688591e-22
relative error = 1.1556864426905683419977332586678e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.2MB, time=6.32
NO POLE
x[1] = 0.1269
y[1] (analytic) = 2.0080735087792803543618029284466
y[1] (numeric) = 2.0080735087792803543620358856704
absolute error = 2.329572238e-22
relative error = 1.1601030678484278226884822090609e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 2.0080862724206431437144751766449
y[1] (numeric) = 2.0080862724206431437147090224148
absolute error = 2.338457699e-22
relative error = 1.1645205343598665971592306204546e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1271
y[1] (analytic) = 2.0080990462250462337906920728367
y[1] (numeric) = 2.0080990462250462337909268073343
absolute error = 2.347344976e-22
relative error = 1.1689388431375883019169748537637e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1272
y[1] (analytic) = 2.0081118301927492692862937891218
y[1] (numeric) = 2.0081118301927492692865294125287
absolute error = 2.356234069e-22
relative error = 1.1733579940982849067854573437459e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1273
y[1] (analytic) = 2.0081246243240121081211189554484
y[1] (numeric) = 2.0081246243240121081213554679465
absolute error = 2.365124981e-22
relative error = 1.1777779886525537027616443168765e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1274
y[1] (analytic) = 2.0081374286190948214603029161898
y[1] (numeric) = 2.0081374286190948214605403179612
absolute error = 2.374017714e-22
relative error = 1.1821988277129541294653212628260e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1275
y[1] (analytic) = 2.0081502430782576937355942758636
y[1] (numeric) = 2.0081502430782576937358325670904
absolute error = 2.382912268e-22
relative error = 1.1866205111960528819130018525697e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1276
y[1] (analytic) = 2.0081630677017612226666897377377
y[1] (numeric) = 2.0081630677017612226669289186023
absolute error = 2.391808646e-22
relative error = 1.1910430405122933075242347190204e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1277
y[1] (analytic) = 2.0081759024898661192825872390716
y[1] (numeric) = 2.0081759024898661192828273097565
absolute error = 2.400706849e-22
relative error = 1.1954664160761259379080654978998e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1278
y[1] (analytic) = 2.0081887474428333079429573867419
y[1] (numeric) = 2.0081887474428333079431983474297
absolute error = 2.409606878e-22
relative error = 1.1998906383019625891126235363790e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.2MB, time=6.53
NO POLE
x[1] = 0.1279
y[1] (analytic) = 2.008201602560923926359533197007
y[1] (numeric) = 2.0082016025609239263597750478806
absolute error = 2.418508736e-22
relative error = 1.2043157086000922850352216752175e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 2.0082144678443993256175181431687
y[1] (numeric) = 2.0082144678443993256177608844112
absolute error = 2.427412425e-22
relative error = 1.2087416278827849837265191332776e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1281
y[1] (analytic) = 2.0082273432935210701970125148905
y[1] (numeric) = 2.0082273432935210701972561466851
absolute error = 2.436317946e-22
relative error = 1.2131683965643074674097049138545e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1282
y[1] (analytic) = 2.0082402289085509379944580929379
y[1] (numeric) = 2.0082402289085509379947026154678
absolute error = 2.445225299e-22
relative error = 1.2175960145609392696979401272639e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1283
y[1] (analytic) = 2.0082531246897509203441011431073
y[1] (numeric) = 2.008253124689750920344346556556
absolute error = 2.454134487e-22
relative error = 1.2220244832827694323918727001353e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1284
y[1] (analytic) = 2.008266030637383222039473733116
y[1] (numeric) = 2.0082660306373832220397200376673
absolute error = 2.463045513e-22
relative error = 1.2264538041398225127747593669927e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1285
y[1] (analytic) = 2.0082789467517102613548933762267
y[1] (numeric) = 2.0082789467517102613551405720644
absolute error = 2.471958377e-22
relative error = 1.2308839770482421239880464957221e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1286
y[1] (analytic) = 2.008291873032994670066981005384
y[1] (numeric) = 2.0082918730329946700672290926922
absolute error = 2.480873082e-22
relative error = 1.2353150034179524805722465545888e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1287
y[1] (analytic) = 2.0083048094814992934761972816462
y[1] (numeric) = 2.0083048094814992934764462606089
absolute error = 2.489789627e-22
relative error = 1.2397468826670836059858686490306e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.2MB, time=6.75
NO POLE
x[1] = 0.1288
y[1] (analytic) = 2.0083177560974871904283972406943
y[1] (numeric) = 2.0083177560974871904286471114959
absolute error = 2.498708016e-22
relative error = 1.2441796167033980178479811981828e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1289
y[1] (analytic) = 2.0083307128812216333364032812091
y[1] (numeric) = 2.0083307128812216333366540440342
absolute error = 2.507628251e-22
relative error = 1.2486132064387287181099781861903e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 2.0083436798329661082015964989065
y[1] (numeric) = 2.0083436798329661082018481539397
absolute error = 2.516550332e-22
relative error = 1.2530476517890112442742714690143e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1291
y[1] (analytic) = 2.0083566569529843146355263700252
y[1] (numeric) = 2.0083566569529843146357789174514
absolute error = 2.525474262e-22
relative error = 1.2574829541639134382714172314049e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1292
y[1] (analytic) = 2.0083696442415401658815387880679
y[1] (numeric) = 2.0083696442415401658817922280721
absolute error = 2.534400042e-22
relative error = 1.2619191139772056064201602248531e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1293
y[1] (analytic) = 2.0083826416988977888364224575948
y[1] (numeric) = 2.0083826416988977888366767903621
absolute error = 2.543327673e-22
relative error = 1.2663561316426188428281322594849e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1294
y[1] (analytic) = 2.0083956493253215240720736488762
y[1] (numeric) = 2.008395649325321524072328874592
absolute error = 2.552257158e-22
relative error = 1.2707940085696647296164585789861e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1295
y[1] (analytic) = 2.0084086671210759258571793172136
y[1] (numeric) = 2.0084086671210759258574354360634
absolute error = 2.561188498e-22
relative error = 1.2752327451719765032735295037407e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1296
y[1] (analytic) = 2.0084216950864257621789185907393
y[1] (numeric) = 2.0084216950864257621791756029088
absolute error = 2.570121695e-22
relative error = 1.2796723423610514934574853183178e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1297
memory used=122.0MB, alloc=4.2MB, time=6.97
y[1] (analytic) = 2.0084347332216360147646826305118
y[1] (numeric) = 2.0084347332216360147649405361868
absolute error = 2.579056750e-22
relative error = 1.2841128005504345937726251801829e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1298
y[1] (analytic) = 2.0084477815269718791038128667251
y[1] (numeric) = 2.0084477815269718791040716660917
absolute error = 2.587993666e-22
relative error = 1.2885541211494252005404392762026e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1299
y[1] (analytic) = 2.0084608400026987644693576148551
y[1] (numeric) = 2.0084608400026987644696173080993
absolute error = 2.596932442e-22
relative error = 1.2929963035756826145123642119016e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 2.008473908649082293939847075567
y[1] (numeric) = 2.0084739086490822939401076628753
absolute error = 2.605873083e-22
relative error = 1.2974393502341953701407824328559e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1301
y[1] (analytic) = 2.0084869874663883044210867222161
y[1] (numeric) = 2.008486987466388304421348203775
absolute error = 2.614815589e-22
relative error = 1.3018832610404245916725779334862e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1302
y[1] (analytic) = 2.0085000764548828466679690797711
y[1] (numeric) = 2.0085000764548828466682314557672
absolute error = 2.623759961e-22
relative error = 1.3063280364076888310342748286250e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1303
y[1] (analytic) = 2.0085131756148321853063038989989
y[1] (numeric) = 2.008513175614832185306567169619
absolute error = 2.632706201e-22
relative error = 1.3107736772471478339076148824439e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1304
y[1] (analytic) = 2.0085262849465027988546667297486
y[1] (numeric) = 2.0085262849465027988549308951798
absolute error = 2.641654312e-22
relative error = 1.3152201849677862686201411056562e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1305
y[1] (analytic) = 2.0085394044501613797462658971789
y[1] (numeric) = 2.0085394044501613797465309576084
absolute error = 2.650604295e-22
relative error = 1.3196675599827747419147799852200e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1306
y[1] (analytic) = 2.0085525341260748343508278847745
y[1] (numeric) = 2.0085525341260748343510938403895
absolute error = 2.659556150e-22
relative error = 1.3241158022073732424343907346359e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.2MB, time=7.20
NO POLE
x[1] = 0.1307
y[1] (analytic) = 2.0085656739745102829965011280011
y[1] (numeric) = 2.0085656739745102829967679789893
absolute error = 2.668509882e-22
relative error = 1.3285649140461536851295479527093e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1308
y[1] (analytic) = 2.008578823995735059991778222454
y[1] (numeric) = 2.008578823995735059992045969003
absolute error = 2.677465490e-22
relative error = 1.3330148949164094286781570406322e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1309
y[1] (analytic) = 2.0085919841900167136474365503546
y[1] (numeric) = 2.0085919841900167136477051926522
absolute error = 2.686422976e-22
relative error = 1.3374657457290037429426267746019e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 2.0086051545576230062984973292569
y[1] (numeric) = 2.0086051545576230062987668674912
absolute error = 2.695382343e-22
relative error = 1.3419174678926050128761435645008e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1311
y[1] (analytic) = 2.0086183350988219143262030868267
y[1] (numeric) = 2.0086183350988219143264735211859
absolute error = 2.704343592e-22
relative error = 1.3463700618201063733192740642429e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1312
y[1] (analytic) = 2.0086315258138816281800135655609
y[1] (numeric) = 2.0086315258138816281802848962333
absolute error = 2.713306724e-22
relative error = 1.3508235279243611133251784229175e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1313
y[1] (analytic) = 2.0086447267030705523996200613169
y[1] (numeric) = 2.008644726703070552399892288491
absolute error = 2.722271741e-22
relative error = 1.3552778671160307725377978924604e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1314
y[1] (analytic) = 2.0086579377666573056369781995266
y[1] (numeric) = 2.0086579377666573056372513233911
absolute error = 2.731238645e-22
relative error = 1.3597330803057239009965611724053e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1315
y[1] (analytic) = 2.0086711590049107206783591529726
y[1] (numeric) = 2.0086711590049107206786331737164
absolute error = 2.740207438e-22
relative error = 1.3641891684039960111965369837497e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.2MB, time=7.41
x[1] = 0.1316
y[1] (analytic) = 2.0086843904180998444664193050063
y[1] (numeric) = 2.0086843904180998444666942228183
absolute error = 2.749178120e-22
relative error = 1.3686461313256729522168336500642e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1317
y[1] (analytic) = 2.0086976320064939381222883620933
y[1] (numeric) = 2.0086976320064939381225641771628
absolute error = 2.758150695e-22
relative error = 1.3731039709768937228363335956463e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1318
y[1] (analytic) = 2.0087108837703624769676759195738
y[1] (numeric) = 2.0087108837703624769679526320901
absolute error = 2.767125163e-22
relative error = 1.3775626872723910044423216973235e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1319
y[1] (analytic) = 2.0087241457099751505469964845279
y[1] (numeric) = 2.0087241457099751505472740946806
absolute error = 2.776101527e-22
relative error = 1.3820222816203558515732802532925e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 2.0087374178256018626495129596427
y[1] (numeric) = 2.0087374178256018626497914676214
absolute error = 2.785079787e-22
relative error = 1.3864827539354374737668743673685e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1321
y[1] (analytic) = 2.0087507001175127313314985919768
y[1] (numeric) = 2.0087507001175127313317779979714
absolute error = 2.794059946e-22
relative error = 1.3909441056257236694520991256994e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1322
y[1] (analytic) = 2.0087639925859780889384173905258
y[1] (numeric) = 2.0087639925859780889386976947263
absolute error = 2.803042005e-22
relative error = 1.3954063371035986099513258574148e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1323
y[1] (analytic) = 2.0087772952312684821271230164923
y[1] (numeric) = 2.0087772952312684821274042190889
absolute error = 2.812025966e-22
relative error = 1.3998694492792215262912272295397e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1324
y[1] (analytic) = 2.0087906080536546718880761501703
y[1] (numeric) = 2.0087906080536546718883582513534
absolute error = 2.821011831e-22
relative error = 1.4043334430626982251855583430151e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1325
y[1] (analytic) = 2.0088039310534076335675803383544
y[1] (numeric) = 2.0088039310534076335678633383145
absolute error = 2.829999601e-22
relative error = 1.4087983188662723776875001158484e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.2MB, time=7.63
NO POLE
x[1] = 0.1326
y[1] (analytic) = 2.0088172642307985568900363261906
y[1] (numeric) = 2.0088172642307985568903202251184
absolute error = 2.838989278e-22
relative error = 1.4132640775999527104748152946927e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1327
y[1] (analytic) = 2.0088306075860988459802148773865
y[1] (numeric) = 2.0088306075860988459804996754729
absolute error = 2.847980864e-22
relative error = 1.4177307201736943970186624951609e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1328
y[1] (analytic) = 2.0088439611195801193855480867037
y[1] (numeric) = 2.0088439611195801193858337841398
absolute error = 2.856974361e-22
relative error = 1.4221982474973990096657107958410e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1329
y[1] (analytic) = 2.0088573248315142100984391886583
y[1] (numeric) = 2.0088573248315142100987257856353
absolute error = 2.865969770e-22
relative error = 1.4266666599831190396428364018155e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 2.0088706987221731655785908663584
y[1] (numeric) = 2.0088706987221731655788783630675
absolute error = 2.874967091e-22
relative error = 1.4311359575450744193025835965969e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1331
y[1] (analytic) = 2.0088840827918292477753520644111
y[1] (numeric) = 2.008884082791829247775640461044
absolute error = 2.883966329e-22
relative error = 1.4356061425864018907658080452946e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1332
y[1] (analytic) = 2.0088974770407549331500833098364
y[1] (numeric) = 2.0088974770407549331503726065848
absolute error = 2.892967484e-22
relative error = 1.4400772150212172073781006318047e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1333
y[1] (analytic) = 2.0089108814692229126985405449261
y[1] (numeric) = 2.0089108814692229126988307419818
absolute error = 2.901970557e-22
relative error = 1.4445491752613910146109540530155e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1334
y[1] (analytic) = 2.0089242960775060919732774759912
y[1] (numeric) = 2.0089242960775060919735685735463
absolute error = 2.910975551e-22
relative error = 1.4490220247143110691320883195710e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.2MB, time=7.85
NO POLE
x[1] = 0.1335
y[1] (analytic) = 2.0089377208658775911060664419457
y[1] (numeric) = 2.0089377208658775911063584401924
absolute error = 2.919982467e-22
relative error = 1.4534957637917469085926317502056e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1336
y[1] (analytic) = 2.0089511558346107448303378066749
y[1] (numeric) = 2.0089511558346107448306307058056
absolute error = 2.928991307e-22
relative error = 1.4579703934031996133928776083311e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1337
y[1] (analytic) = 2.0089646009839791025036378791431
y[1] (numeric) = 2.0089646009839791025039316793504
absolute error = 2.938002073e-22
relative error = 1.4624459144581162762307463114003e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1338
y[1] (analytic) = 2.0089780563142564281301053651971
y[1] (numeric) = 2.0089780563142564281304000666737
absolute error = 2.947014766e-22
relative error = 1.4669223273681244376205332269970e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1339
y[1] (analytic) = 2.0089915218257167003829663550263
y[1] (numeric) = 2.008991521825716700383261957965
absolute error = 2.956029387e-22
relative error = 1.4713996325448108999114036517322e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 2.0090049975186341126270478502428
y[1] (numeric) = 2.0090049975186341126273443548367
absolute error = 2.965045939e-22
relative error = 1.4758778313952393870369244671815e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1341
y[1] (analytic) = 2.0090184833932830729413098345499
y[1] (numeric) = 2.0090184833932830729416072409924
absolute error = 2.974064425e-22
relative error = 1.4803569253264061082098475997893e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1342
y[1] (analytic) = 2.0090319794499382041413958919693
y[1] (numeric) = 2.0090319794499382041416942004537
absolute error = 2.983084844e-22
relative error = 1.4848369137542310597449024178665e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1343
y[1] (analytic) = 2.0090454856888743438022023766007
y[1] (numeric) = 2.0090454856888743438025015873205
absolute error = 2.992107198e-22
relative error = 1.4893177975878665482149186732266e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1344
y[1] (analytic) = 2.0090590021103665442804661378932
y[1] (numeric) = 2.0090590021103665442807662510422
absolute error = 3.001131490e-22
relative error = 1.4937995782341560632287883270692e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.2MB, time=8.07
NO POLE
x[1] = 0.1345
y[1] (analytic) = 2.0090725287146900727373708054091
y[1] (numeric) = 2.0090725287146900727376718211812
absolute error = 3.010157721e-22
relative error = 1.4982822561043911429182812760246e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1346
y[1] (analytic) = 2.0090860655021204111611716370645
y[1] (numeric) = 2.0090860655021204111614735556537
absolute error = 3.019185892e-22
relative error = 1.5027658316098223511162106339209e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1347
y[1] (analytic) = 2.0090996124729332563898389348353
y[1] (numeric) = 2.009099612472933256390141756436
absolute error = 3.028216007e-22
relative error = 1.5072503066548654553615687811289e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1348
y[1] (analytic) = 2.0091131696274045201337200319217
y[1] (numeric) = 2.0091131696274045201340237567282
absolute error = 3.037248065e-22
relative error = 1.5117356806551946903840661383364e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1349
y[1] (analytic) = 2.009126736965810328998219855364
y[1] (numeric) = 2.0091267369658103289985244835709
absolute error = 3.046282069e-22
relative error = 1.5162219550173848140908595555933e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 2.0091403144884270245065000681108
y[1] (numeric) = 2.0091403144884270245068055999129
absolute error = 3.055318021e-22
relative error = 1.5207091306502172770481016350593e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1351
y[1] (analytic) = 2.0091539021955311631221967945406
y[1] (numeric) = 2.0091539021955311631225032301328
absolute error = 3.064355922e-22
relative error = 1.5251972079646969801599279011684e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1352
y[1] (analytic) = 2.0091675000873995162721569334432
y[1] (numeric) = 2.0091675000873995162724642730205
absolute error = 3.073395773e-22
relative error = 1.5296861873717876519381812344069e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1353
y[1] (analytic) = 2.0091811081643090703691930624693
y[1] (numeric) = 2.0091811081643090703695013062271
absolute error = 3.082437578e-22
relative error = 1.5341760707755574596156350147914e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.2MB, time=8.30
NO POLE
x[1] = 0.1354
y[1] (analytic) = 2.0091947264265370268348569380627
y[1] (numeric) = 2.0091947264265370268351660861965
absolute error = 3.091481338e-22
relative error = 1.5386668585868573561291702287556e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1355
y[1] (analytic) = 2.0092083548743608021222315948896
y[1] (numeric) = 2.0092083548743608021225416475949
absolute error = 3.100527053e-22
relative error = 1.5431585507187885462035758783487e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1356
y[1] (analytic) = 2.0092219935080580277387420487853
y[1] (numeric) = 2.009221993508058027739053006258
absolute error = 3.109574727e-22
relative error = 1.5476511490752447729021216648929e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1357
y[1] (analytic) = 2.0092356423279065502689846072427
y[1] (numeric) = 2.0092356423279065502692964696787
absolute error = 3.118624360e-22
relative error = 1.5521446535692310803282401807367e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1358
y[1] (analytic) = 2.0092493013341844313975747914674
y[1] (numeric) = 2.0092493013341844313978875590628
absolute error = 3.127675954e-22
relative error = 1.5566390651091212991967371071477e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1359
y[1] (analytic) = 2.0092629705271699479320138740312
y[1] (numeric) = 2.0092629705271699479323275469823
absolute error = 3.136729511e-22
relative error = 1.5611343846032343231577280499799e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 2.0092766499071415918255740361572
y[1] (numeric) = 2.0092766499071415918258886146604
absolute error = 3.145785032e-22
relative error = 1.5656306124621425160454565292985e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1361
y[1] (analytic) = 2.0092903394743780702002021486734
y[1] (numeric) = 2.0092903394743780702005176329254
absolute error = 3.154842520e-22
relative error = 1.5701277500917530803614185404001e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1362
y[1] (analytic) = 2.0093040392291583053694421806765
y[1] (numeric) = 2.009304039229158305369758570874
absolute error = 3.163901975e-22
relative error = 1.5746257974048502973599496749608e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1363
y[1] (analytic) = 2.009317749171761434861376239949
y[1] (numeric) = 2.009317749171761434861693536289
absolute error = 3.172963400e-22
relative error = 1.5791247558072345809539897794599e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.2MB, time=8.52
NO POLE
x[1] = 0.1364
y[1] (analytic) = 2.0093314693024668114415842491783
y[1] (numeric) = 2.009331469302466811441902451858
absolute error = 3.182026797e-22
relative error = 1.5836246262069596386691588716377e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1365
y[1] (analytic) = 2.009345199621554003136122262029
y[1] (numeric) = 2.0093451996215540031364413712456
absolute error = 3.191092166e-22
relative error = 1.5881254085166748368428411786888e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1366
y[1] (analytic) = 2.0093589401293027932545194231219
y[1] (numeric) = 2.009358940129302793254839439073
absolute error = 3.200159511e-22
relative error = 1.5926271046396861611779679288137e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1367
y[1] (analytic) = 2.0093726908259931804127935759804
y[1] (numeric) = 2.0093726908259931804131144988637
absolute error = 3.209228833e-22
relative error = 1.5971297149862138054572438308180e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1368
y[1] (analytic) = 2.009386451711905378556485523004
y[1] (numeric) = 2.0093864517119053785568073530172
absolute error = 3.218300132e-22
relative error = 1.6016332394687718944648809689564e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1369
y[1] (analytic) = 2.0094002227873198169837119415345
y[1] (numeric) = 2.0094002227873198169840346788757
absolute error = 3.227373412e-22
relative error = 1.6061376799904902049618881521774e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 2.0094140040525171403682369600856
y[1] (numeric) = 2.0094140040525171403685606049529
absolute error = 3.236448673e-22
relative error = 1.6106430364637857045465818131592e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1371
y[1] (analytic) = 2.0094277955077782087825623988053
y[1] (numeric) = 2.009427795507778208782886951397
absolute error = 3.245525917e-22
relative error = 1.6151493097963554229402976284128e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1372
y[1] (analytic) = 2.0094415971533840977210366782494
y[1] (numeric) = 2.0094415971533840977213621387641
absolute error = 3.254605147e-22
