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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> 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_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[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," ");
> ;
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[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[2] := relerr;
> else
> array_last_rel_error[2] := 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 DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, 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_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[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, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[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[2] := relerr
else array_last_rel_error[2] := 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
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y1_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 DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(array_y1_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
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> 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 DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, 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
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> 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_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_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
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #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_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_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[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #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_y2_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_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_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_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_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
> #TOP RADII COMPLEX EQ = 2
> #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_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_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 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> 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 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> 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 3
> 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 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 3
> 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 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> 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 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> 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 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #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 DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or
abs(array_y2_higher[1, m - 1]) < glob_small_float or
abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_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;
m := n - 2;
while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or
abs(array_y1_higher[1, m - 1]) < glob_small_float or
abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_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[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 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_y2_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_y2_higher[1, m]) or
glob_large_float <= abs(array_y2_higher[1, m - 1]) or
glob_large_float <= abs(array_y2_higher[1, m - 2]) or
glob_large_float <= abs(array_y2_higher[1, m - 3]) or
glob_large_float <= abs(array_y2_higher[1, m - 4]) or
glob_large_float <= abs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_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;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y1_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[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_y1_higher[1, m]) or
glob_large_float <= abs(array_y1_higher[1, m - 1]) or
glob_large_float <= abs(array_y1_higher[1, m - 2]) or
glob_large_float <= abs(array_y1_higher[1, m - 3]) or
glob_large_float <= abs(array_y1_higher[1, m - 4]) or
glob_large_float <= abs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_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[2, 1] := glob_large_float;
array_complex_pole[2, 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[2, 1] := rad_c;
array_complex_pole[2, 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;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 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[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 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;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> 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_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_y2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_y1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, 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_y2[iii]) then
array_norms[iii] := abs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y1[iii]) then
array_norms[iii] := abs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_y1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y2_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre sub $eq_no = 2 i = 1
> array_tmp5[1] := (array_y2[1] - (array_const_1D0[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if not array_y1_set_initial[2,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_m1,array_y1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2] + array_const_1D0[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y2_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre sub $eq_no = 2 i = 2
> array_tmp5[2] := (array_y2[2] - (array_const_1D0[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if not array_y1_set_initial[2,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_m1,array_y1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3] + array_const_1D0[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y2_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre sub $eq_no = 2 i = 3
> array_tmp5[3] := (array_y2[3] - (array_const_1D0[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if not array_y1_set_initial[2,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_m1,array_y1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4] + array_const_1D0[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y2_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre sub $eq_no = 2 i = 4
> array_tmp5[4] := (array_y2[4] - (array_const_1D0[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if not array_y1_set_initial[2,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_m1,array_y1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5] + array_const_1D0[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y2_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre sub $eq_no = 2 i = 5
> array_tmp5[5] := (array_y2[5] - (array_const_1D0[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if not array_y1_set_initial[2,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_m1,array_y1,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk] + array_const_1D0[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y2_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp3[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_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_y2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit sub $eq_no = 2
> array_tmp5[kkk] := (array_y2[kkk] - (array_const_1D0[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y1_set_initial[2,kkk + order_d] then # if number 2
> temporary := array_tmp5[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_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_y1_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 DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, glob_last;
array_tmp1[1] := array_m1[1]*array_y1[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
if not array_y2_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*glob_h*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_y2[1] - array_const_1D0[1];
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*glob_h*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_y1, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
array_tmp3[2] := array_tmp2[2] + array_const_1D0[2];
if not array_y2_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*glob_h*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := array_y2[2] - array_const_1D0[2];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*glob_h*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_y1, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
array_tmp3[3] := array_tmp2[3] + array_const_1D0[3];
if not array_y2_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*glob_h*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5[3] := array_y2[3] - array_const_1D0[3];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*glob_h*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_y1, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
array_tmp3[4] := array_tmp2[4] + array_const_1D0[4];
if not array_y2_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*glob_h*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5[4] := array_y2[4] - array_const_1D0[4];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*glob_h*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_y1, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
array_tmp3[5] := array_tmp2[5] + array_const_1D0[5];
if not array_y2_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*glob_h*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp5[5] := array_y2[5] - array_const_1D0[5];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*glob_h*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_m1, array_y1, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk] + array_const_1D0[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_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_y2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
array_tmp5[kkk] := array_y2[kkk] - array_const_1D0[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := array_tmp5[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_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_y1_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_y1 := proc(x)
> 1.0 + cos(x);
> end;
exact_soln_y1 := proc(x) 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> 1.0 - sin(x);
> end;
exact_soln_y2 := proc(x) 1.0 - sin(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
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_warned,
> glob_large_float,
> glob_clock_start_sec,
> glob_clock_sec,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_iter,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_hmin,
> hours_in_day,
> min_in_hour,
> glob_dump,
> glob_normmax,
> glob_current_iter,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_almost_1,
> days_in_year,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_abserr,
> glob_look_poles,
> glob_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> years_in_century,
> djd_debug2,
> glob_html_log,
> glob_subiter_method,
> glob_warned2,
> glob_hmax,
> glob_percent_done,
> glob_orig_start_sec,
> glob_unchanged_h_cnt,
> glob_smallish_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_display_flag,
> glob_start,
> glob_optimal_start,
> glob_optimal_done,
> centuries_in_millinium,
> glob_curr_iter_when_opt,
> sec_in_min,
> glob_max_minutes,
> glob_max_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> djd_debug,
> glob_log10normmin,
> glob_log10abserr,
> glob_relerr,
> glob_dump_analytic,
> glob_hmin_init,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_1D0,
> #END CONST
> array_pole,
> array_norms,
> array_y2,
> array_y1,
> array_1st_rel_error,
> array_y1_init,
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_last_rel_error,
> array_x,
> array_y2_init,
> array_type_pole,
> array_real_pole,
> array_y1_higher,
> array_y2_higher,
> array_y1_higher_work,
> array_poles,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher_work,
> array_complex_pole,
> array_y2_higher_work2,
> array_y2_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_max_terms := 30;
> INFO := 2;
> glob_warned := false;
> glob_large_float := 9.0e100;
> glob_clock_start_sec := 0.0;
> glob_clock_sec := 0.0;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> glob_iter := 0;
> glob_small_float := 0.1e-50;
> glob_optimal_clock_start_sec := 0.0;
> glob_hmin := 0.00000000001;
> hours_in_day := 24.0;
> min_in_hour := 60.0;
> glob_dump := false;
> glob_normmax := 0.0;
> glob_current_iter := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_max_hours := 0.0;
> glob_last_good_h := 0.1;
> glob_not_yet_finished := true;
> glob_almost_1 := 0.9990;
> days_in_year := 365.0;
> glob_max_opt_iter := 10;
> MAX_UNCHANGED := 10;
> glob_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_h := 0.1;
> glob_reached_optimal_h := false;
> glob_not_yet_start_msg := true;
> years_in_century := 100.0;
> djd_debug2 := true;
> glob_html_log := true;
> glob_subiter_method := 3;
> glob_warned2 := false;
> glob_hmax := 1.0;
> glob_percent_done := 0.0;
> glob_orig_start_sec := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_smallish_float := 0.1e-100;
> glob_disp_incr := 0.1;
> glob_initial_pass := true;
> glob_display_flag := true;
> glob_start := 0;
> glob_optimal_start := 0.0;
> glob_optimal_done := false;
> centuries_in_millinium := 10.0;
> glob_curr_iter_when_opt := 0;
> sec_in_min := 60.0;
> glob_max_minutes := 0.0;
> glob_max_sec := 10000.0;
> glob_no_eqs := 0;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> djd_debug := true;
> glob_log10normmin := 0.1;
> glob_log10abserr := 0.0;
> glob_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_hmin_init := 0.001;
> #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 := 2;
> 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/mtest3postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = y2 - 1.0;");
> 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 := 0.5;");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> 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_y1 := proc(x)");
> omniout_str(ALWAYS,"1.0 + cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"1.0 - sin(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_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_y2:= Array(1..(max_terms + 1),[]);
> array_y1:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y1_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> 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_tmp5:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y2_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> 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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y1[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_y1_init[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_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_tmp5[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_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2_init[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
> ;
> ord := 1;
> while ord <=2 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_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 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_y1_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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_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_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_set_initial[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_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> 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 := 0.5;
> glob_h := 0.00001;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_max_iter := 20;
> #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_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := false;
> array_y2_set_initial[1,3] := false;
> array_y2_set_initial[1,4] := false;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #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_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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_y2();
> if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_y1();
> if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> 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;
> if glob_subiter_method = 1 then # if number 3
> atomall();
> elif glob_subiter_method = 2 then # if number 4
> subiter := 1;
> while subiter <= 2 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 2 + glob_max_terms do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_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_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y2_higher[ord,term_no] := array_y2_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
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #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_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y1_higher[ord,term_no] := array_y1_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 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = y2 - 1.0;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T14:37:30-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest3")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;")
> ;
> 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 5
> 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 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 5
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"mtest3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest3 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = y2 - 1.0;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 5
> 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 5
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 5
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if glob_html_log then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `subiter` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp,
subiter;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_warned, glob_large_float, glob_clock_start_sec, glob_clock_sec,
glob_optimal_expect_sec, glob_log10relerr, glob_iter, glob_small_float,
glob_optimal_clock_start_sec, glob_hmin, hours_in_day, min_in_hour,
glob_dump, glob_normmax, glob_current_iter, glob_max_trunc_err,
glob_max_rel_trunc_err, glob_max_iter, glob_max_hours, glob_last_good_h,
glob_not_yet_finished, glob_almost_1, days_in_year, glob_max_opt_iter,
MAX_UNCHANGED, glob_abserr, glob_look_poles, glob_h, glob_reached_optimal_h,
glob_not_yet_start_msg, years_in_century, djd_debug2, glob_html_log,
glob_subiter_method, glob_warned2, glob_hmax, glob_percent_done,
glob_orig_start_sec, glob_unchanged_h_cnt, glob_smallish_float,
glob_disp_incr, glob_initial_pass, glob_display_flag, glob_start,
glob_optimal_start, glob_optimal_done, centuries_in_millinium,
glob_curr_iter_when_opt, sec_in_min, glob_max_minutes, glob_max_sec,
glob_no_eqs, glob_log10_relerr, glob_log10_abserr, djd_debug,
glob_log10normmin, glob_log10abserr, glob_relerr, glob_dump_analytic,
glob_hmin_init, array_const_0D0, array_const_1, array_const_1D0, array_pole,
array_norms, array_y2, array_y1, array_1st_rel_error, array_y1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_last_rel_error, array_x, array_y2_init, array_type_pole,
array_real_pole, array_y1_higher, array_y2_higher, array_y1_higher_work,
array_poles, array_y1_higher_work2, array_y1_set_initial,
array_y2_higher_work, array_complex_pole, array_y2_higher_work2,
array_y2_set_initial, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_max_terms := 30;
INFO := 2;
glob_warned := false;
glob_large_float := 0.90*10^101;
glob_clock_start_sec := 0.;
glob_clock_sec := 0.;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
glob_iter := 0;
glob_small_float := 0.1*10^(-50);
glob_optimal_clock_start_sec := 0.;
glob_hmin := 0.1*10^(-10);
hours_in_day := 24.0;
min_in_hour := 60.0;
glob_dump := false;
glob_normmax := 0.;
glob_current_iter := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_max_hours := 0.;
glob_last_good_h := 0.1;
glob_not_yet_finished := true;
glob_almost_1 := 0.9990;
days_in_year := 365.0;
glob_max_opt_iter := 10;
MAX_UNCHANGED := 10;
glob_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_h := 0.1;
glob_reached_optimal_h := false;
glob_not_yet_start_msg := true;
years_in_century := 100.0;
djd_debug2 := true;
glob_html_log := true;
glob_subiter_method := 3;
glob_warned2 := false;
glob_hmax := 1.0;
glob_percent_done := 0.;
glob_orig_start_sec := 0.;
glob_unchanged_h_cnt := 0;
glob_smallish_float := 0.1*10^(-100);
glob_disp_incr := 0.1;
glob_initial_pass := true;
glob_display_flag := true;
glob_start := 0;
glob_optimal_start := 0.;
glob_optimal_done := false;
centuries_in_millinium := 10.0;
glob_curr_iter_when_opt := 0;
sec_in_min := 60.0;
glob_max_minutes := 0.;
glob_max_sec := 10000.0;
glob_no_eqs := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
djd_debug := true;
glob_log10normmin := 0.1;
glob_log10abserr := 0.;
glob_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_hmin_init := 0.001;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
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/mtest3postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0;");
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 := 0.5;");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_max_iter := 20;");
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_y1 := proc(x)");
omniout_str(ALWAYS, "1.0 + cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "1.0 - sin(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_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_y2 := Array(1 .. max_terms + 1, []);
array_y1 := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y1_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
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_tmp5 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y2_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_y2_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_pole[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_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[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_y1_init[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_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_tmp5[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_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 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_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_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_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_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_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 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 := 0.5;
glob_h := 0.00001;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_max_iter := 20;
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_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := false;
array_y2_set_initial[1, 3] := false;
array_y2_set_initial[1, 4] := false;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 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_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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_y2();
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_y1();
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(array_y1_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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_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 ( y2 , x , 1 ) = m1 * y1 + 1.0;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0;");
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, "2012-06-13T14:37:30-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest3")
;
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
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,
"mtest3 diffeq.mxt");
logitem_str(html_log_file,
"mtest3 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = y2 - 1.0;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 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;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/mtest3postode.ode#################
diff ( y2 , x , 1 ) = m1 * y1 + 1.0;
diff ( y1 , x , 1 ) = y2 - 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 0.5;
glob_h := 0.00001;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_max_iter := 20;
#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_y1 := proc(x)
1.0 + cos(x);
end;
exact_soln_y2 := proc(x)
1.0 - sin(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y2[1] (analytic) = 0.90016658335317184769318580158938
y2[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
h = 0.0001
x[1] = 0.1
y2[1] (analytic) = 0.90016658335317184769318580158938
y2[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1001
y2[1] (analytic) = 0.90006708343597696196220785831547
y2[1] (numeric) = 0.90006708343597696196220786320329
absolute error = 4.88782e-27
relative error = 5.4305063366398261510861738417050e-25 %
h = 0.0001
y1[1] (analytic) = 1.99499417696135689993881931509
y1[1] (numeric) = 1.9949941769613568999388192667253
absolute error = 4.83647e-26
relative error = 2.4243028154430961911904215132473e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.19
NO POLE
NO POLE
x[1] = 0.1002
y2[1] (analytic) = 0.89996758451811124103868599099689
y2[1] (numeric) = 0.89996758451811124103868600078219
absolute error = 9.78530e-27
relative error = 1.0872947168691137934009595886767e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949841786947462724601257815688
y1[1] (numeric) = 1.9949841786947462724601256848403
absolute error = 9.67285e-26
relative error = 4.8485848175140082596311115080848e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1003
y2[1] (analytic) = 0.89986808660056967410044825122023
y2[1] (numeric) = 0.8998680866005696741004482659127
absolute error = 1.469247e-26
relative error = 1.6327359775035163166111398223701e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949741704782938663255043431386
y1[1] (numeric) = 1.9949741704782938663255041980474
absolute error = 1.450912e-25
relative error = 7.2728360169803337064194143601993e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.42
NO POLE
NO POLE
x[1] = 0.1004
y2[1] (analytic) = 0.89976858968434724032208115905533
y2[1] (numeric) = 0.89976858968434724032208117866463
absolute error = 1.960930e-26
relative error = 2.1793714767126118738904601832907e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949641523120997636993956593421
y1[1] (numeric) = 1.9949641523120997636993954658891
absolute error = 1.934530e-25
relative error = 9.6970664748935036726456455407201e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1005
y2[1] (analytic) = 0.89966909377043890886497991131759
y2[1] (numeric) = 0.8996690937704389088649799358534
absolute error = 2.453581e-26
relative error = 2.7272038319302984608311189290073e-24 %
h = 0.0001
y1[1] (analytic) = 1.994954124196264146243657271722
y1[1] (numeric) = 1.9949541241962641462436570299082
absolute error = 2.418138e-25
relative error = 1.2121271214566049366298799002651e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=0.65
NO POLE
NO POLE
x[1] = 0.1006
y2[1] (analytic) = 0.8995695988598396388673986899624
y2[1] (numeric) = 0.8995695988598396388673987194344
absolute error = 2.947200e-26
relative error = 3.2762334384526016667757808219710e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949440861308872951165617872037
y1[1] (numeric) = 1.9949440861308872951165614970301
absolute error = 2.901736e-25
relative error = 1.4545450271881046272923476619281e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1007
y2[1] (analytic) = 0.89947010495354437943450107071087
y2[1] (numeric) = 0.89947010495354437943450110512872
absolute error = 3.441785e-26
relative error = 3.8264584682086354639977063124019e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949340381160695909717940665135
y1[1] (numeric) = 1.994934038116069590971793727981
absolute error = 3.385325e-25
relative error = 1.6969608695418101066944360337451e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=0.88
NO POLE
NO POLE
x[1] = 0.1008
y2[1] (analytic) = 0.89937061205254806962841053200644
y2[1] (numeric) = 0.89937061205254806962841057137982
absolute error = 3.937338e-26
relative error = 4.3778815398628466370417204791365e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949239801519115139574474176422
y1[1] (numeric) = 1.9949239801519115139574470307519
absolute error = 3.868903e-25
relative error = 1.9393736495690361157344891072410e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1009
y2[1] (analytic) = 0.89927112015784563845826106440201
y2[1] (numeric) = 0.89927112015784563845826110874058
absolute error = 4.433857e-26
relative error = 4.9305008251813334662968709560461e-24 %
h = 0.0001
y1[1] (analytic) = 1.9949139122385136437150187943654
y1[1] (numeric) = 1.9949139122385136437150183591182
absolute error = 4.352472e-25
relative error = 2.1817843733998756430046423639389e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.14
NO POLE
NO POLE
x[1] = 0.101
y2[1] (analytic) = 0.89917162927043200487024788047681
y2[1] (numeric) = 0.89917162927043200487024792979025
absolute error = 4.931344e-26
relative error = 5.4843189436494827760196049988447e-24 %
h = 0.0001
y1[1] (analytic) = 1.994903834375976659378402999829
y1[1] (numeric) = 1.9949038343759766593784025162259
absolute error = 4.836031e-25
relative error = 2.4241925433527239317843771646241e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=22.8MB, alloc=4.3MB, time=1.39
x[1] = 0.1011
y2[1] (analytic) = 0.89907213939130207773767822538281
y2[1] (numeric) = 0.89907213939130207773767827968079
absolute error = 5.429798e-26
relative error = 6.0393351791282630283495611359092e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948937465644013395728858952114
y1[1] (numeric) = 1.9948937465644013395728853632534
absolute error = 5.319580e-25
relative error = 2.6665981630156298182566871292699e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1012
y2[1] (analytic) = 0.8989726505214507558510222881199
y2[1] (numeric) = 0.89897265052145075585102234741209
absolute error = 5.929219e-26
relative error = 6.5955499275319950001096094856716e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948836488038885624141366134714
y1[1] (numeric) = 1.9948836488038885624141360331595
absolute error = 5.803119e-25
relative error = 2.9090012359765892363211315934841e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=4.3MB, time=1.63
x[1] = 0.1013
y2[1] (analytic) = 0.89887316266187292790796421363949
y2[1] (numeric) = 0.89887316266187292790796427793556
absolute error = 6.429607e-26
relative error = 7.1529635849397482053389872820539e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948735410945393055071987781922
y1[1] (numeric) = 1.9948735410945393055071981495274
absolute error = 6.286648e-25
relative error = 3.1514017658235453360423722949545e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1014
y2[1] (analytic) = 0.89877367581356347250345321587596
y2[1] (numeric) = 0.89877367581356347250345328518558
absolute error = 6.930962e-26
relative error = 7.7115765475954143911280928475286e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948634234364546459454807275319
y1[1] (numeric) = 1.9948634234364546459454800505152
absolute error = 6.770167e-25
relative error = 3.3937997561443886020973687687854e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=1.86
NO POLE
NO POLE
x[1] = 0.1015
y2[1] (analytic) = 0.89867418997751725811975479180544
y2[1] (numeric) = 0.89867418997751725811975486613828
absolute error = 7.433284e-26
relative error = 8.2713892119077810709600633758015e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948532958297357603097447432905
y1[1] (numeric) = 1.9948532958297357603097440179228
absolute error = 7.253677e-25
relative error = 3.6361957118169526277973876385631e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1016
y2[1] (analytic) = 0.89857470515472914311650203663147
y2[1] (numeric) = 0.89857470515472914311650211599721
absolute error = 7.936574e-26
relative error = 8.8324030873241305391951692769127e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948431582744839246670952851026
y1[1] (numeric) = 1.994843158274483924667094511385
absolute error = 7.737176e-25
relative error = 3.8785886338515791072589332572221e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=2.10
NO POLE
NO POLE
x[1] = 0.1017
y2[1] (analytic) = 0.89847522134619397572074706019696
y2[1] (numeric) = 0.89847522134619397572074714460527
absolute error = 8.440831e-26
relative error = 9.3946174579561833368074717336082e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948330107708005145699662297676
y1[1] (numeric) = 1.9948330107708005145699654077011
absolute error = 8.220665e-25
relative error = 4.1209790271234519251118691060905e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1018
y2[1] (analytic) = 0.89837573855290659401701250472195
y2[1] (numeric) = 0.89837573855290659401701259418249
absolute error = 8.946054e-26
relative error = 9.9580316075879362858915481229673e-24 %
h = 0.0001
y1[1] (analytic) = 1.9948228533187870050551071157262
y1[1] (numeric) = 1.9948228533187870050551062453118
absolute error = 8.704144e-25
relative error = 4.3633668952202520889789176967879e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=2.33
NO POLE
NO POLE
x[1] = 0.1019
y2[1] (analytic) = 0.89827625677586182593734316396666
y2[1] (numeric) = 0.8982762567758618259373432584891
absolute error = 9.452244e-26
relative error = 1.0522647046162021507413130902143e-23 %
h = 0.0001
y1[1] (analytic) = 1.9948126859185449706425683926936
y1[1] (numeric) = 1.9948126859185449706425674739323
absolute error = 9.187613e-25
relative error = 4.6057522417296085333112533152679e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.102
y2[1] (analytic) = 0.89817677601605448925135770391935
y2[1] (numeric) = 0.89817677601605448925135780351336
absolute error = 9.959401e-26
relative error = 1.1088464170912809675179149013221e-23 %
h = 0.0001
y1[1] (analytic) = 1.9948025085701760853346856764599
y1[1] (numeric) = 1.9948025085701760853346847093526
absolute error = 9.671073e-25
relative error = 4.8481355715418566330810053493214e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=2.57
NO POLE
NO POLE
x[1] = 0.1021
y2[1] (analytic) = 0.89807729627447939155630048510842
y2[1] (numeric) = 0.89807729627447939155630058978368
absolute error = 1.0467526e-25
relative error = 1.1655484492729910531154991532538e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947923212737821226150630088674
y1[1] (numeric) = 1.9947923212737821226150619934152
absolute error = 1.0154522e-24
relative error = 5.0905158856415648672548479406004e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1022
y2[1] (analytic) = 0.89797781755213133026709348663827
y2[1] (numeric) = 0.89797781755213133026709359640445
absolute error = 1.0976618e-25
relative error = 1.2223707295935249400375437730186e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947821240294649554475551229758
y1[1] (numeric) = 1.9947821240294649554475540591797
absolute error = 1.0637961e-24
relative error = 5.3328936889164074567621953307443e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=2.80
NO POLE
NO POLE
x[1] = 0.1023
y2[1] (analytic) = 0.89787833985000509260638833204834
y2[1] (numeric) = 0.89787833985000509260638844691511
absolute error = 1.1486677e-25
relative error = 1.2793132978259509853359637356015e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947719168373265562752487134242
y1[1] (numeric) = 1.9947719168373265562752476012853
absolute error = 1.1121389e-24
relative error = 5.5752684836433598758771464806134e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1024
y2[1] (analytic) = 0.89777886316909545559461841709491
y2[1] (numeric) = 0.89777886316909545559461853707193
absolute error = 1.1997702e-25
relative error = 1.3363760823738895237336812195810e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947616996974689970194427120013
y1[1] (numeric) = 1.9947616996974689970194415515205
absolute error = 1.1604808e-24
relative error = 5.8176412760281174689778109887687e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=3.04
NO POLE
NO POLE
x[1] = 0.1025
y2[1] (analytic) = 0.89767938751039718604005113955504
y2[1] (numeric) = 0.89767938751039718604005126465198
absolute error = 1.2509694e-25
relative error = 1.3935592344048458006752010706425e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947514726099944490786275684329
y1[1] (numeric) = 1.9947514726099944490786263596113
absolute error = 1.2088216e-24
relative error = 6.0600110670345337575737272506194e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1026
y2[1] (analytic) = 0.89757991287490504052884023115219
y2[1] (numeric) = 0.89757991287490504052884036137872
absolute error = 1.3022653e-25
relative error = 1.4508627937415703089395176481869e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947412355750051833274635363984
y1[1] (numeric) = 1.9947412355750051833274622792369
absolute error = 1.2571615e-24
relative error = 6.3023788628784722979627143765285e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=3.27
NO POLE
NO POLE
x[1] = 0.1027
y2[1] (analytic) = 0.89748043926361376541507819170298
y2[1] (numeric) = 0.89748043926361376541507832706877
absolute error = 1.3536579e-25
relative error = 1.5082868002233916512884042123709e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947309885926035701157579647845
y1[1] (numeric) = 1.9947309885926035701157566592841
absolute error = 1.3055004e-24
relative error = 6.5447441658341356462811480238945e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1028
y2[1] (analytic) = 0.89738096667751809681084882558455
y2[1] (numeric) = 0.89738096667751809681084896609927
absolute error = 1.4051472e-25
relative error = 1.5658312937062239427544197604367e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947207316628920792674415941882
y1[1] (numeric) = 1.99472073166289207926744024035
absolute error = 1.3538382e-24
relative error = 6.7871064781653792690639204341137e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=3.51
NO POLE
NO POLE
x[1] = 0.1029
y2[1] (analytic) = 0.89728149511761276057627988062199
y2[1] (numeric) = 0.89728149511761276057628002629532
absolute error = 1.4567333e-25
relative error = 1.6234964255103200402121393635829e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947104647859732800795438586784
y1[1] (numeric) = 1.9947104647859732800795424565035
absolute error = 1.4021749e-24
relative error = 7.0294658034515768726895182967996e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.103
y2[1] (analytic) = 0.89718202458489247230959578949541
y2[1] (numeric) = 0.89718202458489247230959594033701
absolute error = 1.5084160e-25
relative error = 1.6812820126416518650359975986628e-23 %
h = 0.0001
y1[1] (analytic) = 1.9947001879619498413211671928266
y1[1] (numeric) = 1.9947001879619498413211657423159
absolute error = 1.4505107e-24
relative error = 7.2718231479289829117232264949020e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=3.75
NO POLE
NO POLE
x[1] = 0.1031
y2[1] (analytic) = 0.89708255508035193733717051376591
y2[1] (numeric) = 0.89708255508035193733717066978545
absolute error = 1.5601954e-25
relative error = 1.7391882064413267497086492086668e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946899011909245312324603440163
y1[1] (numeric) = 1.9946899011909245312324588451708
absolute error = 1.4988455e-24
relative error = 7.5141780138612929614999202505964e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1032
y2[1] (analytic) = 0.89698308660498585070358049062019
y2[1] (numeric) = 0.89698308660498585070358065182734
absolute error = 1.6120715e-25
relative error = 1.7972150468316749575758041378134e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946796044730002175235906900428
y1[1] (numeric) = 1.9946796044730002175235891428635
absolute error = 1.5471793e-24
relative error = 7.7565304048354622025224665714814e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=3.99
NO POLE
NO POLE
x[1] = 0.1033
y2[1] (analytic) = 0.89688361915978889716165768243304
y2[1] (numeric) = 0.89688361915978889716165784883746
absolute error = 1.6640442e-25
relative error = 1.8553624622544630044371694868388e-23 %
h = 0.0001
y1[1] (analytic) = 1.994669297808279867373715562012
y1[1] (numeric) = 1.9946692978082798673737139665
absolute error = 1.5955120e-24
relative error = 7.9988798231021583110298900261213e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1034
y2[1] (analytic) = 0.89678415274575575116254272924732
y2[1] (numeric) = 0.89678415274575575116254290085868
absolute error = 1.7161136e-25
relative error = 1.9136306041377267462724287100616e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946589811968665474299525725501
y1[1] (numeric) = 1.9946589811968665474299509287064
absolute error = 1.6438437e-24
relative error = 8.2412267735792869039292477956822e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=4.23
NO POLE
NO POLE
x[1] = 0.1035
y2[1] (analytic) = 0.89668468736388107684573820427085
y2[1] (numeric) = 0.89668468736388107684573838109882
absolute error = 1.7682797e-25
relative error = 1.9720195124536786209749869208949e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946486546388634238063489493329
y1[1] (numeric) = 1.9946486546388634238063472571586
absolute error = 1.6921743e-24
relative error = 8.4835707585122191344649005682542e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1036
y2[1] (analytic) = 0.89658522301515952802916197248966
y2[1] (numeric) = 0.89658522301515952802916215454391
absolute error = 1.8205425e-25
relative error = 2.0305292271911759304852638304815e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946383181343737620828498739466
y1[1] (numeric) = 1.9946383181343737620828481334426
absolute error = 1.7405040e-24
relative error = 8.7259127841679547397447105032189e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=4.46
NO POLE
NO POLE
x[1] = 0.1037
y2[1] (analytic) = 0.8964857597005857481992006524971
y2[1] (numeric) = 0.8964857597005857481992008397873
absolute error = 1.8729020e-25
relative error = 2.0891597883557282771818335396833e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946279716835009273042658260886
y1[1] (numeric) = 1.994627971683500927304264037256
absolute error = 1.7888326e-24
relative error = 8.9682518514477362371437803484555e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1038
y2[1] (analytic) = 0.8963862974211543705007631816383
y2[1] (numeric) = 0.89638629742115437050076337417411
absolute error = 1.9253581e-25
relative error = 2.1479111244104592135541387241541e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946176152863483839792389331209
y1[1] (numeric) = 1.9946176152863483839792370959608
absolute error = 1.8371601e-24
relative error = 9.2105879639304012769534780923851e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=4.70
NO POLE
NO POLE
x[1] = 0.1039
y2[1] (analytic) = 0.8962868361778600177273344845693
y2[1] (numeric) = 0.89628683617786001772733468236039
absolute error = 1.9779109e-25
relative error = 2.2067833869284915701701896403368e-23 %
h = 0.0001
y1[1] (analytic) = 1.9946072489430196960792083249843
y1[1] (numeric) = 1.9946072489430196960792064394976
absolute error = 1.8854867e-24
relative error = 9.4529221278983882685103120853502e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.104
y2[1] (analytic) = 0.89618737597169730231102924533054
y2[1] (numeric) = 0.89618737597169730231102944838658
absolute error = 2.0305604e-25
relative error = 2.2657766159653286508606274814618e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945968726536185270373744944846
y1[1] (numeric) = 1.9945968726536185270373725606724
absolute error = 1.9338122e-24
relative error = 9.6952533442371721466760228681454e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=4.93
NO POLE
NO POLE
x[1] = 0.1041
y2[1] (analytic) = 0.89608791680366082631264578303401
y2[1] (numeric) = 0.89608791680366082631264599136466
absolute error = 2.0833065e-25
relative error = 2.3248907399969629618433803572446e-23 %
h = 0.0001
y1[1] (analytic) = 1.994586486418248639747662662962
y1[1] (numeric) = 1.9945864864182486397476606808252
absolute error = 1.9821368e-24
relative error = 9.9375826192395146846107019516002e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1042
y2[1] (analytic) = 0.8959884586747451814117200312635
y2[1] (numeric) = 0.89598845867474518141172024487844
absolute error = 2.1361494e-25
relative error = 2.3841260222922675802817109907548e-23 %
h = 0.0001
y1[1] (analytic) = 1.994576090237013896563685151352
y1[1] (numeric) = 1.9945760902370138965636831208918
absolute error = 2.0304602e-24
relative error = 1.0179908452420694680557499957789e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=5.17
NO POLE
NO POLE
x[1] = 0.1043
y2[1] (analytic) = 0.89588900158594494889657962128759
y2[1] (numeric) = 0.89588900158594494889657984019648
absolute error = 2.1890889e-25
relative error = 2.4434822797520358221933293946844e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945656841100182592977027566508
y1[1] (numeric) = 1.9945656841100182592977006778683
absolute error = 2.0787825e-24
relative error = 1.0422231348713690317864994863112e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1044
y2[1] (analytic) = 0.89578954553825469965439806918463
y2[1] (numeric) = 0.89578954553825469965439829339713
absolute error = 2.2421250e-25
relative error = 2.5029595524613655296041673374922e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945552680373657892195851337935
y1[1] (numeric) = 1.9945552680373657892195830066896
absolute error = 2.1271039e-24
relative error = 1.0664552314426772046758791761361e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=5.41
NO POLE
NO POLE
x[1] = 0.1045
y2[1] (analytic) = 0.89569009053266899416124906697927
y2[1] (numeric) = 0.89569009053266899416124929650506
absolute error = 2.2952579e-25
relative error = 2.5625581038135687672528214059815e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945448420191606470557701829557
y1[1] (numeric) = 1.9945448420191606470557680075315
absolute error = 2.1754242e-24
relative error = 1.0906870350419034252393397143634e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1046
y2[1] (analytic) = 0.89559063657018238247216087789009
y2[1] (numeric) = 0.89559063657018238247216111273882
absolute error = 2.3484873e-25
relative error = 2.6222776390270604484927615957184e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945344060555070929882224422906
y1[1] (numeric) = 1.9945344060555070929882202185471
absolute error = 2.2237435e-24
relative error = 1.1149185961638979667761279473377e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=5.64
NO POLE
NO POLE
x[1] = 0.1047
y2[1] (analytic) = 0.89549118365178940421117083578751
y2[1] (numeric) = 0.89549118365178940421117107596885
absolute error = 2.4018134e-25
relative error = 2.6821184215409786251351618183253e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945239601465094866533904861099
y1[1] (numeric) = 1.9945239601465094866533882140481
absolute error = 2.2720618e-24
relative error = 1.1391499151672781763461937822704e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1048
y2[1] (analytic) = 0.89539173177848458856137994896177
y2[1] (numeric) = 0.89539173177848458856138019448539
absolute error = 2.4552362e-25
relative error = 2.7420804915444685927502918580131e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945135042922722871411633285203
y1[1] (numeric) = 1.9945135042922722871411610081413
absolute error = 2.3203790e-24
relative error = 1.1633809422731168388145415318046e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=5.87
NO POLE
NO POLE
x[1] = 0.1049
y2[1] (analytic) = 0.89529228095126245425500760830018
y2[1] (numeric) = 0.89529228095126245425500785917574
absolute error = 2.5087556e-25
relative error = 2.8021637775480503503784914104313e-23 %
h = 0.0001
y1[1] (analytic) = 1.9945030384929000529938258325255
y1[1] (numeric) = 1.9945030384929000529938234638303
absolute error = 2.3686952e-24
relative error = 1.1876117279770351076015910918776e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.105
y2[1] (analytic) = 0.89519283117111750956344639997322
y2[1] (numeric) = 0.89519283117111750956344665621039
absolute error = 2.5623717e-25
relative error = 2.8623684314449102671132969520713e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944925627484974422050131246041
y1[1] (numeric) = 1.9944925627484974422050107075938
absolute error = 2.4170103e-24
relative error = 1.2118422224995688883912891124507e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=6.11
NO POLE
NO POLE
x[1] = 0.1051
y2[1] (analytic) = 0.89509338243904425228731702272891
y2[1] (numeric) = 0.89509338243904425228731728433735
absolute error = 2.6160844e-25
relative error = 2.9226943817542467658400857585116e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944820770591692122186640147742
y1[1] (numeric) = 1.9944820770591692122186615494498
absolute error = 2.4653244e-24
relative error = 1.2360724763368543247781589931111e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1052
y2[1] (analytic) = 0.89499393475603716974652330989487
y2[1] (numeric) = 0.89499393475603716974652357688425
absolute error = 2.6698938e-25
relative error = 2.9831417804275687206757498079947e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944715814250202199279734221549
y1[1] (numeric) = 1.9944715814250202199279709085175
absolute error = 2.5136374e-24
relative error = 1.2603024397088894794832207384841e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.4MB, time=6.35
NO POLE
NO POLE
x[1] = 0.1053
y2[1] (analytic) = 0.89489448812309073877030735618759
y2[1] (numeric) = 0.89489448812309073877030762856758
absolute error = 2.7237999e-25
relative error = 3.0437106677377896703561883616407e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944610758461554216743438060354
y1[1] (numeric) = 1.994461075846155421674341244086
absolute error = 2.5619494e-24
relative error = 1.2845321631123265445867036309684e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1054
y2[1] (analytic) = 0.89479504254119942568730474942828
y2[1] (numeric) = 0.89479504254119942568730502720855
absolute error = 2.7778027e-25
relative error = 3.1044010839746024389011968131994e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944505603226798732463356024613
y1[1] (numeric) = 1.994450560322679873246332992201
absolute error = 2.6102603e-24
relative error = 1.3087615967666247760213588499366e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=6.58
NO POLE
NO POLE
x[1] = 0.1055
y2[1] (analytic) = 0.89469559801135768631559990726483
y2[1] (numeric) = 0.89469559801135768631560019045503
absolute error = 2.8319020e-25
relative error = 3.1652128459047705132154974009024e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944400348546987298786166663504
y1[1] (numeric) = 1.9944400348546987298786140077803
absolute error = 2.6585701e-24
relative error = 1.3329907410295668516961153113694e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1056
y2[1] (analytic) = 0.8945961545345599659527815189992
y2[1] (numeric) = 0.89459615453455996595278180760901
absolute error = 2.8860981e-25
relative error = 3.2261463291238689230323401858297e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944294994423172462509107191469
y1[1] (numeric) = 1.994429499442317246250908012268
absolute error = 2.7068789e-24
relative error = 1.3572196463985806416551327968279e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=6.83
NO POLE
NO POLE
x[1] = 0.1057
y2[1] (analytic) = 0.89449671211180069936599809261988
y2[1] (numeric) = 0.89449671211180069936599838665896
absolute error = 2.9403908e-25
relative error = 3.2872013504198197545372428195997e-23 %
h = 0.0001
y1[1] (analytic) = 1.9944189540856407764869448020247
y1[1] (numeric) = 1.994418954085640776486942046838
absolute error = 2.7551867e-24
relative error = 1.3814483132322315934920720487333e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1058
y2[1] (analytic) = 0.89439727074407431078201360713865
y2[1] (numeric) = 0.89439727074407431078201390661666
absolute error = 2.9947801e-25
relative error = 3.3483779501122113046393408961272e-23 %
h = 0.0001
y1[1] (analytic) = 1.994408398784774774153395734651
y1[1] (numeric) = 1.9944083987847747741533929311577
absolute error = 2.8034933e-24
relative error = 1.4056766416087165067426755319297e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=7.07
NO POLE
NO POLE
x[1] = 0.1059
y2[1] (analytic) = 0.89429783043237521387726327033124
y2[1] (numeric) = 0.89429783043237521387726357525785
absolute error = 3.0492661e-25
relative error = 3.4096762803570042085737911550106e-23 %
h = 0.0001
y1[1] (analytic) = 1.994397833539824792258835579521
y1[1] (numeric) = 1.994397833539824792258832727722
absolute error = 2.8517990e-24
relative error = 1.4299047823063403558870414717874e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.106
y2[1] (analytic) = 0.89419839117769781176790938198128
y2[1] (numeric) = 0.89419839117769781176790969236615
absolute error = 3.1038487e-25
relative error = 3.4710962697126948738116227842107e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943872583508964832526761118722
y1[1] (numeric) = 1.9943872583508964832526732117687
absolute error = 2.9001035e-24
relative error = 1.4541325852623101694767913330124e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=7.31
NO POLE
NO POLE
x[1] = 0.1061
y2[1] (analytic) = 0.89409895298103649699989730272694
y2[1] (numeric) = 0.89409895298103649699989761857973
absolute error = 3.1585279e-25
relative error = 3.5326379585493052137879266897594e-23 %
h = 0.0001
y1[1] (analytic) = 1.994376673218095599024112295192
y1[1] (numeric) = 1.994376673218095599024109346785
absolute error = 2.9484070e-24
relative error = 1.4783601511155341101751245832350e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1062
y2[1] (analytic) = 0.89399951584338565153901152860976
y2[1] (numeric) = 0.89399951584338565153901184994014
absolute error = 3.2133038e-25
relative error = 3.5943014991105646051105414796801e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943660781415279909010647623259
y1[1] (numeric) = 1.9943660781415279909010617656165
absolute error = 2.9967094e-24
relative error = 1.5025874300833058091490039927935e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=7.54
NO POLE
NO POLE
x[1] = 0.1063
y2[1] (analytic) = 0.89390007976573964676093187142512
y2[1] (numeric) = 0.89390007976573964676093219824276
absolute error = 3.2681764e-25
relative error = 3.6560869318374780950069815609230e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943554731212996096491213021998
y1[1] (numeric) = 1.994355473121299609649118257189
absolute error = 3.0450108e-24
relative error = 1.5268144726648728185174047657678e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=125.8MB, alloc=4.4MB, time=7.78
x[1] = 0.1064
y2[1] (analytic) = 0.89380064474909284344128974497372
y2[1] (numeric) = 0.89380064474909284344129007728827
absolute error = 3.3231455e-25
relative error = 3.7179940734243611124995809829645e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943448581575165054704773521646
y1[1] (numeric) = 1.9943448581575165054704742588535
absolute error = 3.0933111e-24
relative error = 1.5510412290769851428348903707051e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1065
y2[1] (analytic) = 0.89370121079443959174572455731352
y2[1] (numeric) = 0.89370121079443959174572489513465
absolute error = 3.3782113e-25
relative error = 3.7800231880596871091720799738547e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943342332502848280028754959752
y1[1] (numeric) = 1.9943342332502848280028723543648
absolute error = 3.1416104e-24
relative error = 1.5752677498194127334011277421046e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=129.7MB, alloc=4.4MB, time=8.03
x[1] = 0.1066
y2[1] (analytic) = 0.89360177790277423121994020911169
y2[1] (numeric) = 0.89360177790277423121994055244906
absolute error = 3.4333737e-25
relative error = 3.8421742043283606143437411460649e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943235983997108263185439674139
y1[1] (numeric) = 1.9943235983997108263185407775055
absolute error = 3.1899084e-24
relative error = 1.5994938848237330928907995868337e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1067
y2[1] (analytic) = 0.89350234607509109077976169819579
y2[1] (numeric) = 0.89350234607509109077976204705906
absolute error = 3.4886327e-25
relative error = 3.9044471627014740973727679673240e-23 %
h = 0.0001
y1[1] (analytic) = 1.9943129536059008489231341595696
y1[1] (numeric) = 1.994312953605900848923130921364
absolute error = 3.2382056e-24
relative error = 1.6237198851589601760806555434090e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=8.27
NO POLE
NO POLE
x[1] = 0.1068
y2[1] (analytic) = 0.89340291531238448870119183040385
y2[1] (numeric) = 0.89340291531238448870119218480269
absolute error = 3.5439884e-25
relative error = 3.9668422155985690092828251544531e-23 %
h = 0.0001
y1[1] (analytic) = 1.994302298868961343754657139781
y1[1] (numeric) = 1.9943022988689613437546538532795
absolute error = 3.2865015e-24
relative error = 1.6479455004709617315380098525869e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1069
y2[1] (analytic) = 0.89330348561564873261046803683264
y2[1] (numeric) = 0.89330348561564873261046839677671
absolute error = 3.5994407e-25
relative error = 4.0293592916178201844620316446931e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942916341889988581824191702586
y1[1] (numeric) = 1.9942916341889988581824158354622
absolute error = 3.3347964e-24
relative error = 1.6721708815451820787721718372148e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=8.50
NO POLE
NO POLE
x[1] = 0.107
y2[1] (analytic) = 0.89320405698587811947411929758354
y2[1] (numeric) = 0.8932040569858781194741196630825
absolute error = 3.6549896e-25
relative error = 4.0919984312809572392690564478114e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942809595661200390059562343918
y1[1] (numeric) = 1.9942809595661200390059528513015
absolute error = 3.3830903e-24
relative error = 1.6963960287401190666636127376009e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1071
y2[1] (analytic) = 0.89310462942406693558902317210554
y2[1] (numeric) = 0.89310462942406693558902354316906
absolute error = 3.7106352e-25
relative error = 4.1547597870955652039038768914009e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942702750004316324539675687545
y1[1] (numeric) = 1.9942702750004316324539641373714
absolute error = 3.4313831e-24
relative error = 1.7206208922706112761881893708220e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=8.73
NO POLE
NO POLE
x[1] = 0.1072
y2[1] (analytic) = 0.89300520293120945657246293623481
y2[1] (numeric) = 0.89300520293120945657246331287254
absolute error = 3.7663773e-25
relative error = 4.2176431756917030706698754074008e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942595804920404841832482008192
y1[1] (numeric) = 1.9942595804920404841832447211445
absolute error = 3.4796747e-24
relative error = 1.7448454223504170974381261688217e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1073
y2[1] (analytic) = 0.89290577750829994735218482603007
y2[1] (numeric) = 0.89290577750829994735218520825167
absolute error = 3.8222160e-25
relative error = 4.2806487495982977226789624199049e-23 %
h = 0.0001
y1[1] (analytic) = 1.99424887604105353927762049239
y1[1] (numeric) = 1.9942488760410535392776169644247
absolute error = 3.5279653e-24
relative error = 1.7690697196247904149655063386872e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=8.98
NO POLE
NO POLE
x[1] = 0.1074
y2[1] (analytic) = 0.89280635315633266215645538850346
y2[1] (numeric) = 0.8928063531563326621564557763186
absolute error = 3.8781514e-25
relative error = 4.3437766614110617005304046968139e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942381616475778422468646887649
y1[1] (numeric) = 1.9942381616475778422468611125101
absolute error = 3.5762548e-24
relative error = 1.7932937343077463620064420918604e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1075
y2[1] (analytic) = 0.89270692987630184450411893934616
y2[1] (numeric) = 0.8927069298763018445041193327645
absolute error = 3.9341834e-25
relative error = 4.4070268397548354321597065891651e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942274373117205370256484736392
y1[1] (numeric) = 1.9942274373117205370256448490959
absolute error = 3.6245433e-24
relative error = 1.8175175169016804895047109069978e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=9.22
NO POLE
NO POLE
x[1] = 0.1076
y2[1] (analytic) = 0.89260750766920172719465512774823
y2[1] (numeric) = 0.89260750766920172719465552677943
absolute error = 3.9903120e-25
relative error = 4.4703993252528191545794299020993e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942167030335888669724555297596
y1[1] (numeric) = 1.9942167030335888669724518569289
absolute error = 3.6728307e-24
relative error = 1.8417410176200585187664256458348e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1077
y2[1] (analytic) = 0.89250808653602653229823660841207
y2[1] (numeric) = 0.8925080865360265322982370130658
absolute error = 4.0465373e-25
relative error = 4.5338942705889528224726479070790e-23 %
h = 0.0001
y1[1] (analytic) = 1.9942059588132901748685131053403
y1[1] (numeric) = 1.9942059588132901748685093842233
absolute error = 3.7211170e-24
relative error = 1.8659642368205328667149821163465e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=9.46
NO POLE
NO POLE
x[1] = 0.1078
y2[1] (analytic) = 0.89240866647777047114578682085902
y2[1] (numeric) = 0.89240866647777047114578723114494
absolute error = 4.1028592e-25
relative error = 4.5975116044014802458976597490282e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941952046509319029167185862516
y1[1] (numeric) = 1.9941952046509319029167148168494
absolute error = 3.7694022e-24
relative error = 1.8901871748607499235561875077220e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1079
y2[1] (analytic) = 0.89230924749542774431903787612839
y2[1] (numeric) = 0.89230924749542774431903829205615
absolute error = 4.1592776e-25
relative error = 4.6612512552956730760906044206450e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941844405466215927405650739918
y1[1] (numeric) = 1.9941844405466215927405612563055
absolute error = 3.8176863e-24
relative error = 1.9144098320983500645608297536300e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=9.70
NO POLE
NO POLE
x[1] = 0.108
y2[1] (analytic) = 0.89220982958999254164058855096841
y2[1] (numeric) = 0.89220982958999254164058897254769
absolute error = 4.2157928e-25
relative error = 4.7251136001688434856907100140821e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941736665004668853830659694533
y1[1] (numeric) = 1.994173666500466885383062103484
absolute error = 3.8659693e-24
relative error = 1.9386322088909676618470821202427e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1081
y2[1] (analytic) = 0.89211041276245904216396238961858
y2[1] (numeric) = 0.89211041276245904216396281685902
absolute error = 4.2724044e-25
relative error = 4.7890982314289015938932830317248e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941628825125755213056785624931
y1[1] (numeric) = 1.9941628825125755213056746482419
absolute error = 3.9142512e-24
relative error = 1.9628543055962310961627437149991e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=9.93
NO POLE
NO POLE
x[1] = 0.1082
y2[1] (analytic) = 0.89201099701382141416366591328264
y2[1] (numeric) = 0.89201099701382141416366634619391
absolute error = 4.3291127e-25
relative error = 4.8532055260445649375813087322054e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941520885830553403872266273193
y1[1] (numeric) = 1.9941520885830553403872226647873
absolute error = 3.9625320e-24
relative error = 1.9870761225717627686673166120844e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1083
y2[1] (analytic) = 0.89191158234507381512524693739185
y2[1] (numeric) = 0.89191158234507381512524737598361
absolute error = 4.3859176e-25
relative error = 4.9174354126765020543434610875951e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941412847120142819228220237039
y1[1] (numeric) = 1.9941412847120142819228180128921
absolute error = 4.0108118e-24
relative error = 2.0112977103220773122773431437379e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=10.16
NO POLE
NO POLE
x[1] = 0.1084
y2[1] (analytic) = 0.89181216875721039173535299675779
y2[1] (numeric) = 0.8918121687572103917353534410397
absolute error = 4.4428191e-25
relative error = 4.9817879320836295299398749108182e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941304708995603846227853040322
y1[1] (numeric) = 1.9941304708995603846227812449418
absolute error = 4.0590904e-24
relative error = 2.0355189689112607428435767918068e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1085
y2[1] (analytic) = 0.89171275625122527987178987871414
y2[1] (numeric) = 0.89171275625122527987179032869586
absolute error = 4.4998172e-25
relative error = 5.0462631250418617249259864616495e-23 %
h = 0.0001
y1[1] (analytic) = 1.9941196471458017866115653262008
y1[1] (numeric) = 1.9941196471458017866115612188329
absolute error = 4.1073679e-24
relative error = 2.0597399488435441083156817724962e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.4MB, time=10.40
NO POLE
NO POLE
x[1] = 0.1086
y2[1] (analytic) = 0.89161334482811260459358026434694
y2[1] (numeric) = 0.89161334482811260459358072003812
absolute error = 4.5569118e-25
relative error = 5.1108609201878787176021374236911e-23 %
h = 0.0001
y1[1] (analytic) = 1.994108813450846725426657872374
y1[1] (numeric) = 1.9941088134508467254266537167297
absolute error = 4.1556443e-24
relative error = 2.0839606504765260093229678445215e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1087
y2[1] (analytic) = 0.89151393448886648013102247791261
y2[1] (numeric) = 0.89151393448886648013102293932292
absolute error = 4.6141031e-25
relative error = 5.1755815826315863831108103628108e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940979698148035380175232736096
y1[1] (numeric) = 1.99409796981480353801751906969
absolute error = 4.2039196e-24
relative error = 2.1081810741677991258144120966365e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=10.64
NO POLE
NO POLE
x[1] = 0.1088
y2[1] (analytic) = 0.89141452523448100987574934454329
y2[1] (numeric) = 0.89141452523448100987574981168239
absolute error = 4.6713910e-25
relative error = 5.2404250410562020449408500764122e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940871162377806607445030403653
y1[1] (numeric) = 1.9940871162377806607444987881715
absolute error = 4.2521938e-24
relative error = 2.1324012202749502288397703891217e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1089
y2[1] (analytic) = 0.89131511706595028637078715633878
y2[1] (numeric) = 0.89131511706595028637078762921633
absolute error = 4.7287755e-25
relative error = 5.3053913363057073809974945683971e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940762527198866293777354988961
y1[1] (numeric) = 1.9940762527198866293777311984292
absolute error = 4.3004669e-24
relative error = 2.1566210891555601923305302838011e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=10.89
NO POLE
NO POLE
x[1] = 0.109
y2[1] (analytic) = 0.89121570998426839130061474694456
y2[1] (numeric) = 0.89121570998426839130061522557021
absolute error = 4.7862565e-25
relative error = 5.3704803970348394062015258319345e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940653792612300790960704335539
y1[1] (numeric) = 1.994065379261230079096066084815
absolute error = 4.3487389e-24
relative error = 2.1808406811672040048807061585538e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1091
y2[1] (analytic) = 0.89111630399042939548122267471527
y2[1] (numeric) = 0.89111630399042939548122315909869
absolute error = 4.8438342e-25
relative error = 5.4356924885217035183920614026219e-23 %
h = 0.0001
y1[1] (analytic) = 1.994054495861919744485982735
y1[1] (numeric) = 1.9940544958619197444859783379902
absolute error = 4.3970098e-24
relative error = 2.2050599966674507815274772022886e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=11.13
NO POLE
NO POLE
x[1] = 0.1092
y2[1] (analytic) = 0.89101689908542735885017251456312
y2[1] (numeric) = 0.89101689908542735885017300471396
absolute error = 4.9015084e-25
relative error = 5.5010274272363287196518602453200e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940436025220644595404850543411
y1[1] (numeric) = 1.9940436025220644595404806090614
absolute error = 4.4452797e-24
relative error = 2.2292790861632185205934593747771e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1093
y2[1] (analytic) = 0.89091749527025633045665625859053
y2[1] (numeric) = 0.89091749527025633045665675451846
absolute error = 4.9592793e-25
relative error = 5.5664854785409978519158451747255e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940326992417731576580394631999
y1[1] (numeric) = 1.9940326992417731576580349696515
absolute error = 4.4935484e-24
relative error = 2.2534978497136293496153614333824e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=11.37
NO POLE
NO POLE
x[1] = 0.1094
y2[1] (analytic) = 0.89081809254591034845155582560653
y2[1] (numeric) = 0.8908180925459103484515563273212
absolute error = 5.0171467e-25
relative error = 5.6320664588897871608619688627216e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940217860211548716414681197318
y1[1] (numeric) = 1.9940217860211548716414635779159
absolute error = 4.5418159e-24
relative error = 2.2777162876754121904556490040784e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1095
y2[1] (analytic) = 0.89071869091338344007750267962617