relative error = 1.6196565013934915814902125311315e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.2MB, time=8.74
NO POLE
x[1] = 0.1373
y[1] (analytic) = 2.0094554089896160981229824005448
y[1] (numeric) = 2.0094554089896160981233087691811
absolute error = 3.263686363e-22
relative error = 1.6241646111674753594666541351248e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1374
y[1] (analytic) = 2.0094692310167557163958426070243
y[1] (numeric) = 2.0094692310167557163961698839811
absolute error = 3.272769568e-22
relative error = 1.6286736405234912533866032952326e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1375
y[1] (analytic) = 2.0094830632350846744383457164216
y[1] (numeric) = 2.0094830632350846744386739018979
absolute error = 3.281854763e-22
relative error = 1.6331835898713735849372717047392e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1376
y[1] (analytic) = 2.0094969056448849096636891477141
y[1] (numeric) = 2.0094969056448849096640182419091
absolute error = 3.290941950e-22
relative error = 1.6376944601185516909416307974473e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1377
y[1] (analytic) = 2.0095107582464385750227416317086
y[1] (numeric) = 2.0095107582464385750230716348217
absolute error = 3.300031131e-22
relative error = 1.6422062521723991842004345422559e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1378
y[1] (analytic) = 2.0095246210400280390272642154664
y[1] (numeric) = 2.0095246210400280390275951276971
absolute error = 3.309122307e-22
relative error = 1.6467189664426037748677572754777e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1379
y[1] (analytic) = 2.009538494025935885773149963668
y[1] (numeric) = 2.009538494025935885773481785216
absolute error = 3.318215480e-22
relative error = 1.6512326038364377904780743966146e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 2.0095523772044449149636823610216
y[1] (numeric) = 2.0095523772044449149640150920868
absolute error = 3.327310652e-22
relative error = 1.6557471652611177059142821563774e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1381
y[1] (analytic) = 2.0095662705758381419328124198236
y[1] (numeric) = 2.009566270575838141933146060606
absolute error = 3.336407824e-22
relative error = 1.6602626511261842784886376837485e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1382
memory used=156.4MB, alloc=4.2MB, time=8.96
y[1] (analytic) = 2.0095801741403987976684544967811
y[1] (numeric) = 2.0095801741403987976687890474809
absolute error = 3.345506998e-22
relative error = 1.6647790623387524628634309453363e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1383
y[1] (analytic) = 2.0095940878984103288358008232119
y[1] (numeric) = 2.0095940878984103288361362840295
absolute error = 3.354608176e-22
relative error = 1.6692963998058812324351648037549e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1384
y[1] (analytic) = 2.0096080118501563978006547527396
y[1] (numeric) = 2.0096080118501563978009911238757
absolute error = 3.363711361e-22
relative error = 1.6738146649321830126180490101384e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1385
y[1] (analytic) = 2.0096219459959208826527827306065
y[1] (numeric) = 2.0096219459959208826531200122617
absolute error = 3.372816552e-22
relative error = 1.6783338571317762275029655247673e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1386
y[1] (analytic) = 2.0096358903359878772292849887275
y[1] (numeric) = 2.0096358903359878772296231811027
absolute error = 3.381923752e-22
relative error = 1.6828539778091749069574175730698e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1387
y[1] (analytic) = 2.0096498448706416911379849706161
y[1] (numeric) = 2.0096498448706416911383240739125
absolute error = 3.391032964e-22
relative error = 1.6873750283688231170867408461590e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1388
y[1] (analytic) = 2.0096638096001668497808374903138
y[1] (numeric) = 2.0096638096001668497811775047326
absolute error = 3.400144188e-22
relative error = 1.6918970087223078923055385240841e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1389
y[1] (analytic) = 2.0096777845248480943773556294575
y[1] (numeric) = 2.0096777845248480943776965552001
absolute error = 3.409257426e-22
relative error = 1.6964199197763720902243822562749e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 2.0096917696449703819880563766269
y[1] (numeric) = 2.0096917696449703819883982138949
absolute error = 3.418372680e-22
relative error = 1.7009437624377022821952719753253e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1391
y[1] (analytic) = 2.0097057649608188855379250131123
y[1] (numeric) = 2.0097057649608188855382677621075
absolute error = 3.427489952e-22
relative error = 1.7054685376129287055031559804672e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.2MB, time=9.19
NO POLE
x[1] = 0.1392
y[1] (analytic) = 2.0097197704726789938398982492511
y[1] (numeric) = 2.0097197704726789938402419101754
absolute error = 3.436609243e-22
relative error = 1.7099942457110434060492365364188e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1393
y[1] (analytic) = 2.0097337861808363116183661154816
y[1] (numeric) = 2.0097337861808363116187106885371
absolute error = 3.445730555e-22
relative error = 1.7145208876385742198428628674021e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1394
y[1] (analytic) = 2.0097478120855766595326926122686
y[1] (numeric) = 2.0097478120855766595330380976576
absolute error = 3.454853890e-22
relative error = 1.7190484643019925202686227857961e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1395
y[1] (analytic) = 2.0097618481871860742007551230576
y[1] (numeric) = 2.0097618481871860742011015209826
absolute error = 3.463979250e-22
relative error = 1.7235769766077131702850373869263e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1396
y[1] (analytic) = 2.0097758944859508082225025944182
y[1] (numeric) = 2.0097758944859508082228499050818
absolute error = 3.473106636e-22
relative error = 1.7281064249645265603399603636006e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1397
y[1] (analytic) = 2.0097899509821573302035324875403
y[1] (numeric) = 2.0097899509821573302038807111453
absolute error = 3.482236050e-22
relative error = 1.7326368102787448291321506224411e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1398
y[1] (analytic) = 2.0098040176760923247786865052525
y[1] (numeric) = 2.0098040176760923247790356420019
absolute error = 3.491367494e-22
relative error = 1.7371681334566234763973306844934e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1399
y[1] (analytic) = 2.0098180945680426926356650987319
y[1] (numeric) = 2.0098180945680426926360151488289
absolute error = 3.500500970e-22
relative error = 1.7417003954043613151140752025769e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 2.0098321816582955505386607580818
y[1] (numeric) = 2.0098321816582955505390117217296
absolute error = 3.509636478e-22
relative error = 1.7462335960329924648222934861032e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=164.0MB, alloc=4.2MB, time=9.41
x[1] = 0.1401
y[1] (analytic) = 2.0098462789471382313520100909542
y[1] (numeric) = 2.0098462789471382313523619683564
absolute error = 3.518774022e-22
relative error = 1.7507677372437241401000412190065e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1402
y[1] (analytic) = 2.0098603864348582840638646934013
y[1] (numeric) = 2.0098603864348582840642174847615
absolute error = 3.527913602e-22
relative error = 1.7553028189474908274250794534152e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1403
y[1] (analytic) = 2.0098745041217434738098808171383
y[1] (numeric) = 2.0098745041217434738102345226604
absolute error = 3.537055221e-22
relative error = 1.7598388425478286011247732398997e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1404
y[1] (analytic) = 2.0098886320080817818969278374097
y[1] (numeric) = 2.0098886320080817818972824572977
absolute error = 3.546198880e-22
relative error = 1.7643758084531226402458034977341e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1405
y[1] (analytic) = 2.0099027700941614058268155256495
y[1] (numeric) = 2.0099027700941614058271710601075
absolute error = 3.555344580e-22
relative error = 1.7689137170717151644177242909862e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1406
y[1] (analytic) = 2.0099169183802707593200401311326
y[1] (numeric) = 2.0099169183802707593203965803651
absolute error = 3.564492325e-22
relative error = 1.7734525703045044195564252920522e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1407
y[1] (analytic) = 2.0099310768666984723395492758173
y[1] (numeric) = 2.0099310768666984723399066400287
absolute error = 3.573642114e-22
relative error = 1.7779923675646560982871903103974e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1408
y[1] (analytic) = 2.0099452455537333911145256665804
y[1] (numeric) = 2.0099452455537333911148839459755
absolute error = 3.582793951e-22
relative error = 1.7825331107529508326525801350715e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1409
y[1] (analytic) = 2.0099594244416645781641896290547
y[1] (numeric) = 2.0099594244416645781645488238384
absolute error = 3.591947837e-22
relative error = 1.7870748002775166282100912634956e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 2.0099736135307813123216204672764
y[1] (numeric) = 2.0099736135307813123219805776537
absolute error = 3.601103773e-22
relative error = 1.7916174365464383565773626218476e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.2MB, time=9.63
NO POLE
x[1] = 0.1411
y[1] (analytic) = 2.0099878128213730887575966533585
y[1] (numeric) = 2.0099878128213730887579576795346
absolute error = 3.610261761e-22
relative error = 1.7961610204652731867980310856724e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1412
y[1] (analytic) = 2.0100020223137296190044548514065
y[1] (numeric) = 2.0100020223137296190048167935868
absolute error = 3.619421803e-22
relative error = 1.8007055529395210394156896318766e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1413
y[1] (analytic) = 2.010016242008140830979967779898
y[1] (numeric) = 2.0100162420081408309803306382881
absolute error = 3.628583901e-22
relative error = 1.8052510348746245387049333910367e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1414
y[1] (analytic) = 2.0100304719048968690112409167512
y[1] (numeric) = 2.0100304719048968690116046915569
absolute error = 3.637748057e-22
relative error = 1.8097974671759689649043094675314e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1415
y[1] (analytic) = 2.01004471200428809385862805131
y[1] (numeric) = 2.0100447120042880938589927427372
absolute error = 3.646914272e-22
relative error = 1.8143448502513808354479050127834e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1416
y[1] (analytic) = 2.0100589623066050827396656874776
y[1] (numeric) = 2.0100589623066050827400312957323
absolute error = 3.656082547e-22
relative error = 1.8188931845086433363386647771307e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1417
y[1] (analytic) = 2.010073222812138629353026302234
y[1] (numeric) = 2.0100732228121386293533928275226
absolute error = 3.665252886e-22
relative error = 1.8234424718479792425239760188115e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1418
y[1] (analytic) = 2.0100874935211797439024904637777
y[1] (numeric) = 2.0100874935211797439028579063066
absolute error = 3.674425289e-22
relative error = 1.8279927121795624377881926795432e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1419
y[1] (analytic) = 2.0101017744340196531209378135313
y[1] (numeric) = 2.0101017744340196531213061735071
absolute error = 3.683599758e-22
relative error = 1.8325439064085119947820558933237e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.2MB, time=9.86
NO POLE
x[1] = 0.142
y[1] (analytic) = 2.0101160655509498002943569162601
y[1] (numeric) = 2.0101160655509498002947261938897
absolute error = 3.692776296e-22
relative error = 1.8370960559373730963439434777835e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 733.2
Order of pole = 1.413e+04
x[1] = 0.1421
y[1] (analytic) = 2.0101303668722618452858739825521
y[1] (numeric) = 2.0101303668722618452862441780423
absolute error = 3.701954902e-22
relative error = 1.8416491601786984323251342773046e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 271.4
Order of pole = 5214
x[1] = 0.1422
y[1] (analytic) = 2.0101446783982476645598004679116
y[1] (numeric) = 2.0101446783982476645601715814696
absolute error = 3.711135580e-22
relative error = 1.8462032210324086328879966154680e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 166.8
Order of pole = 3194
x[1] = 0.1423
y[1] (analytic) = 2.010159000129199351205699552726
y[1] (numeric) = 2.0101590001291993512060715845592
absolute error = 3.720318332e-22
relative error = 1.8507582394033920880042220406356e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 120.4
Order of pole = 2300
x[1] = 0.1424
y[1] (analytic) = 2.0101733320654092149624715073639
y[1] (numeric) = 2.0101733320654092149628444576797
absolute error = 3.729503158e-22
relative error = 1.8553142152015403185514717229547e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 94.33
Order of pole = 1796
x[1] = 0.1425
y[1] (analytic) = 2.0101876742071697822424579466691
y[1] (numeric) = 2.0101876742071697822428318156751
absolute error = 3.738690060e-22
relative error = 1.8598711493316473788078419124241e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 77.57
Order of pole = 1472
x[1] = 0.1426
y[1] (analytic) = 2.0102020265547737961555649781188
y[1] (numeric) = 2.0102020265547737961559397660229
absolute error = 3.747879041e-22
relative error = 1.8644290431959119028584225089528e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 65.9
Order of pole = 1247
x[1] = 0.1427
y[1] (analytic) = 2.0102163891085142165334052479169
y[1] (numeric) = 2.0102163891085142165337809549271
absolute error = 3.757070102e-22
relative error = 1.8689878972015426358285242565605e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 57.3
Order of pole = 1081
x[1] = 0.1428
y[1] (analytic) = 2.0102307618686842199534588892967
y[1] (numeric) = 2.0102307618686842199538355156212
absolute error = 3.766263245e-22
relative error = 1.8735477122531599082597942266997e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 50.71
Order of pole = 953.9
x[1] = 0.1429
y[1] (analytic) = 2.010245144835577199763253377312
y[1] (numeric) = 2.0102451448355771997636309231592
absolute error = 3.775458472e-22
relative error = 1.8781084892553260497747733477997e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.2MB, time=10.09
Real estimate of pole used
Radius of convergence = 45.49
Order of pole = 853.1
x[1] = 0.143
y[1] (analytic) = 2.0102595380094867661045622943983
y[1] (numeric) = 2.0102595380094867661049407599767
absolute error = 3.784655784e-22
relative error = 1.8826702286150971357257182931504e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 41.26
Order of pole = 771.5
x[1] = 0.1431
y[1] (analytic) = 2.0102739413907067459376230109899
y[1] (numeric) = 2.0102739413907067459380023965082
absolute error = 3.793855183e-22
relative error = 1.8872329312369300431627577943207e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 37.76
Order of pole = 703.9
x[1] = 0.1432
y[1] (analytic) = 2.0102883549795311830653732854818
y[1] (numeric) = 2.0102883549795311830657535911489
absolute error = 3.803056671e-22
relative error = 1.8917965980252235198579399334658e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 34.81
Order of pole = 647
x[1] = 0.1433
y[1] (analytic) = 2.010302778776254338157706787829
y[1] (numeric) = 2.010302778776254338158088013854
absolute error = 3.812260250e-22
relative error = 1.8963612298843181365728649309884e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 32.3
Order of pole = 598.6
x[1] = 0.1434
y[1] (analytic) = 2.0103172127811706887757475510807
y[1] (numeric) = 2.0103172127811706887761296976728
absolute error = 3.821465921e-22
relative error = 1.9009268272210623051997359608519e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 30.14
Order of pole = 556.7
x[1] = 0.1435
y[1] (analytic) = 2.0103316569945749293961433551473
y[1] (numeric) = 2.0103316569945749293965264225159
absolute error = 3.830673686e-22
relative error = 1.9054933909396908214638088616274e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 28.25
Order of pole = 520.3
x[1] = 0.1436
y[1] (analytic) = 2.0103461114167619714353780471061
y[1] (numeric) = 2.0103461114167619714357620354607
absolute error = 3.839883546e-22
relative error = 1.9100609214469533922042605620195e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 26.59
Order of pole = 488.2
x[1] = 0.1437
y[1] (analytic) = 2.0103605760480269432741028023507
y[1] (numeric) = 2.0103605760480269432744877119012
absolute error = 3.849095505e-22
relative error = 1.9146294206418253008080808799153e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 25.11
Order of pole = 459.8
x[1] = 0.1438
y[1] (analytic) = 2.0103750508886651902814863308969
y[1] (numeric) = 2.0103750508886651902818721618531
absolute error = 3.858309562e-22
relative error = 1.9191988879360966776145832514698e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.2MB, time=10.31
Real estimate of pole used
Radius of convergence = 23.8
Order of pole = 434.4
x[1] = 0.1439
y[1] (analytic) = 2.0103895359389722748395840331573
y[1] (numeric) = 2.0103895359389722748399707857294
absolute error = 3.867525721e-22
relative error = 1.9237693252286223925372098861688e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 22.62
Order of pole = 411.7
x[1] = 0.144
y[1] (analytic) = 2.0104040311992439763677261095047
y[1] (numeric) = 2.010404031199243976368113783903
absolute error = 3.876743983e-22
relative error = 1.9283407329259327995149557079243e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 21.56
Order of pole = 391.1
x[1] = 0.1441
y[1] (analytic) = 2.0104185366697762913469246279442
y[1] (numeric) = 2.0104185366697762913473132243792
absolute error = 3.885964350e-22
relative error = 1.9329131119319229279103670454026e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 20.59
Order of pole = 372.5
x[1] = 0.1442
y[1] (analytic) = 2.01043305235086543334429955422
y[1] (numeric) = 2.0104330523508654333446890729023
absolute error = 3.895186823e-22
relative error = 1.9374864626530239578863294050431e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 19.71
Order of pole = 355.5
x[1] = 0.1443
y[1] (analytic) = 2.0104475782428078330375237486858
y[1] (numeric) = 2.0104475782428078330379141898261
absolute error = 3.904411403e-22
relative error = 1.9420607854956228204855270248310e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 18.9
Order of pole = 339.9
x[1] = 0.1444
y[1] (analytic) = 2.01046211434590013823928693427
y[1] (numeric) = 2.0104621143459001382396782980794
absolute error = 3.913638094e-22
relative error = 1.9466360823582564212451979376942e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 18.16
Order of pole = 325.6
x[1] = 0.1445
y[1] (analytic) = 2.010476660660439213921778639874
y[1] (numeric) = 2.0104766606604392139221709265636
absolute error = 3.922866896e-22
relative error = 1.9512123531497962514477957797290e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 17.48
Order of pole = 312.5
x[1] = 0.1446
y[1] (analytic) = 2.0104912171867221422411901235405
y[1] (numeric) = 2.0104912171867221422415833333217
absolute error = 3.932097812e-22
relative error = 1.9557895992712564912692340370723e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 16.85
Order of pole = 300.3
x[1] = 0.1447
y[1] (analytic) = 2.0105057839250462225622352797371
y[1] (numeric) = 2.0105057839250462225626294128214
absolute error = 3.941330843e-22
relative error = 1.9603678211288035634723864596463e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 16.26
Order of pole = 289
memory used=183.1MB, alloc=4.2MB, time=10.52
x[1] = 0.1448
y[1] (analytic) = 2.0105203608757089714826905351009
y[1] (numeric) = 2.0105203608757089714830855917
absolute error = 3.950565991e-22
relative error = 1.9649470196259431396284826481157e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 15.72
Order of pole = 278.5
x[1] = 0.1449
y[1] (analytic) = 2.0105349480390081228579537369952
y[1] (numeric) = 2.0105349480390081228583497173209
absolute error = 3.959803257e-22
relative error = 1.9695271951687419467820047494866e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 15.21
Order of pole = 268.7
x[1] = 0.145
y[1] (analytic) = 2.0105495454152416278256220392318
y[1] (numeric) = 2.0105495454152416278260189434962
absolute error = 3.969042644e-22
relative error = 1.9741083491579751324116168274259e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 14.74
Order of pole = 259.5
x[1] = 0.1451
y[1] (analytic) = 2.0105641530047076548300887893172
y[1] (numeric) = 2.0105641530047076548304866177325
absolute error = 3.978284153e-22
relative error = 1.9786904819995987505279886855255e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 14.29
Order of pole = 251
x[1] = 0.1452
y[1] (analytic) = 2.0105787708077045896471594215834
y[1] (numeric) = 2.010578770807704589647558174362
absolute error = 3.987527786e-22
relative error = 1.9832735945968935179386527134650e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 13.88
Order of pole = 242.9
x[1] = 0.1453
y[1] (analytic) = 2.0105933988245310354086863605688
y[1] (numeric) = 2.0105933988245310354090860379234
absolute error = 3.996773546e-22
relative error = 1.9878576883504466983131357209136e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 13.48
Order of pole = 235.4
x[1] = 0.1454
y[1] (analytic) = 2.0106080370554858126272229390177
y[1] (numeric) = 2.0106080370554858126276235411609
absolute error = 4.006021432e-22
relative error = 1.9924427626713240349988477099556e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 13.11
Order of pole = 228.2
x[1] = 0.1455
y[1] (analytic) = 2.0106226855008679592206963348692
y[1] (numeric) = 2.010622685500867959221097862014
absolute error = 4.015271448e-22
relative error = 1.9970288194573673830271501041319e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 12.77
Order of pole = 221.5
x[1] = 0.1456
y[1] (analytic) = 2.0106373441609767305370995316141
y[1] (numeric) = 2.0106373441609767305375019839736
absolute error = 4.024523595e-22
relative error = 2.0016158591142662190644051756476e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 12.44
Order of pole = 215.1
x[1] = 0.1457
y[1] (analytic) = 2.0106520130361115993792023063967
y[1] (numeric) = 2.0106520130361115993796056841841
absolute error = 4.033777874e-22
relative error = 2.0062038820476652859464718687416e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.2MB, time=10.75
Real estimate of pole used
Radius of convergence = 12.12
Order of pole = 209.1
x[1] = 0.1458
y[1] (analytic) = 2.0106666921265722560292812502451
y[1] (numeric) = 2.0106666921265722560296855536738
absolute error = 4.043034287e-22
relative error = 2.0107928891605120435402913188335e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 11.83
Order of pole = 203.4
x[1] = 0.1459
y[1] (analytic) = 2.0106813814326586082738688248179
y[1] (numeric) = 2.0106813814326586082742740541016
absolute error = 4.052292837e-22
relative error = 2.0153828818530384786004468252780e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 11.55
Order of pole = 198
x[1] = 0.146
y[1] (analytic) = 2.0106960809546707814285214600564
y[1] (numeric) = 2.010696080954670781428927615409
absolute error = 4.061553526e-22
relative error = 2.0199738610280624686089565519881e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 11.28
Order of pole = 192.8
x[1] = 0.1461
y[1] (analytic) = 2.0107107906929091183626066971365
y[1] (numeric) = 2.0107107906929091183630137787719
absolute error = 4.070816354e-22
relative error = 2.0245658265936693352244449382148e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 11.03
Order of pole = 187.9
x[1] = 0.1462
y[1] (analytic) = 2.0107255106476741795241093811179
y[1] (numeric) = 2.0107255106476741795245173892502
absolute error = 4.080081323e-22
relative error = 2.0291587794525799060429223319661e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 10.78
Order of pole = 183.3
x[1] = 0.1463
y[1] (analytic) = 2.0107402408192667429644569076922
y[1] (numeric) = 2.0107402408192667429648658425358
absolute error = 4.089348436e-22
relative error = 2.0337527210047848011771565924486e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 10.55
Order of pole = 178.8
x[1] = 0.1464
y[1] (analytic) = 2.0107549812079878043633635284345
y[1] (numeric) = 2.0107549812079878043637733902039
absolute error = 4.098617694e-22
relative error = 2.0383476516555492483462082009588e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 10.33
Order of pole = 174.5
x[1] = 0.1465
y[1] (analytic) = 2.0107697318141385770536937189665
y[1] (numeric) = 2.0107697318141385770541045078764
absolute error = 4.107889099e-22
relative error = 2.0429435723074154566337317395955e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 10.12
Order of pole = 170.5
x[1] = 0.1466
y[1] (analytic) = 2.010784492638020492046344614444
y[1] (numeric) = 2.0107844926380204920467563307094
absolute error = 4.117162654e-22
relative error = 2.0475404843601843397764301078661e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.2MB, time=10.98
Real estimate of pole used
Radius of convergence = 9.92
Order of pole = 166.6
x[1] = 0.1467
y[1] (analytic) = 2.0107992636799351980551475167846
y[1] (numeric) = 2.0107992636799351980555601606204
absolute error = 4.126438358e-22
relative error = 2.0521383872243237833562197808473e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 9.727
Order of pole = 162.8