y2[1] (numeric) = 0.89071869091338344007750318713724
absolute error = 5.0751107e-25
relative error = 5.6977705214603173537723667038036e-23 %
h = 0.0001
y1[1] (analytic) = 1.9940108628603187336968629405976
y1[1] (numeric) = 1.9940108628603187336968583505152
absolute error = 4.5900824e-24
relative error = 2.3019345007056449150374784244893e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.4MB, time=11.61
NO POLE
NO POLE
x[1] = 0.1096
y2[1] (analytic) = 0.89061929037366962165893755745254
y2[1] (numeric) = 0.89061929037366962165893807076967
absolute error = 5.1331713e-25
relative error = 5.7635977072159739829465034844626e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939999297593739754324942789029
y1[1] (numeric) = 1.9939999297593739754324896405552
absolute error = 4.6383477e-24
relative error = 2.3261523888617853671990941781393e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1097
y2[1] (analytic) = 0.89051989092776289859217030544061
y2[1] (numeric) = 0.89051989092776289859217082457346
absolute error = 5.1913285e-25
relative error = 5.8295480571372320465834926597626e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939889867184299278577186081169
y1[1] (numeric) = 1.993988986718429927857713921505
absolute error = 4.6866119e-24
relative error = 2.3503700026512703358313845565733e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.4MB, time=11.85
NO POLE
NO POLE
x[1] = 0.1098
y2[1] (analytic) = 0.89042049257665726533543982554245
y2[1] (numeric) = 0.89042049257665726533544035050068
absolute error = 5.2495823e-25
relative error = 5.8956216122216636537647637365944e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939780337375960213818852119796
y1[1] (numeric) = 1.9939780337375960213818804771046
absolute error = 4.7348750e-24
relative error = 2.3745873424316273918543451579665e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1099
y2[1] (analytic) = 0.89032109532134670539897413073309
y2[1] (numeric) = 0.89032109532134670539897466152635
absolute error = 5.3079326e-25
relative error = 5.9618183011649177319934722550092e-23 %
h = 0.0001
y1[1] (analytic) = 1.993967070816981785813241880409
y1[1] (numeric) = 1.993967070816981785813237097272
absolute error = 4.7831370e-24
relative error = 2.3988044085603783268485294625778e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=12.09
NO POLE
NO POLE
x[1] = 0.11
y2[1] (analytic) = 0.89022169916282519133505050991655
y2[1] (numeric) = 0.89022169916282519133505104655449
absolute error = 5.3663794e-25
relative error = 6.0281381649611612644998879582561e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939560979566968503578396114198
y1[1] (numeric) = 1.9939560979566968503578347800219
absolute error = 4.8313979e-24
relative error = 2.4230212013950391648342784250416e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1101
y2[1] (analytic) = 0.89012230410208668472805580241131
y2[1] (numeric) = 0.8901223041020866847280563449036
absolute error = 5.4249229e-25
relative error = 6.0945814693098897822844692831353e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939451151568509436184363190638
y1[1] (numeric) = 1.9939451151568509436184314394061
absolute error = 4.8796577e-24
relative error = 2.4472377212931201740507999053210e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.4MB, time=12.33
NO POLE
NO POLE
x[1] = 0.1102
y2[1] (analytic) = 0.89002291014012513618454678211479
y2[1] (numeric) = 0.89002291014012513618454733047108
absolute error = 5.4835629e-25
relative error = 6.1611480306014463078920295783505e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939341224175538935933995474028
y1[1] (numeric) = 1.9939341224175538935933946194865
absolute error = 4.9279163e-24
relative error = 2.4714539184600176040873006575308e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1103
y2[1] (analytic) = 0.889923517277934485323310651446
y2[1] (numeric) = 0.88992351727793448532331120567595
absolute error = 5.5422995e-25
relative error = 6.2278380022505563814283788721997e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939231197389156276756081905265
y1[1] (numeric) = 1.9939231197389156276756032143527
absolute error = 4.9761738e-24
relative error = 2.4956698434047850323307608260802e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.4MB, time=12.57
NO POLE
NO POLE
x[1] = 0.1104
y2[1] (analytic) = 0.88982412551650866076542564516599
y2[1] (numeric) = 0.88982412551650866076542620527926
absolute error = 5.6011327e-25
relative error = 6.2946514253575199731783061168196e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939121071210461726513532186242
y1[1] (numeric) = 1.993912107121046172651348194194
absolute error = 5.0244302e-24
relative error = 2.5198854964849147711859728842610e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1105
y2[1] (analytic) = 0.88972473485684158012432174417534
y2[1] (numeric) = 0.88972473485684158012432231018159
absolute error = 5.6600625e-25
relative error = 6.3615883410397879236242582802844e-23 %
h = 0.0001
y1[1] (analytic) = 1.9939010845640556546992374101228
y1[1] (numeric) = 1.9939010845640556546992323374374
absolute error = 5.0726854e-24
relative error = 2.5441008279049541566401992885123e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.4MB, time=12.81
NO POLE
NO POLE
x[1] = 0.1106
y2[1] (analytic) = 0.88962534529992714999584149938814
y2[1] (numeric) = 0.88962534529992714999584207129702
absolute error = 5.7190888e-25
relative error = 6.4286486780251002445028110059780e-23 %
h = 0.0001
y1[1] (analytic) = 1.9938900520680542993890740899021
y1[1] (numeric) = 1.9938900520680542993890689689625
absolute error = 5.1209396e-24
relative error = 2.5683159383279851271394459787415e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1107
y2[1] (analytic) = 0.88952595684675926594830096578185
y2[1] (numeric) = 0.88952595684675926594830154360302
absolute error = 5.7782117e-25
relative error = 6.4958325898469831323259529280056e-23 %
h = 0.0001
y1[1] (analytic) = 1.993879009633152431680784873597
y1[1] (numeric) = 1.9938790096331524316807797044043
absolute error = 5.1691927e-24
relative error = 2.5925307779588208873751655004739e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.4MB, time=13.04
NO POLE
NO POLE
x[1] = 0.1108
y2[1] (analytic) = 0.88942656949833181251255074672242
y2[1] (numeric) = 0.88942656949833181251255133046553
absolute error = 5.8374311e-25
relative error = 6.5631400052423872952843275467796e-23 %
h = 0.0001
y1[1] (analytic) = 1.9938679572594604759232964179994
y1[1] (numeric) = 1.9938679572594604759232912005549
absolute error = 5.2174445e-24
relative error = 2.6167452468473859088568288207605e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1109
y2[1] (analytic) = 0.88932718325563866317203714866406
y2[1] (numeric) = 0.88932718325563866317203773833877
absolute error = 5.8967471e-25
relative error = 6.6305710778042974467395042875029e-23 %
h = 0.0001
y1[1] (analytic) = 1.9938568949470889558534361775704
y1[1] (numeric) = 1.9938568949470889558534309118751
absolute error = 5.2656953e-24
relative error = 2.6409594958116269043833137911522e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.4MB, time=13.28
NO POLE
NO POLE
x[1] = 0.111
y2[1] (analytic) = 0.88922779811967368035286344632307
y2[1] (numeric) = 0.88922779811967368035286404193904
absolute error = 5.9561597e-25
relative error = 6.6981258487360182910241336963638e-23 %
h = 0.0001
y1[1] (analytic) = 1.993845822696148494594827167072
y1[1] (numeric) = 1.9938458226961484945948218531271
absolute error = 5.3139449e-24
relative error = 2.6651734249011775055999819541515e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1111
y2[1] (analytic) = 0.8891284140914307154138512584251
y2[1] (numeric) = 0.88912841409143071541385185999198
absolute error = 6.0156688e-25
relative error = 6.7658042467883583769555106559979e-23 %
h = 0.0001
y1[1] (analytic) = 1.9938347405067498146567817303326
y1[1] (numeric) = 1.9938347405067498146567763681392
absolute error = 5.3621934e-24
relative error = 2.6893870846272613312599783260266e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.4MB, time=13.52
NO POLE
NO POLE
x[1] = 0.1112
y2[1] (analytic) = 0.88902903117190360863660203412518
y2[1] (numeric) = 0.88902903117190360863660264165263
absolute error = 6.0752745e-25
relative error = 6.8336064256435720324971013175275e-23 %
h = 0.0001
y1[1] (analytic) = 1.9938236483790037379331943151542
y1[1] (numeric) = 1.9938236483790037379331889047136
absolute error = 5.4104406e-24
relative error = 2.7136003750375496171283503285041e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1113
y2[1] (analytic) = 0.88892964936208618921555865020002
y2[1] (numeric) = 0.8889296493620861892155592636977
absolute error = 6.1349768e-25
relative error = 6.9015324265565704220543149065197e-23 %
h = 0.0001
y1[1] (analytic) = 1.993812546313021185701433254375
y1[1] (numeric) = 1.9938125463130211857014277956882
absolute error = 5.4586868e-24
relative error = 2.7378134469533057038980775943670e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=13.76
NO POLE
NO POLE
x[1] = 0.1114
y2[1] (analytic) = 0.88883026866297227524806711911186
y2[1] (numeric) = 0.88883026866297227524806773858942
absolute error = 6.1947756e-25
relative error = 6.9695821782920653707185966740094e-23 %
h = 0.0001
y1[1] (analytic) = 1.9938014343089131786212315530961
y1[1] (numeric) = 1.9938014343089131786212260461642
absolute error = 5.5069319e-24
relative error = 2.7620262505773549822308268438464e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1115
y2[1] (analytic) = 0.88873088907555567372443840804326
y2[1] (numeric) = 0.88873088907555567372443903351036
absolute error = 6.2546710e-25
relative error = 7.0377558346216743417444806081137e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937903123667908367335766820852
y1[1] (numeric) = 1.9937903123667908367335711269094
absolute error = 5.5551758e-24
relative error = 2.7862387361113996438368673184591e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.4MB, time=14.00
NO POLE
NO POLE
x[1] = 0.1116
y2[1] (analytic) = 0.88863151060083018051801036900233
y2[1] (numeric) = 0.88863151060083018051801100046862
absolute error = 6.3146629e-25
relative error = 7.1060533243194006235256803364918e-23 %
h = 0.0001
y1[1] (analytic) = 1.993779180486765379459599377368
y1[1] (numeric) = 1.9937791804867653794595937739494
absolute error = 5.6034186e-24
relative error = 2.8104509540680276212386185287341e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1117
y2[1] (analytic) = 0.88853213323978958037520978009757
y2[1] (numeric) = 0.8885321332397895803752104175727
absolute error = 6.3747513e-25
relative error = 7.1744746886713164317164219029315e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937680386689481255994614460173
y1[1] (numeric) = 1.9937680386689481255994557943571
absolute error = 5.6516602e-24
relative error = 2.8346628546483688774413761623900e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.4MB, time=14.23
NO POLE
NO POLE
x[1] = 0.1118
y2[1] (analytic) = 0.88843275699342764690561449808192
y2[1] (numeric) = 0.88843275699342764690561514157555
absolute error = 6.4349363e-25
relative error = 7.2430200815384879887376730436640e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937568869134504933312425781528
y1[1] (numeric) = 1.9937568869134504933312368782521
absolute error = 5.6999007e-24
relative error = 2.8588744883655587726608993483627e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1119
y2[1] (analytic) = 0.88833338186273814257201572226527
y2[1] (numeric) = 0.88833338186273814257201637178705
absolute error = 6.4952178e-25
relative error = 7.3116894317088897514074564082261e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937457252203840002098261651608
y1[1] (numeric) = 1.9937457252203840002098204170208
absolute error = 5.7481400e-24
relative error = 2.8830858054201540756925449587117e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.4MB, time=14.47
NO POLE
NO POLE
x[1] = 0.112
y2[1] (analytic) = 0.88823400784871481868048036989479
y2[1] (numeric) = 0.88823400784871481868048102545438
absolute error = 6.5555959e-25
relative error = 7.3804828931032752043746807372735e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937345535898602631657841241467
y1[1] (numeric) = 1.9937345535898602631657783277685
absolute error = 5.7963782e-24
relative error = 2.9072968563258386339591035551045e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=236.5MB, alloc=4.4MB, time=14.70
x[1] = 0.1121
y2[1] (analytic) = 0.8881346349523514153704135631026
y2[1] (numeric) = 0.88813463495235141537041422470965
absolute error = 6.6160705e-25
relative error = 7.4494003945189609513853846065716e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937233720219909985042607286298
y1[1] (numeric) = 1.9937233720219909985042548840147
absolute error = 5.8446151e-24
relative error = 2.9315075411251853559792080334882e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1122
y2[1] (analytic) = 0.88803526317464166160462122751994
y2[1] (numeric) = 0.8880352631746416616046218951841
absolute error = 6.6766416e-25
relative error = 7.5184419773282885956764688971524e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937121805168880219038554454933
y1[1] (numeric) = 1.9937121805168880219038495526423
absolute error = 5.8928510e-24
relative error = 2.9557180106469654833382676442274e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=240.3MB, alloc=4.4MB, time=14.94
x[1] = 0.1123
y2[1] (analytic) = 0.88793589251657927515937280265742
y2[1] (numeric) = 0.88793589251657927515937347638835
absolute error = 6.7373093e-25
relative error = 7.5876077955416167193132283957371e-23 %
h = 0.0001
y1[1] (analytic) = 1.9937009790746632484155047781987
y1[1] (numeric) = 1.9937009790746632484154988371129
absolute error = 5.9410858e-24
relative error = 2.9799282150914311606084919921790e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1124
y2[1] (analytic) = 0.88783652297915796261446406415063
y2[1] (numeric) = 0.88783652297915796261446474395798
absolute error = 6.7980735e-25
relative error = 7.6568977779703092364738009550670e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936897676954286924613631162776
y1[1] (numeric) = 1.9936897676954286924613571269582
absolute error = 5.9893194e-24
relative error = 3.0041381046577023264144267665909e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.4MB, time=15.18
NO POLE
NO POLE
x[1] = 0.1125
y2[1] (analytic) = 0.88773715456337141934328005797041
y2[1] (numeric) = 0.88773715456337141934328074386384
absolute error = 6.8589343e-25
relative error = 7.7263120786845163382024850105011e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936785463792964678336825911111
y1[1] (numeric) = 1.9936785463792964678336765535594
absolute error = 6.0375517e-24
relative error = 3.0283476295437641935389240633010e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1126
y2[1] (analytic) = 0.88763778727021332950285814669733
y2[1] (numeric) = 0.88763778727021332950285883868649
absolute error = 6.9198916e-25
relative error = 7.7958506265049949320207823535537e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936673151263787876936919380085
y1[1] (numeric) = 1.9936673151263787876936858522255
absolute error = 6.0857830e-24
relative error = 3.0525569405817447303053738866391e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.4MB, time=15.41
NO POLE
NO POLE
x[1] = 0.1127
y2[1] (analytic) = 0.88753842110067736602395116795956
y2[1] (numeric) = 0.8875384211006773660239518660541
absolute error = 6.9809454e-25
relative error = 7.8655134628905499766868711681586e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936560739367879645704743645952
y1[1] (numeric) = 1.9936560739367879645704682305821
absolute error = 6.1340131e-24
relative error = 3.0767659378116431517813073182794e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1128
y2[1] (analytic) = 0.88743905605575719060109070513365
y2[1] (numeric) = 0.88743905605575719060109140934323
absolute error = 7.0420958e-25
relative error = 7.9353007420010934520457577581863e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936448228106364103598444255236
y1[1] (numeric) = 1.9936448228106364103598382432816
absolute error = 6.1822420e-24
relative error = 3.1009746215899619576958609908839e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.4MB, time=15.65
NO POLE
NO POLE
x[1] = 0.1129
y2[1] (analytic) = 0.88733969213644645368265047040748
y2[1] (numeric) = 0.88733969213644645368265118074175
absolute error = 7.1033427e-25
relative error = 8.0052123926715059626156876702229e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936335617480366363232239035154
y1[1] (numeric) = 1.9936335617480366363232176730456
absolute error = 6.2304698e-24
relative error = 3.1251830424328659207619247430089e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.113
y2[1] (analytic) = 0.8872403293437387944609098003048
y2[1] (numeric) = 0.88724032934373879446091051677341
absolute error = 7.1646861e-25
relative error = 8.0752484564125621825971158660522e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936222907491012530865166967484
y1[1] (numeric) = 1.9936222907491012530865104180521
absolute error = 6.2786963e-24
relative error = 3.1493911003777888038398059438334e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.4MB, time=15.89
NO POLE
NO POLE
x[1] = 0.1131
y2[1] (analytic) = 0.88714096767862784086211726377074
y2[1] (numeric) = 0.88714096767862784086211798638334
absolute error = 7.2261260e-25
relative error = 8.1454089747523729163156602769299e-23 %
h = 0.0001
y1[1] (analytic) = 1.9936110098139429706389827125988
y1[1] (numeric) = 1.993611009813942970638976385677
absolute error = 6.3269218e-24
relative error = 3.1735989462610714576283312644032e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1132
y2[1] (analytic) = 0.88704160714210720953655438291757
y2[1] (numeric) = 0.88704160714210720953655511168381
absolute error = 7.2876624e-25
relative error = 8.2156939892363928908504666640958e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935997189426745983321107677489
y1[1] (numeric) = 1.9935997189426745983321043926028
absolute error = 6.3751461e-24
relative error = 3.1978064801198517529130177133071e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.4MB, time=16.13
NO POLE
NO POLE
x[1] = 0.1133
y2[1] (analytic) = 0.88694224773517050584859946653018
y2[1] (numeric) = 0.88694224773517050584860020145972
absolute error = 7.3492954e-25
relative error = 8.2861036541743410549782067016854e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935884181354090448784904946734
y1[1] (numeric) = 1.9935884181354090448784840713043
absolute error = 6.4233691e-24
relative error = 3.2220136521497940447891082583911e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1134
y2[1] (analytic) = 0.88684288945881132386679155643061
y2[1] (numeric) = 0.88684288945881132386679229753309
absolute error = 7.4110248e-25
relative error = 8.3566377856651900768453933366686e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935771073922593183506832545148
y1[1] (numeric) = 1.9935771073922593183506767829238
absolute error = 6.4715910e-24
relative error = 3.2462205630286863716129121247576e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.4MB, time=16.36
NO POLE
NO POLE
x[1] = 0.1135
y2[1] (analytic) = 0.88674353231402324635389448680087
y2[1] (numeric) = 0.88674353231402324635389523408595
absolute error = 7.4728508e-25
relative error = 8.4272966508129353321569191720362e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935657867133385261800920563583
y1[1] (numeric) = 1.9935657867133385261800855365465
absolute error = 6.5198118e-24
relative error = 3.2704272131138381564390014352420e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1136
y2[1] (analytic) = 0.88664417630179984475696105656365
y2[1] (numeric) = 0.88664417630179984475696181004098
absolute error = 7.5347733e-25
relative error = 8.4980801784855808057558862326576e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935544560987598751558304829188
y1[1] (numeric) = 1.9935544560987598751558239148874
absolute error = 6.5680314e-24
relative error = 3.2946335526008938888303563136319e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.4MB, time=16.60
NO POLE
NO POLE
x[1] = 0.1137
y2[1] (analytic) = 0.88654482142313467919739731492003
y2[1] (numeric) = 0.88654482142313467919739807459926
absolute error = 7.5967923e-25
relative error = 8.5689884103154259337272318857829e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935431155486366714235906226508
y1[1] (numeric) = 1.993543115548636671423584006401
absolute error = 6.6162498e-24
relative error = 3.3188395818462962607292226337836e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1138
y2[1] (analytic) = 0.88644546767902129846102696014371
y2[1] (numeric) = 0.8864454676790212984610277260345
absolute error = 7.6589079e-25
relative error = 8.6400215007622588269394581650525e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935317650630823204845100082923
y1[1] (numeric) = 1.9935317650630823204845033438253
absolute error = 6.6644670e-24
relative error = 3.3430453012064811241746416140210e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.4MB, time=16.84
NO POLE
NO POLE
x[1] = 0.1139
y2[1] (analytic) = 0.88634611507045323998815585173106
y2[1] (numeric) = 0.88634611507045323998815662384306
absolute error = 7.7211200e-25
relative error = 8.7111793787083606595962633362495e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935204046422103271940375618546
y1[1] (numeric) = 1.9935204046422103271940308491715
absolute error = 6.7126831e-24
relative error = 3.3672507612003939072324252912192e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.114
y2[1] (analytic) = 0.88624676359842402986363663600634
y2[1] (numeric) = 0.88624676359842402986363741434919
absolute error = 7.7834285e-25
relative error = 8.7824619730028438072743551066436e-23 %
h = 0.0001
y1[1] (analytic) = 1.9935090342861342957607985460685
y1[1] (numeric) = 1.9935090342861342957607917851705
absolute error = 6.7608980e-24
relative error = 3.3914559120225126358818605664173e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.4MB, time=17.07
NO POLE
NO POLE
x[1] = 0.1141
y2[1] (analytic) = 0.88614741326392718280693348528143
y2[1] (numeric) = 0.88614741326392718280693426986479
absolute error = 7.8458336e-25
relative error = 8.8538695510057570437921726039447e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934976539949679297454585222991
y1[1] (numeric) = 1.9934976539949679297454517131874
absolute error = 6.8091117e-24
relative error = 3.4156607540292534725400561325051e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1142
y2[1] (analytic) = 0.8860480640679562021621869506695
y2[1] (numeric) = 0.88604806406795620216218774150302
absolute error = 7.9083352e-25
relative error = 8.9254020416136969003989646625322e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934862637688250320595863149402
y1[1] (numeric) = 1.9934862637688250320595794576159
absolute error = 6.8573243e-24
relative error = 3.4398653377404012848374848696540e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.4MB, time=17.31
NO POLE
NO POLE
x[1] = 0.1143
y2[1] (analytic) = 0.88594871601150457988827892865187
y2[1] (numeric) = 0.8859487160115045798882797257452
absolute error = 7.9709333e-25
relative error = 8.9970594865634328775044279043888e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934748636078195049645159822992
y1[1] (numeric) = 1.9934748636078195049645090767636
absolute error = 6.9055356e-24
relative error = 3.4640695631858945356271103710776e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1144
y2[1] (analytic) = 0.88584936909556579654889774149746
y2[1] (numeric) = 0.88584936909556579654889854486025
absolute error = 8.0336279e-25
relative error = 9.0688419276091722287065129997292e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934634535120653500702077939853
y1[1] (numeric) = 1.9934634535120653500702008402395
absolute error = 6.9537458e-24
relative error = 3.4882735310491674176595342024739e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.4MB, time=17.55
NO POLE
NO POLE
x[1] = 0.1145
y2[1] (analytic) = 0.88575002332113332130260333163422
y2[1] (numeric) = 0.88575002332113332130260414127611
absolute error = 8.0964189e-25
relative error = 9.1407492936238973376172664611087e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934520334816766683341082148102
y1[1] (numeric) = 1.9934520334816766683341012128554
absolute error = 7.0019548e-24
relative error = 3.5124771915232342532054009028223e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1146
y2[1] (analytic) = 0.88565067868920061189289257007174
y2[1] (numeric) = 0.88565067868920061189289338600239
absolute error = 8.1593065e-25
relative error = 9.2127818521813914427340943889990e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934406035167676600600088952151
y1[1] (numeric) = 1.9934406035167676600600018450525
absolute error = 7.0501626e-24
relative error = 3.5366805449644781166318751702054e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.4MB, time=17.79
NO POLE
NO POLE
x[1] = 0.1147
y2[1] (analytic) = 0.88555133520076111463826467897465
y2[1] (numeric) = 0.8855513352007611146382655012037
absolute error = 8.2222905e-25
relative error = 9.2849394192782118191227663176864e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934291636174526248969046682334
y1[1] (numeric) = 1.9934291636174526248968975698642
absolute error = 7.0983692e-24
relative error = 3.5608835917292753478867616638611e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1148
y2[1] (analytic) = 0.88545199285680826442228676848583
y2[1] (numeric) = 0.88545199285680826442228759702294
absolute error = 8.2853711e-25
relative error = 9.3572222625737281456029754623806e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934177137838459618378505530019
y1[1] (numeric) = 1.9934177137838459618378434064273
absolute error = 7.1465746e-24
relative error = 3.5850863321739955642128593154466e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.4MB, time=18.02
NO POLE
NO POLE
x[1] = 0.1149
y2[1] (analytic) = 0.88535265165833548468365948789907
y2[1] (numeric) = 0.88535265165833548468366032275388
absolute error = 8.3485481e-25
relative error = 9.4296301980487771004368815288047e-23 %
h = 0.0001
y1[1] (analytic) = 1.9934062540160621692188177648311
y1[1] (numeric) = 1.9934062540160621692188105700523
absolute error = 7.1947788e-24
relative error = 3.6092887666550016718621217378311e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.115
y2[1] (analytic) = 0.8852533116063361874062827912803
y2[1] (numeric) = 0.88525331160633618740628363246247
absolute error = 8.4118217e-25
relative error = 9.5021634934483678144315369532734e-23 %
h = 0.0001
y1[1] (analytic) = 1.9933947843142158447175487318465
y1[1] (numeric) = 1.9933947843142158447175414888647
absolute error = 7.2429818e-24
relative error = 3.6334908955286498778096244221943e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.4MB, time=18.26
NO POLE
NO POLE
x[1] = 0.1151
y2[1] (analytic) = 0.88515397270180377310932181763692
y2[1] (numeric) = 0.88515397270180377310932266515609
absolute error = 8.4751917e-25
relative error = 9.5748219647376262559403890894839e-23 %
h = 0.0001
y1[1] (analytic) = 1.9933833046784216853524111182121
y1[1] (numeric) = 1.9933833046784216853524038270285
absolute error = 7.2911836e-24
relative error = 3.6576927191512897014673394142038e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1152
y2[1] (analytic) = 0.88505463494573163083727288573437
y2[1] (numeric) = 0.88505463494573163083727373960019
absolute error = 8.5386582e-25
relative error = 9.6476057667598789890377559498005e-23 %
h = 0.0001
y1[1] (analytic) = 1.9933718151087944874812508539478
y1[1] (numeric) = 1.9933718151087944874812435145635
absolute error = 7.3393843e-24
relative error = 3.6818942880455195951348106588592e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.4MB, time=18.50
NO POLE
NO POLE
x[1] = 0.1153
y2[1] (analytic) = 0.88495529833911313815002960365948
y2[1] (numeric) = 0.8849552983391131381500304638816
absolute error = 8.6022212e-25
relative error = 9.7205149414266184479959667040076e-23 %
h = 0.0001
y1[1] (analytic) = 1.9933603156054491468002441713515
y1[1] (numeric) = 1.9933603156054491468002367837678
absolute error = 7.3875837e-24
relative error = 3.7060955022354539250528432467657e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1154
y2[1] (analytic) = 0.88485596288294166111294909322981
y2[1] (numeric) = 0.88485596288294166111294995981787
absolute error = 8.6658806e-25
relative error = 9.7935494176541099114894418771488e-23 %
h = 0.0001
y1[1] (analytic) = 1.9933488061685006583427486480388
y1[1] (numeric) = 1.9933488061685006583427412122569
absolute error = 7.4357819e-24
relative error = 3.7302964122433886760124789217958e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.4MB, time=18.74
NO POLE
NO POLE
x[1] = 0.1155
y2[1] (analytic) = 0.88475662857821055428691832934833
y2[1] (numeric) = 0.88475662857821055428691920231199
absolute error = 8.7296366e-25
relative error = 9.8667094634016852509846685783629e-23 %
h = 0.0001
y1[1] (analytic) = 1.9933372867980641164781532566102
y1[1] (numeric) = 1.9933372867980641164781457726313
absolute error = 7.4839789e-24
relative error = 3.7544970184256467343130185901508e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1156
y2[1] (analytic) = 0.88465729542591316071842059440288
y2[1] (numeric) = 0.88465729542591316071842147375179
absolute error = 8.7934891e-25
relative error = 9.9399950076333517475527717363848e-23 %
h = 0.0001
y1[1] (analytic) = 1.993325757494254714910727420958
y1[1] (numeric) = 1.9933257574942547149107198887833
absolute error = 7.5321747e-24
relative error = 3.7786973211385443572566745990562e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.4MB, time=18.98
NO POLE
NO POLE
x[1] = 0.1157
y2[1] (analytic) = 0.88455796342704281192960204780957
y2[1] (numeric) = 0.88455796342704281192960293355337
absolute error = 8.8574380e-25
relative error = 1.0013405979279898194320615499808e-22 %
h = 0.0001
y1[1] (analytic) = 1.9933142182571877466784690792248
y1[1] (numeric) = 1.9933142182571877466784614988554
absolute error = 7.5803694e-24
relative error = 3.8028973709060963484921005188192e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1158
y2[1] (analytic) = 0.8844586325825928279083384107996
y2[1] (numeric) = 0.88445863258259282790833930294794
absolute error = 8.9214834e-25
relative error = 1.0086942533365901532110842975434e-22 %
h = 0.0001
y1[1] (analytic) = 1.9933026690869786041519517534242
y1[1] (numeric) = 1.9933026690869786041519441248614
absolute error = 7.6285628e-24
relative error = 3.8270970677494860862463041073326e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.4MB, time=19.21
NO POLE
NO POLE
x[1] = 0.1159
y2[1] (analytic) = 0.88435930289355651709830176654879
y2[1] (numeric) = 0.88435930289355651709830266511133
absolute error = 8.9856254e-25
relative error = 1.0160604824984274707131255469538e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932911099837427790331706257364
y1[1] (numeric) = 1.9932911099837427790331629489814
absolute error = 7.6767550e-24
relative error = 3.8512964621924247570615164587044e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.116
y2[1] (analytic) = 0.88425997436092717638902747574917
y2[1] (numeric) = 0.88425997436092717638902838073554
absolute error = 9.0498637e-25
relative error = 1.0234392556940646498567550630088e-22 %
h = 0.0001
y1[1] (analytic) = 1.993279540947595862354387621489
y1[1] (numeric) = 1.9932795409475958623543798965429
absolute error = 7.7249461e-24
relative error = 3.8754956047597801562529544403205e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.4MB, time=19.45
NO POLE
NO POLE
x[1] = 0.1161
y2[1] (analytic) = 0.88416064698569809110598120772183
y2[1] (numeric) = 0.88416064698569809110598211914168
absolute error = 9.1141985e-25
relative error = 1.0308305997413870935636293591211e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932679619786535444769754988352
y1[1] (numeric) = 1.9932679619786535444769677256993
absolute error = 7.7731359e-24
relative error = 3.8996943954709711292526704469769e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1162
y2[1] (analytic) = 0.8840613207688625350006260871706
y2[1] (numeric) = 0.88406132076886253500062700503358
absolute error = 9.1786298e-25
relative error = 1.0382345188473355851762434970838e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932563730770316150902609451413
y1[1] (numeric) = 1.9932563730770316150902531238168
absolute error = 7.8213245e-24
relative error = 3.9238928848505611644362107148910e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.4MB, time=19.69
NO POLE
NO POLE
x[1] = 0.1163
y2[1] (analytic) = 0.88396199571141377024048995667569
y2[1] (numeric) = 0.88396199571141377024049088099144
absolute error = 9.2431575e-25
relative error = 1.0456510059079061148226125637215e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932447742428459632103666800944
y1[1] (numeric) = 1.9932447742428459632103588105825
absolute error = 7.8695119e-24
relative error = 3.9480910732548204440811857726582e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1164
y2[1] (analytic) = 0.88386267181434504739923275502665
y2[1] (numeric) = 0.88386267181434504739923368580483
absolute error = 9.3077818e-25
relative error = 1.0530800877576935772862533692115e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932331654762125771790525655419
y1[1] (numeric) = 1.9932331654762125771790446478438
absolute error = 7.9176981e-24
relative error = 3.9722889610400126151639838196613e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.4MB, time=19.93
NO POLE
NO POLE
x[1] = 0.1165
y2[1] (analytic) = 0.8837633490786496054467140114941
y2[1] (numeric) = 0.88376334907864960544671494874435
absolute error = 9.3725025e-25
relative error = 1.0605217459822384907600831976361e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932215467772475446625557220749
y1[1] (numeric) = 1.9932215467772475446625477561919
absolute error = 7.9658830e-24
relative error = 3.9964864983923571744530426825321e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1166
y2[1] (analytic) = 0.88366402750532067173906045613937
y2[1] (numeric) = 0.88366402750532067173906139987133
absolute error = 9.4373196e-25
relative error = 1.0679759847917059748816396291665e-22 %
h = 0.0001
y1[1] (analytic) = 1.9932099181460670526504296523672
y1[1] (numeric) = 1.9932099181460670526504216383004
absolute error = 8.0140668e-24
relative error = 4.0206837860078872885371911428566e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.4MB, time=20.16
NO POLE
NO POLE
x[1] = 0.1167
y2[1] (analytic) = 0.88356470709535146200873374626153
y2[1] (numeric) = 0.88356470709535146200873469648485
absolute error = 9.5022332e-25
relative error = 1.0754428197158116624878977751642e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931982795827873874543823712802
y1[1] (numeric) = 1.9931982795827873874543743090308
absolute error = 8.0622494e-24
relative error = 4.0448807740731018868762915918078e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1168
y2[1] (analytic) = 0.88346538784973518035459830908104
y2[1] (numeric) = 0.88346538784973518035459926580537
absolute error = 9.5672433e-25
relative error = 1.0829222549720590947852369791175e-22 %
h = 0.0001
y1[1] (analytic) = 1.993186631087524934707113542747
y1[1] (numeric) = 1.9931866310875249347071054323163
absolute error = 8.1104307e-24
relative error = 4.0690774127733221110135092413305e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.4MB, time=20.40
NO POLE
NO POLE
x[1] = 0.1169
y2[1] (analytic) = 0.8833660697694650192319893007594
y2[1] (numeric) = 0.88336606976946501923199026399439
absolute error = 9.6323499e-25
relative error = 1.0904142947797153205988606975086e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931749726603961793611506234465
y1[1] (numeric) = 1.9931749726603961793611424648357
absolute error = 8.1586108e-24
relative error = 4.0932737526351086715735133585361e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.117
y2[1] (analytic) = 0.88326675285553415944278068185407
y2[1] (numeric) = 0.88326675285553415944278165160935
absolute error = 9.6975528e-25
relative error = 1.0979189207165955444323148996053e-22 %
h = 0.0001
y1[1] (analytic) = 1.993163304301517705687684013279
y1[1] (numeric) = 1.9931633043015177056876758064893
absolute error = 8.2067897e-24
relative error = 4.1174697940146854893483184167893e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.4MB, time=20.65
NO POLE
NO POLE
x[1] = 0.1171
y2[1] (analytic) = 0.88316743710893577012545340930797
y2[1] (numeric) = 0.88316743710893577012545438559319
absolute error = 9.7628522e-25
relative error = 1.1054361596436197189918570620090e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931516260110061972754012126552
y1[1] (numeric) = 1.9931516260110061972753929576879
absolute error = 8.2549673e-24
relative error = 4.1416654870964724148890695428899e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1172
y2[1] (analytic) = 0.883068122530663008745163745073
y2[1] (numeric) = 0.88306812253066300874516472789781
absolute error = 9.8282481e-25
relative error = 1.1129660157853485570983271525004e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931399377889784370293199866104
y1[1] (numeric) = 1.9931399377889784370293116834666
absolute error = 8.3031438e-24
relative error = 4.1658609325799814890426034549536e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.4MB, time=20.89
NO POLE
NO POLE
x[1] = 0.1173
y2[1] (analytic) = 0.88296880912170902108381168146673
y2[1] (numeric) = 0.88296880912170902108381267084078
absolute error = 9.8937405e-25
relative error = 1.1205084933681094596355902580019e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931282396355513071696205357551
y1[1] (numeric) = 1.9931282396355513071696121844361
absolute error = 8.3513190e-24
relative error = 4.1900560304775273482621386465391e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1174
y2[1] (analytic) = 0.88286949688306694123010948336167
y2[1] (numeric) = 0.8828694968830669412301104792946
absolute error = 9.9593293e-25
relative error = 1.1280635852932949675973166665418e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931165315508417892304766740745
y1[1] (numeric) = 1.9931165315508417892304682745815
absolute error = 8.3994930e-24
relative error = 4.2142508313171050267162036425180e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.4MB, time=21.14
NO POLE
NO POLE
x[1] = 0.1175
y2[1] (analytic) = 0.88277018581572989156965034730644
y2[1] (numeric) = 0.88277018581572989156965134980789
absolute error = 1.00250145e-24
relative error = 1.1356312957869455074817840839310e-22 %
h = 0.0001
y1[1] (analytic) = 1.9931048135349669640588860135875
y1[1] (numeric) = 1.9931048135349669640588775659218
absolute error = 8.4476657e-24
relative error = 4.2384452852819295225910565961683e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=343.3MB, alloc=4.4MB, time=21.40
x[1] = 0.1176
y2[1] (analytic) = 0.88267087592069098277497717767809
y2[1] (numeric) = 0.88267087592069098277497818675771
absolute error = 1.00907962e-24
relative error = 1.1432116404061200628996572588943e-22 %
h = 0.0001
y1[1] (analytic) = 1.9930930855880440118134991558777
y1[1] (numeric) = 1.9930930855880440118134906600405
absolute error = 8.4958372e-24
relative error = 4.2626394429005709992126580313845e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1177
y2[1] (analytic) = 0.88257156719894331379565147996498
y2[1] (numeric) = 0.88257156719894331379565249563241
absolute error = 1.01566743e-24
relative error = 1.1508046120536932241175622909880e-22 %
h = 0.0001
y1[1] (analytic) = 1.9930813477101902119634478905081
y1[1] (numeric) = 1.9930813477101902119634393465006
absolute error = 8.5440075e-24
relative error = 4.2868333045292069289555368917182e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.4MB, time=21.66
NO POLE
NO POLE
x[1] = 0.1178
y2[1] (analytic) = 0.8824722596514799718483223712794
y2[1] (numeric) = 0.88247225965147997184832339354429
absolute error = 1.02226489e-24
relative error = 1.1584102262928119289310715170577e-22 %
h = 0.0001
y1[1] (analytic) = 1.9930695999015229432871724003303
y1[1] (numeric) = 1.9930695999015229432871638081538
absolute error = 8.5921765e-24
relative error = 4.3110268203501459420574886908144e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1179
y2[1] (analytic) = 0.88237295327929403240679570819939
y2[1] (numeric) = 0.88237295327929403240679673707139
absolute error = 1.02887200e-24
relative error = 1.1660284873604179953416052141608e-22 %
h = 0.0001
y1[1] (analytic) = 1.9930578421621596838712474737017
y1[1] (numeric) = 1.9930578421621596838712388333573
absolute error = 8.6403444e-24
relative error = 4.3352200910669817281300446868399e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.4MB, time=21.91
NO POLE
NO POLE
x[1] = 0.118
y2[1] (analytic) = 0.88227364808337855919210333203896
y2[1] (numeric) = 0.8822736480833785591921043675277
absolute error = 1.03548874e-24
relative error = 1.1736593768265217099376663575427e-22 %
h = 0.0001
y1[1] (analytic) = 1.99304607449221801110920772362
y1[1] (numeric) = 1.9930460744922180111091990351091
absolute error = 8.6885109e-24
relative error = 4.3594129665133965287443148137551e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1181
y2[1] (analytic) = 0.882174344064726604162572431646
y2[1] (numeric) = 0.88217434406472660416257347376113
absolute error = 1.04211513e-24
relative error = 1.1813029215952105192914298490945e-22 %
h = 0.0001
y1[1] (analytic) = 1.9930342968918156017003718137897
y1[1] (numeric) = 1.9930342968918156017003630771134
absolute error = 8.7366763e-24
relative error = 4.3836055975680170314478928311496e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.4MB, time=22.15
NO POLE
NO POLE
x[1] = 0.1182
y2[1] (analytic) = 0.88207504122433120750389502382733
y2[1] (numeric) = 0.88207504122433120750389607257849
absolute error = 1.04875116e-24
relative error = 1.1889591145718398874357644232152e-22 %
h = 0.0001
y1[1] (analytic) = 1.993022509361070231648665691629
y1[1] (numeric) = 1.9930225093610702316486569067886
absolute error = 8.7848404e-24
relative error = 4.4077978842377817805557787658821e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1183
y2[1] (analytic) = 0.88197573956318539761919755150003
y2[1] (numeric) = 0.88197573956318539761919860689687
absolute error = 1.05539684e-24
relative error = 1.1966279713347949587551634130981e-22 %
h = 0.0001
y1[1] (analytic) = 1.9930107119000997762614448282322
y1[1] (numeric) = 1.9930107119000997762614359952289
absolute error = 8.8330033e-24
relative error = 4.4319898770532833846226886902584e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.4MB, time=22.39
NO POLE
NO POLE
x[1] = 0.1184
y2[1] (analytic) = 0.88187643908228219111911059966849
y2[1] (numeric) = 0.88187643908228219111911166172064
absolute error = 1.06205215e-24
relative error = 1.2043094734509703549739033276832e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929989045090222101483154652967
y1[1] (numeric) = 1.9929989045090222101483065841318
absolute error = 8.8811649e-24
relative error = 4.4561815261950112094563007680829e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1185
y2[1] (analytic) = 0.88177713978261459281183872932631
y2[1] (numeric) = 0.88177713978261459281183979804342
absolute error = 1.06871711e-24
relative error = 1.2120036478417572795089893396877e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929870871879556072199548690282
y1[1] (numeric) = 1.992987087187955607219945939703
absolute error = 8.9293252e-24
relative error = 4.4803728320181980204602453285008e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.4MB, time=22.64
NO POLE
NO POLE
x[1] = 0.1186
y2[1] (analytic) = 0.8816778416651755956932304293826
y2[1] (numeric) = 0.88167784166517559569323150477431
absolute error = 1.07539171e-24
relative error = 1.2197104874145048973287923070033e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929752599370181406869305910349
y1[1] (numeric) = 1.9929752599370181406869216135505
absolute error = 8.9774844e-24
relative error = 4.5045638952305438099197187420455e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1187
y2[1] (analytic) = 0.88157854473095818093684818671172
y2[1] (numeric) = 0.88157854473095818093684926878767
absolute error = 1.08207595e-24
relative error = 1.2274299964165189603253992220195e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929634227563280830585187362225
y1[1] (numeric) = 1.9929634227563280830585097105802
absolute error = 9.0256423e-24
relative error = 4.5287546158359828155252277770767e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.4MB, time=22.88
NO POLE
NO POLE
x[1] = 0.1188
y2[1] (analytic) = 0.88147924898095531788403867442595
y2[1] (numeric) = 0.88147924898095531788403976319579
absolute error = 1.08876984e-24
relative error = 1.2351621904414488051988299012321e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929515756460038061415212377028
y1[1] (numeric) = 1.9929515756460038061415121639038
absolute error = 9.0737990e-24
relative error = 4.5529450443665597706186238424696e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1189
y2[1] (analytic) = 0.88137995441615996403400305847032
y2[1] (numeric) = 0.88137995441615996403400415394369
absolute error = 1.09547337e-24
relative error = 1.2429070623981446276627931301568e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929397186061637810390821387263
y1[1] (numeric) = 1.9929397186061637810390730167719
absolute error = 9.1219544e-24
relative error = 4.5771351310012410835325994335743e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.4MB, time=23.11
NO POLE
NO POLE
x[1] = 0.119
y2[1] (analytic) = 0.88128066103756506503386742263883
y2[1] (numeric) = 0.88128066103756506503386852482537
absolute error = 1.10218654e-24
relative error = 1.2506646165392465163196703148983e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929278516369265781495028816522
y1[1] (numeric) = 1.9929278516369265781494937115437
absolute error = 9.1701085e-24
relative error = 4.6013248760952229232078127714318e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1191
y2[1] (analytic) = 0.88118136884616355466875331211147
y2[1] (numeric) = 0.88118136884616355466875442102083
absolute error = 1.10890936e-24
relative error = 1.2584348684675755404514763418873e-22 %
h = 0.0001
y1[1] (analytic) = 1.992915974738410867165056603966
y1[1] (numeric) = 1.9929159747384108671650473857046
absolute error = 9.2182614e-24
relative error = 4.6255143301814238718959351592427e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.4MB, time=23.36
NO POLE
NO POLE
x[1] = 0.1192
y2[1] (analytic) = 0.88108207784294835485184839561134
y2[1] (numeric) = 0.88108207784294835485184951125315
absolute error = 1.11564181e-24
relative error = 1.2662177997438072830323053182121e-22 %
h = 0.0001
y1[1] (analytic) = 1.9929040879107354170708014413578
y1[1] (numeric) = 1.9929040879107354170707921749449
absolute error = 9.2664129e-24
relative error = 4.6497033932598636097252167579627e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1193
y2[1] (analytic) = 0.88098278802891237561447724628095
y2[1] (numeric) = 0.88098278802891237561447836866486
absolute error = 1.12238391e-24
relative error = 1.2740134373240050689414798195275e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928921911540190961433928378731
y1[1] (numeric) = 1.9928921911540190961433835233098
absolute error = 9.3145633e-24
relative error = 4.6738922162198042078565134734939e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.4MB, time=23.61
NO POLE
NO POLE
x[1] = 0.1194
y2[1] (analytic) = 0.88088349940504851509617224137733
y2[1] (numeric) = 0.88088349940504851509617337051297
absolute error = 1.12913564e-24
relative error = 1.2818217627672918849546419525518e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928802844683808719498948631466
y1[1] (numeric) = 1.9928802844683808719498855004341
absolute error = 9.3627125e-24
relative error = 4.6980807492395809372060352635843e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1195
y2[1] (analytic) = 0.88078421197234965953474458088493
y2[1] (numeric) = 0.88078421197234965953474571678195
absolute error = 1.13589702e-24
relative error = 1.2896428030384121628449198771505e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928683678539398113465905367329
y1[1] (numeric) = 1.9928683678539398113465811258726
absolute error = 9.4108603e-24
relative error = 4.7222688923173953881955567817022e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.4MB, time=23.87
NO POLE
NO POLE
x[1] = 0.1196
y2[1] (analytic) = 0.88068492573180868325635542514582
y2[1] (numeric) = 0.88068492573180868325635656781386
absolute error = 1.14266804e-24
relative error = 1.2974765510497359695583472145372e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928564413108150804777911595449
y1[1] (numeric) = 1.992856441310815080477781700538
absolute error = 9.4590069e-24
relative error = 4.7464567461659571014006990771350e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1197
y2[1] (analytic) = 0.88058564068441844866558715160633
y2[1] (numeric) = 0.88058564068441844866558830105503
absolute error = 1.14944870e-24
relative error = 1.3053230110663772006984545721794e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928445048391259447746446524112
y1[1] (numeric) = 1.9928445048391259447746351452589
absolute error = 9.5071523e-24
relative error = 4.7706443111413114975425915960200e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.4MB, time=24.12
NO POLE
NO POLE
x[1] = 0.1198
y2[1] (analytic) = 0.8804863568311718062355147307795
y2[1] (numeric) = 0.8804863568311718062355158870185
absolute error = 1.15623900e-24
relative error = 1.3131821873552348259439074792963e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928325584389917689539429017658
y1[1] (numeric) = 1.9928325584389917689539333464694
absolute error = 9.5552964e-24
relative error = 4.7948315374196673585016702432032e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1199
y2[1] (analytic) = 0.8803870741730615944977772215226
y2[1] (numeric) = 0.88038707417306159449777838456154
absolute error = 1.16303894e-24
relative error = 1.3210540841849936949132719419864e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928206021105320170169281124814
y1[1] (numeric) = 1.9928206021105320170169185090422
absolute error = 9.6034392e-24
relative error = 4.8190184253561546496916652195727e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=389.1MB, alloc=4.4MB, time=24.38
NO POLE
NO POLE
x[1] = 0.12
y2[1] (analytic) = 0.88028779271108064003264938572903
y2[1] (numeric) = 0.88028779271108064003265055557755
absolute error = 1.16984852e-24
relative error = 1.3289387058261253434456330954612e-22 %
h = 0.0001
y1[1] (analytic) = 1.9928086358538662522480981678576
y1[1] (numeric) = 1.9928086358538662522480885162769
absolute error = 9.6515807e-24
relative error = 4.8432049753058957007511220481863e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1201
y2[1] (analytic) = 0.88018851244622175745911342253384
y2[1] (numeric) = 0.88018851244622175745911459920158
absolute error = 1.17666774e-24
relative error = 1.3368360565508888002973068368450e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927966596691141372140109967773
y1[1] (numeric) = 1.9927966596691141372140012970563
absolute error = 9.6997210e-24
relative error = 4.8673912378047396713511072731011e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.4MB, time=24.62
NO POLE
NO POLE
x[1] = 0.1202
y2[1] (analytic) = 0.88008923337947774942493082213217
y2[1] (numeric) = 0.88008923337947774942493200562877
absolute error = 1.18349660e-24
relative error = 1.3447461406333313942548844760594e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927846735563954337620879480417
y1[1] (numeric) = 1.9927846735563954337620782001817
absolute error = 9.7478600e-24
relative error = 4.8915771630276628500526910338734e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1203
y2[1] (analytic) = 0.87998995551184140659671433930993
y2[1] (numeric) = 0.87998995551184140659671552964503
absolute error = 1.19033510e-24
relative error = 1.3526689623492895616648505964855e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927726775158300030194161718975
y1[1] (numeric) = 1.9927726775158300030194063758997
absolute error = 9.7959978e-24
relative error = 4.9157628015111038474228305581536e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.4MB, time=24.88
NO POLE
NO POLE
x[1] = 0.1204
y2[1] (analytic) = 0.87989067884430550765000008678592
y2[1] (numeric) = 0.87989067884430550765000128396916
absolute error = 1.19718324e-24
relative error = 1.3606045259763896543800144713695e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927606715475378053915500087666
y1[1] (numeric) = 1.9927606715475378053915401646324
absolute error = 9.8441342e-24
relative error = 4.9399480532477809444767239673131e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1205
y2[1] (analytic) = 0.87979140337786281925931974846476
y2[1] (numeric) = 0.87979140337786281925932095250578
absolute error = 1.20404102e-24
relative error = 1.3685528357940487481229955363317e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927486556516389005613113851921
y1[1] (numeric) = 1.9927486556516389005613014929227
absolute error = 9.8922694e-24
relative error = 4.9641330189557587819762276128596e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.4MB, time=25.13
NO POLE
NO POLE
x[1] = 0.1206
y2[1] (analytic) = 0.87969212911350609608827291269983
y2[1] (numeric) = 0.87969212911350609608827412360827
absolute error = 1.21090844e-24
relative error = 1.3765138960834754512670035728327e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927366298282534474875892170105
y1[1] (numeric) = 1.9927366298282534474875792766071
absolute error = 9.9404034e-24
relative error = 4.9883176989910233986306308453850e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1207
y2[1] (analytic) = 0.87959285605222808077959952566559
y2[1] (numeric) = 0.87959285605222808077960074345108
absolute error = 1.21778549e-24
relative error = 1.3844876997587743761514097576511e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927245940775017044041378197642
y1[1] (numeric) = 1.9927245940775017044041278312281
absolute error = 9.9885361e-24
relative error = 5.0125020435270055929752996510125e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.4MB, time=25.39
NO POLE
NO POLE
x[1] = 0.1208
y2[1] (analytic) = 0.87949358419502150394525246493838
y2[1] (numeric) = 0.87949358419502150394525368961056
absolute error = 1.22467218e-24
relative error = 1.3924742624710694593626913952037e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927125483995040288183743263647
y1[1] (numeric) = 1.9927125483995040288183642896973
absolute error = 1.00366674e-23
relative error = 5.0366860027359167560247067411430e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1209
y2[1] (analytic) = 0.87939431354287908415647023338523
y2[1] (numeric) = 0.87939431354287908415647146495374
absolute error = 1.23156851e-24
relative error = 1.4004735885069479416635967539518e-22 %
h = 0.0001
y1[1] (analytic) = 1.9927004927943808775101751120199
y1[1] (numeric) = 1.9927004927943808775101650272223
absolute error = 1.00847976e-23
relative error = 5.0608697275213709662128655285448e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.4MB, time=25.66
NO POLE
NO POLE
x[1] = 0.121
y2[1] (analytic) = 0.87929504409679352793384977345972
y2[1] (numeric) = 0.8792950440967935279338510119342
absolute error = 1.23847448e-24
relative error = 1.4084856821547918354694180479113e-22 %
h = 0.0001
y1[1] (analytic) = 1.9926884272622528065306712264356
y1[1] (numeric) = 1.9926884272622528065306610935092
absolute error = 1.01329264e-23
relative error = 5.0850530676898594552036985720930e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1211
y2[1] (analytic) = 0.87919577585775752973741940200428
y2[1] (numeric) = 0.87919577585775752973742064739437
absolute error = 1.24539009e-24
relative error = 1.4165105477047787357187311428299e-22 %
h = 0.0001
y1[1] (analytic) = 1.9926763518032404712010428333059
y1[1] (numeric) = 1.992676351803240471201032652252
absolute error = 1.01810539e-23
relative error = 5.1092360737792761653646825292163e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=411.9MB, alloc=4.4MB, time=25.92
NO POLE
NO POLE
x[1] = 0.1212
y2[1] (analytic) = 0.87909650882676377195671186565819
y2[1] (numeric) = 0.87909650882676377195671311797353
absolute error = 1.25231534e-24
relative error = 1.4245481894488826311628770888892e-22 %
h = 0.0001
y1[1] (analytic) = 1.9926642664174646261113126571021
y1[1] (numeric) = 1.9926642664174646261113024279219
absolute error = 1.02291802e-23
relative error = 5.1334187963287234667146105176723e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1213
y2[1] (analytic) = 0.87899724300480492490083751697053
y2[1] (numeric) = 0.87899724300480492490083877622075
absolute error = 1.25925022e-24
relative error = 1.4325986003042747556291175045364e-22 %
h = 0.0001
y1[1] (analytic) = 1.9926521711050461251191384371732
y1[1] (numeric) = 1.9926521711050461251191281598681
absolute error = 1.02773051e-23
relative error = 5.1576011353253954253835493187262e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.4MB, time=26.19
NO POLE
NO POLE
x[1] = 0.1214
y2[1] (analytic) = 0.87889797839287364678855761131732
y2[1] (numeric) = 0.87889797839287364678855887751206
absolute error = 1.26619474e-24
relative error = 1.4406617959405544865639473971790e-22 %
h = 0.0001
y1[1] (analytic) = 1.992640065866105921348604389171
y1[1] (numeric) = 1.9926400658661059213485940637422
absolute error = 1.03254288e-23
relative error = 5.1817831914927530550799486138594e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1215
y2[1] (analytic) = 0.87879871499196258373835772472221
y2[1] (numeric) = 0.87879871499196258373835899787111
absolute error = 1.27314890e-24
relative error = 1.4487377806550890423151025572012e-22 %
h = 0.0001
y1[1] (analytic) = 1.9926279507007650671890116738096
y1[1] (numeric) = 1.9926279507007650671890013002584
absolute error = 1.03735512e-23
relative error = 5.2059649150017401123753022447849e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.4MB, time=26.42
NO POLE
NO POLE
x[1] = 0.1216
y2[1] (analytic) = 0.87869945280306436975852129267988
y2[1] (numeric) = 0.87869945280306436975852257279258
absolute error = 1.28011270e-24
relative error = 1.4568265587470452840937115820162e-22 %
h = 0.0001
y1[1] (analytic) = 1.9926158256091447142936678729739
y1[1] (numeric) = 1.9926158256091447142936574513015
absolute error = 1.04216724e-23
relative error = 5.2301463563926498435899610922242e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1217
y2[1] (analytic) = 0.87860019182717162673720327008148
y2[1] (numeric) = 0.87860019182717162673720455716762
absolute error = 1.28708614e-24
relative error = 1.4649281345173905293609861500143e-22 %
h = 0.0001
y1[1] (analytic) = 1.992603690591366113578675473187
y1[1] (numeric) = 1.9926036905913661135786650033949
absolute error = 1.04697921e-23
relative error = 5.2543273654646142135845940739868e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.4MB, time=26.67
NO POLE
NO POLE
x[1] = 0.1218
y2[1] (analytic) = 0.87850093206527696443250391234137
y2[1] (numeric) = 0.87850093206527696443250520641058
absolute error = 1.29406921e-24
relative error = 1.4730425008858661712405635799062e-22 %
h = 0.0001
y1[1] (analytic) = 1.992591545647550615221719356451
y1[1] (numeric) = 1.9925915456475506152217088385403
absolute error = 1.05179107e-23
relative error = 5.2785081433143885012037989748368e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1219
y2[1] (analytic) = 0.87840167351837298046254267782436
y2[1] (numeric) = 0.87840167351837298046254397888628
absolute error = 1.30106192e-24
relative error = 1.4811696735374975336114097709021e-22 %
h = 0.0001
y1[1] (analytic) = 1.99257939077781966866085329847
y1[1] (numeric) = 1.9925793907778196686608427324422
absolute error = 1.05660278e-23
relative error = 5.3026884895539668289168708474738e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.4MB, time=26.92
NO POLE
NO POLE
x[1] = 0.122
y2[1] (analytic) = 0.87830241618745226029553225167281
y2[1] (numeric) = 0.87830241618745226029553355973707
absolute error = 1.30806426e-24
relative error = 1.4893096453930573506371110544371e-22 %
h = 0.0001
y1[1] (analytic) = 1.992567225982294822593285474272
y1[1] (numeric) = 1.9925672259822948225932748601282
absolute error = 1.06141438e-23
relative error = 5.3268686052825367276610948764973e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1221
y2[1] (analytic) = 0.87820316007350737723985269113275
y2[1] (numeric) = 0.87820316007350737723985400620899
absolute error = 1.31507624e-24
relative error = 1.4974624321437484512101985264820e-22 %
h = 0.0001
y1[1] (analytic) = 1.9925550512610977249741629712363
y1[1] (numeric) = 1.9925550512610977249741523089779
absolute error = 1.06622584e-23
relative error = 5.3510483402964475745979411349147e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.4MB, time=27.17
NO POLE
NO POLE
x[1] = 0.1222
y2[1] (analytic) = 0.87810390517753089243412569247838
y2[1] (numeric) = 0.87810390517753089243412701457624
absolute error = 1.32209786e-24
relative error = 1.5056280380995509987196161162078e-22 %
h = 0.0001
y1[1] (analytic) = 1.9925428666143501230153553095444
y1[1] (numeric) = 1.9925428666143501230153445991727
absolute error = 1.07103717e-23
relative error = 5.3752277451368658151315353176152e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1223
y2[1] (analytic) = 0.87800465150051535483728897963412
y2[1] (numeric) = 0.87800465150051535483729030876322
absolute error = 1.32912910e-24
relative error = 1.5138064447933279001836319152676e-22 %
h = 0.0001
y1[1] (analytic) = 1.9925306720421738631842369700615
y1[1] (numeric) = 1.9925306720421738631842262115777
absolute error = 1.07584838e-23
relative error = 5.3994068703461776137587061348995e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.4MB, time=27.41
NO POLE
NO POLE
x[1] = 0.1224
y2[1] (analytic) = 0.87790539904345330121867081459346
y2[1] (numeric) = 0.87790539904345330121867215076345
absolute error = 1.33616999e-24
relative error = 1.5219976907031917864896885442272e-22 %
h = 0.0001
y1[1] (analytic) = 1.992518467544690891202468929664
y1[1] (numeric) = 1.9925184675446908912024581230694
absolute error = 1.08065946e-23
relative error = 5.4235856660925101930426096019567e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1225
y2[1] (analytic) = 0.87780614780733725614806462973403
y2[1] (numeric) = 0.87780614780733725614806597295454
absolute error = 1.34322051e-24
relative error = 1.5302017573643296802483379363330e-22 %
h = 0.0001
y1[1] (analytic) = 1.9925062531220232520447792040239
y1[1] (numeric) = 1.9925062531220232520447683493198
absolute error = 1.08547041e-23
relative error = 5.4477641327308025788922235754609e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=438.7MB, alloc=4.4MB, time=27.98
NO POLE
NO POLE
x[1] = 0.1226
y2[1] (analytic) = 0.87770689779315973198580378212786
y2[1] (numeric) = 0.87770689779315973198580513240852
absolute error = 1.35028066e-24
relative error = 1.5384186490900826048832424334635e-22 %
h = 0.0001
y1[1] (analytic) = 1.9924940287742930899377423978626
y1[1] (numeric) = 1.9924940287742930899377314950503
absolute error = 1.09028123e-23
relative error = 5.4719422706159864642383769503622e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1227
y2[1] (analytic) = 0.87760764900191322887283642994635
y2[1] (numeric) = 0.8776076490019132288728377872968
absolute error = 1.35735045e-24
relative error = 1.5466483815902120830993530571965e-22 %
h = 0.0001
y1[1] (analytic) = 1.992481794501622648358558262686
y1[1] (numeric) = 1.9924817945016226483585473117669
absolute error = 1.09509191e-23
relative error = 5.4961200299143218745505181758885e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.4MB, time=28.57
NO POLE
NO POLE
x[1] = 0.1228
y2[1] (analytic) = 0.87750840143459023472080053105907
y2[1] (numeric) = 0.87750840143459023472080189548894
absolute error = 1.36442987e-24
relative error = 1.5548909477896378316665862792749e-22 %
h = 0.0001
y1[1] (analytic) = 1.9924695503041342700338292620138
y1[1] (numeric) = 1.9924695503041342700338182629891
absolute error = 1.09990247e-23
relative error = 5.5202975113577461427270733332565e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1229
y2[1] (analytic) = 0.87740915509218322520209896392561
y2[1] (numeric) = 0.87740915509218322520210033544455
absolute error = 1.37151894e-24
relative error = 1.5631463748015076566050054795023e-22 %
h = 0.0001
y1[1] (analytic) = 1.9924572961819503969383371441142
y1[1] (numeric) = 1.9924572961819503969383260969853
absolute error = 1.10471289e-23
relative error = 5.5444746149235314115360239440593e-22 %
h = 0.0001
memory used=446.3MB, alloc=4.4MB, time=29.17
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.123
y2[1] (analytic) = 0.8773099099756846637399747708799
y2[1] (numeric) = 0.87730990997568466373997614949753
absolute error = 1.37861763e-24
relative error = 1.5714146327586901135078385321734e-22 %
h = 0.0001
y1[1] (analytic) = 1.9924450321351935702938185222573
y1[1] (numeric) = 1.9924450321351935702938074270255
absolute error = 1.10952318e-23
relative error = 5.5686513911552437431097387741804e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=450.1MB, alloc=4.4MB, time=29.80
x[1] = 0.1231
y2[1] (analytic) = 0.87721066608608700149858652390594
y2[1] (numeric) = 0.87721066608608700149858790963191
absolute error = 1.38572597e-24
relative error = 1.5796957601790135195713163901099e-22 %
h = 0.0001
y1[1] (analytic) = 1.9924327581639864305677394624988
y1[1] (numeric) = 1.9924327581639864305677283191653
absolute error = 1.11433335e-23
relative error = 5.5928278905976771324702277657981e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1232
y2[1] (analytic) = 0.8771114234243826773730838130046
y2[1] (numeric) = 0.87711142342438267737308520584853
absolute error = 1.39284393e-24
relative error = 1.5879897271912335679769517094261e-22 %
h = 0.0001
y1[1] (analytic) = 1.992420474268451717472069079006
y1[1] (numeric) = 1.9924204742684517174720578875722
absolute error = 1.11914338e-23
relative error = 5.6170040132262290864222037606997e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.4MB, time=30.43
NO POLE
NO POLE
x[1] = 0.1233
y2[1] (analytic) = 0.8770121819915641179796828572503
y2[1] (numeric) = 0.87701218199156411797968425722182
absolute error = 1.39997152e-24
relative error = 1.5962965495198402721402434454007e-22 %
h = 0.0001
y1[1] (analytic) = 1.9924081804487122699620521369395
y1[1] (numeric) = 1.9924081804487122699620408974067
absolute error = 1.12395328e-23
relative error = 5.6411798095853699026556152921956e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1234
y2[1] (analytic) = 0.87691294178862373764574223863716
y2[1] (numeric) = 0.87691294178862373764574364574592
absolute error = 1.40710876e-24
relative error = 1.6046162542999368645956303417962e-22 %
h = 0.0001
y1[1] (analytic) = 1.9923958767048910262349806629018
y1[1] (numeric) = 1.9923958767048910262349693752713
absolute error = 1.12876305e-23
relative error = 5.6653552800299722677572469529411e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=457.7MB, alloc=4.4MB, time=31.04
NO POLE
NO POLE
x[1] = 0.1235
y2[1] (analytic) = 0.87681370281655393839983875881371
y2[1] (numeric) = 0.87681370281655393839984017306934
absolute error = 1.41425563e-24
relative error = 1.6129488230590405236319582497637e-22 %
h = 0.0001
y1[1] (analytic) = 1.992383563037111023728964562965
y1[1] (numeric) = 1.9923835630371110237289532272382
absolute error = 1.13357268e-23
relative error = 5.6895303747237628175800011839104e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1236
y2[1] (analytic) = 0.87671446507634710996184341880535
y2[1] (numeric) = 0.87671446507634710996184484021747
absolute error = 1.42141212e-24
relative error = 1.6212942487223806324585828431992e-22 %
h = 0.0001
y1[1] (analytic) = 1.9923712394454953991217012482912
y1[1] (numeric) = 1.9923712394454953991216898644694
absolute error = 1.13838218e-23
relative error = 5.7137051442121177128252577784132e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.4MB, time=31.65
NO POLE
NO POLE
x[1] = 0.1237
y2[1] (analytic) = 0.8766152285689956297329975218239
y2[1] (numeric) = 0.87661522856899562973299895040215
absolute error = 1.42857825e-24
relative error = 1.6296525584343771133618055884299e-22 %
h = 0.0001
y1[1] (analytic) = 1.9923589059301673883292442683563
y1[1] (numeric) = 1.9923589059301673883292328364407
absolute error = 1.14319156e-23
relative error = 5.7378796390416472084406319398736e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1238
y2[1] (analytic) = 0.8765159932954918627859888992635
y2[1] (numeric) = 0.87651599329549186278599033501752
absolute error = 1.43575402e-24
relative error = 1.6380237565339863786080047136537e-22 %
h = 0.0001
y1[1] (analytic) = 1.9923465624912503265047709517904
y1[1] (numeric) = 1.9923465624912503265047594717824
absolute error = 1.14800080e-23
relative error = 5.7620537591839853861041392078886e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=465.4MB, alloc=4.4MB, time=32.27
NO POLE
NO POLE
x[1] = 0.1239
y2[1] (analytic) = 0.876416759256828161855028259982
y2[1] (numeric) = 0.87641675925682816185502970292141
absolute error = 1.44293941e-24
relative error = 1.6464078245417898321581459310269e-22 %
h = 0.0001
y1[1] (analytic) = 1.9923342091288676480373490548474
y1[1] (numeric) = 1.9923342091288676480373375267483
absolute error = 1.15280991e-23
relative error = 5.7862275551854174200721937826541e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.124
y2[1] (analytic) = 0.87631752645399686732592566296706
y2[1] (numeric) = 0.87631752645399686732592711310151
absolute error = 1.45013445e-24
relative error = 1.6548048010267956278417887651089e-22 %
h = 0.0001
y1[1] (analytic) = 1.992321845843142886550702417515
y1[1] (numeric) = 1.9923218458431428865506908413261
absolute error = 1.15761889e-23
relative error = 5.8104010274007720402925894188538e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.4MB, time=32.88
NO POLE
NO POLE
x[1] = 0.1241
y2[1] (analytic) = 0.87621829488799030722616711348641
y2[1] (numeric) = 0.87621829488799030722616857082552
absolute error = 1.45733911e-24
relative error = 1.6632146560992499736000297838964e-22 %
h = 0.0001
y1[1] (analytic) = 1.9923094726341996749019756272786
y1[1] (numeric) = 1.9923094726341996749019640030013
absolute error = 1.16242773e-23