x[1] = 0.1468
y[1] (analytic) = 2.0108140449401845615217884780537
y[1] (numeric) = 2.0108140449401845615222020496751
absolute error = 4.135716214e-22
relative error = 2.0567372822995299112182357443429e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 9.541
Order of pole = 159.3
x[1] = 0.1469
y[1] (analytic) = 2.0108288364190706666407479644335
y[1] (numeric) = 2.010828836419070666641162464056
absolute error = 4.144996225e-22
relative error = 2.0613371709854244688103252838189e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 9.363
Order of pole = 155.8
x[1] = 0.147
y[1] (analytic) = 2.0108436381168958153842596052013
y[1] (numeric) = 2.0108436381168958153846750330403
absolute error = 4.154278390e-22
relative error = 2.0659380526923399137000225778038e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 9.192
Order of pole = 152.5
x[1] = 0.1471
y[1] (analytic) = 2.010858450033962527527288031146
y[1] (numeric) = 2.0108584500339625275277043874174
absolute error = 4.163562714e-22
relative error = 2.0705399298143930671188365583208e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 9.028
Order of pole = 149.4
x[1] = 0.1472
y[1] (analytic) = 2.0108732721705735406725258068593
y[1] (numeric) = 2.010873272170573540672943091779
absolute error = 4.172849197e-22
relative error = 2.0751428022591149865447889209601e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 8.87
Order of pole = 146.3
x[1] = 0.1473
y[1] (analytic) = 2.0108881045270318102754094613368
y[1] (numeric) = 2.010888104527031810275827675121
absolute error = 4.182137842e-22
relative error = 2.0797466714258842454439021509965e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 8.718
Order of pole = 143.4
x[1] = 0.1474
y[1] (analytic) = 2.0109029471036405096691546213321
y[1] (numeric) = 2.010902947103640509669573764197
absolute error = 4.191428649e-22
relative error = 2.0843515372221376252986374219248e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 8.572
Order of pole = 140.5
x[1] = 0.1475
y[1] (analytic) = 2.0109177999007030300898102519074
y[1] (numeric) = 2.0109177999007030300902303240694
absolute error = 4.200721620e-22
relative error = 2.0889574005498519830825839054691e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 8.43
Order of pole = 137.8
x[1] = 0.1476
y[1] (analytic) = 2.0109326629185229807013320086304
y[1] (numeric) = 2.0109326629185229807017530103062
absolute error = 4.210016758e-22
relative error = 2.0935642628082258047463160830989e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.2MB, time=11.20
Real estimate of pole used
Radius of convergence = 8.294
Order of pole = 135.2
x[1] = 0.1477
y[1] (analytic) = 2.0109475361574041886206747058693
y[1] (numeric) = 2.0109475361574041886210966372757
absolute error = 4.219314064e-22
relative error = 2.0981721244018267213372060408815e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 8.163
Order of pole = 132.7
x[1] = 0.1478
y[1] (analytic) = 2.010962419617650698942903905641
y[1] (numeric) = 2.0109624196176506989433267669951
absolute error = 4.228613541e-22
relative error = 2.1027809867297255811236201189175e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 8.036
Order of pole = 130.2
x[1] = 0.1479
y[1] (analytic) = 2.010977313299566774766326631474
y[1] (numeric) = 2.0109773132995667747667504229928
absolute error = 4.237915188e-22
relative error = 2.1073908492018356848228331446878e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.913
Order of pole = 127.8
x[1] = 0.148
y[1] (analytic) = 2.0109922172034568972176412117464
y[1] (numeric) = 2.0109922172034568972180659336473
absolute error = 4.247219009e-22
relative error = 2.1120017137143891215812345597403e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.794
Order of pole = 125.6
x[1] = 0.1481
y[1] (analytic) = 2.0110071313296257654771062569691
y[1] (numeric) = 2.0110071313296257654775319094696
absolute error = 4.256525005e-22
relative error = 2.1166135806717383680186658888768e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.68
Order of pole = 123.3
x[1] = 0.1482
y[1] (analytic) = 2.0110220556783782968037287754818
y[1] (numeric) = 2.0110220556783782968041553587997
absolute error = 4.265833179e-22
relative error = 2.1212264514727094888648179982686e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.568
Order of pole = 121.2
x[1] = 0.1483
y[1] (analytic) = 2.0110369902500196265604714320383
y[1] (numeric) = 2.0110369902500196265608989463914
absolute error = 4.275143531e-22
relative error = 2.1258403260242857072262093243499e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.461
Order of pole = 119.1
x[1] = 0.1484
y[1] (analytic) = 2.0110519350448551082394789537568
y[1] (numeric) = 2.0110519350448551082399073993632
absolute error = 4.284456064e-22
relative error = 2.1304552057251759642636160115433e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.357
Order of pole = 117.1
x[1] = 0.1485
y[1] (analytic) = 2.0110668900631903134873236879191
y[1] (numeric) = 2.0110668900631903134877530649971
absolute error = 4.293770780e-22
relative error = 2.1350710914767654438445162016008e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.2MB, time=11.42
Real estimate of pole used
Radius of convergence = 7.256
Order of pole = 115.2
x[1] = 0.1486
y[1] (analytic) = 2.0110818553053310321302703161019
y[1] (numeric) = 2.0110818553053310321307006248699
absolute error = 4.303087680e-22
relative error = 2.1396879836831340012787752512448e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.158
Order of pole = 113.3
x[1] = 0.1487
y[1] (analytic) = 2.0110968307715832721995597291298
y[1] (numeric) = 2.0110968307715832721999909698065
absolute error = 4.312406767e-22
relative error = 2.1443058837427979286432286139358e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 7.062
Order of pole = 111.4
x[1] = 0.1488
y[1] (analytic) = 2.0111118164622532599567120673432
y[1] (numeric) = 2.0111118164622532599571442401472
absolute error = 4.321728040e-22
relative error = 2.1489247910652485122330425978415e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.97
Order of pole = 109.7
x[1] = 0.1489
y[1] (analytic) = 2.0111268123776474399188489306754
y[1] (numeric) = 2.0111268123776474399192820358257
absolute error = 4.331051503e-22
relative error = 2.1535447075461292962188492991111e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.881
Order of pole = 107.9
x[1] = 0.149
y[1] (analytic) = 2.0111418185180724748840347630414
y[1] (numeric) = 2.0111418185180724748844688007571
absolute error = 4.340377157e-22
relative error = 2.1581656335893035410975272008552e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.793
Order of pole = 106.2
x[1] = 0.1491
y[1] (analytic) = 2.0111568348838352459566374155395
y[1] (numeric) = 2.01115683488383524595707238604
absolute error = 4.349705005e-22
relative error = 2.1627875705930411370359300280506e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.709
Order of pole = 104.6
x[1] = 0.1492
y[1] (analytic) = 2.0111718614752428525727078929745
y[1] (numeric) = 2.0111718614752428525731437964793
absolute error = 4.359035048e-22
relative error = 2.1674105189610912333030289019780e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.626
Order of pole = 103
x[1] = 0.1493
y[1] (analytic) = 2.0111868982926026125253792882126
y[1] (numeric) = 2.0111868982926026125258161249413
absolute error = 4.368367287e-22
relative error = 2.1720344790971570047096490830692e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.546
Order of pole = 101.5
x[1] = 0.1494
y[1] (analytic) = 2.0112019453362220619902849088826
y[1] (numeric) = 2.0112019453362220619907226790551
absolute error = 4.377701725e-22
relative error = 2.1766594523993258522150316732465e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.468
Order of pole = 99.98
x[1] = 0.1495
memory used=202.1MB, alloc=4.2MB, time=11.64
y[1] (analytic) = 2.0112170026064089555509956009425
y[1] (numeric) = 2.0112170026064089555514343047788
absolute error = 4.387038363e-22
relative error = 2.1812854392711865981992952006367e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.393
Order of pole = 98.51
x[1] = 0.1496
y[1] (analytic) = 2.011232070103471266224476273632
y[1] (numeric) = 2.0112320701034712662249159113523
absolute error = 4.396377203e-22
relative error = 2.1859124406134896565734887716869e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.319
Order of pole = 97.09
x[1] = 0.1497
y[1] (analytic) = 2.0112471478277171854865616303376
y[1] (numeric) = 2.0112471478277171854870022021623
absolute error = 4.405718247e-22
relative error = 2.1905404573269244358892868301384e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.247
Order of pole = 95.7
x[1] = 0.1498
y[1] (analytic) = 2.0112622357794551232974511098996
y[1] (numeric) = 2.0112622357794551232978926160493
absolute error = 4.415061497e-22
relative error = 2.1951694903121192917292379567617e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.177
Order of pole = 94.35
x[1] = 0.1499
y[1] (analytic) = 2.011277333958993708127223042893
y[1] (numeric) = 2.0112773339589937081276654835884
absolute error = 4.424406954e-22
relative error = 2.1997995399724450044429877518702e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.108
Order of pole = 93.03
x[1] = 0.15
y[1] (analytic) = 2.0112924423666417869813680274198
y[1] (numeric) = 2.0112924423666417869818114028819
absolute error = 4.433754621e-22
relative error = 2.2044306077056116251812532165093e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 6.042
Order of pole = 91.75
x[1] = 0.1501
y[1] (analytic) = 2.0113075610027084254263415289534
y[1] (numeric) = 2.0113075610027084254267858394033
absolute error = 4.443104499e-22
relative error = 2.2090626939148750698856535736014e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.977
Order of pole = 90.49
x[1] = 0.1502
y[1] (analytic) = 2.0113226898675029076151357087776
y[1] (numeric) = 2.0113226898675029076155809544365
absolute error = 4.452456589e-22
relative error = 2.2136957990034449702312787120217e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.913
Order of pole = 89.27
x[1] = 0.1503
y[1] (analytic) = 2.0113378289613347363128704855695
y[1] (numeric) = 2.0113378289613347363133166666589
absolute error = 4.461810894e-22
relative error = 2.2183299243688476917075731929591e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.852
Order of pole = 88.08
x[1] = 0.1504
y[1] (analytic) = 2.0113529782845136329224038346771
y[1] (numeric) = 2.0113529782845136329228509514186
absolute error = 4.471167415e-22
relative error = 2.2229650704141777604770349939889e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=206.0MB, alloc=4.2MB, time=11.87
Real estimate of pole used
Radius of convergence = 5.791
Order of pole = 86.91
x[1] = 0.1505
y[1] (analytic) = 2.0113681378373495375099613296463
y[1] (numeric) = 2.0113681378373495375104093822618
absolute error = 4.480526155e-22
relative error = 2.2276012385368313772560110905653e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.732
Order of pole = 85.77
x[1] = 0.1506
y[1] (analytic) = 2.0113833076201526088307849305573
y[1] (numeric) = 2.0113833076201526088312339192687
absolute error = 4.489887114e-22
relative error = 2.2322384286426175033105953918749e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.674
Order of pole = 84.66
x[1] = 0.1507
y[1] (analytic) = 2.0113984876332332243548010237308
y[1] (numeric) = 2.0113984876332332243552509487604
absolute error = 4.499250296e-22
relative error = 2.2368766426259797574890036641672e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.618
Order of pole = 83.58
x[1] = 0.1508
y[1] (analytic) = 2.0114136778769019802923077173731
y[1] (numeric) = 2.0114136778769019802927585789433
absolute error = 4.508615702e-22
relative error = 2.2415158808897819208729053905205e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.563
Order of pole = 82.52
x[1] = 0.1509
y[1] (analytic) = 2.0114288783514696916196813977271
y[1] (numeric) = 2.0114288783514696916201331960603
absolute error = 4.517983332e-22
relative error = 2.2461561433396822261248001240677e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.509
Order of pole = 81.48
x[1] = 0.151
y[1] (analytic) = 2.0114440890572473921051025503044
y[1] (numeric) = 2.0114440890572473921055552856234
absolute error = 4.527353190e-22
relative error = 2.2507974318699284098612518605287e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.457
Order of pole = 80.46
x[1] = 0.1511
y[1] (analytic) = 2.0114593099945463343343008507761
y[1] (numeric) = 2.0114593099945463343347545233038
absolute error = 4.536725277e-22
relative error = 2.2554397468832220196930706033730e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.405
Order of pole = 79.47
x[1] = 0.1512
y[1] (analytic) = 2.0114745411636779897363195301017
y[1] (numeric) = 2.0114745411636779897367741400611
absolute error = 4.546099594e-22
relative error = 2.2600830887822179716024925743892e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.355
Order of pole = 78.5
x[1] = 0.1513
y[1] (analytic) = 2.0114897825649540486092990184822
y[1] (numeric) = 2.0114897825649540486097545660967
absolute error = 4.555476145e-22
relative error = 2.2647274594609564130417643644392e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.2MB, time=12.09
Real estimate of pole used
Radius of convergence = 5.306
Order of pole = 77.55
x[1] = 0.1514
y[1] (analytic) = 2.0115050341986864201462798727259
y[1] (numeric) = 2.0115050341986864201467363582189
absolute error = 4.564854930e-22
relative error = 2.2693728588248248106064479171952e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.258
Order of pole = 76.62
x[1] = 0.1515
y[1] (analytic) = 2.0115202960651872324610249916173
y[1] (numeric) = 2.0115202960651872324614824152124
absolute error = 4.574235951e-22
relative error = 2.2740192877734518151076401120262e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.21
Order of pole = 75.72
x[1] = 0.1516
y[1] (analytic) = 2.011535568164768832613861123887
y[1] (numeric) = 2.011535568164768832614319485808
absolute error = 4.583619210e-22
relative error = 2.2786667472064042270749331250110e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.164
Order of pole = 74.83
x[1] = 0.1517
y[1] (analytic) = 2.0115508504977437866375396733809
y[1] (numeric) = 2.0115508504977437866379989738517
absolute error = 4.593004708e-22
relative error = 2.2833152375260580798077197635559e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.119
Order of pole = 73.95
x[1] = 0.1518
y[1] (analytic) = 2.011566143064424879563116806032
y[1] (numeric) = 2.0115661430644248795635770452769
absolute error = 4.602392449e-22
relative error = 2.2879647606261178486398928146227e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.075
Order of pole = 73.1
x[1] = 0.1519
y[1] (analytic) = 2.0115814458651251154458528632428
y[1] (numeric) = 2.011581445865125115446314041486
absolute error = 4.611782432e-22
relative error = 2.2926153159145892351112139806409e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 5.031
Order of pole = 72.26
x[1] = 0.152
y[1] (analytic) = 2.0115967589001577173911310862869
y[1] (numeric) = 2.011596758900157717391593203753
absolute error = 4.621174661e-22
relative error = 2.2972669052850489164988118522987e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.989
Order of pole = 71.44
x[1] = 0.1521
y[1] (analytic) = 2.0116120821698361275803956563467
y[1] (numeric) = 2.0116120821698361275808587132604
absolute error = 4.630569137e-22
relative error = 2.3019195291396400059846308893053e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.947
Order of pole = 70.64
x[1] = 0.1522
y[1] (analytic) = 2.011627415674474007297109054803
y[1] (numeric) = 2.0116274156744740072975730513893
absolute error = 4.639965863e-22
relative error = 2.3065731888746785339349851564831e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.906
Order of pole = 69.85
x[1] = 0.1523
y[1] (analytic) = 2.0116427594143852369527287484003
y[1] (numeric) = 2.0116427594143852369531936848842
absolute error = 4.649364839e-22
relative error = 2.3112278843950847266083534510696e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.2MB, time=12.31
Real estimate of pole used
Radius of convergence = 4.866
Order of pole = 69.08
x[1] = 0.1524
y[1] (analytic) = 2.0116581133898839161127032039115
y[1] (numeric) = 2.0116581133898839161131690805182
absolute error = 4.658766067e-22
relative error = 2.3158836165999516570432068936081e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.827
Order of pole = 68.32
x[1] = 0.1525
y[1] (analytic) = 2.0116734776012843635224872369323
y[1] (numeric) = 2.0116734776012843635229540538873
absolute error = 4.668169550e-22
relative error = 2.3205403868854087150861117267796e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.788
Order of pole = 67.58
x[1] = 0.1526
y[1] (analytic) = 2.011688852048901117133576699439
y[1] (numeric) = 2.0116888520489011171340444569678
absolute error = 4.677575288e-22
relative error = 2.3251981951562234986724897260418e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.75
Order of pole = 66.85
x[1] = 0.1527
y[1] (analytic) = 2.011704236733048934129562510744
y[1] (numeric) = 2.0117042367330489341300312090725
absolute error = 4.686983285e-22
relative error = 2.3298570433054955190394362450510e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.713
Order of pole = 66.13
x[1] = 0.1528
y[1] (analytic) = 2.0117196316540427909522040364923
y[1] (numeric) = 2.0117196316540427909526736758464
absolute error = 4.696393541e-22
relative error = 2.3345169312378828353581844186343e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.677
Order of pole = 65.43
x[1] = 0.1529
y[1] (analytic) = 2.0117350368121978833275218203408
y[1] (numeric) = 2.0117350368121978833279924009467
absolute error = 4.705806059e-22
relative error = 2.3391778603492615680118464283310e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.641
Order of pole = 64.74
x[1] = 0.153
y[1] (analytic) = 2.0117504522078296262919096729698
y[1] (numeric) = 2.0117504522078296262923811950538
absolute error = 4.715220840e-22
relative error = 2.3438398310412710392305655268118e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.606
Order of pole = 64.07
x[1] = 0.1531
y[1] (analytic) = 2.0117658778412536542182661230776
y[1] (numeric) = 2.0117658778412536542187385868663
absolute error = 4.724637887e-22
relative error = 2.3485028447096547507182963124333e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.572
Order of pole = 63.4
x[1] = 0.1532
y[1] (analytic) = 2.0117813137127858208421452350137
y[1] (numeric) = 2.0117813137127858208426186407338
absolute error = 4.734057201e-22
relative error = 2.3531669017559345419535311411562e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.2MB, time=12.53
Real estimate of pole used
Radius of convergence = 4.538
Order of pole = 62.75
x[1] = 0.1533
y[1] (analytic) = 2.0117967598227421992879267977096
y[1] (numeric) = 2.0117967598227421992884011455879
absolute error = 4.743478783e-22
relative error = 2.3578320025815848889358759293693e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.505
Order of pole = 62.11
x[1] = 0.1534
y[1] (analytic) = 2.0118122161714390820950058895701
y[1] (numeric) = 2.0118122161714390820954811798337
absolute error = 4.752902636e-22
relative error = 2.3624981485821614505774148262372e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.472
Order of pole = 61.48
x[1] = 0.1535
y[1] (analytic) = 2.0118276827591929812440018239918
y[1] (numeric) = 2.0118276827591929812444780568679
absolute error = 4.762328761e-22
relative error = 2.3671653401590209793659659902943e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.44
Order of pole = 60.86
x[1] = 0.1536
y[1] (analytic) = 2.0118431595863206281829864801786
y[1] (numeric) = 2.0118431595863206281834636558947
absolute error = 4.771757161e-22
relative error = 2.3718335787075860450743353615225e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.408
Order of pole = 60.25
x[1] = 0.1537
y[1] (analytic) = 2.0118586466531389738537320239288
y[1] (numeric) = 2.0118586466531389738542101427124
absolute error = 4.781187836e-22
relative error = 2.3765028641320426832613281447182e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.377
Order of pole = 59.66
x[1] = 0.1538
y[1] (analytic) = 2.0118741439599651887179780230708
y[1] (numeric) = 2.0118741439599651887184570851498
absolute error = 4.790620790e-22
relative error = 2.3811731983247406452203700477388e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.347
Order of pole = 59.07
x[1] = 0.1539
y[1] (analytic) = 2.01188965150711666278371796223
y[1] (numeric) = 2.0118896515071166627841979678324
absolute error = 4.800056024e-22
relative error = 2.3858445816868007030741339820336e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.317
Order of pole = 58.49
x[1] = 0.154
y[1] (analytic) = 2.0119051692949110056315051616113
y[1] (numeric) = 2.0119051692949110056319861109651
absolute error = 4.809493538e-22
relative error = 2.3905170141222546972769285832190e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.287
Order of pole = 57.92
x[1] = 0.1541
y[1] (analytic) = 2.0119206973236660464407781044855
y[1] (numeric) = 2.0119206973236660464412599978192
absolute error = 4.818933337e-22
relative error = 2.3951904980202895944627058586227e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.258
Order of pole = 57.37
x[1] = 0.1542
y[1] (analytic) = 2.0119362355936998340162051780749
y[1] (numeric) = 2.0119362355936998340166880156169
absolute error = 4.828375420e-22
relative error = 2.3998650327877814320355929999740e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.2MB, time=12.75
Real estimate of pole used
Radius of convergence = 4.23
Order of pole = 56.82
x[1] = 0.1543
y[1] (analytic) = 2.0119517841053306368140488325312
y[1] (numeric) = 2.0119517841053306368145326145102
absolute error = 4.837819790e-22
relative error = 2.4045406198197084653740103831780e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.202
Order of pole = 56.28
x[1] = 0.1544
y[1] (analytic) = 2.0119673428588769429685491627085
y[1] (numeric) = 2.0119673428588769429690338893535
absolute error = 4.847266450e-22
relative error = 2.4092172605109704829121798706280e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.174
Order of pole = 55.75
x[1] = 0.1545
y[1] (analytic) = 2.0119829118546574603183269174348
y[1] (numeric) = 2.0119829118546574603188125889747
absolute error = 4.856715399e-22
relative error = 2.4138949542683002782769811437265e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.147
Order of pole = 55.22
x[1] = 0.1546
y[1] (analytic) = 2.011998491092991116432805940988
y[1] (numeric) = 2.0119984910929911164332925576522
absolute error = 4.866166642e-22
relative error = 2.4185737034805232024094594589635e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.121
Order of pole = 54.71
x[1] = 0.1547
y[1] (analytic) = 2.012014080574197058638655051491
y[1] (numeric) = 2.0120140805741970586391426135088
absolute error = 4.875620178e-22
relative error = 2.4232535075542686876358912212857e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.094
Order of pole = 54.21
x[1] = 0.1548
y[1] (analytic) = 2.012029680298594654046249360938
y[1] (numeric) = 2.0120296802985946540467378685391
absolute error = 4.885076011e-22
relative error = 2.4279343683812019001758542973262e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.068
Order of pole = 53.71
x[1] = 0.1549
y[1] (analytic) = 2.0120452902665034895761510415733
y[1] (numeric) = 2.0120452902665034895766404949875
absolute error = 4.894534142e-22
relative error = 2.4326162863618737284411640294923e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.043
Order of pole = 53.22
x[1] = 0.155
y[1] (analytic) = 2.0120609104782433719856095433441
y[1] (numeric) = 2.0120609104782433719860999428013
absolute error = 4.903994572e-22
relative error = 2.4372992618967871019632518330555e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 4.018
Order of pole = 52.73
x[1] = 0.1551
y[1] (analytic) = 2.0120765409341343278950812671537
y[1] (numeric) = 2.0120765409341343278955726128841
absolute error = 4.913457304e-22
relative error = 2.4419832963803949399980006393984e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.2MB, time=12.98
Real estimate of pole used
Radius of convergence = 3.993
Order of pole = 52.26
x[1] = 0.1552
y[1] (analytic) = 2.0120921816344966038147686986468
y[1] (numeric) = 2.0120921816344966038152609908807
absolute error = 4.922922339e-22
relative error = 2.4466683902130810058293511331543e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.969
Order of pole = 51.79
x[1] = 0.1553
y[1] (analytic) = 2.0121078325796506661711790072588
y[1] (numeric) = 2.0121078325796506661716722462268
absolute error = 4.932389680e-22
relative error = 2.4513545447891635188919706462705e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.945
Order of pole = 51.33
x[1] = 0.1554
y[1] (analytic) = 2.0121234937699172013337021152689
y[1] (numeric) = 2.0121234937699172013341963012018
absolute error = 4.941859329e-22
relative error = 2.4560417610058942843463160127507e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.922
Order of pole = 50.88
x[1] = 0.1555
y[1] (analytic) = 2.0121391652056171156412082415974
y[1] (numeric) = 2.0121391652056171156417033747259
absolute error = 4.951331285e-22
relative error = 2.4607300382695109396965309739070e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.898
Order of pole = 50.43
x[1] = 0.1556
y[1] (analytic) = 2.0121548468870715354286649250919
y[1] (numeric) = 2.0121548468870715354291610056472
absolute error = 4.960805553e-22
relative error = 2.4654193789681118040669776229087e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.875