relative error = 5.8345741259918654776663533978406e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1242
y2[1] (analytic) = 0.87611906455980079721499128282118
y2[1] (numeric) = 0.87611906455980079721499274737458
absolute error = 1.46455340e-24
relative error = 1.6716374055116052670898206918950e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922970895021617451804976905511
y1[1] (numeric) = 1.9922970895021617451804860181867
absolute error = 1.16723644e-23
relative error = 5.8587469015058935476710758186888e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.4MB, time=33.50
NO POLE
NO POLE
x[1] = 0.1243
y2[1] (analytic) = 0.87601983547042064057346635168182
y2[1] (numeric) = 0.87601983547042064057346782345915
absolute error = 1.47177733e-24
relative error = 1.6800730650233038987541993200140e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922846964471529287065447117802
y1[1] (numeric) = 1.99228469644715292870653299133
absolute error = 1.17204502e-23
relative error = 5.8829193542976627781019631672193e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1244
y2[1] (analytic) = 0.87592060762084212819456697740569
y2[1] (numeric) = 0.87592060762084212819456845641658
absolute error = 1.47901089e-24
relative error = 1.6885216275676622358975264571212e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922722934692971560301015802472
y1[1] (numeric) = 1.9922722934692971560300898117125
absolute error = 1.17685347e-23
relative error = 5.9070914847219725731588779528098e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.4MB, time=34.11
NO POLE
NO POLE
x[1] = 0.1245
y2[1] (analytic) = 0.87582138101205753857325138503557
y2[1] (numeric) = 0.87582138101205753857325287128965
absolute error = 1.48625408e-24
relative error = 1.6969830974924995132584329673774e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922598805687184569296226645676
y1[1] (numeric) = 1.9922598805687184569296108479498
absolute error = 1.18166178e-23
relative error = 5.9312632429393604617647258330598e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1246
y2[1] (analytic) = 0.87572215564505913779653858237836
y2[1] (numeric) = 0.87572215564505913779654007588526
absolute error = 1.49350690e-24
relative error = 1.7054574791474575277274820901080e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922474577455409604107915149082
y1[1] (numeric) = 1.9922474577455409604107796502086
absolute error = 1.18646996e-23
relative error = 5.9554346794982404183252760885733e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.4MB, time=34.73
NO POLE
NO POLE
x[1] = 0.1247
y2[1] (analytic) = 0.87562293152083917953358569914314
y2[1] (numeric) = 0.87562293152083917953358719991249
absolute error = 1.50076935e-24
relative error = 1.7139447768840014636869555410856e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922350249998888947052795729308
y1[1] (numeric) = 1.9922350249998888947052676601507
absolute error = 1.19127801e-23
relative error = 5.9796057947533897843524450881026e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1248
y2[1] (analytic) = 0.87552370864038990502576545025788
y2[1] (numeric) = 0.87552370864038990502576695829931
absolute error = 1.50804143e-24
relative error = 1.7224449950554207187777878943797e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922225823318865872695038894767
y1[1] (numeric) = 1.9922225823318865872694919286176
absolute error = 1.19608591e-23
relative error = 6.0037764886691898317447629952836e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=484.4MB, alloc=4.4MB, time=35.35
NO POLE
NO POLE
x[1] = 0.1249
y2[1] (analytic) = 0.87542448700470354307674372346399
y2[1] (numeric) = 0.87542448700470354307674523878713
absolute error = 1.51532314e-24
relative error = 1.7309581380168297300938964184687e-22 %
h = 0.0001
y1[1] (analytic) = 1.9922101297416584647833838500039
y1[1] (numeric) = 1.992210129741658464783371841067
absolute error = 1.20089369e-23
relative error = 6.0279469121850459918593756162062e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.125
y2[1] (analytic) = 0.87532526661477231004255729128789
y2[1] (numeric) = 0.87532526661477231004255881390238
absolute error = 1.52261449e-24
relative error = 1.7394842215494934277784669925975e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921976672293290531490969077882
y1[1] (numeric) = 1.9921976672293290531490848507749
absolute error = 1.20570133e-23
relative error = 6.0521169652650103955814889260447e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.4MB, time=36.00
NO POLE
NO POLE
x[1] = 0.1251
y2[1] (analytic) = 0.87522604747158840982169164748898
y2[1] (numeric) = 0.87522604747158840982169317740444
absolute error = 1.52991546e-24
relative error = 1.7480232271648246615425039695158e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921851947950229774898333249033
y1[1] (numeric) = 1.9921851947950229774898212198148
absolute error = 1.21050885e-23
relative error = 6.0762867486551616330314695185570e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1252
y2[1] (analytic) = 0.87512682957614403384515896808298
y2[1] (numeric) = 0.87512682957614403384516050530905
absolute error = 1.53722607e-24
relative error = 1.7565751820733628643534115090165e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921727124388649621485499209891
y1[1] (numeric) = 1.9921727124388649621485377678268
absolute error = 1.21531623e-23
relative error = 6.1004561623182817380320081265240e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.4MB, time=36.62
NO POLE
NO POLE
x[1] = 0.1253
y2[1] (analytic) = 0.87502761292943136106657619704013
y2[1] (numeric) = 0.87502761292943136106657774158643
absolute error = 1.54454630e-24
relative error = 1.7651400677849963257221673784710e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921602201609798306867228298239
y1[1] (numeric) = 1.9921602201609798306867106285892
absolute error = 1.22012347e-23
relative error = 6.1246252066081606986513280847590e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1254
y2[1] (analytic) = 0.87492839753244255795224325675726
y2[1] (numeric) = 0.87492839753244255795224480863342
absolute error = 1.55187616e-24
relative error = 1.7737179000895968223907283112646e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921477179614925058830992637103
y1[1] (numeric) = 1.9921477179614925058830870144045
absolute error = 1.22493058e-23
relative error = 6.1487939320756607900124796134072e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.4MB, time=37.23
NO POLE
NO POLE
x[1] = 0.1255
y2[1] (analytic) = 0.87482918338616977847122138340306
y2[1] (numeric) = 0.87482918338616977847122294261872
absolute error = 1.55921566e-24
relative error = 1.7823086947840493407133080737068e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921352058405280097324482856888
y1[1] (numeric) = 1.9921352058405280097324359883133
absolute error = 1.22973755e-23
relative error = 6.1729622888781046832490609897056e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1256
y2[1] (analytic) = 0.87472997049160516408541158723576
y2[1] (numeric) = 0.87472997049160516408541315380055
absolute error = 1.56656479e-24
relative error = 1.7909124448080568151878111668415e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921226837982114634443105895914
y1[1] (numeric) = 1.9921226837982114634442982441474
absolute error = 1.23454440e-23
relative error = 6.1971303777646808171047068004955e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.4MB, time=37.84
NO POLE
NO POLE
x[1] = 0.1257
y2[1] (analytic) = 0.87463075884974084373963323799236
y2[1] (numeric) = 0.8746307588497408437396348119159
absolute error = 1.57392354e-24
relative error = 1.7995291430979684201888920033500e-22 %
h = 0.0001
y1[1] (analytic) = 1.9921101518346680874417472879467
y1[1] (numeric) = 1.9921101518346680874417348944356
absolute error = 1.23935111e-23
relative error = 6.2212980986949857746883583167597e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1258
y2[1] (analytic) = 0.87453154846156893385170277544872
y2[1] (numeric) = 0.87453154846156893385170435674064
absolute error = 1.58129192e-24
relative error = 1.8081588054561641359232358630131e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920976099500232013600877077509
y1[1] (numeric) = 1.9920976099500232013600752661741
absolute error = 1.24415768e-23
relative error = 6.2454654520227692905611541523818e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=503.5MB, alloc=4.4MB, time=38.46
NO POLE
NO POLE
x[1] = 0.1259
y2[1] (analytic) = 0.87443233932808153830251254524965
y2[1] (numeric) = 0.87443233932808153830251413391958
absolute error = 1.58866993e-24
relative error = 1.8168014362560543292108270336579e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920850581444022240456761941152
y1[1] (numeric) = 1.9920850581444022240456637044741
absolute error = 1.24896411e-23
relative error = 6.2696324381017726262114199072312e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.126
y2[1] (analytic) = 0.87433313145027074842610976010826
y2[1] (numeric) = 0.87433313145027074842611135616583
absolute error = 1.59605757e-24
relative error = 1.8254570398728835227413175195693e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920724964179306735546179218037
y1[1] (numeric) = 1.9920724964179306735546053840996
absolute error = 1.25377041e-23
relative error = 6.2937991074847048637689058168873e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.4MB, time=39.09
NO POLE
NO POLE
x[1] = 0.1261
y2[1] (analytic) = 0.87423392482912864299977558647378
y2[1] (numeric) = 0.87423392482912864299977718992861
absolute error = 1.60345483e-24
relative error = 1.8341256092451451500930729724929e-22 %
h = 0.0001
y1[1] (analytic) = 1.992059924770734167151523714673
y1[1] (numeric) = 1.9920599247707341671515111289073
absolute error = 1.25857657e-23
relative error = 6.3179654103269476703651236153678e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1262
y2[1] (analytic) = 0.87413471946564728823410435676696
y2[1] (numeric) = 0.87413471946564728823410596762869
absolute error = 1.61086173e-24
relative error = 1.8428071716276285300975844680175e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920473432029384213082538730275
y1[1] (numeric) = 1.9920473432029384213082412392015
absolute error = 1.26338260e-23
relative error = 6.3421313971818278550453152753070e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=511.1MB, alloc=4.4MB, time=39.70
NO POLE
NO POLE
x[1] = 0.1263
y2[1] (analytic) = 0.87403551536081873776308290728245
y2[1] (numeric) = 0.8740355153608187377630845255607
absolute error = 1.61827825e-24
relative error = 1.8515017085226147710538726744907e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920347517146692517026610089015
y1[1] (numeric) = 1.9920347517146692517026483270166
absolute error = 1.26818849e-23
relative error = 6.3662970182040781445600440840421e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1264
y2[1] (analytic) = 0.87393631251563503263417004185716
y2[1] (numeric) = 0.87393631251563503263417166756157
absolute error = 1.62570441e-24
relative error = 1.8602092471937599774625919052838e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920221503060525732173318892822
y1[1] (numeric) = 1.9920221503060525732173191593397
absolute error = 1.27299425e-23
relative error = 6.3904623239476441372438618437340e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.4MB, time=40.30
NO POLE
NO POLE
x[1] = 0.1265
y2[1] (analytic) = 0.87383711093108820129837612140398
y2[1] (numeric) = 0.87383711093108820129837775454417
absolute error = 1.63314019e-24
relative error = 1.8689297691418272942159056338118e-22 %
h = 0.0001
y1[1] (analytic) = 1.9920095389772143999383282872844
y1[1] (numeric) = 1.9920095389772143999383155092857
absolute error = 1.27779987e-23
relative error = 6.4146272645666086498570276012570e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1266
y2[1] (analytic) = 0.8737379106081702596003427794099
y2[1] (numeric) = 0.87373791060817025960034441999549
absolute error = 1.64058559e-24
relative error = 1.8776632787491858242949271477064e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919969177282808451539268412912
y1[1] (numeric) = 1.9919969177282808451539140152376
absolute error = 1.28260536e-23
relative error = 6.4387918906155371324464083744359e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.4MB, time=40.91
NO POLE
NO POLE
x[1] = 0.1267
y2[1] (analytic) = 0.87363871154787321076842276349786
y2[1] (numeric) = 0.87363871154787321076842441153849
absolute error = 1.64804063e-24
relative error = 1.8864098032928014384254363379527e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919842865593781213533579220722
y1[1] (numeric) = 1.9919842865593781213533450479651
absolute error = 1.28741071e-23
relative error = 6.4629561522478615221196903252511e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1268
y2[1] (analytic) = 0.87353951375118904540475990315155
y2[1] (numeric) = 0.87353951375118904540476155865684
absolute error = 1.65550529e-24
relative error = 1.8951693242711615775763565961920e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919716454706325402255435078923
y1[1] (numeric) = 1.991971645470632540225530585733
absolute error = 1.29221593e-23
relative error = 6.4871201000187681831083420160008e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.4MB, time=41.52
NO POLE
NO POLE
x[1] = 0.1269
y2[1] (analytic) = 0.87344031721910974147536920370215
y2[1] (numeric) = 0.87344031721910974147537086668173
absolute error = 1.66297958e-24
relative error = 1.9039418575211336298029052208755e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919589944621705126578340676234
y1[1] (numeric) = 1.9919589944621705126578210974133
absolute error = 1.29702101e-23
relative error = 6.5112836840810372031522234011305e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.127
y2[1] (analytic) = 0.87334112195262726430021706667654
y2[1] (numeric) = 0.87334112195262726430021873714003
absolute error = 1.67046349e-24
relative error = 1.9127273959860682357698279344692e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919463335341185487347444518721
y1[1] (numeric) = 1.9919463335341185487347314336126
absolute error = 1.30182595e-23
relative error = 6.5354469047883212142149033851044e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.4MB, time=42.13
NO POLE
NO POLE
x[1] = 0.1271
y2[1] (analytic) = 0.87324192795273356654330163660581
y2[1] (numeric) = 0.87324192795273356654330331456284
absolute error = 1.67795703e-24
relative error = 1.9215259555091171466418529844130e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919336626866032577366887921356
y1[1] (numeric) = 1.9919336626866032577366757258281
absolute error = 1.30663075e-23
relative error = 6.5596097624942645141111383798578e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1272
y2[1] (analytic) = 0.87314273522042058820273327439361
y2[1] (numeric) = 0.87314273522042058820273495985381
absolute error = 1.68546020e-24
relative error = 1.9303375404875972127236520674897e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919209819197513481387144079986
y1[1] (numeric) = 1.9919209819197513481387012936444
absolute error = 1.31143542e-23
relative error = 6.5837723077552977208706503348087e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=530.2MB, alloc=4.4MB, time=42.75
NO POLE
NO POLE
x[1] = 0.1273
y2[1] (analytic) = 0.87304354375668025660081515734331
y2[1] (numeric) = 0.8730435437566802566008168503163
absolute error = 1.69297299e-24
relative error = 1.9391621438664878727457916930593e-22 %
h = 0.0001
y1[1] (analytic) = 1.9919082912336896276092347223836
y1[1] (numeric) = 1.9919082912336896276092215599842
absolute error = 1.31623994e-23
relative error = 6.6079344405197790611177771540717e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1274
y2[1] (analytic) = 0.87294435356250448637412400594317
y2[1] (numeric) = 0.87294435356250448637412570643859
absolute error = 1.70049542e-24
relative error = 1.9479997929538601150760740508930e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918955906285450030087611848684
y1[1] (numeric) = 1.9918955906285450030087479744251
absolute error = 1.32104433e-23
relative error = 6.6320962615472375413670140077509e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.4MB, time=43.36
NO POLE
NO POLE
x[1] = 0.1275
y2[1] (analytic) = 0.87284516463888517946359093750894
y2[1] (numeric) = 0.8728451646388851794635926455364
absolute error = 1.70802746e-24
relative error = 1.9568504577861157103161854516617e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918828801044444803886342030816
y1[1] (numeric) = 1.9918828801044444803886209445957
absolute error = 1.32584859e-23
relative error = 6.6562577711922453069906487295407e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1276
y2[1] (analytic) = 0.87274597698681422510458244678271
y2[1] (numeric) = 0.87274597698681422510458416235184
absolute error = 1.71556913e-24
relative error = 1.9657141656763196566385793568644e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918701596615151649897530821902
y1[1] (numeric) = 1.9918701596615151649897397756631
absolute error = 1.33065271e-23
relative error = 6.6804189196052921922390409706329e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.4MB, time=43.98
NO POLE
NO POLE
x[1] = 0.1277
y2[1] (analytic) = 0.87264679060728349981698151358759
y2[1] (numeric) = 0.87264679060728349981698323670802
absolute error = 1.72312043e-24
relative error = 1.9745909210310204828341199928823e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918574292998842612413049724921
y1[1] (numeric) = 1.9918574292998842612412916179252
absolute error = 1.33545669e-23
relative error = 6.7045797071399742574602130193124e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1278
y2[1] (analytic) = 0.87254760550128486739526883763711
y2[1] (numeric) = 0.87254760550128486739527056831846
absolute error = 1.73068135e-24
relative error = 1.9834807167979231710788780400184e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918446890196790727594928251248
y1[1] (numeric) = 1.9918446890196790727594794225195
absolute error = 1.34026053e-23
relative error = 6.7287401341498793098523280558116e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=541.7MB, alloc=4.4MB, time=44.61
NO POLE
NO POLE
x[1] = 0.1279
y2[1] (analytic) = 0.87244842166981017889860420059869
y2[1] (numeric) = 0.87244842166981017889860593885058
absolute error = 1.73825189e-24
relative error = 1.9923835573833667503358455489139e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918319388210270023462623559048
y1[1] (numeric) = 1.9918319388210270023462489052624
absolute error = 1.34506424e-23
relative error = 6.7529002511936258297004851587849e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.128
y2[1] (analytic) = 0.87234923911385127264090795551028
y2[1] (numeric) = 0.87234923911385127264090970134235
absolute error = 1.74583207e-24
relative error = 2.0012994701221370680774101617360e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918191787040555519880280173089
y1[1] (numeric) = 1.9918191787040555519880145186309
absolute error = 1.34986780e-23
relative error = 6.7770599582150289499135225730259e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=545.5MB, alloc=4.4MB, time=45.25
NO POLE
NO POLE
x[1] = 0.1281
y2[1] (analytic) = 0.87225005783439997418094264364948
y2[1] (numeric) = 0.87225005783439997418094439707134
absolute error = 1.75342186e-24
relative error = 2.0102284250382863019408858749896e-22 %
h = 0.0001
y1[1] (analytic) = 1.9918064086688923228543979786115
y1[1] (numeric) = 1.9918064086688923228543844318992
absolute error = 1.35467123e-23
relative error = 6.8012193559780517518736430899222e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1282
y2[1] (analytic) = 0.87215087783244809631239473895411
y2[1] (numeric) = 0.87215087783244809631239649997539
absolute error = 1.76102128e-24
relative error = 2.0191704494716060501159355161118e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917936287156650152968981141892
y1[1] (numeric) = 1.991793628715665015296884519444
absolute error = 1.35947452e-23
relative error = 6.8253783946312109935111894488232e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=549.3MB, alloc=4.4MB, time=45.86
NO POLE
NO POLE
x[1] = 0.1283
y2[1] (analytic) = 0.87205169910898743905395652009366
y2[1] (numeric) = 0.87205169910898743905395828872399
absolute error = 1.76863033e-24
relative error = 2.0281255478397500266335047474319e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917808388445014288476950000068
y1[1] (numeric) = 1.9917808388445014288476813572301
absolute error = 1.36427767e-23
relative error = 6.8495370745280541521184157069574e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1284
y2[1] (analytic) = 0.87195252166500978963940807029062
y2[1] (numeric) = 0.87195252166500978963940984653962
absolute error = 1.77624900e-24
relative error = 2.0370937130937118288115942030802e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917680390555294622183179182967
y1[1] (numeric) = 1.9917680390555294622183042274899
absolute error = 1.36908068e-23
relative error = 6.8736953960221205212372442519605e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=553.1MB, alloc=4.4MB, time=46.48
NO POLE
NO POLE
x[1] = 0.1285
y2[1] (analytic) = 0.87185334550150692250769940499094
y2[1] (numeric) = 0.87185334550150692250770118886823
absolute error = 1.78387729e-24
relative error = 2.0460749496509407196005662062397e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917552293488771132983798704446
y1[1] (numeric) = 1.991755229348877113298366131609
absolute error = 1.37388356e-23
relative error = 6.8978534096739137088403637910692e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=556.9MB, alloc=4.4MB, time=47.08
x[1] = 0.1286
y2[1] (analytic) = 0.87175417061947059929303272748278
y2[1] (numeric) = 0.87175417061947059929303451899799
absolute error = 1.79151521e-24
relative error = 2.0550692734018639745847731380470e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917424097246724791542975980945
y1[1] (numeric) = 1.9917424097246724791542838112315
absolute error = 1.37868630e-23
relative error = 6.9220110656306304920055400706262e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1287
y2[1] (analytic) = 0.87165499701989256881494481256279
y2[1] (numeric) = 0.87165499701989256881494661172554
absolute error = 1.79916275e-24
relative error = 2.0640766772991266551042378591171e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917295801830437560280106124855
y1[1] (numeric) = 1.9917295801830437560279967775965
absolute error = 1.38348890e-23
relative error = 6.9461683642457864448674346201394e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=560.7MB, alloc=4.4MB, time=47.69
x[1] = 0.1288
y2[1] (analytic) = 0.87155582470376456706838951834897
y2[1] (numeric) = 0.87155582470376456706839132516888
absolute error = 1.80681991e-24
relative error = 2.0730971657657440777358235851133e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917167407241192393356992320336
y1[1] (numeric) = 1.99171674072411923933568534912
absolute error = 1.38829136e-23
relative error = 6.9703253058728890040804439548105e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1289
y2[1] (analytic) = 0.87145665367207831721382042633941
y2[1] (numeric) = 0.87145665367207831721382224082611
absolute error = 1.81448670e-24
relative error = 2.0821307547016283621865787597785e-22 %
h = 0.0001
y1[1] (analytic) = 1.9917038913480273236665016281709
y1[1] (numeric) = 1.9917038913480273236664876972342
absolute error = 1.39309367e-23
relative error = 6.9944818406571708628359248050712e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=564.5MB, alloc=4.4MB, time=48.31
NO POLE
NO POLE
x[1] = 0.129
y2[1] (analytic) = 0.87135748392582552956727360981603
y2[1] (numeric) = 0.87135748392582552956727543197914
absolute error = 1.82216311e-24
relative error = 2.0911774370610810969690044133118e-22 %
h = 0.0001
y1[1] (analytic) = 1.9916910320548965027812298794554
y1[1] (numeric) = 1.9916910320548965027812159004969
absolute error = 1.39789585e-23
relative error = 7.0186380693683322844346047319739e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1291
y2[1] (analytic) = 0.87125831546599790159045053069248
y2[1] (numeric) = 0.87125831546599790159045236054161
absolute error = 1.82984913e-24
relative error = 2.1002372057950389480728463879774e-22 %
h = 0.0001
y1[1] (analytic) = 1.9916781628448553696110850339637
y1[1] (numeric) = 1.9916781628448553696110710069848
absolute error = 1.40269789e-23
relative error = 7.0427939421519136588838766191826e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=568.4MB, alloc=4.4MB, time=48.93
NO POLE
NO POLE
x[1] = 0.1292
y2[1] (analytic) = 0.87115914829358711788080106490534
y2[1] (numeric) = 0.87115914829358711788080290245013
absolute error = 1.83754479e-24
relative error = 2.1093100997669070302784317554836e-22 %
h = 0.0001
y1[1] (analytic) = 1.9916652837180326162563711799802
y1[1] (numeric) = 1.9916652837180326162563571049824
absolute error = 1.40749978e-23
relative error = 7.0669494091521501039264061721200e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1293
y2[1] (analytic) = 0.87105998240958485016160665644799
y2[1] (numeric) = 0.87105998240958485016160850169804
absolute error = 1.84525005e-24
relative error = 2.1183960774957711925009077886539e-22 %
h = 0.0001
y1[1] (analytic) = 1.9916523946745570339852085249954
y1[1] (numeric) = 1.99165239467455703398519440198
absolute error = 1.41230154e-23
relative error = 7.0911045711406633806463318062207e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=572.2MB, alloc=4.4MB, time=49.55
NO POLE
NO POLE
x[1] = 0.1294
y2[1] (analytic) = 0.87096081781498275727206360014593
y2[1] (numeric) = 0.87096081781498275727206545311088
absolute error = 1.85296495e-24
relative error = 2.1274951893342500441249148685965e-22 %
h = 0.0001
y1[1] (analytic) = 1.9916394957145575132322454830252
y1[1] (numeric) = 1.9916394957145575132322313119936
absolute error = 1.41710316e-23
relative error = 7.1152593782619971355140726476103e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1295
y2[1] (analytic) = 0.87086165451077248515736645327321
y2[1] (numeric) = 0.87086165451077248515736831396267
absolute error = 1.86068946e-24
relative error = 2.1366074052775777928565667981014e-22 %
h = 0.0001
y1[1] (analytic) = 1.991626586838163043597369770266
y1[1] (numeric) = 1.9916265868381630435973555512196
absolute error = 1.42190464e-23
relative error = 7.1394138308696021664862315269164e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=576.0MB, alloc=4.4MB, time=50.16
NO POLE
NO POLE
x[1] = 0.1296
y2[1] (analytic) = 0.87076249249794566685879157610865
y2[1] (numeric) = 0.87076249249794566685879344453224
absolute error = 1.86842359e-24
relative error = 2.1457327412439139365922026917486e-22 %
h = 0.0001
y1[1] (analytic) = 1.9916136680455027138444185090966
y1[1] (numeric) = 1.9916136680455027138444042420368
absolute error = 1.42670598e-23
relative error = 7.1635679293169212265153215933344e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1297
y2[1] (analytic) = 0.87066333177749392250378080153137
y2[1] (numeric) = 0.87066333177749392250378267769872
absolute error = 1.87616735e-24
relative error = 2.1548712131585115854510565953573e-22 %
h = 0.0001
y1[1] (analytic) = 1.991600739336705711899887340441
y1[1] (numeric) = 1.9916007393367057118998730253693
absolute error = 1.43150717e-23
relative error = 7.1877216237465219547391487213286e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=579.8MB, alloc=4.4MB, time=50.78
NO POLE
NO POLE
x[1] = 0.1298
y2[1] (analytic) = 0.87056417235040885929602523375467
y2[1] (numeric) = 0.8705641723504088592960271176754
absolute error = 1.88392073e-24
relative error = 2.1640228139801131561644991989156e-22 %
h = 0.0001
y1[1] (analytic) = 1.9915878007119013248516385445047
y1[1] (numeric) = 1.9915878007119013248516241814224
absolute error = 1.43630823e-23
relative error = 7.2118750149332390076925539702280e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1299
y2[1] (analytic) = 0.87046501421768207150554917629734
y2[1] (numeric) = 0.87046501421768207150555106798107
absolute error = 1.89168373e-24
relative error = 2.1731875481522064168200587887834e-22 %
h = 0.0001
y1[1] (analytic) = 1.9915748521712189389476081698967
y1[1] (numeric) = 1.9915748521712189389475937588053
absolute error = 1.44110914e-23
relative error = 7.2360280028084302016301822184121e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=583.6MB, alloc=4.4MB, time=51.40
NO POLE
NO POLE
x[1] = 0.13
y2[1] (analytic) = 0.87036585738030514045879418929169
y2[1] (numeric) = 0.87036585738030514045879608874804
absolute error = 1.89945635e-24
relative error = 2.1823654201201451912753429533363e-22 %
h = 0.0001
y1[1] (analytic) = 1.9915618937147880395945121711518
y1[1] (numeric) = 1.9915618937147880395944977120526
absolute error = 1.44590992e-23
relative error = 7.2601806881482189912621501550431e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1301
y2[1] (analytic) = 0.8702667018392696345287032762274
y2[1] (numeric) = 0.87026670183926963452870518346599
absolute error = 1.90723859e-24
relative error = 2.1915564343311502071476677860159e-22 %
h = 0.0001
y1[1] (analytic) = 1.991548925342738211356551554664
y1[1] (numeric) = 1.9915489253427382113565370475584
absolute error = 1.45071056e-23
relative error = 7.2843330210948147956869789940954e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=587.4MB, alloc=4.4MB, time=52.04
NO POLE
NO POLE
x[1] = 0.1302
y2[1] (analytic) = 0.87016754759556710912480520023036
y2[1] (numeric) = 0.87016754759556710912480711526081
absolute error = 1.91503045e-24
relative error = 2.2007605952343099442440094610301e-22 %
h = 0.0001
y1[1] (analytic) = 1.9915359470551991379541165330459
y1[1] (numeric) = 1.9915359470551991379541019779353
absolute error = 1.45551106e-23
relative error = 7.3084850020016123405373417315806e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1303
y2[1] (analytic) = 0.87006839465018910668329892997564
y2[1] (numeric) = 0.87006839465018910668330085280757
absolute error = 1.92283193e-24
relative error = 2.2099779072805814834315338833155e-22 %
h = 0.0001
y1[1] (analytic) = 1.9915229588523006022624896879256
y1[1] (numeric) = 1.9915229588523006022624750848115
absolute error = 1.46031141e-23
relative error = 7.3326365810091702823512822958934e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=591.2MB, alloc=4.4MB, time=52.68
NO POLE
NO POLE
x[1] = 0.1304
y2[1] (analytic) = 0.86996924300412715665713821533376
y2[1] (numeric) = 0.86996924300412715665714014597679
absolute error = 1.93064303e-24
relative error = 2.2192083749227913559489602797004e-22 %
h = 0.0001
y1[1] (analytic) = 1.9915099607341724863105481411954
y1[1] (numeric) = 1.9915099607341724863105334900792
absolute error = 1.46511162e-23
relative error = 7.3567878086830400804222155629908e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1305
y2[1] (analytic) = 0.86987009265837277550611629284942
y2[1] (numeric) = 0.86987009265837277550611823131317
absolute error = 1.93846375e-24
relative error = 2.2284520026156363931590147636530e-22 %
h = 0.0001
y1[1] (analytic) = 1.9914969527009447712794647347236
y1[1] (numeric) = 1.9914969527009447712794500356067
absolute error = 1.46991169e-23
relative error = 7.3809386853765918399211045904157e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=595.1MB, alloc=4.4MB, time=53.30
NO POLE
NO POLE
x[1] = 0.1306
y2[1] (analytic) = 0.86977094361391746668695072115183
y2[1] (numeric) = 0.86977094361391746668695266744592
absolute error = 1.94629409e-24
relative error = 2.2377087948156845767422300715612e-22 %
h = 0.0001
y1[1] (analytic) = 1.9914839347527475375014082185443
y1[1] (numeric) = 1.9914839347527475375013934714281
absolute error = 1.47471162e-23
relative error = 7.4050892114431877365614216530272e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1307
y2[1] (analytic) = 0.86967179587175272064336834639579
y2[1] (numeric) = 0.86967179587175272064337030052984
absolute error = 1.95413405e-24
relative error = 2.2469787559813758893323478341734e-22 %
h = 0.0001
y1[1] (analytic) = 1.9914709068897109644582424475362
y1[1] (numeric) = 1.9914709068897109644582276524222
absolute error = 1.47951140e-23
relative error = 7.4292393370220414880954358071096e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=598.9MB, alloc=4.4MB, time=53.92
NO POLE
NO POLE
x[1] = 0.1308
y2[1] (analytic) = 0.8695726494328700147961903978327
y2[1] (numeric) = 0.86957264943287001479619235981633
absolute error = 1.96198363e-24
relative error = 2.2562618905730231655935799126280e-22 %
h = 0.0001
y1[1] (analytic) = 1.991457869111965330780224586606
y1[1] (numeric) = 1.9914578691119653307802097434955
absolute error = 1.48431105e-23
relative error = 7.4533891628944517816172697915454e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1309
y2[1] (analytic) = 0.86947350429826081353341771361058
y2[1] (numeric) = 0.86947350429826081353341968345341
absolute error = 1.96984283e-24
relative error = 2.2655582030528129437399854944160e-22 %
h = 0.0001
y1[1] (analytic) = 1.9914448214196410142447023243858
y1[1] (numeric) = 1.9914448214196410142446874332803
absolute error = 1.48911055e-23
relative error = 7.4775385889851467405856748653708e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=602.7MB, alloc=4.4MB, time=54.57
NO POLE
NO POLE
x[1] = 0.131
y2[1] (analytic) = 0.86937436046891656820031609690237
y2[1] (numeric) = 0.86937436046891656820031807461401
absolute error = 1.97771164e-24
relative error = 2.2748676863822816805775448938118e-22 %
h = 0.0001
y1[1] (analytic) = 1.9914317638128684917748100954616
y1[1] (numeric) = 1.9914317638128684917747951563625
absolute error = 1.49390991e-23
relative error = 7.5016876658615967155714128912654e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1311
y2[1] (analytic) = 0.86927521794582871708950180246149
y2[1] (numeric) = 0.86927521794582871708950378805156
absolute error = 1.98559007e-24
relative error = 2.2841903565272667442187110756253e-22 %
h = 0.0001
y1[1] (analytic) = 1.9914186962917783394381643111425
y1[1] (numeric) = 1.9914186962917783394381493240513
absolute error = 1.49870912e-23
relative error = 7.5258363436616666015086025102520e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=606.5MB, alloc=4.4MB, time=55.19
NO POLE
NO POLE
x[1] = 0.1312
y2[1] (analytic) = 0.86917607672998868543102715370395
y2[1] (numeric) = 0.86917607672998868543102914718207
absolute error = 1.99347812e-24
relative error = 2.2935262179555800511391556667580e-22 %
h = 0.0001
y1[1] (analytic) = 1.991405618856501232445557598786
y1[1] (numeric) = 1.9914056188565012324455425637041
absolute error = 1.50350819e-23
relative error = 7.5499846729534679974324972200486e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1313
y2[1] (analytic) = 0.86907693682238788538246629041611
y2[1] (numeric) = 0.8690769368223878853824682917919
absolute error = 2.00137579e-24
relative error = 2.3028752751369106315583903799584e-22 %
h = 0.0001
y1[1] (analytic) = 1.9913925315071679451496520496909
y1[1] (numeric) = 1.9913925315071679451496369666197
absolute error = 1.50830712e-23
relative error = 7.5741326540903063704089683549104e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=610.3MB, alloc=4.4MB, time=55.80
NO POLE
NO POLE
x[1] = 0.1314
y2[1] (analytic) = 0.86897779822401771601900104718718
y2[1] (numeric) = 0.86897779822401771601900305647026
absolute error = 2.00928308e-24
relative error = 2.3122375325428254831734442409875e-22 %
h = 0.0001
y1[1] (analytic) = 1.9913794342439093510436714755718
y1[1] (numeric) = 1.9913794342439093510436563445127
absolute error = 1.51310591e-23
relative error = 7.5982802874254793504340919887253e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1315
y2[1] (analytic) = 0.86887866093586956332350696266567
y2[1] (numeric) = 0.86887866093586956332350897986566
absolute error = 2.01719999e-24
relative error = 2.3216129946467704253362001712598e-22 %
h = 0.0001
y1[1] (analytic) = 1.991366327066856422760092673628
y1[1] (numeric) = 1.9913663270668564227600774945825
absolute error = 1.51790455e-23
relative error = 7.6224275230954991251379943860143e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=614.1MB, alloc=4.4MB, time=56.40
NO POLE
NO POLE
x[1] = 0.1316
y2[1] (analytic) = 0.8687795249589348001766394197389
y2[1] (numeric) = 0.86877952495893480017664144486541
absolute error = 2.02512651e-24
relative error = 2.3310016544136707742129183965646e-22 %
h = 0.0001
y1[1] (analytic) = 1.99135320997614023206933570022
y1[1] (numeric) = 1.9913532099761402320693204731895
absolute error = 1.52270305e-23
relative error = 7.6465744116697637436841234531275e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1317
y2[1] (analytic) = 0.86868039029420478634691991673469
y2[1] (numeric) = 0.86868039029420478634692194979734
absolute error = 2.03306265e-24
relative error = 2.3404035278285055797445098009080e-22 %
h = 0.0001
y1[1] (analytic) = 1.9913400829718919498784531531661
y1[1] (numeric) = 1.991340082971891949878437878152
absolute error = 1.52750141e-23
relative error = 7.6707209535015466311132457090332e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=617.9MB, alloc=4.4MB, time=57.01
NO POLE
NO POLE
x[1] = 0.1318
y2[1] (analytic) = 0.86858125694267086848082246974444
y2[1] (numeric) = 0.86858125694267086848082451075284
absolute error = 2.04100840e-24
relative error = 2.3498186078573337900337213234795e-22 %
h = 0.0001
y1[1] (analytic) = 1.991326946054242846229818462673
y1[1] (numeric) = 1.9913269460542428462298031396768
absolute error = 1.53229962e-23
relative error = 7.6948670987263427043511204861898e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1319
y2[1] (analytic) = 0.8684821249053243800928601461666
y2[1] (numeric) = 0.86848212490532438009286219513038
absolute error = 2.04896378e-24
relative error = 2.3592469220058653076537607813380e-22 %
h = 0.0001
y1[1] (analytic) = 1.9913137992233242902998131909134
y1[1] (numeric) = 1.9913137992233242902997978199365
absolute error = 1.53709769e-23
relative error = 7.7190128979145174510781040501994e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=621.8MB, alloc=4.4MB, time=57.64
NO POLE
NO POLE
x[1] = 0.132
y2[1] (analytic) = 0.86838299418315664155567172956986
y2[1] (numeric) = 0.86838299418315664155567378649863
absolute error = 2.05692877e-24
relative error = 2.3686884517295820953047197678142e-22 %
h = 0.0001
y1[1] (analytic) = 1.991300642479267750397513340263
y1[1] (numeric) = 1.9913006424792677503974979213069
absolute error = 1.54189561e-23
relative error = 7.7431583012008861392269968853608e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1321
y2[1] (analytic) = 0.86828386477715896009010851597497
y2[1] (numeric) = 0.86828386477715896009011058087835
absolute error = 2.06490338e-24
relative error = 2.3781432130262467869829867512351e-22 %
h = 0.0001
y1[1] (analytic) = 1.9912874758222047939633746702112
y1[1] (numeric) = 1.9912874758222047939633592032772
absolute error = 1.54669340e-23
relative error = 7.7673034093752263975062788762195e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=625.6MB, alloc=4.4MB, time=58.25
NO POLE
NO POLE
x[1] = 0.1322
y2[1] (analytic) = 0.86818473668832262975532124165454
y2[1] (numeric) = 0.86818473668832262975532331454214
absolute error = 2.07288760e-24
relative error = 2.3876111988641933239016807386180e-22 %
h = 0.0001
y1[1] (analytic) = 1.991274299252267087567917022957
y1[1] (numeric) = 1.9912742992522670875679015080467
absolute error = 1.55149103e-23
relative error = 7.7914480721344729648951164609065e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1323
y2[1] (analytic) = 0.86808560991763893143884714254974
y2[1] (numeric) = 0.86808560991763893143884922343117
absolute error = 2.08088143e-24
relative error = 2.3970924137279813826593320279733e-22 %
h = 0.0001
y1[1] (analytic) = 1.9912611127695863969104076577057
y1[1] (numeric) = 1.9912611127695863969103920948205
absolute error = 1.55628852e-23
relative error = 7.8155923902687185168374323595396e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=629.4MB, alloc=4.4MB, time=58.87
NO POLE
NO POLE
x[1] = 0.1324
y2[1] (analytic) = 0.86798648446609913284669714540321
y2[1] (numeric) = 0.8679864844660991328466992342881
absolute error = 2.08888489e-24
relative error = 2.4065868851458889073130627701285e-22 %
h = 0.0001
y1[1] (analytic) = 1.9912479163742945868175435936767
y1[1] (numeric) = 1.991247916374294586817527982818
absolute error = 1.56108587e-23
relative error = 7.8397363641311798951452354116841e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1325
y2[1] (analytic) = 0.86788736033469448849344319070725
y2[1] (numeric) = 0.86788736033469448849344528760521
absolute error = 2.09689796e-24
relative error = 2.4160945945696760182320540754931e-22 %
h = 0.0001
y1[1] (analytic) = 1.9912347100665236212421329618379
y1[1] (numeric) = 1.9912347100665236212421173030072
absolute error = 1.56588307e-23
relative error = 7.8638799438549693768251891289431e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=633.2MB, alloc=4.4MB, time=59.60
NO POLE
NO POLE
x[1] = 0.1326
y2[1] (analytic) = 0.86778823752441623969230568756629
y2[1] (numeric) = 0.86778823752441623969230779248693
absolute error = 2.10492064e-24
relative error = 2.4256155464895611579611066404644e-22 %
h = 0.0001
y1[1] (analytic) = 1.9912214938464055632617753653787
y1[1] (numeric) = 1.9912214938464055632617596585774
absolute error = 1.57068013e-23
relative error = 7.8880231800127186038260558354191e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1327
y2[1] (analytic) = 0.86768911603625561454524110057299
y2[1] (numeric) = 0.86768911603625561454524321352593
absolute error = 2.11295294e-24
relative error = 2.4351497569225152630047277499686e-22 %
h = 0.0001
y1[1] (analytic) = 1.9912082677140725750775412489351
y1[1] (numeric) = 1.9912082677140725750775254941646
absolute error = 1.57547705e-23
relative error = 7.9121660729576205590562640941681e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=637.0MB, alloc=4.4MB, time=60.21
NO POLE
NO POLE
x[1] = 0.1328
y2[1] (analytic) = 0.86758999587120382793302966879695
y2[1] (numeric) = 0.8675899958712038279330317897918
absolute error = 2.12099485e-24
relative error = 2.4446972188403007399930867772210e-22 %
h = 0.0001
y1[1] (analytic) = 1.99119503166965691801265027658
y1[1] (numeric) = 1.9911950316696569180126344738418
absolute error = 1.58027382e-23
relative error = 7.9363085728217629630709957071769e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1329
y2[1] (analytic) = 0.86749087703025208150536325698511
y2[1] (numeric) = 0.86749087703025208150536538603149
absolute error = 2.12904638e-24
relative error = 2.4542579482663004287869442108733e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911817857132909525111487185922
y1[1] (numeric) = 1.9911817857132909525111328678878
absolute error = 1.58507044e-23
relative error = 7.9604506799573212006231871375627e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=640.8MB, alloc=4.4MB, time=60.81
NO POLE
NO POLE
x[1] = 0.133
y2[1] (analytic) = 0.86739175951439156367093333907315
y2[1] (numeric) = 0.86739175951439156367093547618068
absolute error = 2.13710753e-24
relative error = 2.4638319497022401740045357006482e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911685298451071381365858470171
y1[1] (numeric) = 1.9911685298451071381365699483479
absolute error = 1.58986692e-23
relative error = 7.9845924449382274912759278829867e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1331
y2[1] (analytic) = 0.86729264332461344958751911410682
y2[1] (numeric) = 0.8672926433246134495875212592851
absolute error = 2.14517828e-24
relative error = 2.4734192045914712777305835080802e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911552640652380335706893400321
y1[1] (numeric) = 1.9911552640652380335706733933995
absolute error = 1.59466326e-23
relative error = 8.0087338681176426586555856523420e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=644.7MB, alloc=4.4MB, time=61.38
NO POLE
NO POLE
x[1] = 0.1332
y2[1] (analytic) = 0.86719352846190890115207575467236
y2[1] (numeric) = 0.86719352846190890115207790793102
absolute error = 2.15325866e-24
relative error = 2.4830197520259527061447263930353e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911419883738162966120396951306
y1[1] (numeric) = 1.9911419883738162966120237005361
absolute error = 1.59945945e-23
relative error = 8.0328748996262844384726481205509e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1333
y2[1] (analytic) = 0.8670944149272690669908227879353
y2[1] (numeric) = 0.86709441492726906699082494928394
absolute error = 2.16134864e-24
relative error = 2.4926335619187347258006941188571e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911287027709746841747436511374
y1[1] (numeric) = 1.9911287027709746841747276085824
absolute error = 1.60425550e-23
relative error = 8.0570155900390636577135971732700e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=648.5MB, alloc=4.4MB, time=61.96
NO POLE
NO POLE
x[1] = 0.1334
y2[1] (analytic) = 0.86699530272168508244933260938644
y2[1] (numeric) = 0.86699530272168508244933477883467
absolute error = 2.16944823e-24
relative error = 2.5022606503052952140157068475928e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911154072568460522871066190683
y1[1] (numeric) = 1.9911154072568460522870905285544
absolute error = 1.60905139e-23
relative error = 8.0811558392629056808701710551554e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1335
y2[1] (analytic) = 0.86689619184614806958261912939442
y2[1] (numeric) = 0.86689619184614806958262130695186
absolute error = 2.17755744e-24
relative error = 2.5119010332282793358718368283326e-22 %
h = 0.0001
y1[1] (analytic) = 1.9911021018315633560903041218489
y1[1] (numeric) = 1.9911021018315633560902879833774
absolute error = 1.61384715e-23
relative error = 8.1052957983192510446981858829707e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=652.3MB, alloc=4.4MB, time=62.54
NO POLE
NO POLE
x[1] = 0.1336
y2[1] (analytic) = 0.86679708230164913714522655266383
y2[1] (numeric) = 0.8667970823016491371452287383401
absolute error = 2.18567627e-24
relative error = 2.5215547152007777477672772230391e-22 %
h = 0.0001
y1[1] (analytic) = 1.991088786495259649837052242903
y1[1] (numeric) = 1.9910887864952596498370360564755
absolute error = 1.61864275e-23
relative error = 8.1294353168908956486803543195690e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1337
y2[1] (analytic) = 0.86669797408917938058131829069807
y2[1] (numeric) = 0.86669797408917938058132048450278
absolute error = 2.19380471e-24
relative error = 2.5312216891997340905785589754867e-22 %
h = 0.0001
y1[1] (analytic) = 1.9910754612480680868902770836274
y1[1] (numeric) = 1.9910754612480680868902608492453
absolute error = 1.62343821e-23
relative error = 8.1535744957771635022502059977166e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=656.1MB, alloc=4.4MB, time=63.13
NO POLE
NO POLE
x[1] = 0.1338
y2[1] (analytic) = 0.8665988672097298820147660073659
y2[1] (numeric) = 0.86659886720972988201476820930866
absolute error = 2.20194276e-24
relative error = 2.5409019597380767539972394568382e-22 %
h = 0.0001
y1[1] (analytic) = 1.9910621260901219197217832297633
y1[1] (numeric) = 1.9910621260901219197217669474281
absolute error = 1.62823352e-23
relative error = 8.1777132851067093120990102797103e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1339
y2[1] (analytic) = 0.86649976166429171023923879767105
y2[1] (numeric) = 0.86649976166429171023924100776147
absolute error = 2.21009042e-24
relative error = 2.5505955313306318758047696306063e-22 %
h = 0.0001
y1[1] (analytic) = 1.9910487810215544999109212266794
y1[1] (numeric) = 1.9910487810215544999109048963926
absolute error = 1.63302868e-23
relative error = 8.2018516852316202435530814493582e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=659.9MB, alloc=4.4MB, time=63.72
NO POLE
NO POLE
x[1] = 0.134
y2[1] (analytic) = 0.86640065745385592070829249982374
y2[1] (numeric) = 0.86640065745385592070829471807144
absolute error = 2.21824770e-24
relative error = 2.5603024200361283750305760926036e-22 %
h = 0.0001
y1[1] (analytic) = 1.9910354260424992781432540635797
y1[1] (numeric) = 1.9910354260424992781432376853427
absolute error = 1.63782370e-23
relative error = 8.2259897467290978145309022859682e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1341
y2[1] (analytic) = 0.86630155457941355552545914071341
y2[1] (numeric) = 0.866301554579413555525461367128
absolute error = 2.22641459e-24
relative error = 2.5700226188338270678441382865842e-22 %
h = 0.0001
y1[1] (analytic) = 1.9910220611530898042092226666487
y1[1] (numeric) = 1.991022061153089804209206240463
absolute error = 1.64261857e-23
relative error = 8.2501274197267619369752883027282e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=663.7MB, alloc=4.4MB, time=64.29
NO POLE
NO POLE
x[1] = 0.1342
y2[1] (analytic) = 0.86620245304195564343433651488166
y2[1] (numeric) = 0.86620245304195564343433874947275
absolute error = 2.23459109e-24
relative error = 2.5797561322442533784512580094582e-22 %
h = 0.0001
y1[1] (analytic) = 1.9910086863534597270028104011484
y1[1] (numeric) = 1.9910086863534597270027939270155
absolute error = 1.64741329e-23
relative error = 8.2742647045766733819117750312182e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1343
y2[1] (analytic) = 0.8661033528424731998086778970945
y2[1] (numeric) = 0.8661033528424731998086801398717
absolute error = 2.24277720e-24
relative error = 2.5895029647898339404411523688821e-22 %
h = 0.0001
y1[1] (analytic) = 1.9909953016437427945202065824794
y1[1] (numeric) = 1.9909953016437427945201900604007
absolute error = 1.65220787e-23
relative error = 8.2984016518570194910683336770734e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=667.5MB, alloc=4.4MB, time=64.86
NO POLE
NO POLE
x[1] = 0.1344
y2[1] (analytic) = 0.8660042539819572266424818886131
y2[1] (numeric) = 0.86600425398195722664248413958603
absolute error = 2.25097293e-24
relative error = 2.5992631325421848512039886588575e-22 %
h = 0.0001
y1[1] (analytic) = 1.9909819070240728538584689962201
y1[1] (numeric) = 1.990981907024072853858452426197
absolute error = 1.65700231e-23
relative error = 8.3225382619208566985180858558892e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1345
y2[1] (analytic) = 0.86590515646139871254008239726208
y2[1] (numeric) = 0.86590515646139871254008465644034
absolute error = 2.25917826e-24
relative error = 2.6090366169342845026050277857891e-22 %
h = 0.0001
y1[1] (analytic) = 1.9909685024945838512141854271572
y1[1] (numeric) = 1.9909685024945838512141688091913
absolute error = 1.66179659e-23
relative error = 8.3466744346676106346915523418935e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=671.4MB, alloc=4.4MB, time=65.43
NO POLE
NO POLE
x[1] = 0.1346
y2[1] (analytic) = 0.86580606028178863270623875139437
y2[1] (numeric) = 0.86580606028178863270624101878758
absolute error = 2.26739321e-24
relative error = 2.6188234455901652177949716710087e-22 %
h = 0.0001
y1[1] (analytic) = 1.9909550880554098318821341973214
y1[1] (numeric) = 1.9909550880554098318821175314141
absolute error = 1.66659073e-23
relative error = 8.3708102709025924597712699057578e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=675.2MB, alloc=4.4MB, time=66.00
x[1] = 0.1347
y2[1] (analytic) = 0.86570696544411794893622594785194
y2[1] (numeric) = 0.86570696544411794893622822346971
absolute error = 2.27561777e-24
relative error = 2.6286236114925806021886173152318e-22 %
h = 0.0001
y1[1] (analytic) = 1.99094166370668494025394371304
y1[1] (numeric) = 1.9909416637066849402539269991928
absolute error = 1.67138472e-23
relative error = 8.3949457207513459347883136122096e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1348
y2[1] (analytic) = 0.86560787194937760960592503402127
y2[1] (numeric) = 0.86560787194937760960592731787321
absolute error = 2.28385194e-24
relative error = 2.6384371191734771953148529802333e-22 %
h = 0.0001
y1[1] (analytic) = 1.9909282294485434198167510210223
y1[1] (numeric) = 1.9909282294485434198167342592366
absolute error = 1.67617857e-23
relative error = 8.4190808347937070164712419813003e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=679.0MB, alloc=4.4MB, time=66.57
x[1] = 0.1349
y2[1] (analytic) = 0.8655087797985585496619136240828
y2[1] (numeric) = 0.86550877979855854966191591617852
absolute error = 2.29209572e-24
relative error = 2.6482639731667079514003367020917e-22 %
h = 0.0001
y1[1] (analytic) = 1.990914785281119613151859373489
y1[1] (numeric) = 1.9909147852811196131518425637664
absolute error = 1.68097226e-23
relative error = 8.4432155129263588854448956611666e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.135
y2[1] (analytic) = 0.86540968899265169061155654955344
y2[1] (numeric) = 0.86540968899265169061155884990255
absolute error = 2.30034911e-24
relative error = 2.6581041780080331084515015064905e-22 %
h = 0.0001
y1[1] (analytic) = 1.9909013312045479619333948023605
y1[1] (numeric) = 1.9909013312045479619333779447025
absolute error = 1.68576580e-23
relative error = 8.4673498057287806666602964349432e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=682.8MB, alloc=4.4MB, time=67.15
NO POLE
NO POLE
x[1] = 0.1351
y2[1] (analytic) = 0.86531059953264794051309664422115
y2[1] (numeric) = 0.86531059953264794051309895283325
absolute error = 2.30861210e-24
relative error = 2.6679577266785770776264959641253e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908878672189630069269617025168
y1[1] (numeric) = 1.9908878672189630069269447969249
absolute error = 1.69055919e-23
relative error = 8.4914837135529538052125374144052e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1352
y2[1] (analytic) = 0.86521151141953819396574566357075
y2[1] (numeric) = 0.86521151141953819396574798045546
absolute error = 2.31688471e-24
relative error = 2.6778246468296817238162179402007e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908743933244993879882974241424
y1[1] (numeric) = 1.990874393324499387988280470618
absolute error = 1.69535244e-23
relative error = 8.5156172869800367169785644906821e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=686.6MB, alloc=4.4MB, time=67.71
NO POLE
NO POLE
x[1] = 0.1353
y2[1] (analytic) = 0.86511242465431333209977533880013
y2[1] (numeric) = 0.86511242465431333209977766396706
absolute error = 2.32516693e-24
relative error = 2.6877049314476136001065148172416e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908609095212918440619258741701
y1[1] (numeric) = 1.9908609095212918440619088727147
absolute error = 1.70014554e-23
relative error = 8.5397504761334874984315967592101e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1354
y2[1] (analytic) = 0.86501333923796422256660856552572
y2[1] (numeric) = 0.86501333923796422256661089898448
absolute error = 2.33345876e-24
relative error = 2.6975985850757707794210800381319e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908474158094752131798101268369
y1[1] (numeric) = 1.990847415809475213179793077452
absolute error = 1.70493849e-23
relative error = 8.5638832813652616140699275966919e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=690.4MB, alloc=4.4MB, time=68.29
NO POLE
NO POLE
x[1] = 0.1355
y2[1] (analytic) = 0.86491425517148171952891072727656
y2[1] (numeric) = 0.86491425517148171952891306903675
absolute error = 2.34176019e-24
relative error = 2.7075056006976232389165735410453e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908339121891844324600040433656
y1[1] (numeric) = 1.9908339121891844324599869460526
absolute error = 1.70973130e-23
relative error = 8.5880157532575128817488233065360e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1356
y2[1] (analytic) = 0.86481517245585666365068115387588
y2[1] (numeric) = 0.86481517245585666365068350394711
absolute error = 2.35007123e-24
relative error = 2.7174259944195836245877681080099e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908203986605545381053029007851
y1[1] (numeric) = 1.9908203986605545381052857555456
absolute error = 1.71452395e-23
relative error = 8.6121477917021054620305389037133e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=694.2MB, alloc=4.4MB, time=68.85
NO POLE
NO POLE
x[1] = 0.1357
y2[1] (analytic) = 0.86471609109207988208734471480937
y2[1] (numeric) = 0.86471609109207988208734707320125
absolute error = 2.35839188e-24
relative error = 2.7273597707907866767056805639569e-22 %
h = 0.0001
y1[1] (analytic) = 1.9908068752237206654018930299039
y1[1] (numeric) = 1.9908068752237206654018758367394
absolute error = 1.71931645e-23
relative error = 8.6362794472808347195694904864232e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1358
y2[1] (analytic) = 0.8646170110811421884758435476792
y2[1] (numeric) = 0.86461701108114218847584591440134
absolute error = 2.36672214e-24
relative error = 2.7373069343622813879794718274099e-22 %
h = 0.0001
y1[1] (analytic) = 1.9907933418788180487180004624492
y1[1] (numeric) = 1.9907933418788180487179832213612
absolute error = 1.72410880e-23
relative error = 8.6604107203456206204225036629774e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=698.1MB, alloc=4.4MB, time=69.45
NO POLE
NO POLE
x[1] = 0.1359
y2[1] (analytic) = 0.86451793242403438292472892184285
y2[1] (numeric) = 0.86451793242403438292473129690485
absolute error = 2.37506200e-24
relative error = 2.7472674781198918268201468078417e-22 %
h = 0.0001
y1[1] (analytic) = 1.9907797986259820215025385873858
y1[1] (numeric) = 1.9907797986259820215025212983757
absolute error = 1.72890101e-23
relative error = 8.6845416614799468921091431001409e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.136
y2[1] (analytic) = 0.86441885512174725200425323733583
y2[1] (numeric) = 0.86441885512174725200425562074731
absolute error = 2.38341148e-24
relative error = 2.7572414297514524169136528414100e-22 %
h = 0.0001
y1[1] (analytic) = 1.990766245465348016283754816428
y1[1] (numeric) = 1.9907662454653480162837374794974
absolute error = 1.73369306e-23
relative error = 8.7086721705729125826916730111678e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=701.9MB, alloc=4.4MB, time=70.04
NO POLE
NO POLE
x[1] = 0.1361
y2[1] (analytic) = 0.86431977917527156873646215917745
y2[1] (numeric) = 0.86431977917527156873646455094802
absolute error = 2.39177057e-24
relative error = 2.7672287822479456070421740571584e-22 %
h = 0.0001
y1[1] (analytic) = 1.9907526823970515646678762587584
y1[1] (numeric) = 1.9907526823970515646678588739088
absolute error = 1.73848496e-23
relative error = 8.7328022982076420397666604796039e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1362
y2[1] (analytic) = 0.8642207045855980925852868871586
y2[1] (numeric) = 0.86422070458559809258528928729787
absolute error = 2.40013927e-24
relative error = 2.7772295401680861357911362501901e-22 %
h = 0.0001
y1[1] (analytic) = 1.9907391094212282973377544049668
y1[1] (numeric) = 1.9907391094212282973377369721996
absolute error = 1.74327672e-23
relative error = 8.7569320949686192173632702111936e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=705.7MB, alloc=4.4MB, time=70.61
NO POLE
NO POLE
x[1] = 0.1363
y2[1] (analytic) = 0.8641216313537175694466365612107
y2[1] (numeric) = 0.86412163135371756944663896972827
absolute error = 2.40851757e-24
relative error = 2.7872436965000624249140445031287e-22 %
h = 0.0001
y1[1] (analytic) = 1.9907255265380139440515088202224
y1[1] (numeric) = 1.9907255265380139440514913395392
absolute error = 1.74806832e-23
relative error = 8.7810614607428641021740876589282e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1364
y2[1] (analytic) = 0.86402255948062073163849080245486
y2[1] (numeric) = 0.86402255948062073163849321936033
absolute error = 2.41690547e-24
relative error = 2.7972712558024465220530291642319e-22 %
h = 0.0001
y1[1] (analytic) = 1.9907119337475443336411698466945
y1[1] (numeric) = 1.9907119337475443336411523180967
absolute error = 1.75285978e-23
relative error = 8.8051904963477856129494216616431e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=709.5MB, alloc=4.4MB, time=71.18
NO POLE
NO POLE
x[1] = 0.1365
y2[1] (analytic) = 0.86392348896729829789099239003033
y2[1] (numeric) = 0.86392348896729829789099481533331
absolute error = 2.42530298e-24
relative error = 2.8073122342108282327419565126910e-22 %
h = 0.0001
y1[1] (analytic) = 1.9906983310499553940113203152323
y1[1] (numeric) = 1.9906983310499553940113027387215
absolute error = 1.75765108e-23
relative error = 8.8293191016690152062143099331629e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1366
y2[1] (analytic) = 0.86382441981474097333654007380135
y2[1] (numeric) = 0.86382441981474097333654250751145
absolute error = 2.43371010e-24
relative error = 2.8173666362916003240490561595876e-22 %
h = 0.0001
y1[1] (analytic) = 1.9906847184453831521377362663213
y1[1] (numeric) = 1.990684718445383152137718641899
absolute error = 1.76244223e-23
relative error = 8.8534473272913444458790307594270e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=713.3MB, alloc=4.4MB, time=71.75
NO POLE
NO POLE
x[1] = 0.1367
y2[1] (analytic) = 0.86372535202393944949988152304141
y2[1] (numeric) = 0.86372535202393944949988396516824
absolute error = 2.44212683e-24
relative error = 2.8274344666130776897379895090114e-22 %
h = 0.0001
y1[1] (analytic) = 1.9906710959339637340660266803259
y1[1] (numeric) = 1.9906710959339637340660090079936
absolute error = 1.76723323e-23
relative error = 8.8775751735666140977667986792456e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1368
y2[1] (analytic) = 0.86362628559588440428820641119402
y2[1] (numeric) = 0.86362628559588440428820886174719
absolute error = 2.45055317e-24
relative error = 2.8375157297454982275373757201291e-22 %
h = 0.0001
y1[1] (analytic) = 1.9906574635158333649102722170348
y1[1] (numeric) = 1.9906574635158333649102544967939
absolute error = 1.77202409e-23
relative error = 8.9017026910813157549389497617393e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=717.1MB, alloc=4.4MB, time=72.32
NO POLE
NO POLE
x[1] = 0.1369
y2[1] (analytic) = 0.86352722053156650198123963680909
y2[1] (numeric) = 0.8635272205315665019812420957982
absolute error = 2.45898911e-24
relative error = 2.8476104186806128598199989255347e-22 %
h = 0.0001
y1[1] (analytic) = 1.990643821191128368851662964521
y1[1] (numeric) = 1.9906438211911283688516451963731
absolute error = 1.77681479e-23
relative error = 8.9258297797182978388552431968777e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.137
y2[1] (analytic) = 0.86342815683197639322133468075391
y2[1] (numeric) = 0.86342815683197639322133714818856
absolute error = 2.46743465e-24
relative error = 2.8577185379885221601721355464915e-22 %
h = 0.0001
y1[1] (analytic) = 1.9906301689599851691371351973316
y1[1] (numeric) = 1.9906301689599851691371173812781
absolute error = 1.78160535e-23
relative error = 8.9499565402990388402930191260422e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=720.9MB, alloc=4.4MB, time=72.90
NO POLE
NO POLE
x[1] = 0.1371
y2[1] (analytic) = 0.86332909449810471500356709979788
y2[1] (numeric) = 0.86332909449810471500356957568768
absolute error = 2.47588980e-24
relative error = 2.8678401038243190752572822074906e-22 %
h = 0.0001
y1[1] (analytic) = 1.9906165068225402880780071440189
y1[1] (numeric) = 1.9906165068225402880779892800614
absolute error = 1.78639575e-23
relative error = 8.9740828727049926755954094407018e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1372
y2[1] (analytic) = 0.86323003353094209066582815667003
y2[1] (numeric) = 0.86323003353094209066583064102459
absolute error = 2.48435456e-24
relative error = 2.8779751207659405804018084225110e-22 %
h = 0.0001
y1[1] (analytic) = 1.990602834778930347048613764029
y1[1] (numeric) = 1.990602834778930347048595852169
absolute error = 1.79118600e-23
relative error = 8.9982088275229603511966267714810e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=724.8MB, alloc=4.4MB, time=73.49
NO POLE
NO POLE
x[1] = 0.1373
y2[1] (analytic) = 0.86313097393147912987891858668834
y2[1] (numeric) = 0.86313097393147912987892107951725
absolute error = 2.49282891e-24
relative error = 2.8881235702217966517429157666188e-22 %
h = 0.0001
y1[1] (analytic) = 1.990589152829292066484940533959
y1[1] (numeric) = 1.990589152829292066484922574198
absolute error = 1.79597610e-23
relative error = 9.0223344051047303490341343719472e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1374
y2[1] (analytic) = 0.86303191570070642863664250105997
y2[1] (numeric) = 0.86303191570070642863664500237285
absolute error = 2.50131288e-24
relative error = 2.8982854915268721250740877214432e-22 %
h = 0.0001
y1[1] (analytic) = 1.9905754609737622658832562431987
y1[1] (numeric) = 1.9905754609737622658832382355383
absolute error = 1.80076604e-23
relative error = 9.0464595555653534706749806749714e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=728.6MB, alloc=4.4MB, time=74.08
NO POLE
NO POLE
x[1] = 0.1375
y2[1] (analytic) = 0.86293285883961456924590142695153
y2[1] (numeric) = 0.86293285883961456924590393675798
absolute error = 2.50980645e-24
relative error = 2.9084608660921031735096097157370e-22 %
h = 0.0001
y1[1] (analytic) = 1.9905617592124778637987447989689
y1[1] (numeric) = 1.9905617592124778637987267434106
absolute error = 1.80555583e-23
relative error = 9.0705843294926382730047384019542e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1376
y2[1] (analytic) = 0.86283380334919412031678848442828
y2[1] (numeric) = 0.8628338033491941203167910027379
absolute error = 2.51830962e-24
relative error = 2.9186496984991496514418889800402e-22 %
h = 0.0001
y1[1] (analytic) = 1.9905480475455758778441360407708
y1[1] (numeric) = 1.9905480475455758778441179373161
absolute error = 1.81034547e-23
relative error = 9.0947087272383464865946106502455e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=732.4MB, alloc=4.4MB, time=74.64
NO POLE
NO POLE
x[1] = 0.1377
y2[1] (analytic) = 0.86273474923043563675268270036144
y2[1] (numeric) = 0.86273474923043563675268522718384
absolute error = 2.52682240e-24
relative error = 2.9288520049226487378814019130896e-22 %
h = 0.0001
y1[1] (analytic) = 1.9905343259731934246883355642596
y1[1] (numeric) = 1.99053432597319342468831741291
absolute error = 1.81513496e-23
relative error = 9.1188327491542312025643887080976e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1378
y2[1] (analytic) = 0.8626356964843296597403434594027
y2[1] (numeric) = 0.86263569648432965974034599474748
absolute error = 2.53534478e-24
relative error = 2.9390677783597333340043270926281e-22 %
h = 0.0001
y1[1] (analytic) = 1.9905205944954677200550535545568
y1[1] (numeric) = 1.9905205944954677200550353553139
absolute error = 1.81992429e-23
relative error = 9.1429563453539231581567886324533e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=736.2MB, alloc=4.4MB, time=75.24
NO POLE
NO POLE
x[1] = 0.1379
y2[1] (analytic) = 0.86253664511186671674000509212484
y2[1] (numeric) = 0.86253664511186671674000763600161
absolute error = 2.54387677e-24
relative error = 2.9492970349915647050618489892227e-22 %
h = 0.0001
y1[1] (analytic) = 1.9905068531125360787214326290143
y1[1] (numeric) = 1.9905068531125360787214143818795
absolute error = 1.82471348e-23
relative error = 9.1670796166650388350174360045549e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.138
y2[1] (analytic) = 0.86243759511403732147547160042766
y2[1] (numeric) = 0.86243759511403732147547415284602
absolute error = 2.55241836e-24
relative error = 2.9595397678164783761288486924075e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904931018245359145166746894438
y1[1] (numeric) = 1.9904931018245359145166563944187
absolute error = 1.82950251e-23
relative error = 9.1912024629627306965949197826337e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=740.0MB, alloc=4.4MB, time=75.81
NO POLE
NO POLE
x[1] = 0.1381
y2[1] (analytic) = 0.86233854649183197392421152030819
y2[1] (numeric) = 0.86233854649183197392421408127775
absolute error = 2.56096956e-24
relative error = 2.9697959930221643769588550806052e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904793406316047403206667838264
y1[1] (numeric) = 1.9904793406316047403206484409125
absolute error = 1.83429139e-23
relative error = 9.2153249348368303524124084674353e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1382
y2[1] (analytic) = 0.86223949924624116030745292209427
y2[1] (numeric) = 0.86223949924624116030745549162462
absolute error = 2.56953035e-24
relative error = 2.9800656920104574868321038390173e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904655695338801680626059775144
y1[1] (numeric) = 1.9904655695338801680625875867132
absolute error = 1.83908012e-23
relative error = 9.2394470326390471039638060856128e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=743.8MB, alloc=4.4MB, time=76.38
NO POLE
NO POLE
x[1] = 0.1383
y2[1] (analytic) = 0.86214045337825535308027854824049
y2[1] (numeric) = 0.86214045337825535308028112634125
absolute error = 2.57810076e-24
relative error = 2.9903489041696602994455256152838e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904517885314999087196232339406
y1[1] (numeric) = 1.9904517885314999087196047952537
absolute error = 1.84386869e-23
relative error = 9.2635687064812313243968244645408e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1384
y2[1] (analytic) = 0.86204140888886501092172108878567
y2[1] (numeric) = 0.86204140888886501092172367546643
absolute error = 2.58668076e-24
relative error = 3.0006455993037762712700624501202e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904379976246017723154063048486
y1[1] (numeric) = 1.9904379976246017723153878182774
absolute error = 1.84865712e-23
relative error = 9.2876900571944278099310134099456e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=747.6MB, alloc=4.4MB, time=76.95
NO POLE
NO POLE
x[1] = 0.1385
y2[1] (analytic) = 0.86194236577906057872485859457073
y2[1] (numeric) = 0.8619423657790605787248611898411
absolute error = 2.59527037e-24
relative error = 3.0109558052112719020106801533353e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904241968133236679188216300562
y1[1] (numeric) = 1.9904241968133236679188030956024
absolute error = 1.85344538e-23
relative error = 9.3118109344097240746460928942713e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1386
y2[1] (analytic) = 0.8618433240498324875869100283162
y2[1] (numeric) = 0.86184332404983248758691263218578
absolute error = 2.60386958e-24
relative error = 3.0212795148941040309983929385998e-22 %
h = 0.0001
y1[1] (analytic) = 1.9904103860978036036425352467689
y1[1] (numeric) = 1.9904103860978036036425166644339