Order of pole = 49.99
x[1] = 0.1557
y[1] (analytic) = 2.0121705388146018070537735320539
y[1] (numeric) = 2.0121705388146018070542705602673
absolute error = 4.970282134e-22
relative error = 2.4701097835017819482347689108388e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.853
Order of pole = 49.56
x[1] = 0.1558
y[1] (analytic) = 2.0121862409885294969236252527561
y[1] (numeric) = 2.012186240988529496924123228859
absolute error = 4.979761029e-22
relative error = 2.4748012522705581979861999835346e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.831
Order of pole = 49.13
x[1] = 0.1559
y[1] (analytic) = 2.012201953409176391521376591708
y[1] (numeric) = 2.012201953409176391521875515932
absolute error = 4.989242240e-22
relative error = 2.4794937861713971210794824226938e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.809
Order of pole = 48.71
x[1] = 0.156
y[1] (analytic) = 2.0122176760768644974329443564304
y[1] (numeric) = 2.0122176760768644974334442290074
absolute error = 4.998725770e-22
relative error = 2.4841873865981555889085000365475e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.2MB, time=13.20
Real estimate of pole used
Radius of convergence = 3.787
Order of pole = 48.29
x[1] = 0.1561
y[1] (analytic) = 2.0122334089919160413737201495033
y[1] (numeric) = 2.0122334089919160413742209706652
absolute error = 5.008211619e-22
relative error = 2.4888820534537303368795276727898e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.766
Order of pole = 47.89
x[1] = 0.1562
y[1] (analytic) = 2.0122491521546534702153043686534
y[1] (numeric) = 2.0122491521546534702158061386324
absolute error = 5.017699790e-22
relative error = 2.4935777881318543310354471049164e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.745
Order of pole = 47.48
x[1] = 0.1563
y[1] (analytic) = 2.0122649055653994510122597196556
y[1] (numeric) = 2.0122649055653994510127624386841
absolute error = 5.027190285e-22
relative error = 2.4982745915292285622163135496092e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.725
Order of pole = 47.09
x[1] = 0.1564
y[1] (analytic) = 2.0122806692244768710288842468214
y[1] (numeric) = 2.0122806692244768710293879151319
absolute error = 5.036683105e-22
relative error = 2.5029724640455414388317618837452e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.704
Order of pole = 46.69
x[1] = 0.1565
y[1] (analytic) = 2.012296443132208837766003885855
y[1] (numeric) = 2.0122964431322088377665085036802
absolute error = 5.046178252e-22
relative error = 2.5076714065773775647613986861116e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.684
Order of pole = 46.31
x[1] = 0.1566
y[1] (analytic) = 2.0123122272889186789877845438599
y[1] (numeric) = 2.0123122272889186789882901114328
absolute error = 5.055675729e-22
relative error = 2.5123714205181982269281408265830e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.664
Order of pole = 45.93
x[1] = 0.1567
y[1] (analytic) = 2.0123280216949299427485637112828
y[1] (numeric) = 2.0123280216949299427490702288364
absolute error = 5.065175536e-22
relative error = 2.5170725057705743429941887044015e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.645
Order of pole = 45.55
x[1] = 0.1568
y[1] (analytic) = 2.0123438263505663974197016105846
y[1] (numeric) = 2.0123438263505663974202090783522
absolute error = 5.074677676e-22
relative error = 2.5217746637278427692667319982612e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.626
Order of pole = 45.18
x[1] = 0.1569
y[1] (analytic) = 2.0123596412561520317164518864344
y[1] (numeric) = 2.0123596412561520317169603046495
absolute error = 5.084182151e-22
relative error = 2.5264778952863314525376634791001e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.607
Order of pole = 44.81
x[1] = 0.157
y[1] (analytic) = 2.0123754664120110547248518422239
y[1] (numeric) = 2.0123754664120110547253612111201
absolute error = 5.093688962e-22
relative error = 2.5311822008453788969662004756047e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.2MB, time=13.41
Real estimate of pole used
Radius of convergence = 3.588
Order of pole = 44.45
x[1] = 0.1571
y[1] (analytic) = 2.0123913018184678959286322277035
y[1] (numeric) = 2.0123913018184678959291425475146
absolute error = 5.103198111e-22
relative error = 2.5358875813011961668288197785865e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.569
Order of pole = 44.1
x[1] = 0.1572
y[1] (analytic) = 2.0124071474758472052361465825471
y[1] (numeric) = 2.0124071474758472052366578535073
absolute error = 5.112709602e-22
relative error = 2.5405940385437646366693880200284e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.551
Order of pole = 43.75
x[1] = 0.1573
y[1] (analytic) = 2.012423003384473853007320140655
y[1] (numeric) = 2.0124230033844738530078323629983
absolute error = 5.122223433e-22
relative error = 2.5453015714814894201181643315552e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.533
Order of pole = 43.4
x[1] = 0.1574
y[1] (analytic) = 2.0124388695446729300806183000065
y[1] (numeric) = 2.0124388695446729300811314739674
absolute error = 5.131739609e-22
relative error = 2.5500101825011403524832692296599e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.515
Order of pole = 43.06
x[1] = 0.1575
y[1] (analytic) = 2.0124547459567697478000346628826
y[1] (numeric) = 2.0124547459567697478005487886957
absolute error = 5.141258131e-22
relative error = 2.5547198720017534170017550124350e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.498
Order of pole = 42.72
x[1] = 0.1576
y[1] (analytic) = 2.0124706326210898380420986512764
y[1] (numeric) = 2.0124706326210898380426137291764
absolute error = 5.150779000e-22
relative error = 2.5594306403823157197182704992535e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.481
Order of pole = 42.39
x[1] = 0.1577
y[1] (analytic) = 2.0124865295379589532429027023178
y[1] (numeric) = 2.0124865295379589532434187325397
absolute error = 5.160302219e-22
relative error = 2.5641424890355609384716425687227e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.463
Order of pole = 42.06
x[1] = 0.1578
y[1] (analytic) = 2.0125024367077030664251490485412
y[1] (numeric) = 2.01250243670770306642566603132
absolute error = 5.169827788e-22
relative error = 2.5688554178634609829486790525561e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.447
Order of pole = 41.74
x[1] = 0.1579
y[1] (analytic) = 2.012518354130648371225216087827
y[1] (numeric) = 2.0125183541306483712257340233981
absolute error = 5.179355711e-22
relative error = 2.5735694287555140209658342809815e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.2MB, time=13.63
Real estimate of pole used
Radius of convergence = 3.43
Order of pole = 41.42
x[1] = 0.158
y[1] (analytic) = 2.0125342818071212819202443478551
y[1] (numeric) = 2.012534281807121281920763236454
absolute error = 5.188885989e-22
relative error = 2.5782845221104642099555259922162e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.414
Order of pole = 41.1
x[1] = 0.1581
y[1] (analytic) = 2.0125502197374484334552420499082
y[1] (numeric) = 2.0125502197374484334557618917706
absolute error = 5.198418624e-22
relative error = 2.5830006988238886679123050622543e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.397
Order of pole = 40.79
x[1] = 0.1582
y[1] (analytic) = 2.0125661679219566814702102768707
y[1] (numeric) = 2.0125661679219566814707310722324
absolute error = 5.207953617e-22
relative error = 2.5877179592944216167318936979428e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.381
Order of pole = 40.48
x[1] = 0.1583
y[1] (analytic) = 2.0125821263609731023272877502688
y[1] (numeric) = 2.0125821263609731023278094993659
absolute error = 5.217490971e-22
relative error = 2.5924363049143964346373012698517e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.365
Order of pole = 40.18
x[1] = 0.1584
y[1] (analytic) = 2.0125980950548249931379152212051
y[1] (numeric) = 2.0125980950548249931384379242738
absolute error = 5.227030687e-22
relative error = 2.5971557360823254454045328668494e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.35
Order of pole = 39.88
x[1] = 0.1585
y[1] (analytic) = 2.012614074003839871790019480041
y[1] (numeric) = 2.0126140740038398717905431373178
absolute error = 5.236572768e-22
relative error = 2.6018762541904042795491316397612e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.334
Order of pole = 39.58
x[1] = 0.1586
y[1] (analytic) = 2.0126300632083454769752169896874
y[1] (numeric) = 2.0126300632083454769757416014088
absolute error = 5.246117214e-22
relative error = 2.6065978591401608839800301206145e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.319
Order of pole = 39.29
x[1] = 0.1587
y[1] (analytic) = 2.0126460626686697682160371473654
y[1] (numeric) = 2.0126460626686697682165627137683
absolute error = 5.255664029e-22
relative error = 2.6113205528205231403512053790085e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.304
Order of pole = 39
x[1] = 0.1588
y[1] (analytic) = 2.0126620723851409258931651797046
y[1] (numeric) = 2.0126620723851409258936917010259
absolute error = 5.265213213e-22
relative error = 2.6160443351329046471887524084772e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.289
Order of pole = 38.71
x[1] = 0.1589
y[1] (analytic) = 2.012678092358087351272704676048
y[1] (numeric) = 2.012678092358087351273232152525
absolute error = 5.274764770e-22
relative error = 2.6207692079660872544651118005804e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.2MB, time=13.86
Real estimate of pole used
Radius of convergence = 3.275
Order of pole = 38.43
x[1] = 0.159
y[1] (analytic) = 2.01269412258783766653345976484
y[1] (numeric) = 2.0126941225878376665339881967099
absolute error = 5.284318699e-22
relative error = 2.6254951707245235574580907464182e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.26
Order of pole = 38.15
x[1] = 0.1591
y[1] (analytic) = 2.0127101630747207147942369379727
y[1] (numeric) = 2.012710163074720714794766325473
absolute error = 5.293875003e-22
relative error = 2.6302222248000185187594019532221e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.246
Order of pole = 37.87
x[1] = 0.1592
y[1] (analytic) = 2.0127262138190655601411665279745
y[1] (numeric) = 2.0127262138190655601416968713431
absolute error = 5.303433686e-22
relative error = 2.6349503720811345629089744251191e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.232
Order of pole = 37.6
x[1] = 0.1593
y[1] (analytic) = 2.0127422748212014876550438429267
y[1] (numeric) = 2.0127422748212014876555751424013
absolute error = 5.312994746e-22
relative error = 2.6396796114753294917498072486771e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.218
Order of pole = 37.33
x[1] = 0.1594
y[1] (analytic) = 2.0127583460814580034386899639954
y[1] (numeric) = 2.0127583460814580034392222198142
absolute error = 5.322558188e-22
relative error = 2.6444099453678736083983515683213e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.204
Order of pole = 37.07
x[1] = 0.1595
y[1] (analytic) = 2.0127744276001648346443322104752
y[1] (numeric) = 2.0127744276001648346448654228765
absolute error = 5.332124013e-22
relative error = 2.6491413741566175538605621494783e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.19
Order of pole = 36.8
x[1] = 0.1596
y[1] (analytic) = 2.0127905193776519295010042772393
y[1] (numeric) = 2.0127905193776519295015384464615
absolute error = 5.341692222e-22
relative error = 2.6538738982393623852704330614948e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.176
Order of pole = 36.54
x[1] = 0.1597
y[1] (analytic) = 2.0128066214142494573419660494982
y[1] (numeric) = 2.01280662141424945734250117578
absolute error = 5.351262818e-22
relative error = 2.6586075190074969839667840028540e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.163
Order of pole = 36.29
x[1] = 0.1598
y[1] (analytic) = 2.0128227337102878086321430997717
y[1] (numeric) = 2.012822733710287808632679183352
absolute error = 5.360835803e-22
relative error = 2.6633422373555140479384295549397e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.2MB, time=14.08
Real estimate of pole used
Radius of convergence = 3.15
Order of pole = 36.03
x[1] = 0.1599
y[1] (analytic) = 2.0128388562660975949955858719827
y[1] (numeric) = 2.0128388562660975949961229131004
absolute error = 5.370411177e-22
relative error = 2.6680780531842191577740361487985e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.137
Order of pole = 35.78
x[1] = 0.16
y[1] (analytic) = 2.0128549890820096492429485575849
y[1] (numeric) = 2.0128549890820096492434865564793
absolute error = 5.379988944e-22
relative error = 2.6728149683816112110159175630860e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.124
Order of pole = 35.53
x[1] = 0.1601
y[1] (analytic) = 2.0128711321583550253989876686422
y[1] (numeric) = 2.0128711321583550253995266255527
absolute error = 5.389569105e-22
relative error = 2.6775529833451831874725491916029e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.111
Order of pole = 35.29
x[1] = 0.1602
y[1] (analytic) = 2.0128872854954649987300803127776
y[1] (numeric) = 2.0128872854954649987306202279438
absolute error = 5.399151662e-22
relative error = 2.6822920989691770786810510465683e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.099
Order of pole = 35.05
x[1] = 0.1603
y[1] (analytic) = 2.0129034490936710657717621749178
y[1] (numeric) = 2.0129034490936710657723030485794
absolute error = 5.408736616e-22
relative error = 2.6870323156509742853691176552804e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.086
Order of pole = 34.81
x[1] = 0.1604
y[1] (analytic) = 2.0129196229533049443562852107599
y[1] (numeric) = 2.0129196229533049443568270431569
absolute error = 5.418323970e-22
relative error = 2.6917736347814880036352082366813e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.074
Order of pole = 34.57
x[1] = 0.1605
y[1] (analytic) = 2.0129358070746985736401950568927
y[1] (numeric) = 2.0129358070746985736407378482653
absolute error = 5.427913726e-22
relative error = 2.6965160572547627678646518672121e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.062
Order of pole = 34.34
x[1] = 0.1606
y[1] (analytic) = 2.0129520014581841141319281625079
y[1] (numeric) = 2.0129520014581841141324719130963
absolute error = 5.437505884e-22
relative error = 2.7012595829712115281262256711111e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.049
Order of pole = 34.1
x[1] = 0.1607
y[1] (analytic) = 2.0129682061040939477194286476396
y[1] (numeric) = 2.0129682061040939477199733576844
absolute error = 5.447100448e-22
relative error = 2.7060042138183286034663983573458e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.037
Order of pole = 33.87
memory used=247.9MB, alloc=4.2MB, time=14.30
x[1] = 0.1608
y[1] (analytic) = 2.0129844210127606776977848928773
y[1] (numeric) = 2.0129844210127606776983305626192
absolute error = 5.456697419e-22
relative error = 2.7107499501931858187820015446373e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.026
Order of pole = 33.65
x[1] = 0.1609
y[1] (analytic) = 2.0130006461845171287968858654974
y[1] (numeric) = 2.0130006461845171287974324951772
absolute error = 5.466296798e-22
relative error = 2.7154967924928049569001850469091e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.014
Order of pole = 33.42
x[1] = 0.161
y[1] (analytic) = 2.0130168816196963472090971869651
y[1] (numeric) = 2.013016881619696347209644776824
absolute error = 5.475898589e-22
relative error = 2.7202447426044582034944526934869e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 3.002
Order of pole = 33.2
x[1] = 0.1611
y[1] (analytic) = 2.0130331273186316006169569467619
y[1] (numeric) = 2.0130331273186316006175054970411
absolute error = 5.485502792e-22
relative error = 2.7249938004282682943141930386603e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.991
Order of pole = 32.98
x[1] = 0.1612
y[1] (analytic) = 2.0130493832816563782208912674958
y[1] (numeric) = 2.0130493832816563782214407784367
absolute error = 5.495109409e-22
relative error = 2.7297439668578414605264016658014e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.98
Order of pole = 32.76
x[1] = 0.1613
y[1] (analytic) = 2.0130656495091043907669496262579
y[1] (numeric) = 2.0130656495091043907675000981022
absolute error = 5.504718443e-22
relative error = 2.7344952432834725029442127396147e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.968
Order of pole = 32.55
x[1] = 0.1614
y[1] (analytic) = 2.0130819260013095705745599371914
y[1] (numeric) = 2.013081926001309570575111370181
absolute error = 5.514329896e-22
relative error = 2.7392476305986231192791182083929e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.957
Order of pole = 32.34
x[1] = 0.1615
y[1] (analytic) = 2.0130982127586060715643034002433
y[1] (numeric) = 2.0130982127586060715648557946201
absolute error = 5.523943768e-22
relative error = 2.7440011287031951739602730404378e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.946
Order of pole = 32.13
x[1] = 0.1616
y[1] (analytic) = 2.0131145097813282692857091210714
y[1] (numeric) = 2.0131145097813282692862624770777
absolute error = 5.533560063e-22
relative error = 2.7487557394840272523115501759243e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.936
Order of pole = 31.92
x[1] = 0.1617
y[1] (analytic) = 2.0131308170698107609450685070872
y[1] (numeric) = 2.0131308170698107609456228249653
absolute error = 5.543178781e-22
relative error = 2.7535114628409045260311604124213e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.2MB, time=14.53
Real estimate of pole used
Radius of convergence = 2.925
Order of pole = 31.71
x[1] = 0.1618
y[1] (analytic) = 2.0131471346243883654332694446133
y[1] (numeric) = 2.0131471346243883654338247246058
absolute error = 5.552799925e-22
relative error = 2.7582683001637819506909094013022e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.914
Order of pole = 31.51
x[1] = 0.1619
y[1] (analytic) = 2.0131634624453961233536502621437
y[1] (numeric) = 2.0131634624453961233542065044935
absolute error = 5.562423498e-22
relative error = 2.7630262528425318789436551044393e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.904
Order of pole = 31.31
x[1] = 0.162
y[1] (analytic) = 2.0131798005331692970498734846944
y[1] (numeric) = 2.0131798005331692970504306896443
absolute error = 5.572049499e-22
relative error = 2.7677853202800375040527097788395e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.893
Order of pole = 31.11
x[1] = 0.1621
y[1] (analytic) = 2.0131961488880433706338193842382
y[1] (numeric) = 2.0131961488880433706343775520314
absolute error = 5.581677932e-22
relative error = 2.7725455043627767487016058751061e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.883
Order of pole = 30.91
x[1] = 0.1622
y[1] (analytic) = 2.0132125075103540500134993312217
y[1] (numeric) = 2.0132125075103540500140584621015
absolute error = 5.591308798e-22
relative error = 2.7773068054869729774084248396076e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.873
Order of pole = 30.71
x[1] = 0.1623
y[1] (analytic) = 2.0132288764004372629209889521643
y[1] (numeric) = 2.0132288764004372629215490463742
absolute error = 5.600942099e-22
relative error = 2.7820692245455135298120353146452e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.863
Order of pole = 30.52
x[1] = 0.1624
y[1] (analytic) = 2.0132452555586291589403810983448
y[1] (numeric) = 2.0132452555586291589409421561285
absolute error = 5.610577837e-22
relative error = 2.7868327624312190209610349889381e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.853
Order of pole = 30.33
x[1] = 0.1625
y[1] (analytic) = 2.0132616449852661095357586305844
y[1] (numeric) = 2.0132616449852661095363206521859
absolute error = 5.620216015e-22
relative error = 2.7915974205335497218069736148359e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.843
Order of pole = 30.14
x[1] = 0.1626
y[1] (analytic) = 2.0132780446806847080791870251385
y[1] (numeric) = 2.0132780446806847080797500108019
absolute error = 5.629856634e-22
relative error = 2.7963631992484781362052981080727e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.2MB, time=14.76
Real estimate of pole used
Radius of convergence = 2.833
Order of pole = 29.95
x[1] = 0.1627
y[1] (analytic) = 2.0132944546452217698787268057139
y[1] (numeric) = 2.0132944546452217698792907556833
absolute error = 5.639499694e-22
relative error = 2.8011300984752277473870403093709e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.823
Order of pole = 29.77
x[1] = 0.1628
y[1] (analytic) = 2.0133108748792143322064658066315
y[1] (numeric) = 2.0133108748792143322070307211515
absolute error = 5.649145200e-22
relative error = 2.8058981205964589439059508547976e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.814
Order of pole = 29.58
x[1] = 0.1629
y[1] (analytic) = 2.0133273053829996543265712721599
y[1] (numeric) = 2.0133273053829996543271371514751
absolute error = 5.658793152e-22
relative error = 2.8106672655112653970002041150138e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.804
Order of pole = 29.4
x[1] = 0.163
y[1] (analytic) = 2.0133437461569152175233617970464
y[1] (numeric) = 2.0133437461569152175239286414017
absolute error = 5.668443553e-22
relative error = 2.8154375346087647205145604709837e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.795
Order of pole = 29.22
x[1] = 0.1631
y[1] (analytic) = 2.0133601972012987251293991132787
y[1] (numeric) = 2.0133601972012987251299669229191
absolute error = 5.678096404e-22
relative error = 2.8202089282846270245093931437669e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.786
Order of pole = 29.04
x[1] = 0.1632
y[1] (analytic) = 2.0133766585164881025535997281127
y[1] (numeric) = 2.0133766585164881025541685032834
absolute error = 5.687751707e-22
relative error = 2.8249814474311496127751192989138e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.776
Order of pole = 28.86
x[1] = 0.1633
y[1] (analytic) = 2.0133931301028214973093664184062
y[1] (numeric) = 2.0133931301028214973099361593526
absolute error = 5.697409464e-22
relative error = 2.8297550929405626532186717146015e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.767
Order of pole = 28.69
x[1] = 0.1634
y[1] (analytic) = 2.0134096119606372790427395863025
y[1] (numeric) = 2.0134096119606372790433102932702
absolute error = 5.707069677e-22
relative error = 2.8345298657050291305298327423201e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.758
Order of pole = 28.52
x[1] = 0.1635
y[1] (analytic) = 2.013426104090274039560568481311
y[1] (numeric) = 2.0134261040902740395611401545458
absolute error = 5.716732348e-22
relative error = 2.8393057666166447988497415387685e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.749
Order of pole = 28.34
x[1] = 0.1636
y[1] (analytic) = 2.0134426064920705928587022938365
y[1] (numeric) = 2.0134426064920705928592749335843
absolute error = 5.726397478e-22
relative error = 2.8440827960707763489128318303025e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.2MB, time=14.98
Real estimate of pole used
Radius of convergence = 2.74
Order of pole = 28.17
x[1] = 0.1637
y[1] (analytic) = 2.0134591191663659751502011252126
y[1] (numeric) = 2.0134591191663659751507747317196
absolute error = 5.736065070e-22
relative error = 2.8488609554560548636985858474058e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.732
Order of pole = 28
x[1] = 0.1638
y[1] (analytic) = 2.0134756421134994448935668392985
y[1] (numeric) = 2.013475642113499444894141412811
absolute error = 5.745735125e-22
relative error = 2.8536402451677204924674831218981e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.723
Order of pole = 27.84
x[1] = 0.1639
y[1] (analytic) = 2.0134921753338104828209938007017
y[1] (numeric) = 2.0134921753338104828215693414663
absolute error = 5.755407646e-22
relative error = 2.8584206665942613942260106665117e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.714
Order of pole = 27.67
x[1] = 0.164
y[1] (analytic) = 2.0135087188276387919666395046947
y[1] (numeric) = 2.0135087188276387919672160129582
absolute error = 5.765082635e-22
relative error = 2.8632022206274364752781312952743e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.706
Order of pole = 27.51
x[1] = 0.1641
y[1] (analytic) = 2.0135252725953242976949151038959
y[1] (numeric) = 2.0135252725953242976954925799051
absolute error = 5.774760092e-22
relative error = 2.8679849071656543376834212087002e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.697
Order of pole = 27.35
x[1] = 0.1642
y[1] (analytic) = 2.013541836637207147728795836789
y[1] (numeric) = 2.0135418366372071477293742807911
absolute error = 5.784440021e-22
relative error = 2.8727687280938379433238877519711e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.689
Order of pole = 27.19
x[1] = 0.1643
y[1] (analytic) = 2.0135584109536277121781513631614
y[1] (numeric) = 2.0135584109536277121787307754036
absolute error = 5.794122422e-22
relative error = 2.8775536833102770851901970730078e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.681
Order of pole = 27.03
x[1] = 0.1644
y[1] (analytic) = 2.0135749955449265835680960115416
y[1] (numeric) = 2.0135749955449265835686763922715
absolute error = 5.803807299e-22
relative error = 2.8823397746997431470837436506642e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.672
Order of pole = 26.87
x[1] = 0.1645
y[1] (analytic) = 2.0135915904114445768673589437253
y[1] (numeric) = 2.0135915904114445768679402931905
absolute error = 5.813494652e-22
relative error = 2.8871270021604069434128818814670e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.2MB, time=15.20
Real estimate of pole used