absolute error = 1.85823350e-23
relative error = 9.3359314891993897870448908771899e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=751.5MB, alloc=4.4MB, time=77.52
NO POLE
NO POLE
x[1] = 0.1387
y2[1] (analytic) = 0.86174428370217115479933095365828
y2[1] (numeric) = 0.86174428370217115479933356613667
absolute error = 2.61247839e-24
relative error = 3.0316167329552056659386834748064e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903965654781796866416327084534
y1[1] (numeric) = 1.9903965654781796866416140782388
absolute error = 1.86302146e-23
relative error = 9.3600516214336480472741129523582e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1388
y2[1] (analytic) = 0.86164524473706698383790936224252
y2[1] (numeric) = 0.86164524473706698383791198333932
absolute error = 2.62109680e-24
relative error = 3.0419674639994487294783608108419e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903827349545901231122380132886
y1[1] (numeric) = 1.990382734954590123112219335196
absolute error = 1.86780926e-23
relative error = 9.3841713314631088100025170558448e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=755.3MB, alloc=4.4MB, time=78.10
NO POLE
NO POLE
x[1] = 0.1389
y2[1] (analytic) = 0.86154620715551036435286163897421
y2[1] (numeric) = 0.86154620715551036435286426869902
absolute error = 2.62972481e-24
relative error = 3.0523317126336449453401722249014e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903688945271732182901315422053
y1[1] (numeric) = 1.9903688945271732182901128162362
absolute error = 1.87259691e-23
relative error = 9.4082906698803147236836675215317e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.139
y2[1] (analytic) = 0.86144717095849167215892866552446
y2[1] (numeric) = 0.86144717095849167215893130388689
absolute error = 2.63836243e-24
relative error = 3.0627094950749196317269371074480e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903550441960673764493670065295
y1[1] (numeric) = 1.9903550441960673764493482326854
absolute error = 1.87738441e-23
relative error = 9.4324096370369045518244975123172e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=759.1MB, alloc=4.4MB, time=78.66
NO POLE
NO POLE
x[1] = 0.1391
y2[1] (analytic) = 0.86134813614700126922547206219106
y2[1] (numeric) = 0.86134813614700126922547470920071
absolute error = 2.64700965e-24
relative error = 3.0731008043282632486081402911582e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903411839614111009008874052429
y1[1] (numeric) = 1.9903411839614111009008685835253
absolute error = 1.88217176e-23
relative error = 9.4565282332845085789181586820901e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1392
y2[1] (analytic) = 0.86124910272202950366657056821309
y2[1] (numeric) = 0.86124910272202950366657322387956
absolute error = 2.65566647e-24
relative error = 3.0835056450063131091462353757678e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903273138233429939911399918749
y1[1] (numeric) = 1.9903273138233429939911211222854
absolute error = 1.88695895e-23
relative error = 9.4806464087317562731268445650969e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=762.9MB, alloc=4.4MB, time=79.25
NO POLE
NO POLE
x[1] = 0.1393
y2[1] (analytic) = 0.86115007068456670973111656063842
y2[1] (numeric) = 0.8611500706845667097311192249713
absolute error = 2.66433288e-24
relative error = 3.0939240101112720344318437998107e-22 %
h = 0.0001
y1[1] (analytic) = 1.9903134337820017571006902510391
y1[1] (numeric) = 1.9903134337820017571006713335792
absolute error = 1.89174599e-23
relative error = 9.5047642139725525752635076756761e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1394
y2[1] (analytic) = 0.86105104003560320779291271184299
y2[1] (numeric) = 0.8610510400356032077929153848519
absolute error = 2.67300891e-24
relative error = 3.1043559390967984551033978257207e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902995438375261906428348846289
y1[1] (numeric) = 1.9902995438375261906428159193002
absolute error = 1.89653287e-23
relative error = 9.5288815991148082644195079123880e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=766.7MB, alloc=4.4MB, time=79.84
NO POLE
NO POLE
x[1] = 0.1395
y2[1] (analytic) = 0.8609520107761293043407687858011
y2[1] (numeric) = 0.86095201077612930434077146749563
absolute error = 2.68169453e-24
relative error = 3.1148014017442288739236466459739e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902856439900551940622138076855
y1[1] (numeric) = 1.9902856439900551940621947944896
absolute error = 1.90131959e-23
relative error = 9.5529985645090663764281227638913e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1396
y2[1] (analytic) = 0.86085298290713529196859857320552
y2[1] (numeric) = 0.86085298290713529196860126359526
absolute error = 2.69038974e-24
relative error = 3.1252604026699718072720519201578e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902717342397277658334211539531
y1[1] (numeric) = 1.9902717342397277658334020928914
absolute error = 1.90610617e-23
relative error = 9.5771152109946508275834150591716e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=770.5MB, alloc=4.4MB, time=80.41
NO POLE
NO POLE
x[1] = 0.1397
y2[1] (analytic) = 0.86075395642961144936551696553659
y2[1] (numeric) = 0.86075395642961144936551966463115
absolute error = 2.69909456e-24
relative error = 3.1357329697278245376452182869044e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902578145866830034596152911334
y1[1] (numeric) = 1.9902578145866830034595961822075
absolute error = 1.91089259e-23
relative error = 9.6012314384346995473161589443017e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1398
y2[1] (analytic) = 0.86065493134454804130593716817938
y2[1] (numeric) = 0.86065493134454804130593987598836
absolute error = 2.70780898e-24
relative error = 3.1462190959270485757305200098138e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902438850310601034711278458558
y1[1] (numeric) = 1.9902438850310601034711086890673
absolute error = 1.91567885e-23
relative error = 9.6253472471797272817934381428524e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=774.4MB, alloc=4.4MB, time=80.99
NO POLE
NO POLE
x[1] = 0.1399
y2[1] (analytic) = 0.86055590765293531863966805268778
y2[1] (numeric) = 0.86055590765293531863967076922077
absolute error = 2.71653299e-24
relative error = 3.1567187742735078585241815976478e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902299455729983614240717383751
y1[1] (numeric) = 1.9902299455729983614240525337255
absolute error = 1.92046496e-23
relative error = 9.6494626878256892528331247613800e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.14
y2[1] (analytic) = 0.86045688535576351828201164829463
y2[1] (numeric) = 0.86045688535576351828201437356124
absolute error = 2.72526661e-24
relative error = 3.1672320326348651261641462107720e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902159962126371718989482270114
y1[1] (numeric) = 1.9902159962126371718989289745023
absolute error = 1.92525091e-23
relative error = 9.6735777104783343292449270414495e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=778.2MB, alloc=4.4MB, time=81.58
NO POLE
NO POLE
x[1] = 0.1401
y2[1] (analytic) = 0.86035786445402286320386077276701
y2[1] (numeric) = 0.86035786445402286320386350677684
absolute error = 2.73400983e-24
relative error = 3.1777588640222213648356714301280e-22 %
h = 0.0001
y1[1] (analytic) = 1.9902020369501160284992529623462
y1[1] (numeric) = 1.9902020369501160284992336619792
absolute error = 1.93003670e-23
relative error = 9.6976923154881483055626197914383e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1402
y2[1] (analytic) = 0.86025884494870356242179680270554
y2[1] (numeric) = 0.86025884494870356242179954546818
absolute error = 2.74276264e-24
relative error = 3.1882992614432791958625621887585e-22 %
h = 0.0001
y1[1] (analytic) = 1.990188067785574523850081051189
y1[1] (numeric) = 1.9901880677855745238500617029655
absolute error = 1.93482235e-23
relative error = 9.7218066036986224208613351508184e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=782.0MB, alloc=4.4MB, time=82.18
NO POLE
NO POLE
x[1] = 0.1403
y2[1] (analytic) = 0.8601598268407958109881875833868
y2[1] (numeric) = 0.86015982684079581098819033491185
absolute error = 2.75152505e-24
relative error = 3.1988532411538336537840934278608e-22 %
h = 0.0001
y1[1] (analytic) = 1.9901740887191523495967311303268
y1[1] (numeric) = 1.9901740887191523495967117342485
absolute error = 1.93960783e-23
relative error = 9.7459204247217585256685221065623e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1404
y2[1] (analytic) = 0.86006081013128978998128547824793
y2[1] (numeric) = 0.86006081013128978998128823854499
absolute error = 2.76029706e-24
relative error = 3.2094208077899001306473857624617e-22 %
h = 0.0001
y1[1] (analytic) = 1.9901600997509892964033084500731
y1[1] (numeric) = 1.9901600997509892964032890061415
absolute error = 1.94439316e-23
relative error = 9.7700338794013823362619178693527e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=785.8MB, alloc=4.4MB, time=82.78
NO POLE
NO POLE
x[1] = 0.1405
y2[1] (analytic) = 0.85996179482117566649532555811233
y2[1] (numeric) = 0.85996179482117566649532832719101
absolute error = 2.76907868e-24
relative error = 3.2200019776178716259496731750991e-22 %
h = 0.0001
y1[1] (analytic) = 1.9901461008812252539513269676275
y1[1] (numeric) = 1.9901461008812252539513074758441
absolute error = 1.94917834e-23
relative error = 9.7941469680890012802623640468573e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1406
y2[1] (analytic) = 0.85986278091144359363062393025561
y2[1] (numeric) = 0.8598627809114435936306267081255
absolute error = 2.77786989e-24
relative error = 3.2305967320221644027833937792628e-22 %
h = 0.0001
y1[1] (analytic) = 1.9901320921100002109383104502617
y1[1] (numeric) = 1.9901320921100002109382909106282
absolute error = 1.95396335e-23
relative error = 9.8182595906402726226588985630861e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=789.6MB, alloc=4.4MB, time=83.35
NO POLE
NO POLE
x[1] = 0.1407
y2[1] (analytic) = 0.85976376840308371048367620741061
y2[1] (numeric) = 0.85976376840308371048367899408131
absolute error = 2.78667070e-24
relative error = 3.2412050872717434947595257002181e-22 %
h = 0.0001
y1[1] (analytic) = 1.9901180734374542550763925883458
y1[1] (numeric) = 1.9901180734374542550763730008637
absolute error = 1.95874821e-23
relative error = 9.8423718479011132296227134145230e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1408
y2[1] (analytic) = 0.85966475729708614213725611681077
y2[1] (numeric) = 0.85966475729708614213725891229187
absolute error = 2.79548110e-24
relative error = 3.2518270363780043281044169744307e-22 %
h = 0.0001
y1[1] (analytic) = 1.9901040448637275730909161182278
y1[1] (numeric) = 1.9901040448637275730908964828986
absolute error = 1.96353292e-23
relative error = 9.8664837402230041114956901106574e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=793.4MB, alloc=4.4MB, time=83.92
NO POLE
NO POLE
x[1] = 0.1409
y2[1] (analytic) = 0.85956574759444099965051424937056
y2[1] (numeric) = 0.85956574759444099965051705367167
absolute error = 2.80430111e-24
relative error = 3.2624626072502845630768460428605e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900900063889604507190309549814
y1[1] (numeric) = 1.9900900063889604507190112718067
absolute error = 1.96831747e-23
relative error = 9.8905952177084344527081833110596e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=797.2MB, alloc=4.4MB, time=84.49
x[1] = 0.141
y2[1] (analytic) = 0.85946673929613838004907694910232
y2[1] (numeric) = 0.85946673929613838004907976223302
absolute error = 2.81313070e-24
relative error = 3.2731117696349922190772828420127e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900759580132932727082913350357
y1[1] (numeric) = 1.9900759580132932727082716040171
absolute error = 1.97310186e-23
relative error = 9.9147062807078045739538260645759e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1411
y2[1] (analytic) = 0.85936773240316836631514534286816
y2[1] (numeric) = 0.85936773240316836631514816483806
absolute error = 2.82196990e-24
relative error = 3.2837745630831830837866773585656e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900618997368665228152519687011
y1[1] (numeric) = 1.9900618997368665228152321898401
absolute error = 1.97788610e-23
relative error = 9.9388169798211982607190095981996e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=801.1MB, alloc=4.4MB, time=85.08
x[1] = 0.1412
y2[1] (analytic) = 0.85926872691652102737759451056627
y2[1] (numeric) = 0.85926872691652102737759734138496
absolute error = 2.83081869e-24
relative error = 3.2944509689749448803632727345024e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900478315598207838040632026043
y1[1] (numeric) = 1.9900478315598207838040433759025
absolute error = 1.98267018e-23
relative error = 9.9629272651500134970579245476870e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1413
y2[1] (analytic) = 0.85916972283718641810207279585035
y2[1] (numeric) = 0.85916972283718641810207563552744
absolute error = 2.83967709e-24
relative error = 3.3051410152381752951607198556321e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900337534822967374450651920485
y1[1] (numeric) = 1.9900337534822967374450453175076
absolute error = 1.98745409e-23
relative error = 9.9870370867942181060565560356870e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=804.9MB, alloc=4.4MB, time=85.67
NO POLE
NO POLE
x[1] = 0.1414
y2[1] (analytic) = 0.85907072016615457928110125748146
y2[1] (numeric) = 0.85907072016615457928110410602653
absolute error = 2.84854507e-24
relative error = 3.3158446716110371258224081572732e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900196655044351645133810833112
y1[1] (numeric) = 1.9900196655044351645133611609327
absolute error = 1.99223785e-23
relative error = 1.0011146545604626296645346766522e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1415
y2[1] (analytic) = 0.85897171890441553762417326141098
y2[1] (numeric) = 0.85897171890441553762417611883363
absolute error = 2.85742265e-24
relative error = 3.3265619660266924772671527413641e-22 %
h = 0.0001
y1[1] (analytic) = 1.9900055676263769447875092058936
y1[1] (numeric) = 1.9900055676263769447874892356791
absolute error = 1.99702145e-23
relative error = 1.0035255591681541895063828132807e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=808.7MB, alloc=4.4MB, time=86.23
NO POLE
NO POLE
x[1] = 0.1416
y2[1] (analytic) = 0.85887271905295930574785421369398
y2[1] (numeric) = 0.8588727190529593057478570800038
absolute error = 2.86630982e-24
relative error = 3.3372928915014929999061152773933e-22 %
h = 0.0001
y1[1] (analytic) = 1.9899914598482630570479142747374
y1[1] (numeric) = 1.9899914598482630570478942566884
absolute error = 2.00180490e-23
relative error = 1.0059364275626779415035796070093e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1417
y2[1] (analytic) = 0.85877372061277588216588143433178
y2[1] (numeric) = 0.85877372061277588216588430953837
absolute error = 2.87520659e-24
relative error = 3.3480374643374082165278926767138e-22 %
h = 0.0001
y1[1] (analytic) = 1.989977342170234579075617602421
y1[1] (numeric) = 1.989977342170234579075597536539
absolute error = 2.00658820e-23
relative error = 1.0083472597791741232144339952865e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=812.5MB, alloc=4.4MB, time=86.80
NO POLE
NO POLE
x[1] = 0.1418
y2[1] (analytic) = 0.85867472358485525127926417214287
y2[1] (numeric) = 0.85867472358485525127926705625582
absolute error = 2.88411295e-24
relative error = 3.3587956775520346952260272700193e-22 %
h = 0.0001
y1[1] (analytic) = 1.9899632145924326876507863213504
y1[1] (numeric) = 1.9899632145924326876507662076371
absolute error = 2.01137133e-23
relative error = 1.0107580458023451152904880291139e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1419
y2[1] (analytic) = 0.85857572797018738336638376076101
y2[1] (numeric) = 0.85857572797018738336638665378992
absolute error = 2.89302891e-24
relative error = 3.3695675474539569391522786132000e-22 %
h = 0.0001
y1[1] (analytic) = 1.9899490771149986585513216159589
y1[1] (numeric) = 1.9899490771149986585513014544159
absolute error = 2.01615430e-23
relative error = 1.0131687906923695355367692947499e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=816.3MB, alloc=4.4MB, time=87.39
NO POLE
NO POLE
x[1] = 0.142
y2[1] (analytic) = 0.85847673376976223457309391585971
y2[1] (numeric) = 0.85847673376976223457309681781418
absolute error = 2.90195447e-24
relative error = 3.3803530787105582050593828893203e-22 %
h = 0.0001
y1[1] (analytic) = 1.9899349297380738665514459649294
y1[1] (numeric) = 1.9899349297380738665514257555582
absolute error = 2.02093712e-23
relative error = 1.0155794995095677884885204612093e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1421
y2[1] (analytic) = 0.85837774098456974690282117370195
y2[1] (numeric) = 0.85837774098456974690282408459157
absolute error = 2.91088962e-24
relative error = 3.3911522643413074451214799721556e-22 %
h = 0.0001
y1[1] (analytic) = 1.9899207724617997854202893934529
y1[1] (numeric) = 1.9899207724617997854202691362551
absolute error = 2.02571978e-23
relative error = 1.0179901672637509204299292156500e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=820.1MB, alloc=4.4MB, time=87.95
NO POLE
NO POLE
x[1] = 0.1422
y2[1] (analytic) = 0.85827874961559984820666547111412
y2[1] (numeric) = 0.85827874961559984820666839094849
absolute error = 2.91983437e-24
relative error = 3.4019651206647209997674396214193e-22 %
h = 0.0001
y1[1] (analytic) = 1.9899066052863179879204747355387
y1[1] (numeric) = 1.9899066052863179879204544305159
absolute error = 2.03050228e-23
relative error = 1.0204007939899475321317119671418e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1423
y2[1] (analytic) = 0.85817975966384245217350086698331
y2[1] (numeric) = 0.85817975966384245217350379577201
absolute error = 2.92878870e-24
relative error = 3.4127916290489485154764053145082e-22 %
h = 0.0001
y1[1] (analytic) = 1.9898924282117701458067019063893
y1[1] (numeric) = 1.9898924282117701458066815535431
absolute error = 2.03528462e-23
relative error = 1.0228113797231852600342007571684e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=823.9MB, alloc=4.4MB, time=88.55
NO POLE
NO POLE
x[1] = 0.1424
y2[1] (analytic) = 0.85808077113028745832007640537679
y2[1] (numeric) = 0.85808077113028745832007934312942
absolute error = 2.93775263e-24
relative error = 3.4236318174690150611453548915975e-22 %
h = 0.0001
y1[1] (analytic) = 1.9898782412382980298243311848546
y1[1] (numeric) = 1.9898782412382980298243107841866
absolute error = 2.04006680e-23
relative error = 1.0252219244984907773858613847286e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1425
y2[1] (analytic) = 0.85798178401592475198111712038278
y2[1] (numeric) = 0.85798178401592475198112006710894
absolute error = 2.94672616e-24
relative error = 3.4344856906021523030312552343777e-22 %
h = 0.0001
y1[1] (analytic) = 1.9898640443660435097079655059794
y1[1] (numeric) = 1.9898640443660435097079450574912
absolute error = 2.04484882e-23
relative error = 1.0276324283508897953817798136604e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=827.8MB, alloc=4.4MB, time=89.12
NO POLE
NO POLE
x[1] = 0.1426
y2[1] (analytic) = 0.85788279832174420429942518277147
y2[1] (numeric) = 0.85788279832174420429942813848075
absolute error = 2.95570928e-24
relative error = 3.4453532414709608885204391005497e-22 %
h = 0.0001
y1[1] (analytic) = 1.9898498375951485541800317636587
y1[1] (numeric) = 1.9898498375951485541800112673518
absolute error = 2.04963069e-23
relative error = 1.0300428963409119094745509415857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1427
y2[1] (analytic) = 0.85778381404873567221598118857522
y2[1] (numeric) = 0.85778381404873567221598415327721
absolute error = 2.96470199e-24
relative error = 3.4562344747525838597099993332457e-22 %
h = 0.0001
y1[1] (analytic) = 1.9898356209257552309493611234143
y1[1] (numeric) = 1.9898356209257552309493405792904
absolute error = 2.05441239e-23
relative error = 1.0324533184526071252717208893695e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=831.6MB, alloc=4.4MB, time=89.70
NO POLE
NO POLE
x[1] = 0.1428
y2[1] (analytic) = 0.85768483119788899846004558968699
y2[1] (numeric) = 0.85768483119788899846004856339129
absolute error = 2.97370430e-24
relative error = 3.4671294067854316921688206107187e-22 %
h = 0.0001
y1[1] (analytic) = 1.989821394358005706709768345308
y1[1] (numeric) = 1.9898213943580057067097477533687
absolute error = 2.05919393e-23
relative error = 1.0348636997464672398752892687987e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1429
y2[1] (analytic) = 0.85758584977019401153926026657604
y2[1] (numeric) = 0.85758584977019401153926324929223
absolute error = 2.98271619e-24
relative error = 3.4780380189333510631559648015428e-22 %
h = 0.0001
y1[1] (analytic) = 1.9898071578920422471386301170046
y1[1] (numeric) = 1.9898071578920422471386094772515
absolute error = 2.06397531e-23
relative error = 1.0372740402575141276517788790768e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=835.4MB, alloc=4.4MB, time=90.27
NO POLE
NO POLE
x[1] = 0.143
y2[1] (analytic) = 0.85748686976664052572975024321969
y2[1] (numeric) = 0.85748686976664052572975323495738
absolute error = 2.99173769e-24
relative error = 3.4889603508613280028727969163286e-22 %
h = 0.0001
y1[1] (analytic) = 1.9897929115280072168954623969991
y1[1] (numeric) = 1.9897929115280072168954417094338
absolute error = 2.06875653e-23
relative error = 1.0396843400207687066062918051111e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1431
y2[1] (analytic) = 0.85738789118821834106622554435039
y2[1] (numeric) = 0.85738789118821834106622854511916
absolute error = 3.00076877e-24
relative error = 3.4998963722724832731597001944968e-22 %
h = 0.0001
y1[1] (analytic) = 1.989778655266043079620496768023
y1[1] (numeric) = 1.989778655266043079620476032647
absolute error = 2.07353760e-23
relative error = 1.0420946040969355670719811362411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=839.2MB, alloc=4.4MB, time=90.84
NO POLE
NO POLE
x[1] = 0.1432
y2[1] (analytic) = 0.85728891403591724333208319511679
y2[1] (numeric) = 0.85728891403591724333208620492624
absolute error = 3.00980945e-24
relative error = 3.5108461111791538761497157532731e-22 %
h = 0.0001
y1[1] (analytic) = 1.9897643891062923979332558006428
y1[1] (numeric) = 1.9897643891062923979332350174578
absolute error = 2.07831850e-23
relative error = 1.0445048224697004956634822405974e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1433
y2[1] (analytic) = 0.85718993831072700404950936325809
y2[1] (numeric) = 0.85718993831072700404951238211781
absolute error = 3.01885972e-24
relative error = 3.5218095606083498688936412585292e-22 %
h = 0.0001
y1[1] (analytic) = 1.9897501130488978334311274270666
y1[1] (numeric) = 1.9897501130488978334311065960741
absolute error = 2.08309925e-23
relative error = 1.0469150052254868872863012835429e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=843.0MB, alloc=4.4MB, time=91.42
NO POLE
NO POLE
x[1] = 0.1434
y2[1] (analytic) = 0.85709096401363738046958164389038
y2[1] (numeric) = 0.85709096401363738046958467180996
absolute error = 3.02791958e-24
relative error = 3.5327867252510458660136616423018e-22 %
h = 0.0001
y1[1] (analytic) = 1.9897358270940021466879383251705
y1[1] (numeric) = 1.9897358270940021466879174463722
absolute error = 2.08787983e-23
relative error = 1.0493251423478344917220395903035e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1435
y2[1] (analytic) = 0.85699199114563811556237148700414
y2[1] (numeric) = 0.85699199114563811556237452399317
absolute error = 3.03698903e-24
relative error = 3.5437776098001957954547261033665e-22 %
h = 0.0001
y1[1] (analytic) = 1.9897215312417481972525263127625
y1[1] (numeric) = 1.98972153124174819725250538616
absolute error = 2.09266025e-23
relative error = 1.0517352388974801228150247576453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=846.8MB, alloc=4.4MB, time=92.01
NO POLE
NO POLE
x[1] = 0.1436
y2[1] (analytic) = 0.85689301970771893800704676777175
y2[1] (numeric) = 0.85689301970771893800704981383982
absolute error = 3.04606807e-24
relative error = 3.5547822189507338058473008423808e-22 %
h = 0.0001
y1[1] (analytic) = 1.9897072254922789436473117520946
y1[1] (numeric) = 1.9897072254922789436472907776894
absolute error = 2.09744052e-23
relative error = 1.0541452999353040321281790197133e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1437
y2[1] (analytic) = 0.85679404970086956218197449976406
y2[1] (numeric) = 0.85679404970086956218197755492077
absolute error = 3.05515671e-24
relative error = 3.5658005690709914306687472268687e-22 %
h = 0.0001
y1[1] (analytic) = 1.98969290984573744336686796464
y1[1] (numeric) = 1.9896929098457374433668469424338
absolute error = 2.10222062e-23
relative error = 1.0565553154446265399743588491049e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=850.6MB, alloc=4.4MB, time=92.60
NO POLE
NO POLE
x[1] = 0.1438
y2[1] (analytic) = 0.85669508112607968815482369117501
y2[1] (numeric) = 0.85669508112607968815482675542994
absolute error = 3.06425493e-24
relative error = 3.5768326415183817963060863478703e-22 %
h = 0.0001
y1[1] (analytic) = 1.9896785843022668528764906561488
y1[1] (numeric) = 1.9896785843022668528764695861431
absolute error = 2.10700057e-23
relative error = 1.0589652955122272617375149630618e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1439
y2[1] (analytic) = 0.85659611398433900167266834415311
y2[1] (numeric) = 0.85659611398433900167267141751586
absolute error = 3.07336275e-24
relative error = 3.5878784643379665841312305611362e-22 %
h = 0.0001
y1[1] (analytic) = 1.9896642488620104276107663519958
y1[1] (numeric) = 1.9896642488620104276107452341923
absolute error = 2.11178035e-23
relative error = 1.0613752301212799819216935055453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=854.5MB, alloc=4.4MB, time=93.17
NO POLE
NO POLE
x[1] = 0.144
y2[1] (analytic) = 0.85649714827663717415209059733904
y2[1] (numeric) = 0.85649714827663717415209367981919
absolute error = 3.08248015e-24
relative error = 3.5989380188857324210342002458675e-22 %
h = 0.0001
y1[1] (analytic) = 1.9896499035251115219721398428361
y1[1] (numeric) = 1.9896499035251115219721186772364
absolute error = 2.11655997e-23
relative error = 1.0637851243326973259527936626930e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1441
y2[1] (analytic) = 0.85639818400396386266928401170799
y2[1] (numeric) = 0.85639818400396386266928710331513
absolute error = 3.09160714e-24
relative error = 3.6100113215392927676816018987497e-22 %
h = 0.0001
y1[1] (analytic) = 1.9896355482917135893294806405819
y1[1] (numeric) = 1.9896355482917135893294594271876
absolute error = 2.12133943e-23
relative error = 1.0661949781814897669840036062272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=858.3MB, alloc=4.4MB, time=93.75
NO POLE
NO POLE
x[1] = 0.1442
y2[1] (analytic) = 0.85629922116730870995015699981602
y2[1] (numeric) = 0.85629922116730870995016010055975
absolute error = 3.10074373e-24
relative error = 3.6210983886836429808999528476956e-22 %
h = 0.0001
y1[1] (analytic) = 1.9896211831619601820166484447149
y1[1] (numeric) = 1.9896211831619601820166271835276
absolute error = 2.12611873e-23
relative error = 1.0686047917026668354646148646509e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1443
y2[1] (analytic) = 0.85620025976766134436043639854923
y2[1] (numeric) = 0.85620025976766134436043950843913
absolute error = 3.10988990e-24
relative error = 3.6321992016726323810409909947106e-22 %
h = 0.0001
y1[1] (analytic) = 1.9896068081359949513310576189487
y1[1] (numeric) = 1.9896068081359949513310363099701
absolute error = 2.13089786e-23
relative error = 1.0710145599051184122460287273081e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=862.1MB, alloc=4.4MB, time=94.34
NO POLE
NO POLE
x[1] = 0.1444
y2[1] (analytic) = 0.8561012998060113798957711854747
y2[1] (numeric) = 0.85610129980601137989577430452035
absolute error = 3.11904565e-24
relative error = 3.6433137652130202464596375199227e-22 %
h = 0.0001
y1[1] (analytic) = 1.9895924232139616475322406782564
y1[1] (numeric) = 1.989592423213961647532219321488
absolute error = 2.13567684e-23
relative error = 1.0734242928760532225826179736810e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1445
y2[1] (analytic) = 0.85600234128334841617183633889226
y2[1] (numeric) = 0.85600234128334841617183946710326
absolute error = 3.12821100e-24
relative error = 3.6544421073779745853321013704241e-22 %
h = 0.0001
y1[1] (analytic) = 1.9895780283960041198404107862758
y1[1] (numeric) = 1.9895780283960041198403893817193
absolute error = 2.14045565e-23
relative error = 1.0758339805982041692605596986584e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=865.9MB, alloc=4.4MB, time=94.91
NO POLE
NO POLE
x[1] = 0.1446
y2[1] (analytic) = 0.85590338420066203841443684168603
y2[1] (numeric) = 0.85590338420066203841443997907196
absolute error = 3.13738593e-24
relative error = 3.6655842095192094725239493671252e-22 %
h = 0.0001
y1[1] (analytic) = 1.989563623682266316435023263109
y1[1] (numeric) = 1.989563623682266316435001810766
absolute error = 2.14523430e-23
relative error = 1.0782436281326956547467850013811e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1447
y2[1] (analytic) = 0.85580442855894181744961182907454
y2[1] (numeric) = 0.855804428558941817449614975645
absolute error = 3.14657046e-24
relative error = 3.6767400997192739535264965761881e-22 %
h = 0.0001
y1[1] (analytic) = 1.9895492090728922844533361035288
y1[1] (numeric) = 1.9895492090728922844533146034008
absolute error = 2.15001280e-23
relative error = 1.0806532405407966547034428276494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=869.7MB, alloc=4.4MB, time=95.48
NO POLE
NO POLE
x[1] = 0.1448
y2[1] (analytic) = 0.85570547435917730969373888035867
y2[1] (numeric) = 0.85570547435917730969374203612324
absolute error = 3.15576457e-24
relative error = 3.6879097593284608276925892442019e-22 %
h = 0.0001
y1[1] (analytic) = 1.9895347845680261699889695056071
y1[1] (numeric) = 1.9895347845680261699889479576959
absolute error = 2.15479112e-23
relative error = 1.0830628027787183359344000211778e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1449
y2[1] (analytic) = 0.85560652160235805714363845476603
y2[1] (numeric) = 0.85560652160235805714364161973431
absolute error = 3.16496828e-24
relative error = 3.6990932164387061712831060311978e-22 %
h = 0.0001
y1[1] (analytic) = 1.9895203501678122180904644097807
y1[1] (numeric) = 1.9895203501678122180904428140878
absolute error = 2.15956929e-23
relative error = 1.0854723299602562399693699714402e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=873.5MB, alloc=4.4MB, time=96.05
NO POLE
NO POLE
x[1] = 0.145
y2[1] (analytic) = 0.85550757028947358736667847149108
y2[1] (numeric) = 0.85550757028947358736668164567266
absolute error = 3.17418158e-24
relative error = 3.7102904640878501042230540532243e-22 %
h = 0.0001
y1[1] (analytic) = 1.989505905872394772759840048366
y1[1] (numeric) = 1.9895059058723947727598184048931
absolute error = 2.16434729e-23
relative error = 1.0878818120677744828164110740942e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1451
y2[1] (analytic) = 0.85540862042151341349087903402967
y2[1] (numeric) = 0.85540862042151341349088221743412
absolute error = 3.18340445e-24
relative error = 3.7215014836200004698666269618204e-22 %
h = 0.0001
y1[1] (analytic) = 1.9894914516819182769511505055409
y1[1] (numeric) = 1.9894914516819182769511288142896
absolute error = 2.16912513e-23
relative error = 1.0902912541625746682268845702810e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=877.4MB, alloc=4.4MB, time=96.63
NO POLE
NO POLE
x[1] = 0.1452
y2[1] (analytic) = 0.85530967199946703419501729890705
y2[1] (numeric) = 0.85530967199946703419502049154397
absolute error = 3.19263692e-24
relative error = 3.7327263148287997092650237709327e-22 %
h = 0.0001
y1[1] (analytic) = 1.989476987596527272569040287805
y1[1] (numeric) = 1.989476987596527272569018548777
absolute error = 2.17390280e-23
relative error = 1.0927006512532101286243772407381e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1453
y2[1] (analytic) = 0.85521072502432393369873248889841
y2[1] (numeric) = 0.85521072502432393369873569077737
absolute error = 3.20187896e-24
relative error = 3.7439649273679677547733299929541e-22 %
h = 0.0001
y1[1] (analytic) = 1.9894625136163664004672989049346
y1[1] (numeric) = 1.9894625136163664004672771181315
absolute error = 2.17868031e-23
relative error = 1.0951100084010534889662076266977e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=881.2MB, alloc=4.4MB, time=97.19
NO POLE
NO POLE
x[1] = 0.1454
y2[1] (analytic) = 0.85511177949707358175263105084066
y2[1] (numeric) = 0.85511177949707358175263426197126
absolute error = 3.21113060e-24
relative error = 3.7552173610432521665527981940107e-22 %
h = 0.0001
y1[1] (analytic) = 1.9894480297415804004474144614458
y1[1] (numeric) = 1.9894480297415804004473926268692
absolute error = 2.18345766e-23
relative error = 1.0975193256411028262112469044493e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1455
y2[1] (analytic) = 0.85501283541870543362839195813468
y2[1] (numeric) = 0.85501283541870543362839517852651
absolute error = 3.22039183e-24
relative error = 3.7664836088957107261238841850829e-22 %
h = 0.0001
y1[1] (analytic) = 1.9894335359723141112571262585808
y1[1] (numeric) = 1.9894335359723141112571043762324
absolute error = 2.18823484e-23
relative error = 1.0999285979817988253661514536741e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=885.0MB, alloc=4.4MB, time=97.75
NO POLE
NO POLE
x[1] = 0.1456
y2[1] (analytic) = 0.85491389279020893010887215803674
y2[1] (numeric) = 0.85491389279020893010887538769938
absolute error = 3.22966264e-24
relative error = 3.7777636639629870664163159346519e-22 %
h = 0.0001
y1[1] (analytic) = 1.9894190323087124705889764068321
y1[1] (numeric) = 1.9894190323087124705889544767135
absolute error = 2.19301186e-23
relative error = 1.1023378304846208814832532556921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1457
y2[1] (analytic) = 0.85481495161257349747821216383817
y2[1] (numeric) = 0.85481495161257349747821540278121
absolute error = 3.23894304e-24
relative error = 3.7890575426761853267311991708410e-22 %
h = 0.0001
y1[1] (analytic) = 1.9894045187509205150788604490178
y1[1] (numeric) = 1.9894045187509205150788384711307
absolute error = 2.19778871e-23
relative error = 1.1047470181579344337716079710607e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=888.8MB, alloc=4.4MB, time=98.35
NO POLE
NO POLE
x[1] = 0.1458
y2[1] (analytic) = 0.85471601188678854751194179203221
y2[1] (numeric) = 0.85471601188678854751194504026524
absolute error = 3.24823303e-24
relative error = 3.8003652497740323951156543125272e-22 %
h = 0.0001
y1[1] (analytic) = 1.9893899952990833803045769939243
y1[1] (numeric) = 1.9893899952990833803045549682702
absolute error = 2.20256541e-23
relative error = 1.1071561710899566426266978309974e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1459
y2[1] (analytic) = 0.85461707361384347746708604456697