Radius of convergence = 2.664
Order of pole = 26.71
x[1] = 0.1646
y[1] (analytic) = 2.0136081955535227295166742414772
y[1] (numeric) = 2.0136081955535227295172565599255
absolute error = 5.823184483e-22
relative error = 2.8919153665836461858248479059284e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.656
Order of pole = 26.56
x[1] = 0.1647
y[1] (analytic) = 2.0136248109715023014571909205055
y[1] (numeric) = 2.0136248109715023014577742081851
absolute error = 5.832876796e-22
relative error = 2.8967048698540045065766655516700e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.648
Order of pole = 26.41
x[1] = 0.1648
y[1] (analytic) = 2.0136414366657247751589028768064
y[1] (numeric) = 2.0136414366657247751594871339655
absolute error = 5.842571591e-22
relative error = 2.9014955118694739418026798326413e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.64
Order of pole = 26.25
x[1] = 0.1649
y[1] (analytic) = 2.0136580726365318556490987704801
y[1] (numeric) = 2.0136580726365318556496839973671
absolute error = 5.852268870e-22
relative error = 2.9062872935212287401718990945214e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.632
Order of pole = 26.1
x[1] = 0.165
y[1] (analytic) = 2.0136747188842654705408318521251
y[1] (numeric) = 2.0136747188842654705414180489887
absolute error = 5.861968636e-22
relative error = 2.9110802161969797759771402964024e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.625
Order of pole = 25.95
x[1] = 0.1651
y[1] (analytic) = 2.013691375409267770061409736921
y[1] (numeric) = 2.0136913754092677700619969040099
absolute error = 5.871670889e-22
relative error = 2.9158742797945522489656909170108e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.617
Order of pole = 25.81
x[1] = 0.1652
y[1] (analytic) = 2.0137080422118811270809041315125
y[1] (numeric) = 2.0137080422118811270814922690758
absolute error = 5.881375633e-22
relative error = 2.9206694861981214938374551341176e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.609
Order of pole = 25.66
x[1] = 0.1653
y[1] (analytic) = 2.0137247192924481371406805188141
y[1] (numeric) = 2.013724719292448137141269627101
absolute error = 5.891082869e-22
relative error = 2.9254658358019852891575918772495e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.602
Order of pole = 25.51
x[1] = 0.1654
y[1] (analytic) = 2.0137414066513116184819478058553
y[1] (numeric) = 2.0137414066513116184825378851151
absolute error = 5.900792598e-22
relative error = 2.9302633290003897593842572263198e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.594
Order of pole = 25.37
memory used=267.0MB, alloc=4.2MB, time=15.42
x[1] = 0.1655
y[1] (analytic) = 2.013758104288814612074327939793
y[1] (numeric) = 2.0137581042888146120749189902754
absolute error = 5.910504824e-22
relative error = 2.9350619676772812711129739340562e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.587
Order of pole = 25.23
x[1] = 0.1656
y[1] (analytic) = 2.0137748122053003816444454972214
y[1] (numeric) = 2.0137748122053003816450375191761
absolute error = 5.920219547e-22
relative error = 2.9398617517301856392411192849437e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.579
Order of pole = 25.09
x[1] = 0.1657
y[1] (analytic) = 2.0137915304011124137045372519107
y[1] (numeric) = 2.0137915304011124137051302455877
absolute error = 5.929936770e-22
relative error = 2.9446626825463205935016360945285e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.572
Order of pole = 24.95
x[1] = 0.1658
y[1] (analytic) = 2.013808258876594417581081726114
y[1] (numeric) = 2.0138082588765944175816756917634
absolute error = 5.939656494e-22
relative error = 2.9494647605196758787332026284191e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.565
Order of pole = 24.81
x[1] = 0.1659
y[1] (analytic) = 2.0138249976320903254434487305825
y[1] (numeric) = 2.0138249976320903254440436684548
absolute error = 5.949378723e-22
relative error = 2.9542679875338918470642759456232e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.557
Order of pole = 24.67
x[1] = 0.166
y[1] (analytic) = 2.0138417466679442923325688984354
y[1] (numeric) = 2.013841746667944292333164808781
absolute error = 5.959103456e-22
relative error = 2.9590723629896907026089569424373e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.55
Order of pole = 24.53
x[1] = 0.1661
y[1] (analytic) = 2.0138585059845006961896232180317
y[1] (numeric) = 2.0138585059845006961902201011013
absolute error = 5.968830696e-22
relative error = 2.9638778882740126549125179176867e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.543
Order of pole = 24.4
x[1] = 0.1662
y[1] (analytic) = 2.0138752755821041378847525699994
y[1] (numeric) = 2.0138752755821041378853504260439
absolute error = 5.978560445e-22
relative error = 2.9686845642771578448718343325092e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.536
Order of pole = 24.26
x[1] = 0.1663
y[1] (analytic) = 2.0138920554610994412457872735772
y[1] (numeric) = 2.0138920554610994412463861028477
absolute error = 5.988292705e-22
relative error = 2.9734923918893579028252423137710e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.529
Order of pole = 24.13
x[1] = 0.1664
y[1] (analytic) = 2.0139088456218316530869966474306
y[1] (numeric) = 2.0139088456218316530875964501784
absolute error = 5.998027478e-22
relative error = 2.9783013720007759012834006246297e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.2MB, time=15.65
Real estimate of pole used
Radius of convergence = 2.522
Order of pole = 24
x[1] = 0.1665
y[1] (analytic) = 2.0139256460646460432378585901071
y[1] (numeric) = 2.0139256460646460432384593665838
absolute error = 6.007764767e-22
relative error = 2.9831115059980489689835831563198e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.516
Order of pole = 23.87
x[1] = 0.1666
y[1] (analytic) = 2.0139424567898881045718491852993
y[1] (numeric) = 2.0139424567898881045724509357565
absolute error = 6.017504572e-22
relative error = 2.9879227937781134536127887022755e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.509
Order of pole = 23.74
x[1] = 0.1667
y[1] (analytic) = 2.0139592777979035530352523370883
y[1] (numeric) = 2.0139592777979035530358550617779
absolute error = 6.027246896e-22
relative error = 2.9927352367274732741884294170022e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.502
Order of pole = 23.61
x[1] = 0.1668
y[1] (analytic) = 2.0139761090890383276759894403449
y[1] (numeric) = 2.013976109089038327676593139519
absolute error = 6.036991741e-22
relative error = 2.9975488357360167992633103726028e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.495
Order of pole = 23.48
x[1] = 0.1669
y[1] (analytic) = 2.0139929506636385906724690914686
y[1] (numeric) = 2.0139929506636385906730737653794
absolute error = 6.046739108e-22
relative error = 3.0023635911970375356337095823718e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.489
Order of pole = 23.36
x[1] = 0.167
y[1] (analytic) = 2.0140098025220507273624568446486
y[1] (numeric) = 2.0140098025220507273630624935486
absolute error = 6.056489000e-22
relative error = 3.0071795044968205931144530972269e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.482
Order of pole = 23.23
x[1] = 0.1671
y[1] (analytic) = 2.0140266646646213462719650188369
y[1] (numeric) = 2.0140266646646213462725716429787
absolute error = 6.066241418e-22
relative error = 3.0119965760285300675013155171413e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.476
Order of pole = 23.11
x[1] = 0.1672
y[1] (analytic) = 2.014043537091697279144162560624
y[1] (numeric) = 2.0140435370916972791447701602604
absolute error = 6.075996364e-22
relative error = 3.0168148066817913532250802414525e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.469
Order of pole = 22.98
x[1] = 0.1673
y[1] (analytic) = 2.0140604198036255809683049682149
y[1] (numeric) = 2.014060419803625580968913543599
absolute error = 6.085753841e-22
relative error = 3.0216341978426703108180122161574e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.2MB, time=15.87
Real estimate of pole used
Radius of convergence = 2.463
Order of pole = 22.86
x[1] = 0.1674
y[1] (analytic) = 2.0140773128007535300086842817055
y[1] (numeric) = 2.0140773128007535300092938330905
absolute error = 6.095513850e-22
relative error = 3.0264547499041365873857343170507e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.457
Order of pole = 22.74
x[1] = 0.1675
y[1] (analytic) = 2.0140942160834286278335991448633
y[1] (numeric) = 2.0140942160834286278342096725026
absolute error = 6.105276393e-22
relative error = 3.0312764637556085231539063460241e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.45
Order of pole = 22.62
x[1] = 0.1676
y[1] (analytic) = 2.0141111296519985993443449436211
y[1] (numeric) = 2.0141111296519985993449564477683
absolute error = 6.115041472e-22
relative error = 3.0360993402864353482567716044200e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.444
Order of pole = 22.5
x[1] = 0.1677
y[1] (analytic) = 2.014128053506811392804224026496
y[1] (numeric) = 2.0141280535068113928048365074049
absolute error = 6.124809089e-22
relative error = 3.0409233803858971354964263190025e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.438
Order of pole = 22.38
x[1] = 0.1678
y[1] (analytic) = 2.0141449876482151798675760121493
y[1] (numeric) = 2.0141449876482151798681894700739
absolute error = 6.134579246e-22
relative error = 3.0457485849432047531043133464346e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.432
Order of pole = 22.27
x[1] = 0.1679
y[1] (analytic) = 2.014161932076558355608828189308
y[1] (numeric) = 2.0141619320765583556094426245024
absolute error = 6.144351944e-22
relative error = 3.0505749543510154067559897374097e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.426
Order of pole = 22.15
x[1] = 0.168
y[1] (analytic) = 2.0141788867921895385515660142714
y[1] (numeric) = 2.0141788867921895385521814269901
absolute error = 6.154127187e-22
relative error = 3.0554024904913744145803405745031e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.42
Order of pole = 22.04
x[1] = 0.1681
y[1] (analytic) = 2.0141958517954575706976237112318
y[1] (numeric) = 2.0141958517954575706982401017294
absolute error = 6.163904976e-22
relative error = 3.0602311937567961601570839065541e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.414
Order of pole = 21.92
x[1] = 0.1682
y[1] (analytic) = 2.0142128270867115175561949806404
y[1] (numeric) = 2.0142128270867115175568123491715
absolute error = 6.173685311e-22
relative error = 3.0650610640432704898738102828120e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.408
Order of pole = 21.81
x[1] = 0.1683
y[1] (analytic) = 2.014229812666300668172963820854
y[1] (numeric) = 2.0142298126663006681735821676737
absolute error = 6.183468197e-22
relative error = 3.0698921037290896973708390210935e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.2MB, time=16.09
Real estimate of pole used
Radius of convergence = 2.402
Order of pole = 21.7
x[1] = 0.1684
y[1] (analytic) = 2.0142468085345745351592554683048
y[1] (numeric) = 2.0142468085345745351598747936681
absolute error = 6.193253633e-22
relative error = 3.0747243122136454094634112108924e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.396
Order of pole = 21.58
x[1] = 0.1685
y[1] (analytic) = 2.0142638146918828547212074614335
y[1] (numeric) = 2.0142638146918828547218277655958
absolute error = 6.203041623e-22
relative error = 3.0795576913786064933053096886602e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.39
Order of pole = 21.47
x[1] = 0.1686
y[1] (analytic) = 2.014280831138575586688960833637
y[1] (numeric) = 2.0142808311385755866895821168539
absolute error = 6.212832169e-22
relative error = 3.0843922421126285024306837465436e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.385
Order of pole = 21.36
x[1] = 0.1687
y[1] (analytic) = 2.0142978578750029145458714404807
y[1] (numeric) = 2.0142978578750029145464937030078
absolute error = 6.222625271e-22
relative error = 3.0892279643113955452770556046042e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.379
Order of pole = 21.26
x[1] = 0.1688
y[1] (analytic) = 2.0143148949015152454577414264311
y[1] (numeric) = 2.0143148949015152454583646685243
absolute error = 6.232420932e-22
relative error = 3.0940648593598957715158468952738e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.373
Order of pole = 21.15
x[1] = 0.1689
y[1] (analytic) = 2.0143319422184632103020708363699
y[1] (numeric) = 2.0143319422184632103026950582854
absolute error = 6.242219155e-22
relative error = 3.0989029286430308306127999340096e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.368
Order of pole = 21.04
x[1] = 0.169
y[1] (analytic) = 2.0143489998261976636973293771518
y[1] (numeric) = 2.0143489998261976636979545791459
absolute error = 6.252019941e-22
relative error = 3.1037421725527391930945395914439e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.362
Order of pole = 20.93
x[1] = 0.1691
y[1] (analytic) = 2.0143660677250696840322483344746
y[1] (numeric) = 2.0143660677250696840328745168038
absolute error = 6.261823292e-22
relative error = 3.1085825919773404335483388707812e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.356
Order of pole = 20.83
x[1] = 0.1692
y[1] (analytic) = 2.0143831459154305734951326503331
y[1] (numeric) = 2.014383145915430573495759813254
absolute error = 6.271629209e-22
relative error = 3.1134241873086543874345320819186e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.2MB, time=16.31
Real estimate of pole used
Radius of convergence = 2.351
Order of pole = 20.72
x[1] = 0.1693
y[1] (analytic) = 2.0144002343976318581031931663323
y[1] (numeric) = 2.0144002343976318581038213101019
absolute error = 6.281437696e-22
relative error = 3.1182669604277248681372658363451e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.346
Order of pole = 20.62
x[1] = 0.1694
y[1] (analytic) = 2.0144173331720252877318990381402
y[1] (numeric) = 2.0144173331720252877325281630155
absolute error = 6.291248753e-22
relative error = 3.1231109112298061957139936872722e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.34
Order of pole = 20.52
x[1] = 0.1695
y[1] (analytic) = 2.0144344422389628361443503263627
y[1] (numeric) = 2.014434442238962836144980432601
absolute error = 6.301062383e-22
relative error = 3.1279560410993681536170046048204e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.335
Order of pole = 20.42
x[1] = 0.1696
y[1] (analytic) = 2.0144515615987967010206707691298
y[1] (numeric) = 2.0144515615987967010213018569885
absolute error = 6.310878587e-22
relative error = 3.1328023504279675690915904070120e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.329
Order of pole = 20.31
x[1] = 0.1697
y[1] (analytic) = 2.0144686912518793039874207416829
y[1] (numeric) = 2.0144686912518793039880528114198
absolute error = 6.320697369e-22
relative error = 3.1376498410963344884611135313768e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.324
Order of pole = 20.21
x[1] = 0.1698
y[1] (analytic) = 2.0144858311985632906470304082609
y[1] (numeric) = 2.0144858311985632906476634601337
absolute error = 6.330518728e-22
relative error = 3.1424985125030721323072893664833e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.319
Order of pole = 20.11
x[1] = 0.1699
y[1] (analytic) = 2.0145029814392015306072530715823
y[1] (numeric) = 2.0145029814392015306078871058491
absolute error = 6.340342668e-22
relative error = 3.1473483665287660252245256964429e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.314
Order of pole = 20.01
x[1] = 0.17
y[1] (analytic) = 2.0145201419741471175106387252292
y[1] (numeric) = 2.0145201419741471175112737421482
absolute error = 6.350169190e-22
relative error = 3.1521994035647092779295691583047e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.309
Order of pole = 19.92
x[1] = 0.1701
y[1] (analytic) = 2.0145373128037533690640278142393
y[1] (numeric) = 2.014537312803753369064663814069
absolute error = 6.359998297e-22
relative error = 3.1570516249949254452435105607479e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.303
Order of pole = 19.82
memory used=286.1MB, alloc=4.3MB, time=16.53
x[1] = 0.1702
y[1] (analytic) = 2.0145544939283738270680652092181
y[1] (numeric) = 2.014554493928373827068702192217
absolute error = 6.369829989e-22
relative error = 3.1619050307141878468958849642480e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.298
Order of pole = 19.72
x[1] = 0.1703
y[1] (analytic) = 2.0145716853483622574467343992862
y[1] (numeric) = 2.0145716853483622574473723657132
absolute error = 6.379664270e-22
relative error = 3.1667596226027670338665220562503e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.293
Order of pole = 19.63
x[1] = 0.1704
y[1] (analytic) = 2.0145888870640726502769119091827
y[1] (numeric) = 2.0145888870640726502775508592968
absolute error = 6.389501141e-22
relative error = 3.1716154010516916921698214700820e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.288
Order of pole = 19.53
x[1] = 0.1705
y[1] (analytic) = 2.0146060990758592198179419458464
y[1] (numeric) = 2.0146060990758592198185818799069
absolute error = 6.399340605e-22
relative error = 3.1764723674446869052352625864429e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.283
Order of pole = 19.44
x[1] = 0.1706
y[1] (analytic) = 2.014623321384076404541231279804
y[1] (numeric) = 2.0146233213840764045418721980702
absolute error = 6.409182662e-22
relative error = 3.1813305216762781689139869929330e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.278
Order of pole = 19.34
x[1] = 0.1707
y[1] (analytic) = 2.0146405539890788671598643666956
y[1] (numeric) = 2.0146405539890788671605062694272
absolute error = 6.419027316e-22
relative error = 3.1861898656264202268095512776869e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.273
Order of pole = 19.25
x[1] = 0.1708
y[1] (analytic) = 2.0146577968912214946582387142745
y[1] (numeric) = 2.0146577968912214946588816017313
absolute error = 6.428874568e-22
relative error = 3.1910503996858766248072945642155e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.269
Order of pole = 19.16
x[1] = 0.1709
y[1] (analytic) = 2.0146750500908593983217205002191
y[1] (numeric) = 2.014675050090859398322364372661
absolute error = 6.438724419e-22
relative error = 3.1959121242453572586318449657265e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.264
Order of pole = 19.06
x[1] = 0.171
y[1] (analytic) = 2.0146923135883479137663204461019
y[1] (numeric) = 2.0146923135883479137669653037891
absolute error = 6.448576872e-22
relative error = 3.2007750406882257669961998456600e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.259
Order of pole = 18.97
x[1] = 0.1711
y[1] (analytic) = 2.0147095873840426009683899528632
y[1] (numeric) = 2.0147095873840426009690357960561
absolute error = 6.458431929e-22
relative error = 3.2056391499014085959703950889433e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.3MB, time=16.75
Real estimate of pole used
Radius of convergence = 2.254
Order of pole = 18.88
x[1] = 0.1712
y[1] (analytic) = 2.0147268714782992442943375031397
y[1] (numeric) = 2.0147268714782992442949843320989
absolute error = 6.468289592e-22
relative error = 3.2105044527717614118403550829102e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.25
Order of pole = 18.79
x[1] = 0.1713
y[1] (analytic) = 2.0147441658714738525303653358056
y[1] (numeric) = 2.0147441658714738525310131507919
absolute error = 6.478149863e-22
relative error = 3.2153709501860690539471670295586e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.245
Order of pole = 18.7
x[1] = 0.1714
y[1] (analytic) = 2.014761470563922658912226398084
y[1] (numeric) = 2.0147614705639226589128751993583
absolute error = 6.488012743e-22
relative error = 3.2202386425347088171037579196670e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.24
Order of pole = 18.61
x[1] = 0.1715
y[1] (analytic) = 2.0147787855560021211550015805935
y[1] (numeric) = 2.014778785556002121155651368417
absolute error = 6.497878235e-22
relative error = 3.2251075312006689467397075178523e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.236
Order of pole = 18.53
x[1] = 0.1716
y[1] (analytic) = 2.0147961108480689214828972406974
y[1] (numeric) = 2.0147961108480689214835480153314
absolute error = 6.507746340e-22
relative error = 3.2299776165741933888774605673084e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.231
Order of pole = 18.44
x[1] = 0.1717
y[1] (analytic) = 2.0148134464404799666590630195267
y[1] (numeric) = 2.0148134464404799666597147812328
absolute error = 6.517617061e-22
relative error = 3.2348489000381198887254707495825e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.226
Order of pole = 18.35
x[1] = 0.1718
y[1] (analytic) = 2.0148307923335923880154299580533
y[1] (numeric) = 2.0148307923335923880160827070932
absolute error = 6.527490399e-22
relative error = 3.2397213819825588647643564745184e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.222
Order of pole = 18.27
x[1] = 0.1719
y[1] (analytic) = 2.0148481485277635414825689175925
y[1] (numeric) = 2.0148481485277635414832226542282
absolute error = 6.537366357e-22
relative error = 3.2445950637901973635271812207938e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.217
Order of pole = 18.18
x[1] = 0.172
y[1] (analytic) = 2.0148655150233510076195693101194
y[1] (numeric) = 2.014865515023351007620224034613
absolute error = 6.547244936e-22
relative error = 3.2494699458510120972192387455478e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.3MB, time=16.97
Real estimate of pole used
Radius of convergence = 2.213
Order of pole = 18.1
x[1] = 0.1721
y[1] (analytic) = 2.0148828918207125916439381437856
y[1] (numeric) = 2.0148828918207125916445938563995
absolute error = 6.557126139e-22
relative error = 3.2543460295475392152624511969539e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.209
Order of pole = 18.01
x[1] = 0.1722
y[1] (analytic) = 2.0149002789202063234615193890298
y[1] (numeric) = 2.0149002789202063234621760900266
absolute error = 6.567009968e-22
relative error = 3.2592233157659240222006542268338e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.204
Order of pole = 17.93
x[1] = 0.1723
y[1] (analytic) = 2.014917676322190457696433670677
y[1] (numeric) = 2.0149176763221904576970913603193
absolute error = 6.576896423e-22
relative error = 3.2641018043996441399389081754297e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.2
Order of pole = 17.85
x[1] = 0.1724
y[1] (analytic) = 2.0149350840270234737210382914257
y[1] (numeric) = 2.0149350840270234737216969699764
absolute error = 6.586785507e-22
relative error = 3.2689814968310218595736290539662e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.195
Order of pole = 17.76
x[1] = 0.1725
y[1] (analytic) = 2.0149525020350640756859075921287
y[1] (numeric) = 2.014952502035064075686567259851
absolute error = 6.596677223e-22
relative error = 3.2738623944422909484622823407272e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.191
Order of pole = 17.68
x[1] = 0.1726
y[1] (analytic) = 2.014969930346671192549833654274
y[1] (numeric) = 2.0149699303466711925504943114312
absolute error = 6.606571572e-22
relative error = 3.2787444976230259351526999531228e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.187
Order of pole = 17.6
x[1] = 0.1727
y[1] (analytic) = 2.0149873689622039781098473500784
y[1] (numeric) = 2.014987368962203978110508996934
absolute error = 6.616468556e-22
relative error = 3.2836278072590280681219874045226e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.183
Order of pole = 17.52
x[1] = 0.1728
y[1] (analytic) = 2.0150048178820218110312597456092
y[1] (numeric) = 2.0150048178820218110319223824269
absolute error = 6.626368177e-22
relative error = 3.2885123242360270765440667171434e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.178
Order of pole = 17.44
x[1] = 0.1729
y[1] (analytic) = 2.0150222771064842948777238623554
y[1] (numeric) = 2.0150222771064842948783874893991
absolute error = 6.636270437e-22
relative error = 3.2933980494396811231649447435795e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.174
Order of pole = 17.36
x[1] = 0.173
y[1] (analytic) = 2.0150397466359512581413168026708
y[1] (numeric) = 2.0150397466359512581419814202046
absolute error = 6.646175338e-22
relative error = 3.2982849837555767571802667105080e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.3MB, time=17.19
Real estimate of pole used
Radius of convergence = 2.17
Order of pole = 17.28
x[1] = 0.1731
y[1] (analytic) = 2.0150572264707827542726422445185
y[1] (numeric) = 2.0150572264707827542733078528067
absolute error = 6.656082882e-22
relative error = 3.3031731280692288671151561606386e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.166
Order of pole = 17.2
x[1] = 0.1732
y[1] (analytic) = 2.0150747166113390617109533109483
y[1] (numeric) = 2.0150747166113390617116199102554
absolute error = 6.665993071e-22
relative error = 3.3080624832660806337063424684139e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.162
Order of pole = 17.12
x[1] = 0.1733
y[1] (analytic) = 2.0150922170579806839142958197434
y[1] (numeric) = 2.0150922170579806839149634103341
absolute error = 6.675905907e-22
relative error = 3.3129530502315034827865771043859e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.158
Order of pole = 17.05
x[1] = 0.1734
y[1] (analytic) = 2.0151097278110683493896719186767
y[1] (numeric) = 2.0151097278110683493903405008159
absolute error = 6.685821392e-22
relative error = 3.3178448298507970381713398226263e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.154
Order of pole = 16.97
x[1] = 0.1735
y[1] (analytic) = 2.015127248870963011723224111821
y[1] (numeric) = 2.0151272488709630117238936857738
absolute error = 6.695739528e-22
relative error = 3.3227378230091890745478359449505e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.15
Order of pole = 16.89
x[1] = 0.1736
y[1] (analytic) = 2.0151447802380258496104396823616
y[1] (numeric) = 2.0151447802380258496111102483933
absolute error = 6.705660317e-22
relative error = 3.3276320305918354703662859151624e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.146
Order of pole = 16.82
x[1] = 0.1737
y[1] (analytic) = 2.0151623219126182668863755173636
y[1] (numeric) = 2.0151623219126182668870470757397
absolute error = 6.715583761e-22
relative error = 3.3325274534838201607335082959530e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.142
Order of pole = 16.74
x[1] = 0.1738
y[1] (analytic) = 2.0151798738951018925559033399505
y[1] (numeric) = 2.0151798738951018925565758909366
absolute error = 6.725509861e-22
relative error = 3.3374240920739214721816375975564e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.138
Order of pole = 16.67
x[1] = 0.1739
y[1] (analytic) = 2.0151974361858385808239753543545
y[1] (numeric) = 2.0151974361858385808246488982165
absolute error = 6.735438620e-22
relative error = 3.3423219477433215792234443880938e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.3MB, time=17.42
Real estimate of pole used
Radius of convergence = 2.134
Order of pole = 16.59
x[1] = 0.174
y[1] (analytic) = 2.0152150087851904111259103093034
y[1] (numeric) = 2.0152150087851904111265848463074
absolute error = 6.745370040e-22
relative error = 3.3472210213768883117090162354129e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.13
Order of pole = 16.52
x[1] = 0.1741
y[1] (analytic) = 2.0152325916935196881576999852122
y[1] (numeric) = 2.0152325916935196881583755156245
absolute error = 6.755304123e-22
relative error = 3.3521213138594173677421621798476e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.126
Order of pole = 16.45
x[1] = 0.1742
y[1] (analytic) = 2.0152501849111889419063361106532
y[1] (numeric) = 2.0152501849111889419070126347403
absolute error = 6.765240871e-22
relative error = 3.3570228260756322665854804048216e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.122
Order of pole = 16.37
x[1] = 0.1743
y[1] (analytic) = 2.01526778843856092768015771358
y[1] (numeric) = 2.0152677884385609276808352316085
absolute error = 6.775180285e-22
relative error = 3.3619255584139723312594008690688e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.119
Order of pole = 16.3
x[1] = 0.1744
y[1] (analytic) = 2.0152854022759986261392189127874
y[1] (numeric) = 2.0152854022759986261398974250241
absolute error = 6.785122367e-22
relative error = 3.3668295117590295929258810981510e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.115
Order of pole = 16.23
x[1] = 0.1745
y[1] (analytic) = 2.0153030264238652433256771550914
y[1] (numeric) = 2.0153030264238652433263566618035
absolute error = 6.795067121e-22
relative error = 3.3717346879877303652926954553136e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.111
Order of pole = 16.16
x[1] = 0.1746
y[1] (analytic) = 2.0153206608825242106942019037193
y[1] (numeric) = 2.015320660882524210694882405174
absolute error = 6.805014547e-22
relative error = 3.3766410869920980663715751849466e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.107
Order of pole = 16.09
x[1] = 0.1747
y[1] (analytic) = 2.0153383056523391851424037834014
y[1] (numeric) = 2.0153383056523391851430852798661
absolute error = 6.814964647e-22
relative error = 3.3815487096565076552858587363541e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.104
Order of pole = 16.02
x[1] = 0.1748
y[1] (analytic) = 2.0153559607336740490412841876626
y[1] (numeric) = 2.0153559607336740490419666794051
absolute error = 6.824917425e-22
relative error = 3.3864575578576421664092157480941e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.1
Order of pole = 15.95
memory used=305.1MB, alloc=4.3MB, time=17.64
x[1] = 0.1749
y[1] (analytic) = 2.0153736261268929102657053538156
y[1] (numeric) = 2.0153736261268929102663888411036
absolute error = 6.834872880e-22
relative error = 3.3913676309911477880591370488748e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.096
Order of pole = 15.88
x[1] = 0.175
y[1] (analytic) = 2.0153913018323601022248809111587
y[1] (numeric) = 2.0153913018323601022255653942603
absolute error = 6.844831016e-22
relative error = 3.3962789309335581586217902780008e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.093
Order of pole = 15.81
x[1] = 0.1751
y[1] (analytic) = 2.0154089878504401838928869078908
y[1] (numeric) = 2.0154089878504401838935723870743
absolute error = 6.854791835e-22
relative error = 3.4011914585689450984470131708178e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.089
Order of pole = 15.74
x[1] = 0.1752
y[1] (analytic) = 2.015426684181497939839193322254
y[1] (numeric) = 2.0154266841814979398398797977878
absolute error = 6.864755338e-22
relative error = 3.4061052142851349291412447634842e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.085
Order of pole = 15.67
x[1] = 0.1753
y[1] (analytic) = 2.0154443908258983802592160634235
y[1] (numeric) = 2.0154443908258983802599035355763
absolute error = 6.874721528e-22
relative error = 3.4110201994622356919670065629862e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.082
Order of pole = 15.61
x[1] = 0.1754
y[1] (analytic) = 2.0154621077840067410048894676653
y[1] (numeric) = 2.0154621077840067410055779367059
absolute error = 6.884690406e-22
relative error = 3.4159364144879369960773890259236e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.078
Order of pole = 15.54
x[1] = 0.1755
y[1] (analytic) = 2.0154798350561884836152592952874
y[1] (numeric) = 2.0154798350561884836159487614849
absolute error = 6.894661975e-22
relative error = 3.4208538607421926446093621202438e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.075
Order of pole = 15.47
x[1] = 0.1756
y[1] (analytic) = 2.0154975726428092953470962339154
y[1] (numeric) = 2.015497572642809295347786697539
absolute error = 6.904636236e-22
relative error = 3.4257725386125553558518651825760e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.071
Order of pole = 15.41
x[1] = 0.1757
y[1] (analytic) = 2.0155153205442350892055299136246
y[1] (numeric) = 2.0155153205442350892062213749438
absolute error = 6.914613192e-22
relative error = 3.4306924494788244967153879155832e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.068
Order of pole = 15.34
x[1] = 0.1758
y[1] (analytic) = 2.0155330787608320039747034394682
y[1] (numeric) = 2.0155330787608320039753958987526
absolute error = 6.924592844e-22
relative error = 3.4356135937284157162321088168773e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=309.0MB, alloc=4.3MB, time=17.85
Real estimate of pole used
Radius of convergence = 2.064
Order of pole = 15.28
x[1] = 0.1759
y[1] (analytic) = 2.0155508472929664042484484469425
y[1] (numeric) = 2.0155508472929664042491419044619
absolute error = 6.934575194e-22
relative error = 3.4405359722448314634475664506090e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.061
Order of pole = 15.21
x[1] = 0.176
y[1] (analytic) = 2.0155686261410048804609806859361
y[1] (numeric) = 2.0155686261410048804616751419605
absolute error = 6.944560244e-22
relative error = 3.4454595859115011760236680538489e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.057
Order of pole = 15.15
x[1] = 0.1761
y[1] (analytic) = 2.0155864153053142489176161387125
y[1] (numeric) = 2.0155864153053142489183115935123
absolute error = 6.954547998e-22
relative error = 3.4503844366040482899668694575929e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.054
Order of pole = 15.08
x[1] = 0.1762
y[1] (analytic) = 2.0156042147862615518255076774816
y[1] (numeric) = 2.0156042147862615518262041313272
absolute error = 6.964538456e-22
relative error = 3.4553105242134714971343612599471e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.051
Order of pole = 15.02
x[1] = 0.1763
y[1] (analytic) = 2.015622024584214057324402267117
y[1] (numeric) = 2.0156220245842140573250997202789
absolute error = 6.974531619e-22
relative error = 3.4602378491268561405906410474057e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.047
Order of pole = 14.96
x[1] = 0.1764
y[1] (analytic) = 2.0156398446995392595174187185828
y[1] (numeric) = 2.0156398446995392595181171713319
absolute error = 6.984527491e-22
relative error = 3.4651664132195930401501510084296e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.044
Order of pole = 14.89
x[1] = 0.1765
y[1] (analytic) = 2.0156576751326048785018459986365
y[1] (numeric) = 2.0156576751326048785025454512439
absolute error = 6.994526074e-22
relative error = 3.4700962173747326974583162732718e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.041
Order of pole = 14.83
x[1] = 0.1766
y[1] (analytic) = 2.0156755158837788603999621013782
y[1] (numeric) = 2.0156755158837788604006625541151
absolute error = 7.004527369e-22
relative error = 3.4750272619791407083442567267342e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.037
Order of pole = 14.77
x[1] = 0.1767
y[1] (analytic) = 2.0156933669534293773898734872208
y[1] (numeric) = 2.0156933669534293773905749403587
absolute error = 7.014531379e-22
relative error = 3.4799595484118412951187699895647e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.3MB, time=18.08
Real estimate of pole used
Radius of convergence = 2.034
Order of pole = 14.71
x[1] = 0.1768
y[1] (analytic) = 2.0157112283419248277363750948614
y[1] (numeric) = 2.0157112283419248277370775486719
absolute error = 7.024538105e-22
relative error = 3.4848930770595620926643581173565e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.031
Order of pole = 14.65
x[1] = 0.1769
y[1] (analytic) = 2.0157291000496338358218309318353
y[1] (numeric) = 2.0157291000496338358225343865903
absolute error = 7.034547550e-22
relative error = 3.4898278493011716988564248565228e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.028
Order of pole = 14.58
x[1] = 0.177
y[1] (analytic) = 2.0157469820769252521770752492412
y[1] (numeric) = 2.0157469820769252521777797052126
absolute error = 7.044559714e-22
relative error = 3.4947638650271656010761449409193e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.025
Order of pole = 14.52
x[1] = 0.1771
y[1] (analytic) = 2.0157648744241681535123343062277
y[1] (numeric) = 2.0157648744241681535130397636878
absolute error = 7.054574601e-22
relative error = 3.4997011261123593899334330292773e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.021
Order of pole = 14.46
x[1] = 0.1772
y[1] (analytic) = 2.0157827770917318427481687298376
y[1] (numeric) = 2.0157827770917318427488751890588
absolute error = 7.064592212e-22
relative error = 3.5046396329432042509716582472609e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.018
Order of pole = 14.4
x[1] = 0.1773
y[1] (analytic) = 2.0158006900799858490464364758087
y[1] (numeric) = 2.0158006900799858490471439370637
absolute error = 7.074612550e-22
relative error = 3.5095793868982569466940062130845e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.015
Order of pole = 14.34
x[1] = 0.1774
y[1] (analytic) = 2.0158186133892999278412763959354
y[1] (numeric) = 2.015818613389299927841984859497
absolute error = 7.084635616e-22
relative error = 3.5145203883638301669026538653258e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.012
Order of pole = 14.29
x[1] = 0.1775
y[1] (analytic) = 2.0158365470200440608701124175976
y[1] (numeric) = 2.0158365470200440608708218837389
absolute error = 7.094661413e-22
relative error = 3.5194626387183244558168254284996e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.009
Order of pole = 14.23
x[1] = 0.1776
y[1] (analytic) = 2.0158544909725884562046783410708
y[1] (numeric) = 2.0158544909725884562053888100651
absolute error = 7.104689943e-22
relative error = 3.5244061388439813800168884823419e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2.006
Order of pole = 14.17
x[1] = 0.1777
y[1] (analytic) = 2.0158724452473035482820632602317
y[1] (numeric) = 2.0158724452473035482827747323523
absolute error = 7.114721206e-22
relative error = 3.5293508886308424152844351172836e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.3MB, time=18.30
Real estimate of pole used
Radius of convergence = 2.003
Order of pole = 14.11
x[1] = 0.1778
y[1] (analytic) = 2.0158904098445599979357776122798
y[1] (numeric) = 2.0158904098445599979364900878003
absolute error = 7.124755205e-22
relative error = 3.5342968894570866656351544007660e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 2
Order of pole = 14.05
x[1] = 0.1779
y[1] (analytic) = 2.0159083847647286924268398620996
y[1] (numeric) = 2.015908384764728692427553341294
absolute error = 7.134791944e-22
relative error = 3.5392441431968559411446533155532e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.997
Order of pole = 14
x[1] = 0.178
y[1] (analytic) = 2.0159263700081807454748838268924
y[1] (numeric) = 2.0159263700081807454755983100346
absolute error = 7.144831422e-22
relative error = 3.5441926492439333793835839201356e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.994
Order of pole = 13.94
x[1] = 0.1781
y[1] (analytic) = 2.0159443655752874972892866467076
y[1] (numeric) = 2.015944365575287497290002134072
absolute error = 7.154873644e-22
relative error = 3.5491424099683538367121745274950e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.991
Order of pole = 13.88
x[1] = 0.1782
y[1] (analytic) = 2.0159623714664205146003174065143
y[1] (numeric) = 2.0159623714664205146010338983753
absolute error = 7.164918610e-22
relative error = 3.5540934252598199491158607782488e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.988
Order of pole = 13.83
x[1] = 0.1783
y[1] (analytic) = 2.0159803876819515906903064154497
y[1] (numeric) = 2.0159803876819515906910239120819
absolute error = 7.174966322e-22
relative error = 3.5590456960000688371147652140292e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.985
Order of pole = 13.77
x[1] = 0.1784
y[1] (analytic) = 2.0159984142222527454248351488922
y[1] (numeric) = 2.0159984142222527454255536505704
absolute error = 7.185016782e-22
relative error = 3.5639992230707634812556669731885e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.982
Order of pole = 13.72
x[1] = 0.1785
y[1] (analytic) = 2.0160164510876962252839468590068
y[1] (numeric) = 2.0160164510876962252846663660062
absolute error = 7.195069994e-22
relative error = 3.5689540083455480717483905382785e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.979
Order of pole = 13.66
x[1] = 0.1786
y[1] (analytic) = 2.0160344982786545033933778594171
y[1] (numeric) = 2.0160344982786545033940983720128
absolute error = 7.205125957e-22
relative error = 3.5739100512178407521999114891958e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.3MB, time=18.52
Real estimate of pole used
Radius of convergence = 1.976
Order of pole = 13.61
x[1] = 0.1787
y[1] (analytic) = 2.0160525557955002795558094896591
y[1] (numeric) = 2.0160525557955002795565310081266
absolute error = 7.215184675e-22
relative error = 3.5788673535611327452467918527351e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.973
Order of pole = 13.55
x[1] = 0.1788
y[1] (analytic) = 2.0160706236386064802821407650815
y[1] (numeric) = 2.0160706236386064802828632896964
absolute error = 7.225246149e-22
relative error = 3.5838259157607622885302563565073e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.97
Order of pole = 13.5
x[1] = 0.1789
y[1] (analytic) = 2.0160887018083462588227817178548
y[1] (numeric) = 2.0160887018083462588235052488931
absolute error = 7.235310383e-22
relative error = 3.5887857396900407873497655963320e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.967
Order of pole = 13.44
x[1] = 0.179
y[1] (analytic) = 2.0161067903050929951989674347616
y[1] (numeric) = 2.0161067903050929951996919724993
absolute error = 7.245377377e-22
relative error = 3.5937468252381477357661760228695e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.964
Order of pole = 13.39
x[1] = 0.1791
y[1] (analytic) = 2.01612488912922029623409279744
y[1] (numeric) = 2.0161248891292202962348183421533
absolute error = 7.255447133e-22
relative error = 3.5987091732862257892435584694791e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.962
Order of pole = 13.34
x[1] = 0.1792
y[1] (analytic) = 2.0161429982811019955850679307598
y[1] (numeric) = 2.0161429982811019955857944827251
absolute error = 7.265519653e-22
relative error = 3.6036727847153430873760464146107e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.959
Order of pole = 13.28
x[1] = 0.1793
y[1] (analytic) = 2.0161611177611121537736943650124
y[1] (numeric) = 2.0161611177611121537744219245064
absolute error = 7.275594940e-22
relative error = 3.6086376609024853134897764504339e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.956
Order of pole = 13.23
x[1] = 0.1794
y[1] (analytic) = 2.0161792475696250582180619176017
y[1] (numeric) = 2.0161792475696250582187904849013
absolute error = 7.285672996e-22
relative error = 3.6136038027285580543889683164349e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.953
Order of pole = 13.18
x[1] = 0.1795
y[1] (analytic) = 2.0161973877070152232639662999262
y[1] (numeric) = 2.0161973877070152232646958753085
absolute error = 7.295753823e-22
relative error = 3.6185712110743922253211796557190e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.951
Order of pole = 13.13
x[1] = 0.1796
y[1] (analytic) = 2.0162155381736573902163474551466
y[1] (numeric) = 2.0162155381736573902170780388889
absolute error = 7.305837423e-22
memory used=324.2MB, alloc=4.3MB, time=18.74
relative error = 3.6235398868207440230082536750941e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.948
Order of pole = 13.08
x[1] = 0.1797
y[1] (analytic) = 2.0162336989699265273707486325384
y[1] (numeric) = 2.016233698969926527371480224918
absolute error = 7.315923796e-22
relative error = 3.6285098298563463753777653574608e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.945
Order of pole = 13.03
x[1] = 0.1798
y[1] (analytic) = 2.0162518700961978300447962041316
y[1] (numeric) = 2.0162518700961978300455288054264
absolute error = 7.326012948e-22
relative error = 3.6334810430457118475729422489987e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.942
Order of pole = 12.97
x[1] = 0.1799
y[1] (analytic) = 2.0162700515528467206097002293467
y[1] (numeric) = 2.0162700515528467206104338398344
absolute error = 7.336104877e-22
relative error = 3.6384535252854841419529258681011e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.94
Order of pole = 12.92
x[1] = 0.18
y[1] (analytic) = 2.0162882433402488485217757733345
y[1] (numeric) = 2.0162882433402488485225103932932
absolute error = 7.346199587e-22
relative error = 3.6434272784480686295581486139567e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.937
Order of pole = 12.87
x[1] = 0.1801
y[1] (analytic) = 2.0163064454587800903539849847399
y[1] (numeric) = 2.016306445458780090354720614448
absolute error = 7.356297081e-22
relative error = 3.6484023039098035821457552930781e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.934
Order of pole = 12.82
x[1] = 0.1802
y[1] (analytic) = 2.0163246579088165498274999386058
y[1] (numeric) = 2.0163246579088165498282365783417
absolute error = 7.366397359e-22
relative error = 3.6533786015590787193936802063952e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.932
Order of pole = 12.77
x[1] = 0.1803
y[1] (analytic) = 2.0163428806907345578432862501419
y[1] (numeric) = 2.0163428806907345578440239001843
absolute error = 7.376500424e-22
relative error = 3.6583561727720867427900039219187e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.929
Order of pole = 12.72
x[1] = 0.1804
y[1] (analytic) = 2.0163611138049106725137074650875
y[1] (numeric) = 2.0163611138049106725144461257153
absolute error = 7.386606278e-22
relative error = 3.6633350184289844250102393321171e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.926
Order of pole = 12.68
x[1] = 0.1805
y[1] (analytic) = 2.016379357251721679194150232399
y[1] (numeric) = 2.0163793572517216791948899038913
absolute error = 7.396714923e-22
relative error = 3.6683151394098533975888290135803e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.3MB, time=18.96
Real estimate of pole used
Radius of convergence = 1.924
Order of pole = 12.63
x[1] = 0.1806
y[1] (analytic) = 2.0163976110315445905146702649994
y[1] (numeric) = 2.0163976110315445905154109476355
absolute error = 7.406826361e-22
relative error = 3.6732965365947001039737711170779e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.921
Order of pole = 12.58
x[1] = 0.1807
y[1] (analytic) = 2.0164158751447566464116590943297
y[1] (numeric) = 2.016415875144756646412400788389
absolute error = 7.416940593e-22
relative error = 3.6782792103675263104846719060600e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.919
Order of pole = 12.53
x[1] = 0.1808
y[1] (analytic) = 2.0164341495917353141595316244471
y[1] (numeric) = 2.0164341495917353141602743302094
absolute error = 7.427057623e-22
relative error = 3.6832631626000513222545253665082e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.916
Order of pole = 12.48
x[1] = 0.1809
y[1] (analytic) = 2.0164524343728582884024344914196
y[1] (numeric) = 2.0164524343728582884031782091648
absolute error = 7.437177452e-22
relative error = 3.6882483936761218026980213070716e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.914
Order of pole = 12.43
x[1] = 0.181
y[1] (analytic) = 2.0164707294885034911859752337688
y[1] (numeric) = 2.0164707294885034911867199637771
absolute error = 7.447300083e-22
relative error = 3.6932349049713589247699849380857e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.911
Order of pole = 12.39
x[1] = 0.1811
y[1] (analytic) = 2.0164890349390490719889722797192
y[1] (numeric) = 2.0164890349390490719897180222708
absolute error = 7.457425516e-22
relative error = 3.6982226963735560830041475744255e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.909
Order of pole = 12.34
x[1] = 0.1812
y[1] (analytic) = 2.0165073507248734077552257570144
y[1] (numeric) = 2.0165073507248734077559725123898
absolute error = 7.467553754e-22
relative error = 3.7032117692581880572756446677237e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.906
Order of pole = 12.29
x[1] = 0.1813
y[1] (analytic) = 2.0165256768463551029253091310674
y[1] (numeric) = 2.0165256768463551029260568995473
absolute error = 7.477684799e-22
relative error = 3.7082021245047336601564532510955e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.904
Order of pole = 12.25
x[1] = 0.1814
y[1] (analytic) = 2.0165440133038729894683816772131
y[1] (numeric) = 2.0165440133038729894691304590784
absolute error = 7.487818653e-22
relative error = 3.7131937629925961406546747677367e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.3MB, time=19.18
Real estimate of pole used
Radius of convergence = 1.901
Order of pole = 12.2
x[1] = 0.1815
y[1] (analytic) = 2.0165623600978061269140217928379
y[1] (numeric) = 2.0165623600978061269147715883699
absolute error = 7.497955320e-22
relative error = 3.7181866865928899719426825120917e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.899
Order of pole = 12.15
x[1] = 0.1816
y[1] (analytic) = 2.0165807172285338023840811551652
y[1] (numeric) = 2.0165807172285338023848319646451
absolute error = 7.508094799e-22
relative error = 3.7231808946971733406548733347244e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.896
Order of pole = 12.11
x[1] = 0.1817
y[1] (analytic) = 2.016599084696435530624559730477
y[1] (numeric) = 2.0165990846964355306253115541864
absolute error = 7.518237094e-22
relative error = 3.7281763891764048317607861199958e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.894
Order of pole = 12.06
x[1] = 0.1818
y[1] (analytic) = 2.0166174625018910540375016405613
y[1] (numeric) = 2.0166174625018910540382544787819
absolute error = 7.528382206e-22
relative error = 3.7331731704137915387130077474798e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.891
Order of pole = 12.02
x[1] = 0.1819
y[1] (analytic) = 2.0166358506452803427129118921734
y[1] (numeric) = 2.0166358506452803427136657451871
absolute error = 7.538530137e-22
relative error = 3.7381712392883581741306729568004e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.889
Order of pole = 11.97
x[1] = 0.182
y[1] (analytic) = 2.0166542491269835944606939753071
y[1] (numeric) = 2.0166542491269835944614488433961
absolute error = 7.548680890e-22
relative error = 3.7431705971749244274600220312022e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.887
Order of pole = 11.93
x[1] = 0.1821
y[1] (analytic) = 2.016672657947381234842608336076
y[1] (numeric) = 2.0166726579473812348433642195227
absolute error = 7.558834467e-22
relative error = 3.7481712449523496948743954427668e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.884
Order of pole = 11.88
x[1] = 0.1822
y[1] (analytic) = 2.0166910771068539172042517300062
y[1] (numeric) = 2.0166910771068539172050086290931
absolute error = 7.568990869e-22
relative error = 3.7531731830035556523911372162893e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.882
Order of pole = 11.84
x[1] = 0.1823
y[1] (analytic) = 2.0167095066057825227070574615498
y[1] (numeric) = 2.0167095066057825227078153765596
absolute error = 7.579150098e-22
relative error = 3.7581764122072633361380733013932e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.879
Order of pole = 11.79
x[1] = 0.1824
y[1] (analytic) = 2.01672794644454816036031651563
y[1] (numeric) = 2.0167279464445481603610754468457
absolute error = 7.589312157e-22
relative error = 3.7631809339379704508318731058763e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.3MB, time=19.40
Real estimate of pole used
Radius of convergence = 1.877
Order of pole = 11.75
x[1] = 0.1825
y[1] (analytic) = 2.0167463966235321670532195870346
y[1] (numeric) = 2.0167463966235321670539795347395
absolute error = 7.599477049e-22
relative error = 3.7681867495700804763849643986243e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.875
Order of pole = 11.71
x[1] = 0.1826
y[1] (analytic) = 2.0167648571431161075869200134774
y[1] (numeric) = 2.0167648571431161075876809779548
absolute error = 7.609644774e-22
relative error = 3.7731938589903717177527295928585e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.872
Order of pole = 11.66
x[1] = 0.1827
y[1] (analytic) = 2.0167833280036817747066176181521
y[1] (numeric) = 2.0167833280036817747073795996855
absolute error = 7.619815334e-22
relative error = 3.7782022630772607767567368036317e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.87
Order of pole = 11.62
x[1] = 0.1828
y[1] (analytic) = 2.0168018092056111891336634676077
y[1] (numeric) = 2.016801809205611189134426466481
absolute error = 7.629988733e-22
relative error = 3.7832119637007571175769335394778e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.868
Order of pole = 11.58
x[1] = 0.1829
y[1] (analytic) = 2.0168203007492865995976855507784
y[1] (numeric) = 2.0168203007492865995984495672755
absolute error = 7.640164971e-22
relative error = 3.7882229607474375873862811998753e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.866
Order of pole = 11.54
x[1] = 0.183
y[1] (analytic) = 2.0168388026350904828687353850041
y[1] (numeric) = 2.0168388026350904828695004194092
absolute error = 7.650344051e-22
relative error = 3.7932352555913154183215682726571e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.863
Order of pole = 11.49
x[1] = 0.1831
y[1] (analytic) = 2.0168573148634055437894555548841
y[1] (numeric) = 2.0168573148634055437902216074817
absolute error = 7.660525976e-22
relative error = 3.7982488496063092773443419453592e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.861
Order of pole = 11.45
x[1] = 0.1832
y[1] (analytic) = 2.0168758374346147153072681898088
y[1] (numeric) = 2.0168758374346147153080352608834
absolute error = 7.670710746e-22
relative error = 3.8032637426787941687444592902965e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.859
Order of pole = 11.41
x[1] = 0.1833
y[1] (analytic) = 2.016894370349101158506584386019
y[1] (numeric) = 2.0168943703491011585073524758555
absolute error = 7.680898365e-22
relative error = 3.8082799366783522045273027453376e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.3MB, time=19.62
Real estimate of pole used
Radius of convergence = 1.857
Order of pole = 11.37
x[1] = 0.1834
y[1] (analytic) = 2.0169129136072482626410345790476
y[1] (numeric) = 2.016912913607248262641803687931
absolute error = 7.691088834e-22
relative error = 3.8132974319870308448426086301882e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.854
Order of pole = 11.33
x[1] = 0.1835
y[1] (analytic) = 2.0169314672094396451657198724011
y[1] (numeric) = 2.0169314672094396451664900006166
absolute error = 7.701282155e-22
relative error = 3.8183162294826218821477935030882e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.852
Order of pole = 11.29
x[1] = 0.1836
y[1] (analytic) = 2.0169500311560591517694843283438
y[1] (numeric) = 2.0169500311560591517702554761769
absolute error = 7.711478331e-22
relative error = 3.8233363305386386021611297413019e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.85
Order of pole = 11.24
x[1] = 0.1837
y[1] (analytic) = 2.0169686054474908564072082266513
y[1] (numeric) = 2.0169686054474908564079803943876
absolute error = 7.721677363e-22
relative error = 3.8283577355369122953162807077492e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.848
Order of pole = 11.2
x[1] = 0.1838
y[1] (analytic) = 2.0169871900841190613321222972039
y[1] (numeric) = 2.0169871900841190613328954851293
absolute error = 7.731879254e-22
relative error = 3.8333804458507937450837844757588e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.846
Order of pole = 11.16
x[1] = 0.1839
y[1] (analytic) = 2.017005785066328297128142932296
y[1] (numeric) = 2.0170057850663282971289171406965
absolute error = 7.742084005e-22
relative error = 3.8384044618619699042437945630906e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.844
Order of pole = 11.12
x[1] = 0.184
y[1] (analytic) = 2.0170243903945033227422283845393
y[1] (numeric) = 2.0170243903945033227430036137012
absolute error = 7.752291619e-22
relative error = 3.8434297849436288567206121651904e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.841
Order of pole = 11.08
x[1] = 0.1841
y[1] (analytic) = 2.0170430060690291255167559562454
y[1] (numeric) = 2.0170430060690291255175322064551
absolute error = 7.762502097e-22
relative error = 3.8484564154773130400226339291287e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.839
Order of pole = 11.04
x[1] = 0.1842
y[1] (analytic) = 2.0170616320902909212219201861736
y[1] (numeric) = 2.0170616320902909212226974577178
absolute error = 7.772715442e-22
relative error = 3.8534843548360476412490684315537e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.837
Order of pole = 11
x[1] = 0.1843
y[1] (analytic) = 2.0170802684586741540881520395378
y[1] (numeric) = 2.0170802684586741540889303327033
absolute error = 7.782931655e-22
relative error = 3.8585136034012304050372641281950e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.3MB, time=19.84
Real estimate of pole used
Radius of convergence = 1.835
Order of pole = 10.96
x[1] = 0.1844
y[1] (analytic) = 2.0170989151745644968385591071677
y[1] (numeric) = 2.0170989151745644968393384222417
absolute error = 7.793150740e-22
relative error = 3.8635441630414849324159748565519e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.833
Order of pole = 10.93
x[1] = 0.1845
y[1] (analytic) = 2.0171175722383478507213868197259
y[1] (numeric) = 2.0171175722383478507221671569956
absolute error = 7.803372697e-22
relative error = 3.8685760336422934185955779938204e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.831
Order of pole = 10.89
x[1] = 0.1846
y[1] (analytic) = 2.017136239650410345542500682884
y[1] (numeric) = 2.0171362396504103455432820426369
absolute error = 7.813597529e-22
relative error = 3.8736092165763546578917805079897e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.829
Order of pole = 10.85
x[1] = 0.1847
y[1] (analytic) = 2.0171549174111383396978895393694
y[1] (numeric) = 2.0171549174111383396986719218932
absolute error = 7.823825238e-22
relative error = 3.8786437127205242132984006352779e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.827
Order of pole = 10.81
x[1] = 0.1848
y[1] (analytic) = 2.0171736055209184202061898637934
y[1] (numeric) = 2.0171736055209184202069732693761
absolute error = 7.834055827e-22
relative error = 3.8836795234473236120193491619882e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.825
Order of pole = 10.77
x[1] = 0.1849
y[1] (analytic) = 2.0171923039801374027412310961809
y[1] (numeric) = 2.0171923039801374027420155251106
absolute error = 7.844289297e-22
relative error = 3.8887166491377016539793875348930e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.823
Order of pole = 10.73
x[1] = 0.185
y[1] (analytic) = 2.017211012789182331664602020121
y[1] (numeric) = 2.0172110127891823316653874726859
absolute error = 7.854525649e-22
relative error = 3.8937550901725482346349176549091e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.821
Order of pole = 10.69
x[1] = 0.1851
y[1] (analytic) = 2.0172297319484404800582381914664
y[1] (numeric) = 2.0172297319484404800590246679551
absolute error = 7.864764887e-22
relative error = 3.8987948484198823967839192715033e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.819
Order of pole = 10.66
x[1] = 0.1852
y[1] (analytic) = 2.0172484614582993497570304235115
y[1] (numeric) = 2.0172484614582993497578179242128
absolute error = 7.875007013e-22
relative error = 3.9038359247561594913151933037725e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.3MB, time=20.06
Real estimate of pole used
Radius of convergence = 1.817
Order of pole = 10.62
x[1] = 0.1853
y[1] (analytic) = 2.0172672013191466713814543345839
y[1] (numeric) = 2.0172672013191466713822428597867
absolute error = 7.885252028e-22
relative error = 3.9088783195620372828719000447554e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.815
Order of pole = 10.58
x[1] = 0.1854
y[1] (analytic) = 2.0172859515313704043702209639874
y[1] (numeric) = 2.0172859515313704043710105139808
absolute error = 7.895499934e-22
relative error = 3.9139220337138300262082995740316e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.813
Order of pole = 10.55
x[1] = 0.1855
y[1] (analytic) = 2.0173047120953587370129484622411
y[1] (numeric) = 2.0173047120953587370137390373145
absolute error = 7.905750734e-22
relative error = 3.9189670685834853936258202011746e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.811
Order of pole = 10.51
x[1] = 0.1856
y[1] (analytic) = 2.0173234830115000864828548615613
y[1] (numeric) = 2.0173234830115000864836464620042
absolute error = 7.916004429e-22
relative error = 3.9240134245514424055597904037463e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.809
Order of pole = 10.47
x[1] = 0.1857
y[1] (analytic) = 2.0173422642801830988694719325372
y[1] (numeric) = 2.0173422642801830988702645586395
absolute error = 7.926261023e-22
relative error = 3.9290611034851860340432612029842e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.807
Order of pole = 10.44
x[1] = 0.1858
y[1] (analytic) = 2.0173610559017966492113801329582
y[1] (numeric) = 2.0173610559017966492121737850098
absolute error = 7.936520516e-22
relative error = 3.9341101052692983058699508938726e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.805
Order of pole = 10.4
x[1] = 0.1859
y[1] (analytic) = 2.0173798578767298415289646547511
y[1] (numeric) = 2.0173798578767298415297593330422
absolute error = 7.946782911e-22
relative error = 3.9391604312753978782939500487998e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.803
Order of pole = 10.36
x[1] = 0.186
y[1] (analytic) = 2.0173986702053720088571925749931
y[1] (numeric) = 2.0173986702053720088579882798141
absolute error = 7.957048210e-22
relative error = 3.9442120823793193247633837596346e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.801
Order of pole = 10.33
x[1] = 0.1861
y[1] (analytic) = 2.0174174928881127132784111169689
y[1] (numeric) = 2.0174174928881127132792078486104
absolute error = 7.967316415e-22
relative error = 3.9492650594568194081020580903686e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.3MB, time=20.29
Real estimate of pole used
Radius of convergence = 1.799
Order of pole = 10.29
x[1] = 0.1862
y[1] (analytic) = 2.0174363259253417459551670272446
y[1] (numeric) = 2.0174363259253417459559647859975
absolute error = 7.977587529e-22
relative error = 3.9543193638792556269470582459585e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.797
Order of pole = 10.26
x[1] = 0.1863
y[1] (analytic) = 2.0174551693174491271630470747371
y[1] (numeric) = 2.0174551693174491271638458608924
absolute error = 7.987861553e-22
relative error = 3.9593749960265411297474940513252e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.795
Order of pole = 10.22
x[1] = 0.1864
y[1] (analytic) = 2.0174740230648251063235396777589
y[1] (numeric) = 2.0174740230648251063243394916078
absolute error = 7.998138489e-22
relative error = 3.9644319567741989592347153094475e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.793
Order of pole = 10.19
x[1] = 0.1865
y[1] (analytic) = 2.0174928871678601620369176650255
y[1] (numeric) = 2.0174928871678601620377185068594
absolute error = 8.008418339e-22
relative error = 3.9694902469976741602930895937128e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.791
Order of pole = 10.15
x[1] = 0.1866
y[1] (analytic) = 2.0175117616269450021151421766151
y[1] (numeric) = 2.0175117616269450021159440467257
absolute error = 8.018701106e-22
relative error = 3.9745498680679937927545858666203e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.789
Order of pole = 10.12
x[1] = 0.1867
y[1] (analytic) = 2.0175306464424705636147877108755
y[1] (numeric) = 2.0175306464424705636155906095547
absolute error = 8.028986792e-22
relative error = 3.9796108208604328467416877627674e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.788
Order of pole = 10.08
x[1] = 0.1868
y[1] (analytic) = 2.0175495416148280128699883232765
y[1] (numeric) = 2.0175495416148280128707922508163
absolute error = 8.039275398e-22
relative error = 3.9846731057545373813710247562895e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.786
Order of pole = 10.05
x[1] = 0.1869
y[1] (analytic) = 2.0175684471444087455254049832113
y[1] (numeric) = 2.017568447144408745526209939904
absolute error = 8.049566927e-22
relative error = 3.9897367241210861009728286911335e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.784
Order of pole = 10.01
x[1] = 0.187
y[1] (analytic) = 2.0175873630316043865692140947539
y[1] (numeric) = 2.017587363031604386570020080892
absolute error = 8.059861381e-22
relative error = 3.9948016768351194037182112385226e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.782
Order of pole = 9.978
x[1] = 0.1871
y[1] (analytic) = 2.0176062892768067903661171873849
y[1] (numeric) = 2.0176062892768067903669242032611
absolute error = 8.070158762e-22
relative error = 3.9998679647715993944264118415869e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.3MB, time=20.52
Real estimate of pole used
Radius of convergence = 1.78
Order of pole = 9.945
x[1] = 0.1872
y[1] (analytic) = 2.0176252258804080406903717827008
y[1] (numeric) = 2.017625225880408040691179828608
absolute error = 8.080459072e-22
relative error = 4.0049355888054098377802986980784e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.778
Order of pole = 9.911
x[1] = 0.1873
y[1] (analytic) = 2.0176441728428004507588434431277
y[1] (numeric) = 2.017644172842800450759652519359
absolute error = 8.090762313e-22
relative error = 4.0100045498113561115443184272948e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.777
Order of pole = 9.877
x[1] = 0.1874
y[1] (analytic) = 2.0176631301643765632640790086638
y[1] (numeric) = 2.0176631301643765632648891155125
absolute error = 8.101068487e-22
relative error = 4.0150748486641651597848955112859e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.775
Order of pole = 9.844
x[1] = 0.1875
y[1] (analytic) = 2.0176820978455291504074010276796
y[1] (numeric) = 2.0176820978455291504082121654393
absolute error = 8.111377597e-22
relative error = 4.0201464867341036612064537960809e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.773
Order of pole = 9.811
x[1] = 0.1876
y[1] (analytic) = 2.0177010758866512139320233878089
y[1] (numeric) = 2.0177010758866512139328355567733
absolute error = 8.121689644e-22
relative error = 4.0252194644001140136909675337007e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.771
Order of pole = 9.778
x[1] = 0.1877
y[1] (analytic) = 2.0177200642881359851561881529683
y[1] (numeric) = 2.0177200642881359851570013534313
absolute error = 8.132004630e-22
relative error = 4.0302937825366875721863920494458e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.769
Order of pole = 9.745
x[1] = 0.1878
y[1] (analytic) = 2.0177390630503769250063236125469
y[1] (numeric) = 2.0177390630503769250071378448027
absolute error = 8.142322558e-22
relative error = 4.0353694425138412935715019622702e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.768
Order of pole = 9.712
x[1] = 0.1879
y[1] (analytic) = 2.0177580721737677240502235488123
y[1] (numeric) = 2.0177580721737677240510388131552
absolute error = 8.152643429e-22
relative error = 4.0404464447102956836323212689141e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.766
Order of pole = 9.68
x[1] = 0.188
y[1] (analytic) = 2.0177770916587023025302477285834
y[1] (numeric) = 2.017777091658702302531064025308
absolute error = 8.162967246e-22
relative error = 4.0455247904959009694481420687178e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.3MB, time=20.73
Real estimate of pole used
Radius of convergence = 1.764
Order of pole = 9.648
x[1] = 0.1881
y[1] (analytic) = 2.0177961215055748103965436252249
y[1] (numeric) = 2.017796121505574810397360954626
absolute error = 8.173294011e-22
relative error = 4.0506044807448197129605086251372e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.762
Order of pole = 9.615
x[1] = 0.1882
y[1] (analytic) = 2.0178151617147796273402893770218
y[1] (numeric) = 2.0178151617147796273411077393945
absolute error = 8.183623727e-22
relative error = 4.0556855168267211853272358823363e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.761
Order of pole = 9.583
x[1] = 0.1883
y[1] (analytic) = 2.0178342122867113628269579879992
y[1] (numeric) = 2.0178342122867113628277773836386
absolute error = 8.193956394e-22
relative error = 4.0607678986244345140786154947057e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.759
Order of pole = 9.552
x[1] = 0.1884
y[1] (analytic) = 2.017853273221764856129602777252
y[1] (numeric) = 2.0178532732217648561304232064536
absolute error = 8.204292016e-22
relative error = 4.0658516280030520329470912603214e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.757
Order of pole = 9.52
x[1] = 0.1885
y[1] (analytic) = 2.0178723445203351763621640828602
y[1] (numeric) = 2.0178723445203351763629855459196
absolute error = 8.214630594e-22
relative error = 4.0709367053408351938180234661891e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.756
Order of pole = 9.488
x[1] = 0.1886
y[1] (analytic) = 2.0178914261828176225127972264629
y[1] (numeric) = 2.0178914261828176225136197236759
absolute error = 8.224972130e-22
relative error = 4.0760231315115519707797655543113e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.754
Order of pole = 9.457
x[1] = 0.1887
y[1] (analytic) = 2.0179105182096077234772217445737
y[1] (numeric) = 2.0179105182096077234780452762364
absolute error = 8.235316627e-22
relative error = 4.0811109078844533944494173599577e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.752
Order of pole = 9.426
x[1] = 0.1888
y[1] (analytic) = 2.0179296206011012380920918927223
y[1] (numeric) = 2.0179296206011012380929164591309
absolute error = 8.245664086e-22
relative error = 4.0862000348375777842872354337579e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.75
Order of pole = 9.395
x[1] = 0.1889
y[1] (analytic) = 2.0179487333576941551683884285103
y[1] (numeric) = 2.0179487333576941551692140299614
absolute error = 8.256014511e-22
relative error = 4.0912905142355612539548443850603e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.749
Order of pole = 9.364
x[1] = 0.189
y[1] (analytic) = 2.0179678564797826935248316796769
y[1] (numeric) = 2.017967856479782693525658316467
absolute error = 8.266367901e-22
relative error = 4.0963823454651829917875297115204e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.3MB, time=20.95
Real estimate of pole used
Radius of convergence = 1.747
Order of pole = 9.333
x[1] = 0.1891
y[1] (analytic) = 2.0179869899677633020213159032704
y[1] (numeric) = 2.0179869899677633020221435756965
absolute error = 8.276724261e-22
relative error = 4.1014755308864592967252726465573e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.745
Order of pole = 9.303
x[1] = 0.1892
y[1] (analytic) = 2.0180061338220326595923649420299
y[1] (numeric) = 2.0180061338220326595931936503891
absolute error = 8.287083592e-22
relative error = 4.1065700708771162504858836939839e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.744
Order of pole = 9.272
x[1] = 0.1893
y[1] (analytic) = 2.0180252880429876752806091840824
y[1] (numeric) = 2.018025288042987675281438928672
absolute error = 8.297445896e-22
relative error = 4.1116659663103533113792766063145e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.742
Order of pole = 9.242
x[1] = 0.1894
y[1] (analytic) = 2.0180444526310254882702838320669
y[1] (numeric) = 2.0180444526310254882711146131844
absolute error = 8.307811175e-22
relative error = 4.1167632180592905394687466656997e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.741
Order of pole = 9.212
x[1] = 0.1895
y[1] (analytic) = 2.0180636275865434679207484878004
y[1] (numeric) = 2.0180636275865434679215803057437
absolute error = 8.318179433e-22
relative error = 4.1218618279880175795476801829267e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.739
Order of pole = 9.182
x[1] = 0.1896
y[1] (analytic) = 2.0180828129099392138000280586072
y[1] (numeric) = 2.0180828129099392138008609136741
absolute error = 8.328550669e-22
relative error = 4.1269617954829078780318805952577e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.737
Order of pole = 9.152
x[1] = 0.1897
y[1] (analytic) = 2.0181020086016105557183749914327
y[1] (numeric) = 2.0181020086016105557192088839213
absolute error = 8.338924886e-22
relative error = 4.1320631219123722357263985577952e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.736
Order of pole = 9.123
x[1] = 0.1898
y[1] (analytic) = 2.0181212146619555537618528408725
y[1] (numeric) = 2.0181212146619555537626877710813
absolute error = 8.349302088e-22
relative error = 4.1371658091402333952206167252864e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.734
Order of pole = 9.093
x[1] = 0.1899
y[1] (analytic) = 2.0181404310913724983259411772493
y[1] (numeric) = 2.0181404310913724983267771454768
absolute error = 8.359682275e-22
relative error = 4.1422698570481740942938718187619e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.3MB, time=21.17
Real estimate of pole used
Radius of convergence = 1.732
Order of pole = 9.064
x[1] = 0.19
y[1] (analytic) = 2.0181596578902599101491618408727
y[1] (numeric) = 2.0181596578902599101499988474178
absolute error = 8.370065451e-22
relative error = 4.1473752674998388727580918987886e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.731
Order of pole = 9.035
x[1] = 0.1901
y[1] (analytic) = 2.0181788950590165403467265486265
y[1] (numeric) = 2.0181788950590165403475645937881
absolute error = 8.380451616e-22
relative error = 4.1524820403767699077663018458897e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.729
Order of pole = 9.006
x[1] = 0.1902
y[1] (analytic) = 2.0181981425980413704442058590264
y[1] (numeric) = 2.0181981425980413704450449431037
absolute error = 8.390840773e-22
relative error = 4.1575901770469418422314048638574e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.728
Order of pole = 8.977
x[1] = 0.1903
y[1] (analytic) = 2.0182174005077336124112195019001
y[1] (numeric) = 2.0182174005077336124120596251927
absolute error = 8.401232926e-22
relative error = 4.1626996793737173479965821840218e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.726
Order of pole = 8.948
x[1] = 0.1904
y[1] (analytic) = 2.0182366687884927086951480788442
y[1] (numeric) = 2.0182366687884927086959892416516
absolute error = 8.411628074e-22
relative error = 4.1678105467429312272659888479443e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.725
Order of pole = 8.919
x[1] = 0.1905
y[1] (analytic) = 2.0182559474407183322548661406152
y[1] (numeric) = 2.0182559474407183322557083432373
absolute error = 8.422026221e-22
relative error = 4.1729227810177816021673812541821e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.723
Order of pole = 8.891
x[1] = 0.1906
y[1] (analytic) = 2.0182752364648103865944966476205
y[1] (numeric) = 2.0182752364648103865953398903573
absolute error = 8.432427368e-22
relative error = 4.1780363825749310704070264835591e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.722
Order of pole = 8.863
x[1] = 0.1907
y[1] (analytic) = 2.0182945358611690057971868196743
y[1] (numeric) = 2.0182945358611690057980311028262
absolute error = 8.442831519e-22
relative error = 4.1831513532773846152236437970487e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.72
Order of pole = 8.834
x[1] = 0.1908
y[1] (analytic) = 2.0183138456301945545589053811929
y[1] (numeric) = 2.0183138456301945545597507050604
absolute error = 8.453238675e-22
relative error = 4.1882676935016399823191422151194e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.718
Order of pole = 8.806
memory used=370.0MB, alloc=4.3MB, time=21.39
x[1] = 0.1909
y[1] (analytic) = 2.0183331657722876282222612080037
y[1] (numeric) = 2.0183331657722876282231075728874
absolute error = 8.463648837e-22
relative error = 4.1933854036241337452398589709045e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.717
Order of pole = 8.779
x[1] = 0.191
y[1] (analytic) = 2.0183524962878490528103433819497
y[1] (numeric) = 2.0183524962878490528111907881506
absolute error = 8.474062009e-22
relative error = 4.1985044855076020678533937721342e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.715
Order of pole = 8.751
x[1] = 0.1911
y[1] (analytic) = 2.0183718371772798850605826594749
y[1] (numeric) = 2.0183718371772798850614311072941
absolute error = 8.484478192e-22
relative error = 4.2036249395283163841938908994472e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.714
Order of pole = 8.723
x[1] = 0.1912
y[1] (analytic) = 2.0183911884409814124586343603789
y[1] (numeric) = 2.0183911884409814124594838501178
absolute error = 8.494897389e-22
relative error = 4.2087467670533750397963448273243e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.712
Order of pole = 8.696
x[1] = 0.1913
y[1] (analytic) = 2.0184105500793551532722826829362
y[1] (numeric) = 2.0184105500793551532731332148963
absolute error = 8.505319601e-22
relative error = 4.2138699684588983657380680681733e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.711
Order of pole = 8.668
x[1] = 0.1914
y[1] (analytic) = 2.0184299220928028565853664515764
y[1] (numeric) = 2.0184299220928028565862180260595
absolute error = 8.515744831e-22
relative error = 4.2189945451118145157459397332023e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.709
Order of pole = 8.641
x[1] = 0.1915
y[1] (analytic) = 2.0184493044817265023317263033305
y[1] (numeric) = 2.0184493044817265023325789206385
absolute error = 8.526173080e-22
relative error = 4.2241204973880925410477796009721e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.708
Order of pole = 8.614
x[1] = 0.1916
y[1] (analytic) = 2.0184686972465283013291733192474
y[1] (numeric) = 2.0184686972465283013300269796826
absolute error = 8.536604352e-22
relative error = 4.2292478271499152792026846917911e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.706
Order of pole = 8.587
x[1] = 0.1917
y[1] (analytic) = 2.0184881003876106953134791069949
y[1] (numeric) = 2.0184881003876106953143338108597
absolute error = 8.547038648e-22
relative error = 4.2343765347730860375830424161910e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.705
Order of pole = 8.56
x[1] = 0.1918
y[1] (analytic) = 2.0185075139053763569723873408586
y[1] (numeric) = 2.0185075139053763569732430884556
absolute error = 8.557475970e-22
relative error = 4.2395066211287621499192934378954e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.3MB, time=21.61
Real estimate of pole used
Radius of convergence = 1.704
Order of pole = 8.533
x[1] = 0.1919
y[1] (analytic) = 2.0185269378002281899796467653602
y[1] (numeric) = 2.0185269378002281899805035569922
absolute error = 8.567916320e-22
relative error = 4.2446380870880203400777718863426e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.702
Order of pole = 8.507
x[1] = 0.192
y[1] (analytic) = 2.0185463720725693290290656687196
y[1] (numeric) = 2.0185463720725693290299235046897
absolute error = 8.578359701e-22
relative error = 4.2497709340172626833222643143480e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.701
Order of pole = 8.48
x[1] = 0.1921
y[1] (analytic) = 2.0185658167228031398685878323895
y[1] (numeric) = 2.018565816722803139869446713001
absolute error = 8.588806115e-22
relative error = 4.2549051627873902272078353187508e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.699
Order of pole = 8.454
x[1] = 0.1922
y[1] (analytic) = 2.018585271751333219334389962896
y[1] (numeric) = 2.0185852717513332193352498884523
absolute error = 8.599255563e-22
relative error = 4.2600407737738267936389520306319e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.698
Order of pole = 8.428
x[1] = 0.1923
y[1] (analytic) = 2.0186047371585633953850006122226
y[1] (numeric) = 2.0186047371585633953858615830274
absolute error = 8.609708048e-22
relative error = 4.2651777683427178696504560313092e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.696
Order of pole = 8.402
x[1] = 0.1924
y[1] (analytic) = 2.0186242129448977271354405929807
y[1] (numeric) = 2.018624212944897727136302609338
absolute error = 8.620163573e-22
relative error = 4.2703161478601089808672189644404e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.695
Order of pole = 8.376
x[1] = 0.1925
y[1] (analytic) = 2.0186436991107405048913848946121
y[1] (numeric) = 2.018643699110740504892247956826
absolute error = 8.630622139e-22
relative error = 4.2754559127011813755383358293759e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.694
Order of pole = 8.35
x[1] = 0.1926
y[1] (analytic) = 2.018663195656496250183346106875
y[1] (numeric) = 2.0186631956564962501842102152498
absolute error = 8.641083748e-22
relative error = 4.2805970637364318118016664589929e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.692
Order of pole = 8.325
x[1] = 0.1927
y[1] (analytic) = 2.0186827025825697158008793568687
y[1] (numeric) = 2.018682702582569715801744511709
absolute error = 8.651548403e-22
relative error = 4.2857396023316486009464392599944e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.3MB, time=21.83
Real estimate of pole used
Radius of convergence = 1.691
Order of pole = 8.299
x[1] = 0.1928
y[1] (analytic) = 2.0187022198893658858268087658574
y[1] (numeric) = 2.0187022198893658858276749674679
absolute error = 8.662016105e-22
relative error = 4.2908835288617843290606577683510e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.689
Order of pole = 8.274
x[1] = 0.1929
y[1] (analytic) = 2.0187217475772899756714754321555
y[1] (numeric) = 2.0187217475772899756723426808412
absolute error = 8.672486857e-22
relative error = 4.2960288446924555832624790208927e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.688
Order of pole = 8.248
x[1] = 0.193
y[1] (analytic) = 2.0187412856467474321070069463458
y[1] (numeric) = 2.0187412856467474321078752424119
absolute error = 8.682960661e-22
relative error = 4.3011755506938204602811846381133e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.687
Order of pole = 8.223
x[1] = 0.1931
y[1] (analytic) = 2.0187608340981439333016084451008
y[1] (numeric) = 2.0187608340981439333024777888527
absolute error = 8.693437519e-22
relative error = 4.3063236477359558577316163481272e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.685
Order of pole = 8.198
x[1] = 0.1932
y[1] (analytic) = 2.0187803929318853888538752098863
y[1] (numeric) = 2.0187803929318853888547456016297
absolute error = 8.703917434e-22
relative error = 4.3114731371842060070009135138072e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.684
Order of pole = 8.173
x[1] = 0.1933
y[1] (analytic) = 2.0187999621483779398271268168287
y[1] (numeric) = 2.0187999621483779398279982568694
absolute error = 8.714400407e-22
relative error = 4.3166240194131270847483742567043e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.682
Order of pole = 8.148
x[1] = 0.1934
y[1] (analytic) = 2.0188195417480279587837628440318
y[1] (numeric) = 2.0188195417480279587846353326759
absolute error = 8.724886441e-22
relative error = 4.3217762957878910778493064700596e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.681
Order of pole = 8.124
x[1] = 0.1935
y[1] (analytic) = 2.0188391317312420498196401426346
y[1] (numeric) = 2.0188391317312420498205136801883
absolute error = 8.735375537e-22
relative error = 4.3269299666829010269153378247810e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.68
Order of pole = 8.099
x[1] = 0.1936
y[1] (analytic) = 2.0188587320984270485984716779042
y[1] (numeric) = 2.018858732098427048599346264674
absolute error = 8.745867698e-22
relative error = 4.3320850334631564779930377477787e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.678
Order of pole = 8.075
x[1] = 0.1937
y[1] (analytic) = 2.0188783428499900223862469466646
y[1] (numeric) = 2.0188783428499900223871225829572
absolute error = 8.756362926e-22
relative error = 4.3372414969982317056685299828607e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.3MB, time=22.06
Real estimate of pole used
Radius of convergence = 1.677
Order of pole = 8.05
x[1] = 0.1938
y[1] (analytic) = 2.018897963986338270085673977364
y[1] (numeric) = 2.0188979639863382700865506634863
absolute error = 8.766861223e-22
relative error = 4.3423993581576194443134779792045e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.676
Order of pole = 8.026
x[1] = 0.1939
y[1] (analytic) = 2.0189175955078793222706429190902
y[1] (numeric) = 2.0189175955078793222715206553494
absolute error = 8.777362592e-22
relative error = 4.3475586183060457578521587636305e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.674
Order of pole = 8.002
x[1] = 0.194
y[1] (analytic) = 2.0189372374150209412207112258461
y[1] (numeric) = 2.0189372374150209412215900125494
absolute error = 8.787867033e-22
relative error = 4.3527192773222055087868015295248e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.673
Order of pole = 7.978
x[1] = 0.1941
y[1] (analytic) = 2.0189568897081711209556104424024
y[1] (numeric) = 2.0189568897081711209564902798574
absolute error = 8.798374550e-22
relative error = 4.3578813370659715401869863839608e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.672
Order of pole = 7.954
x[1] = 0.1942
y[1] (analytic) = 2.0189765523877380872697745980507
y[1] (numeric) = 2.0189765523877380872706554865652
absolute error = 8.808885145e-22
relative error = 4.3630447984064954882118542475571e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.67
Order of pole = 7.93
x[1] = 0.1943
y[1] (analytic) = 2.0189962254541302977668902145811
y[1] (numeric) = 2.0189962254541302977677721544632
absolute error = 8.819398821e-22
relative error = 4.3682096627081428273429010635871e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.669
Order of pole = 7.906
x[1] = 0.1944
y[1] (analytic) = 2.0190159089077564418944679348163
y[1] (numeric) = 2.0190159089077564418953509263741
absolute error = 8.829915578e-22
relative error = 4.3733759298493054898966572412078e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.668
Order of pole = 7.883
x[1] = 0.1945
y[1] (analytic) = 2.0190356027490254409784357780363
y[1] (numeric) = 2.0190356027490254409793198215783
absolute error = 8.840435420e-22
relative error = 4.3785436016894760273282351757540e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.667
Order of pole = 7.859
x[1] = 0.1946
y[1] (analytic) = 2.0190553069783464482577540286343
y[1] (numeric) = 2.019055306978346448258639124469
absolute error = 8.850958347e-22
relative error = 4.3837126781069018776009821598256e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.3MB, time=22.29
Real estimate of pole used
Radius of convergence = 1.665
Order of pole = 7.836
x[1] = 0.1947
y[1] (analytic) = 2.0190750215961288489190517643461
y[1] (numeric) = 2.0190750215961288489199379127824
absolute error = 8.861484363e-22
relative error = 4.3888831609608923655819789612778e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.664
Order of pole = 7.813
x[1] = 0.1948
y[1] (analytic) = 2.019094746602782260131285030403
y[1] (numeric) = 2.0190947466027822601321722317501
absolute error = 8.872013471e-22
relative error = 4.3940550516153646436391649143241e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.663
Order of pole = 7.79
x[1] = 0.1949
y[1] (analytic) = 2.01911448199871653108041666596
y[1] (numeric) = 2.0191144819987165310813049205271
absolute error = 8.882545671e-22
relative error = 4.3992283499483345654381317850985e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.662
Order of pole = 7.767
x[1] = 0.195
y[1] (analytic) = 2.0191342277843417430041177891565
y[1] (numeric) = 2.0191342277843417430050070972531
absolute error = 8.893080966e-22
relative error = 4.4044030573235599106736224434013e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.66
Order of pole = 7.744
x[1] = 0.1951
y[1] (analytic) = 2.0191539839600682092264909471717
y[1] (numeric) = 2.0191539839600682092273813091076
absolute error = 8.903619359e-22
relative error = 4.4095791751046969149924443782935e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.659
Order of pole = 7.721
x[1] = 0.1952
y[1] (analytic) = 2.019173750526306475192814937641
y[1] (numeric) = 2.0191737505263064751937063537261
absolute error = 8.914160851e-22
relative error = 4.4147567036647960387065900479129e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.658
Order of pole = 7.698
x[1] = 0.1953
y[1] (analytic) = 2.019193527483467318504311307803
y[1] (numeric) = 2.0191935274834673185052037783474
absolute error = 8.924705444e-22
relative error = 4.4199356438720920910992663739363e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.656
Order of pole = 7.676
x[1] = 0.1954
y[1] (analytic) = 2.0192133148319617489529325377533
y[1] (numeric) = 2.0192133148319617489538260630674
absolute error = 8.935253141e-22
relative error = 4.4251159970899799424269348675926e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.655
Order of pole = 7.653
x[1] = 0.1955
y[1] (analytic) = 2.019233112572201008556171914184
y[1] (numeric) = 2.0192331125722010085570664945785
absolute error = 8.945803945e-22
relative error = 4.4302977646817526786104660163201e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.654
Order of pole = 7.631
memory used=389.1MB, alloc=4.3MB, time=22.52
x[1] = 0.1956
y[1] (analytic) = 2.0192529207045965715918951009936
y[1] (numeric) = 2.0192529207045965715927907367792
absolute error = 8.956357856e-22
relative error = 4.4354809465249035428991129822256e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.653
Order of pole = 7.609
x[1] = 0.1957
y[1] (analytic) = 2.0192727392295601446331934131542
y[1] (numeric) = 2.019272739229560144634090104642
absolute error = 8.966914878e-22
relative error = 4.4406655444777933860583056050013e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.652
Order of pole = 7.587
x[1] = 0.1958
y[1] (analytic) = 2.0192925681475036665832588002312
y[1] (numeric) = 2.0192925681475036665841565477323
absolute error = 8.977475011e-22
relative error = 4.4458515584177698979420419154142e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.65
Order of pole = 7.565
x[1] = 0.1959
y[1] (analytic) = 2.0193124074588393087102805459507
y[1] (numeric) = 2.0193124074588393087111793497767
absolute error = 8.988038260e-22
relative error = 4.4510389906982274815813185171816e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.649
Order of pole = 7.543
x[1] = 0.196
y[1] (analytic) = 2.0193322571639794746823636902184
y[1] (numeric) = 2.019332257163979474683263550681
absolute error = 8.998604626e-22
relative error = 4.4562278416915667085560222130322e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.648
Order of pole = 7.521
x[1] = 0.1961
y[1] (analytic) = 2.0193521172633368006024691799948
y[1] (numeric) = 2.0193521172633368006033700974059
absolute error = 9.009174111e-22
relative error = 4.4614181122653332817270815137121e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.647
Order of pole = 7.499
x[1] = 0.1962
y[1] (analytic) = 2.0193719877573241550433757554385
y[1] (numeric) = 2.0193719877573241550442777301102
absolute error = 9.019746717e-22
relative error = 4.4666098032869901868244651250593e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.646
Order of pole = 7.477
x[1] = 0.1963
y[1] (analytic) = 2.0193918686463546390826635777324
y[1] (numeric) = 2.019391868646354639083566609977
absolute error = 9.030322446e-22
relative error = 4.4718029156239176458955117582467e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.644
Order of pole = 7.456
x[1] = 0.1964
y[1] (analytic) = 2.0194117599308415863377196050131
y[1] (numeric) = 2.0194117599308415863386236951431
absolute error = 9.040901300e-22
relative error = 4.4769974501434130707558089639001e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.643
Order of pole = 7.434
x[1] = 0.1965
y[1] (analytic) = 2.0194316616111985630007647228271
y[1] (numeric) = 2.0194316616111985630016698711553
absolute error = 9.051483282e-22
relative error = 4.4821934082078798455620746046633e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.3MB, time=22.75
Real estimate of pole used
Radius of convergence = 1.642
Order of pole = 7.413
x[1] = 0.1966
y[1] (analytic) = 2.019451573687839367873902635543
y[1] (numeric) = 2.0194515736878393678748088423825
absolute error = 9.062068395e-22
relative error = 4.4873907911796189206225838519845e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.641
Order of pole = 7.392
x[1] = 0.1967
y[1] (analytic) = 2.0194714961611780324041905251536
y[1] (numeric) = 2.0194714961611780324050977908174
absolute error = 9.072656638e-22
relative error = 4.4925895984401124957120416068449e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.64
Order of pole = 7.371
x[1] = 0.1968
y[1] (analytic) = 2.0194914290316288207187314839033
y[1] (numeric) = 2.019491429031628820719639808705
absolute error = 9.083248017e-22
relative error = 4.4977898328370376122783059789792e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.638
Order of pole = 7.35
x[1] = 0.1969
y[1] (analytic) = 2.0195113722996062296597887271867
y[1] (numeric) = 2.0195113722996062296606981114398
absolute error = 9.093842531e-22
relative error = 4.5029914937517250565732122885814e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.637
Order of pole = 7.329
x[1] = 0.197
y[1] (analytic) = 2.019531325965524988819921593161
y[1] (numeric) = 2.0195313259655249888208320371795
absolute error = 9.104440185e-22
relative error = 4.5081945835364675391370426484963e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.636
Order of pole = 7.308
x[1] = 0.1971
y[1] (analytic) = 2.0195512900298000605771433355272
y[1] (numeric) = 2.0195512900298000605780548396252
absolute error = 9.115040980e-22
relative error = 4.5133991025627779096092205966744e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.635
Order of pole = 7.287
x[1] = 0.1972
y[1] (analytic) = 2.019571264492846640130100715933
y[1] (numeric) = 2.0195712644928466401310132804247
absolute error = 9.125644917e-22
relative error = 4.5186050512021053803428154987812e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.634
Order of pole = 7.266
x[1] = 0.1973
y[1] (analytic) = 2.019591249355080155533275402459
y[1] (numeric) = 2.0195912493550801555341890276589
absolute error = 9.136251999e-22
relative error = 4.5238124308161349031783421771927e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.633
Order of pole = 7.246
x[1] = 0.1974
y[1] (analytic) = 2.0196112446169162677322071806526
y[1] (numeric) = 2.0196112446169162677331218668755
absolute error = 9.146862229e-22
relative error = 4.5290212427664485306423853245029e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.3MB, time=22.98
Real estimate of pole used
Radius of convergence = 1.632
Order of pole = 7.225
x[1] = 0.1975
y[1] (analytic) = 2.019631250278770870598738983579
y[1] (numeric) = 2.0196312502787708705996547311399
absolute error = 9.157475609e-22
relative error = 4.5342314879193854524762860919087e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.63
Order of pole = 7.205
x[1] = 0.1976
y[1] (analytic) = 2.0196512663410600909662837473629
y[1] (numeric) = 2.0196512663410600909672005565768
absolute error = 9.168092139e-22
relative error = 4.5394431661509314751254131632746e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.629
Order of pole = 7.185
x[1] = 0.1977
y[1] (analytic) = 2.019671292804200288665113098698
y[1] (numeric) = 2.0196712928042002886660309698804
absolute error = 9.178711824e-22
relative error = 4.5446562798126786009150863656031e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.628
Order of pole = 7.165
x[1] = 0.1978
y[1] (analytic) = 2.0196913296686080565576678808099
y[1] (numeric) = 2.0196913296686080565585868142765
absolute error = 9.189334666e-22
relative error = 4.5498708297707009202684891599814e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.627
Order of pole = 7.144
x[1] = 0.1979
y[1] (analytic) = 2.0197113769347002205738905243565
y[1] (numeric) = 2.0197113769347002205748105204231
absolute error = 9.199960666e-22
relative error = 4.5550868163958687075204951216944e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.626
Order of pole = 7.124
x[1] = 0.198
y[1] (analytic) = 2.0197314346028938397465792697594
y[1] (numeric) = 2.0197314346028938397475003287419
absolute error = 9.210589825e-22
relative error = 4.5603042400589882913602414889889e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.625
Order of pole = 7.104
x[1] = 0.1981
y[1] (analytic) = 2.0197515026736062062467642474619
y[1] (numeric) = 2.0197515026736062062476863696768
absolute error = 9.221222149e-22
relative error = 4.5655231036063540962514759039898e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.624
Order of pole = 7.085
x[1] = 0.1982
y[1] (analytic) = 2.019771581147254845419105422616
y[1] (numeric) = 2.0197715811472548454200286083796
absolute error = 9.231857636e-22
relative error = 4.5707434059232541931237202485855e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.623
Order of pole = 7.065
x[1] = 0.1983
y[1] (analytic) = 2.0197916700242575158173124107001
y[1] (numeric) = 2.0197916700242575158182366603292
absolute error = 9.242496291e-22
relative error = 4.5759651493606756250311266325363e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.621
Order of pole = 7.045
x[1] = 0.1984
y[1] (analytic) = 2.019811769305032209239586170582
y[1] (numeric) = 2.0198117693050322092405114843935
absolute error = 9.253138115e-22
relative error = 4.5811883342890799847840584188300e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.3MB, time=23.21
Real estimate of pole used
Radius of convergence = 1.62
Order of pole = 7.026
x[1] = 0.1985
y[1] (analytic) = 2.0198318789899971507640825815373
y[1] (numeric) = 2.0198318789899971507650089598483
absolute error = 9.263783110e-22
relative error = 4.5864129615739554318561588483652e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.619
Order of pole = 7.006
x[1] = 0.1986
y[1] (analytic) = 2.0198519990795707987843979107446
y[1] (numeric) = 2.0198519990795707987853253538726
absolute error = 9.274431280e-22
relative error = 4.5916390330708777907885367789228e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.618
Order of pole = 6.987
x[1] = 0.1987
y[1] (analytic) = 2.0198721295741718450450761777806
y[1] (numeric) = 2.0198721295741718450460046860432
absolute error = 9.285082626e-22
relative error = 4.5968665491500569400888641357410e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.617
Order of pole = 6.968
x[1] = 0.1988
y[1] (analytic) = 2.0198922704742192146771384226419
y[1] (numeric) = 2.0198922704742192146780679963568
absolute error = 9.295737149e-22
relative error = 4.6020955101816384897064231567001e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.616
Order of pole = 6.948
x[1] = 0.1989
y[1] (analytic) = 2.0199124217801320662336338838268
y[1] (numeric) = 2.0199124217801320662345645233122
absolute error = 9.306394854e-22
relative error = 4.6073259185159876351769547654760e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.615
Order of pole = 6.929
x[1] = 0.199
y[1] (analytic) = 2.0199325834923297917252130930153
y[1] (numeric) = 2.0199325834923297917261447985893
absolute error = 9.317055740e-22
relative error = 4.6125577735329300304850916585358e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.614
Order of pole = 6.91
x[1] = 0.1991
y[1] (analytic) = 2.0199527556112320166557228928855
y[1] (numeric) = 2.0199527556112320166566556648666
absolute error = 9.327719811e-22
relative error = 4.6177910770875719058374514762556e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.613
Order of pole = 6.891
x[1] = 0.1992
y[1] (analytic) = 2.0199729381372586000578233846165
y[1] (numeric) = 2.0199729381372586000587572233235
absolute error = 9.338387070e-22
relative error = 4.6230258305398396116873845811809e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.612
Order of pole = 6.872
x[1] = 0.1993
y[1] (analytic) = 2.0199931310708296345286268116257
y[1] (numeric) = 2.0199931310708296345295617173774
absolute error = 9.349057517e-22
relative error = 4.6282620337644018907536316615187e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.3MB, time=23.43
Real estimate of pole used
Radius of convergence = 1.611
Order of pole = 6.854
x[1] = 0.1994
y[1] (analytic) = 2.0200133344123654462653583860963
y[1] (numeric) = 2.0200133344123654462662943592119
absolute error = 9.359731156e-22
relative error = 4.6334996886160677358842801113792e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.61
Order of pole = 6.835
x[1] = 0.1995
y[1] (analytic) = 2.0200335481622865951010390648555
y[1] (numeric) = 2.0200335481622865951019761056543
absolute error = 9.370407988e-22
relative error = 4.6387387954643983344978523696122e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.609
Order of pole = 6.816
x[1] = 0.1996
y[1] (analytic) = 2.0200537723210138745401902811666
y[1] (numeric) = 2.0200537723210138745411283899682
absolute error = 9.381088016e-22
relative error = 4.6439793556689629516218887204289e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.608
Order of pole = 6.798
x[1] = 0.1997
y[1] (analytic) = 2.0200740068889683117945606390047
y[1] (numeric) = 2.0200740068889683117954998161289
absolute error = 9.391771242e-22
relative error = 4.6492213700941952160678261136793e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.607
Order of pole = 6.779
x[1] = 0.1998
y[1] (analytic) = 2.0200942518665711678188745763887
y[1] (numeric) = 2.0200942518665711678198148221555
absolute error = 9.402457668e-22
relative error = 4.6544648396044442623247116965156e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.606
Order of pole = 6.761
x[1] = 0.1999
y[1] (analytic) = 2.0201145072542439373466030043479
y[1] (numeric) = 2.0201145072542439373475443190776
absolute error = 9.413147297e-22
relative error = 4.6597097655589961278922019119706e-20 %
h = 0.0001
TOP MAIN SOLVE Loop
Real estimate of pole used
Radius of convergence = 1.605
Order of pole = 6.743
x[1] = 0.2
y[1] (analytic) = 2.0201347730524083489257559281057
y[1] (numeric) = 2.0201347730524083489266983121188
absolute error = 9.423840131e-22
relative error = 4.6649561488220159212264523454217e-20 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ;
Iterations = 1000
Total Elapsed Time = 23 Seconds
Elapsed Time(since restart) = 23 Seconds
Expected Time Remaining = 3 Minutes 8 Seconds
Optimized Time Remaining = 3 Minutes 8 Seconds
Time to Timeout = 14 Minutes 36 Seconds
Percent Done = 11.12 %
> quit
memory used=407.1MB, alloc=4.3MB, time=23.59