y2[1] (numeric) = 0.85461707361384347746708930209957
absolute error = 3.25753260e-24
relative error = 3.8116867782961093886260359988279e-22 %
h = 0.0001
y1[1] (analytic) = 1.989375461953346300784376360529
y1[1] (numeric) = 1.9893754619533463007843542871097
absolute error = 2.20734193e-23
relative error = 1.1095652742356813711238449147060e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=892.6MB, alloc=4.4MB, time=98.92
NO POLE
NO POLE
x[1] = 0.146
y2[1] (analytic) = 0.85451813679472767007227113628341
y2[1] (numeric) = 0.85451813679472767007227440312517
absolute error = 3.26684176e-24
relative error = 3.8230221446835840103467601976969e-22 %
h = 0.0001
y1[1] (analytic) = 1.9893609187138546099755082328197
y1[1] (numeric) = 1.9893609187138546099754861116366
absolute error = 2.21211831e-23
relative error = 1.1119743477368403724183082851486e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1461
y2[1] (analytic) = 0.85441920143043049351783066763732
y2[1] (numeric) = 0.85441920143043049351783394379782
absolute error = 3.27616050e-24
relative error = 3.8343713419773318635217215573485e-22 %
h = 0.0001
y1[1] (analytic) = 1.9893463655807537402727683252224
y1[1] (numeric) = 1.9893463655807537402727461562773
absolute error = 2.21689451e-23
relative error = 1.1143833715215387788395955762727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=896.4MB, alloc=4.4MB, time=99.50
NO POLE
NO POLE
x[1] = 0.1462
y2[1] (analytic) = 0.85432026752194130144591194280423
y2[1] (numeric) = 0.85432026752194130144591522829306
absolute error = 3.28548883e-24
relative error = 3.8457343866252354624633161271374e-22 %
h = 0.0001
y1[1] (analytic) = 1.9893318025541892230070440586556
y1[1] (numeric) = 1.9893318025541892230070218419501
absolute error = 2.22167055e-23
relative error = 1.1167923556781734453700281565155e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1463
y2[1] (analytic) = 0.8542213350702494329405824332662
y2[1] (numeric) = 0.85422133507024943294058572809294
absolute error = 3.29482674e-24
relative error = 3.8571112716694673990746099992775e-22 %
h = 0.0001
y1[1] (analytic) = 1.9893172296343066884438592472218
y1[1] (numeric) = 1.9893172296343066884438369827575
absolute error = 2.22644643e-23
relative error = 1.1192013002417339087659428894125e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=900.2MB, alloc=4.4MB, time=100.07
NO POLE
NO POLE
x[1] = 0.1464
y2[1] (analytic) = 0.85412240407634421251793638697937
y2[1] (numeric) = 0.8541224040763442125179396911536
absolute error = 3.30417423e-24
relative error = 3.8685020018567060805539873035579e-22 %
h = 0.0001
y1[1] (analytic) = 1.9893026468212518657819177955538
y1[1] (numeric) = 1.9893026468212518657818954833324
absolute error = 2.23122214e-23
relative error = 1.1216102002203215942382205551066e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1465
y2[1] (analytic) = 0.85402347454121495011620158322126
y2[1] (numeric) = 0.85402347454121495011620489675257
absolute error = 3.31353131e-24
relative error = 3.8799065936449149013261733540972e-22 %
h = 0.0001
y1[1] (analytic) = 1.989288054115170583151646406829
y1[1] (numeric) = 1.9892880541151705831516240468522
absolute error = 2.23599768e-23
relative error = 1.1240190556488135779492109924332e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=904.1MB, alloc=4.4MB, time=100.64
NO POLE
NO POLE
x[1] = 0.1466
y2[1] (analytic) = 0.85392454646585094108584623321674
y2[1] (numeric) = 0.85392454646585094108584955611472
absolute error = 3.32289798e-24
relative error = 3.8913250517888527384634211235783e-22 %
h = 0.0001
y1[1] (analytic) = 1.9892734515162087676137363014662
y1[1] (numeric) = 1.9892734515162087676137138937356
absolute error = 2.24077306e-23
relative error = 1.1264278715890468376844859050181e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=907.9MB, alloc=4.4MB, time=101.24
x[1] = 0.1467
y2[1] (analytic) = 0.85382561985124146617968602664162
y2[1] (numeric) = 0.85382561985124146617968935891585
absolute error = 3.33227423e-24
relative error = 3.9027573693332936813473064450641e-22 %
h = 0.0001
y1[1] (analytic) = 1.9892588390245124451576839465197
y1[1] (numeric) = 1.989258839024512445157661491037
absolute error = 2.24554827e-23
relative error = 1.1288366430490091961809687416561e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1468
y2[1] (analytic) = 0.85372669469837579154299132410269
y2[1] (numeric) = 0.85372669469837579154299466576275
absolute error = 3.34166006e-24
relative error = 3.9142035510329433330182138638415e-22 %
h = 0.0001
y1[1] (analytic) = 1.9892442166402277407003307957861
y1[1] (numeric) = 1.9892442166402277407003082925529
absolute error = 2.25032332e-23
relative error = 1.1312453750906094525138188669882e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=911.7MB, alloc=4.4MB, time=101.83
x[1] = 0.1469
y2[1] (analytic) = 0.8536277710082431687035944956933
y2[1] (numeric) = 0.85362777100824316870359784674877
absolute error = 3.35105547e-24
relative error = 3.9256636016445159592377927411744e-22 %
h = 0.0001
y1[1] (analytic) = 1.9892295843635008780844020406365
y1[1] (numeric) = 1.9892295843635008780843794896545
absolute error = 2.25509820e-23
relative error = 1.1336540627217595979392445030993e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.147
y2[1] (analytic) = 0.85352884878183283456199740572324
y2[1] (numeric) = 0.85352884878183283456200076618371
absolute error = 3.36046047e-24
relative error = 3.9371375376428010302989619732834e-22 %
h = 0.0001
y1[1] (analytic) = 1.9892149421944781800770443715908
y1[1] (numeric) = 1.9892149421944781800770217728617
absolute error = 2.25987291e-23
relative error = 1.1360627059773315298614553668209e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=915.5MB, alloc=4.4MB, time=102.40
NO POLE
NO POLE
x[1] = 0.1471
y2[1] (analytic) = 0.85342992802013401138147904372201
y2[1] (numeric) = 0.85342992802013401138148241359706
absolute error = 3.36987505e-24
relative error = 3.9486253520751832975561194091776e-22 %
h = 0.0001
y1[1] (analytic) = 1.9892002901333060683683627506476
y1[1] (numeric) = 1.9892002901333060683683401041729
absolute error = 2.26464747e-23
relative error = 1.1384713149464877994032082389976e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1472
y2[1] (analytic) = 0.85333100872413590677820330181425
y2[1] (numeric) = 0.85333100872413590677820668111346
absolute error = 3.37929921e-24
relative error = 3.9601270497044094381548672067274e-22 %
h = 0.0001
y1[1] (analytic) = 1.9891856281801310635699561943838
y1[1] (numeric) = 1.9891856281801310635699335001652
absolute error = 2.26942186e-23
relative error = 1.1408798796099546793429251962183e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=919.3MB, alloc=4.4MB, time=102.97
NO POLE
NO POLE
x[1] = 0.1473
y2[1] (analytic) = 0.85323209089482771371132689856633
y2[1] (numeric) = 0.85323209089482771371133028729929
absolute error = 3.38873296e-24
relative error = 3.9716426470153790048998577666037e-22 %
h = 0.0001
y1[1] (analytic) = 1.9891709563350997852134525678404
y1[1] (numeric) = 1.9891709563350997852134298258797
absolute error = 2.27419607e-23
relative error = 1.1432883949753810423153578805508e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1474
y2[1] (analytic) = 0.85313317453319861047310744940307
y2[1] (numeric) = 0.85313317453319861047311084757935
absolute error = 3.39817628e-24
relative error = 3.9831721253359421673311480542516e-22 %
h = 0.0001
y1[1] (analytic) = 1.9891562745983589517490423892074
y1[1] (numeric) = 1.9891562745983589517490195995061
absolute error = 2.27897013e-23
relative error = 1.1456968761592946709621729832763e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=923.1MB, alloc=4.4MB, time=103.54
NO POLE
NO POLE
x[1] = 0.1475
y2[1] (analytic) = 0.85303425964023776067901168369335
y2[1] (numeric) = 0.85303425964023776067901509132254
absolute error = 3.40762919e-24
relative error = 3.9947155128765259655136820864582e-22 %
h = 0.0001
y1[1] (analytic) = 1.9891415829700553805440116453226
y1[1] (numeric) = 1.9891415829700553805439888078824
absolute error = 2.28374402e-23
relative error = 1.1481053131421965636407096425662e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1476
y2[1] (analytic) = 0.85293534621693431325782380860373
y2[1] (numeric) = 0.85293534621693431325782722569541
absolute error = 3.41709168e-24
relative error = 4.0062728026877924236304620031524e-22 %
h = 0.0001
y1[1] (analytic) = 1.9891268814503359878812736180005
y1[1] (numeric) = 1.9891268814503359878812507328231
absolute error = 2.28851774e-23
relative error = 1.1505137059589524865789745336314e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=926.9MB, alloc=4.4MB, time=104.12
NO POLE
NO POLE
x[1] = 0.1477
y2[1] (analytic) = 0.85283643426427740244175401981884
y2[1] (numeric) = 0.85283643426427740244175744638259
absolute error = 3.42656375e-24
relative error = 4.0178439995425601439357646848950e-22 %
h = 0.0001
y1[1] (analytic) = 1.9891121700393477889578997212043
y1[1] (numeric) = 1.9891121700393477889578767882913
absolute error = 2.29329130e-23
relative error = 1.1529220596717957168353794311282e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1478
y2[1] (analytic) = 0.85273752378325614775654715922751
y2[1] (numeric) = 0.85273752378325614775655059527291
absolute error = 3.43604540e-24
relative error = 4.0294291082156647152032258641407e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890974487372378978836493490761
y1[1] (numeric) = 1.9890974487372378978836263684292
absolute error = 2.29806469e-23
relative error = 1.1553303692882957573352416871427e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=930.8MB, alloc=4.4MB, time=104.69
NO POLE
NO POLE
x[1] = 0.1479
y2[1] (analytic) = 0.85263861477485965401159151967357
y2[1] (numeric) = 0.85263861477485965401159496521021
absolute error = 3.44553664e-24
relative error = 4.0410281452122579209739220343928e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890827175441535276794987348408
y1[1] (numeric) = 1.9890827175441535276794757064618
absolute error = 2.30283790e-23
relative error = 1.1577386298158722780028377297026e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.148
y2[1] (analytic) = 0.85253970724007701129002779687021
y2[1] (numeric) = 0.85253970724007701129003125190767
absolute error = 3.45503746e-24
relative error = 4.0526411035856351451088960963165e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890679764602419902761688205978
y1[1] (numeric) = 1.9890679764602419902761457444882
absolute error = 2.30761096e-23
relative error = 1.1601468563717159266209215230827e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=934.6MB, alloc=4.4MB, time=105.25
NO POLE
NO POLE
x[1] = 0.1481
y2[1] (analytic) = 0.85244080117989729493885818857684
y2[1] (numeric) = 0.85244080117989729493886165312469
absolute error = 3.46454785e-24
relative error = 4.0642679763856694901932443847623e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890532254856506965126521380143
y1[1] (numeric) = 1.9890532254856506965126290141758
absolute error = 2.31238385e-23
relative error = 1.1625550389358758037289316329279e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1482
y2[1] (analytic) = 0.85234189659530956555905564113724
y2[1] (numeric) = 0.85234189659530956555905911520507
absolute error = 3.47406783e-24
relative error = 4.0759087918559531982244565812786e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890384646205271561347386999374
y1[1] (numeric) = 1.9890384646205271561347155283717
absolute error = 2.31715657e-23
relative error = 1.1649631775432115084715738667206e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=938.4MB, alloc=4.4MB, time=105.82
NO POLE
NO POLE
x[1] = 0.1483
y2[1] (analytic) = 0.85224299348730286899567324347816
y2[1] (numeric) = 0.85224299348730286899567672707555
absolute error = 3.48359739e-24
relative error = 4.0875635430517626541151942745993e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890236938650189777935409029368
y1[1] (numeric) = 1.9890236938650189777935176836456
absolute error = 2.32192912e-23
relative error = 1.1673712722285815905518662863676e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1484
y2[1] (analytic) = 0.85214409185686623632795376866698
y2[1] (numeric) = 0.8521440918568662363279572618035
absolute error = 3.49313652e-24
relative error = 4.0992322230249512030264596089265e-22 %
h = 0.0001
y1[1] (analytic) = 1.9890089132192738690440174407954
y1[1] (numeric) = 1.9890089132192738690439941737803
absolute error = 2.32670151e-23
relative error = 1.1697793280544731077380469971748e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=942.2MB, alloc=4.4MB, time=106.38
NO POLE
NO POLE
x[1] = 0.1485
y2[1] (analytic) = 0.85204519170498868385943936312752
y2[1] (numeric) = 0.85204519170498868385944286581276
absolute error = 3.50268524e-24
relative error = 4.1109148600333471553704000703351e-22 %
h = 0.0001
y1[1] (analytic) = 1.9889941226834396363434962289604
y1[1] (numeric) = 1.9889941226834396363434729142232
absolute error = 2.33147372e-23
relative error = 1.1721873350005207878843555897196e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1486
y2[1] (analytic) = 0.85194629303265921310808138361289
y2[1] (numeric) = 0.85194629303265921310808489585643
absolute error = 3.51224354e-24
relative error = 4.1226114471342136049252437195412e-22 %
h = 0.0001
y1[1] (analytic) = 1.988979322257664185050196339972
y1[1] (numeric) = 1.9889793222576641850501729775142
absolute error = 2.33624578e-23
relative error = 1.1745953081845809441516334356539e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=946.0MB, alloc=4.4MB, time=106.94
NO POLE
NO POLE
x[1] = 0.1487
y2[1] (analytic) = 0.85184739584086681079635038203421
y2[1] (numeric) = 0.85184739584086681079635390384562
absolute error = 3.52181141e-24
relative error = 4.1343219773813898486759470320824e-22 %
h = 0.0001
y1[1] (analytic) = 1.9889645119420955194217489498816
y1[1] (numeric) = 1.988964511942095519421725539705
absolute error = 2.34101766e-23
relative error = 1.1770032325585071880961859934496e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1488
y2[1] (analytic) = 0.85174850013060044884134623824411
y2[1] (numeric) = 0.85174850013060044884134976963297
absolute error = 3.53138886e-24
relative error = 4.1460464673063990960391551331608e-22 %
h = 0.0001
y1[1] (analytic) = 1.9889496917368817426137172956774
y1[1] (numeric) = 1.9889496917368817426136938377837
absolute error = 2.34578937e-23
relative error = 1.1794111131848198586026406314774e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=949.8MB, alloc=4.4MB, time=107.51
NO POLE
NO POLE
x[1] = 0.1489
y2[1] (analytic) = 0.85164960590284908434490844087403
y2[1] (numeric) = 0.85164960590284908434491198184992
absolute error = 3.54097589e-24
relative error = 4.1577849217063250919189677295975e-22 %
h = 0.0001
y1[1] (analytic) = 1.9889348616421710566781156437297
y1[1] (numeric) = 1.9889348616421710566780921381205
absolute error = 2.35056092e-23
relative error = 1.1818189551261880530658511511608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.149
y2[1] (analytic) = 0.85155071315860165958372651632402
y2[1] (numeric) = 0.85155071315860165958373006689652
absolute error = 3.55057250e-24
relative error = 4.1695373453802797266008068508015e-22 %
h = 0.0001
y1[1] (analytic) = 1.9889200216581117625619272692718
y1[1] (numeric) = 1.9889200216581117625619037159488
absolute error = 2.35533230e-23
relative error = 1.1842267533897213678124574986160e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=953.6MB, alloc=4.4MB, time=108.08
NO POLE
NO POLE
x[1] = 0.1491
y2[1] (analytic) = 0.85145182189884710199945060600412
y2[1] (numeric) = 0.85145182189884710199945416618281
absolute error = 3.56017869e-24
relative error = 4.1813037431294039688344033910961e-22 %
h = 0.0001
y1[1] (analytic) = 1.9889051717848522601056214469319
y1[1] (numeric) = 1.9889051717848522601055978458968
absolute error = 2.36010351e-23
relative error = 1.1866345080102701510190891424088e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1492
y2[1] (analytic) = 0.85135293212457432418880219192608
y2[1] (numeric) = 0.85135293212457432418880576172053
absolute error = 3.56979445e-24
relative error = 4.1930841080108588631462430929189e-22 %
h = 0.0001
y1[1] (analytic) = 1.9888903120225410480416694523293
y1[1] (numeric) = 1.9888903120225410480416458035838
absolute error = 2.36487455e-23
relative error = 1.1890422190226837115879301619853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=957.5MB, alloc=4.4MB, time=108.65
NO POLE
NO POLE
x[1] = 0.1493
y2[1] (analytic) = 0.85125404383677222389368497074437
y2[1] (numeric) = 0.85125404383677222389368855016417
absolute error = 3.57941980e-24
relative error = 4.2048784683205017011129567394487e-22 %
h = 0.0001
y1[1] (analytic) = 1.988875442371326723993059574751
y1[1] (numeric) = 1.9888754423713267239930358782967
absolute error = 2.36964543e-23
relative error = 1.1914498914897772743433646832360e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1494
y2[1] (analytic) = 0.85115515703642968399129587634543
y2[1] (numeric) = 0.85115515703642968399129946540015
absolute error = 3.58905472e-24
relative error = 4.2166868053721813168665610230244e-22 %
h = 0.0001
y1[1] (analytic) = 1.9888605628313579844718111409228
y1[1] (numeric) = 1.9888605628313579844717873967615
absolute error = 2.37441613e-23
relative error = 1.1938575153905017813201668734671e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=961.3MB, alloc=4.4MB, time=109.24
NO POLE
NO POLE
x[1] = 0.1495
y2[1] (analytic) = 0.85105627172453557248423625108391
y2[1] (numeric) = 0.85105627172453557248423984978312
absolute error = 3.59869921e-24
relative error = 4.2285091239710690306502719871980e-22 %
h = 0.0001
y1[1] (analytic) = 1.9888456734027836248774875498911
y1[1] (numeric) = 1.9888456734027836248774637580244
absolute error = 2.37918667e-23
relative error = 1.1962651008156750060611813658392e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1496
y2[1] (analytic) = 0.85095738790207874249062316576489
y2[1] (numeric) = 0.85095738790207874249062677411817
absolute error = 3.60835328e-24
relative error = 4.2403454406758378808800361592944e-22 %
h = 0.0001
y1[1] (analytic) = 1.9888307740857525394957083190275
y1[1] (numeric) = 1.9888307740857525394956844794572
absolute error = 2.38395703e-23
relative error = 1.1986726377440953542332026449205e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=965.1MB, alloc=4.4MB, time=109.85
NO POLE
NO POLE
x[1] = 0.1497
y2[1] (analytic) = 0.85085850557004803223420088847096
y2[1] (numeric) = 0.8508585055700480322342045064879
absolute error = 3.61801694e-24
relative error = 4.2521957720526565900246768794036e-22 %
h = 0.0001
y1[1] (analytic) = 1.9888158648804137214966601411747
y1[1] (numeric) = 1.9888158648804137214966362539024
absolute error = 2.38872723e-23
relative error = 1.2010801362667290989658423980875e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1498
y2[1] (analytic) = 0.85075962472943226503445250233304
y2[1] (numeric) = 0.85075962472943226503445613002321
absolute error = 3.62769017e-24
relative error = 4.2640600994125891703605839802127e-22 %
h = 0.0001
y1[1] (analytic) = 1.9888009457869162629336069529454
y1[1] (numeric) = 1.9888009457869162629335830179728
absolute error = 2.39349726e-23
relative error = 1.2034875913903772014227983016072e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=968.9MB, alloc=4.4MB, time=110.43
NO POLE
NO POLE
x[1] = 0.1499
y2[1] (analytic) = 0.85066074538122024929671167234376
y2[1] (numeric) = 0.85066074538122024929671530971673
absolute error = 3.63737297e-24
relative error = 4.2759384275689431121742642543440e-22 %
h = 0.0001
y1[1] (analytic) = 1.988786016805409354741399014191
y1[1] (numeric) = 1.9887860168054093547413750315198
absolute error = 2.39826712e-23
relative error = 1.2058950031498818038889390323430e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.15
y2[1] (analytic) = 0.85056186752640077850227456131236
y2[1] (numeric) = 0.85056186752640077850227820837771
absolute error = 3.64706535e-24
relative error = 4.2878307730939959279379623961759e-22 %
h = 0.0001
y1[1] (analytic) = 1.9887710779360422867349809986543
y1[1] (numeric) = 1.9887710779360422867349569682863
absolute error = 2.40303680e-23
relative error = 1.2083023665518532124879218069007e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=972.7MB, alloc=4.4MB, time=111.06
NO POLE
NO POLE
x[1] = 0.1501
y2[1] (analytic) = 0.85046299116596263119851189505999
y2[1] (numeric) = 0.8504629911659626311985155518273
absolute error = 3.65676731e-24
relative error = 4.2997371408092281238953219345876e-22 %
h = 0.0001
y1[1] (analytic) = 1.9887561291789644476078990958217
y1[1] (numeric) = 1.9887561291789644476078750177584
absolute error = 2.40780633e-23
relative error = 1.2107096967158239279089233794418e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1502
y2[1] (analytic) = 0.85036411630089457098898117695424
y2[1] (numeric) = 0.85036411630089457098898484343308
absolute error = 3.66647884e-24
relative error = 4.3116575237784912117943344390702e-22 %
h = 0.0001
y1[1] (analytic) = 1.9887411705343253249308071239882
y1[1] (numeric) = 1.9887411705343253249307829982314
absolute error = 2.41257568e-23
relative error = 1.2131169785919405873388653969370e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=976.5MB, alloc=4.4MB, time=111.66
NO POLE
NO POLE
x[1] = 0.1503
y2[1] (analytic) = 0.85026524293218534652353905188179
y2[1] (numeric) = 0.85026524293218534652354272808173
absolute error = 3.67619994e-24
relative error = 4.3235919268232429539533022191141e-22 %
h = 0.0001
y1[1] (analytic) = 1.9887262020022745051499716545528
y1[1] (numeric) = 1.9887262020022745051499474811043
absolute error = 2.41734485e-23
relative error = 1.2155242122149277560126408534589e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1504
y2[1] (analytic) = 0.85016637106082369148845381975808
y2[1] (numeric) = 0.85016637106082369148845750568871
absolute error = 3.68593063e-24
relative error = 4.3355403782917878194867412972960e-22 %
h = 0.0001
y1[1] (analytic) = 1.9887112235829616735857761475568
y1[1] (numeric) = 1.9887112235829616735857519264183
absolute error = 2.42211385e-23
relative error = 1.2179314026478909608887512626499e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=980.3MB, alloc=4.4MB, time=112.27
NO POLE
NO POLE
x[1] = 0.1505
y2[1] (analytic) = 0.85006750068779832459651809867291
y2[1] (numeric) = 0.85006750068779832459652179434379
absolute error = 3.69567088e-24
relative error = 4.3475028477265568030245632116132e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886962352765366144312240984814
y1[1] (numeric) = 1.9886962352765366144311998296545
absolute error = 2.42688269e-23
relative error = 1.2203385549540861415434342086694e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1506
y2[1] (analytic) = 0.84996863181409794957716163777069
y2[1] (numeric) = 0.8499686318140979495771653431914
absolute error = 3.70542071e-24
relative error = 4.3594793634813056871106097220508e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886812370831492107504411963185
y1[1] (numeric) = 1.9886812370831492107504168798049
absolute error = 2.43165136e-23
relative error = 1.2227456641400039834932251741183e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=984.2MB, alloc=4.4MB, time=112.89
NO POLE
NO POLE
x[1] = 0.1507
y2[1] (analytic) = 0.84986976444071125516656427996442
y2[1] (numeric) = 0.84986976444071125516656799514454
absolute error = 3.71518012e-24
relative error = 4.3714699303897626366844536051681e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886662290029494444771764929311
y1[1] (numeric) = 1.9886662290029494444771521287325
absolute error = 2.43641986e-23
relative error = 1.2251527302404784186869673640190e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1508
y2[1] (analytic) = 0.84977089856862691509776907458214
y2[1] (numeric) = 0.84977089856862691509777279953123
absolute error = 3.72494909e-24
relative error = 4.3834745297519454481689102235308e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886512110360873964133025837168
y1[1] (numeric) = 1.988651211036087396413278171835
absolute error = 2.44118818e-23
relative error = 1.2275597482618084729305817873448e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=988.0MB, alloc=4.4MB, time=113.51
NO POLE
NO POLE
x[1] = 0.1509
y2[1] (analytic) = 0.84967203419883358809079554004469
y2[1] (numeric) = 0.84967203419883358809079927477233
absolute error = 3.73472764e-24
relative error = 4.3954931899359515904890640158762e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886361831827132462273147995907
y1[1] (numeric) = 1.9886361831827132462272903400273
absolute error = 2.44595634e-23
relative error = 1.2299667282958558067840780592137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.151
y2[1] (analytic) = 0.8495731713323199178427530766738
y2[1] (numeric) = 0.84957317133231991784275682118957
absolute error = 3.74451577e-24
relative error = 4.4075259157816453101926386212929e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886211454429772724528294103012
y1[1] (numeric) = 1.9886211454429772724528049030579
absolute error = 2.45072433e-23
relative error = 1.2323736653489553813836288947608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=991.8MB, alloc=4.4MB, time=114.12
NO POLE
NO POLE
x[1] = 0.1511
y2[1] (analytic) = 0.84947430997007453301795452972924
y2[1] (numeric) = 0.84947430997007453301795828404271
absolute error = 3.75431347e-24
relative error = 4.4195727003589523230188578233260e-22 %
h = 0.0001
y1[1] (analytic) = 1.9886060978170298524870808390954
y1[1] (numeric) = 1.9886060978170298524870562841739
absolute error = 2.45549215e-23
relative error = 1.2347805594559370505911712489513e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1512
y2[1] (analytic) = 0.84937545011308604723802990277388
y2[1] (numeric) = 0.84937545011308604723803366689462
absolute error = 3.76412074e-24
relative error = 4.4316335485077230324844184637132e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885910403050214625894178887478
y1[1] (numeric) = 1.98859104030502146258939328615
absolute error = 2.46025978e-23
relative error = 1.2371874005942575752395723858598e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=995.6MB, alloc=4.4MB, time=114.73
NO POLE
NO POLE
x[1] = 0.1513
y2[1] (analytic) = 0.84927659176234305907204022146568
y2[1] (numeric) = 0.84927659176234305907204399540326
absolute error = 3.77393758e-24
relative error = 4.4437084650698557816652758215067e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885759729071026778797989789685
y1[1] (numeric) = 1.988575972907102677879774328696
absolute error = 2.46502725e-23
relative error = 1.2395942038846885846672200817601e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1514
y2[1] (analytic) = 0.84917773491883415202659154787527
y2[1] (numeric) = 0.84917773491883415202659533163927
absolute error = 3.78376400e-24
relative error = 4.4557974666653955308657050562693e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885608956234241723372863952044
y1[1] (numeric) = 1.9885608956234241723372616972589
absolute error = 2.46979455e-23
relative error = 1.2420009643334088477930835651008e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=999.4MB, alloc=4.4MB, time=115.36
NO POLE
NO POLE
x[1] = 0.1515
y2[1] (analytic) = 0.84907887958354789453594914542818
y2[1] (numeric) = 0.84907887958354789453595293902817
absolute error = 3.79359999e-24
relative error = 4.4679005463669837006645525458435e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885458084541367187985395488499
y1[1] (numeric) = 1.9885458084541367187985148032332
absolute error = 2.47456167e-23
relative error = 1.2444076769464436600717367379394e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1516
y2[1] (analytic) = 0.8489800257574728399521517945704
y2[1] (numeric) = 0.84898002575747283995215559801594
absolute error = 3.80344554e-24
relative error = 4.4800176972438288778735607760725e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885307113993911889563072488819
y1[1] (numeric) = 1.9885307113993911889562824555957
absolute error = 2.47932862e-23
relative error = 1.2468143467873417900805163784343e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1003.2MB, alloc=4.4MB, time=115.98
NO POLE
NO POLE
x[1] = 0.1517
y2[1] (analytic) = 0.8488811734415975265351262592562
y2[1] (numeric) = 0.84888117344159752653513007255688
absolute error = 3.81330068e-24
relative error = 4.4921489594825519008950431413192e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885156044593385533579189849331
y1[1] (numeric) = 1.9885156044593385533578941439792
absolute error = 2.48409539e-23
relative error = 1.2492209688620500497407854247878e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1518
y2[1] (analytic) = 0.84878232263691047744280190435716
y2[1] (numeric) = 0.84878232263691047744280572752254
absolute error = 3.82316538e-24
relative error = 4.5042943025987854695080644151530e-22 %
h = 0.0001
y1[1] (analytic) = 1.9885004876341298814037752218205
y1[1] (numeric) = 1.9885004876341298814037503332005
absolute error = 2.48886200e-23
relative error = 1.2516275532631064264293383435126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1007.1MB, alloc=4.4MB, time=116.60
NO POLE
NO POLE
x[1] = 0.1519
y2[1] (analytic) = 0.84868347334440020072122546409107
y2[1] (numeric) = 0.84868347334440020072122929713073
absolute error = 3.83303966e-24
relative error = 4.5164537550085323980698384412823e-22 %
h = 0.0001
y1[1] (analytic) = 1.988485360923916341345836705542
y1[1] (numeric) = 1.9884853609239163413458117692577
absolute error = 2.49362843e-23
relative error = 1.2540340899675406268388287439896e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.152
y2[1] (analytic) = 0.84858462556505518929467596156972
y2[1] (numeric) = 0.84858462556505518929467980449322
absolute error = 3.84292350e-24
relative error = 4.5286272980035145521067944855411e-22 %
h = 0.0001
y1[1] (analytic) = 1.9884702243288492002861127807586
y1[1] (numeric) = 1.9884702243288492002860877968117
absolute error = 2.49839469e-23
relative error = 1.2564405840390499700697262938875e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1010.9MB, alloc=4.4MB, time=117.22
NO POLE
NO POLE
x[1] = 0.1521
y2[1] (analytic) = 0.84848577929986392095577977956433
y2[1] (numeric) = 0.84848577929986392095578363238125
absolute error = 3.85281692e-24
relative error = 4.5408149600093337825488042903974e-22 %
h = 0.0001
y1[1] (analytic) = 1.9884550778490798241751487197755
y1[1] (numeric) = 1.9884550778490798241751236881676
absolute error = 2.50316079e-23
relative error = 1.2588470405414838427117408730816e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1522
y2[1] (analytic) = 0.84838693454981485835562588258755
y2[1] (numeric) = 0.84838693454981485835562974530746
absolute error = 3.86271991e-24
relative error = 4.5530167341034082324140794121162e-22 %
h = 0.0001
y1[1] (analytic) = 1.9884399214847596778105120630374
y1[1] (numeric) = 1.9884399214847596778104869837704
absolute error = 2.50792670e-23
relative error = 1.2612534444225711090238747255709e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1014.7MB, alloc=4.4MB, time=117.83
NO POLE
NO POLE
x[1] = 0.1523
y2[1] (analytic) = 0.84828809131589644899388119039079
y2[1] (numeric) = 0.84828809131589644899388506302325
absolute error = 3.87263246e-24
relative error = 4.5652326133597214776985567922454e-22 %
h = 0.0001
y1[1] (analytic) = 1.988424755236040324835277971155
y1[1] (numeric) = 1.9884247552360403248352528442305
absolute error = 2.51269245e-23
relative error = 1.2636598108042189043137748837070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1018.5MB, alloc=4.4MB, time=118.45
x[1] = 0.1524
y2[1] (analytic) = 0.84818924959909712520890610297577
y2[1] (numeric) = 0.84818924959909712520890998553036
absolute error = 3.88255459e-24
relative error = 4.5774626262182855136394397373327e-22 %
h = 0.0001
y1[1] (analytic) = 1.9884095791030734277365135884744
y1[1] (numeric) = 1.9884095791030734277364884138942
absolute error = 2.51745802e-23
relative error = 1.2660661296630688904333256713414e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1525
y2[1] (analytic) = 0.84809040940040530416787017721919
y2[1] (numeric) = 0.84809040940040530416787406970548
absolute error = 3.89248629e-24
relative error = 4.5897067657585749993018799704947e-22 %
h = 0.0001
y1[1] (analytic) = 1.9883943930860107478437614182088
y1[1] (numeric) = 1.9883943930860107478437361959746
absolute error = 2.52222342e-23
relative error = 1.2684724060630046947307729412025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1022.3MB, alloc=4.4MB, time=119.06
NO POLE
NO POLE
x[1] = 0.1526
y2[1] (analytic) = 0.84799157072080938785686795520926
y2[1] (numeric) = 0.84799157072080938785687185763682
absolute error = 3.90242756e-24
relative error = 4.6019650368491993367929587360591e-22 %
h = 0.0001
y1[1] (analytic) = 1.9883791971850041453275217091434
y1[1] (numeric) = 1.988379197185004145327496439257
absolute error = 2.52698864e-23
relative error = 1.2708786350096189345291355105590e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1527
y2[1] (analytic) = 0.84789273356129776307103494439298
y2[1] (numeric) = 0.84789273356129776307103885677137
absolute error = 3.91237839e-24
relative error = 4.6142374325668844372812572720046e-22 %
h = 0.0001
y1[1] (analytic) = 1.9883639914002055791977338539323
y1[1] (numeric) = 1.9883639914002055791977085363954
absolute error = 2.53175369e-23
relative error = 1.2732848215668699013877623722142e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1026.1MB, alloc=4.4MB, time=119.68
NO POLE
NO POLE
x[1] = 0.1528
y2[1] (analytic) = 0.84779389792285880140466374963302
y2[1] (numeric) = 0.84779389792285880140466767197181
absolute error = 3.92233879e-24
relative error = 4.6265239695755578608129018607085e-22 %
h = 0.0001
y1[1] (analytic) = 1.9883487757317671073022567990002
y1[1] (numeric) = 1.9883487757317671073022314338145
absolute error = 2.53651857e-23
relative error = 1.2756909657695699348154749723619e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1529
y2[1] (analytic) = 0.84769506380648085924132035727303
y2[1] (numeric) = 0.8476950638064808592413242895818
absolute error = 3.93230877e-24
relative error = 4.6388246645467094087187577793617e-22 %
h = 0.0001
y1[1] (analytic) = 1.9883335501798408863253484660648
y1[1] (numeric) = 1.9883335501798408863253230532321
absolute error = 2.54128327e-23
relative error = 1.2780970626231931214197037243014e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1029.9MB, alloc=4.4MB, time=120.31
NO POLE
NO POLE
x[1] = 0.153
y2[1] (analytic) = 0.84759623121315227774396057131025
y2[1] (numeric) = 0.84759623121315227774396451359857
absolute error = 3.94228832e-24
relative error = 4.6511395105632542851863063429080e-22 %
h = 0.0001
y1[1] (analytic) = 1.9883183147445791717861441852958
y1[1] (numeric) = 1.9883183147445791717861187248179
absolute error = 2.54604779e-23
relative error = 1.2805031121624341952706646213910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1531
y2[1] (analytic) = 0.84749740014386138284504660177415
y2[1] (numeric) = 0.84749740014386138284505055405158
absolute error = 3.95227743e-24
relative error = 4.6634685007046711560817883625711e-22 %
h = 0.0001
y1[1] (analytic) = 1.988303069426134318037134140125
y1[1] (numeric) = 1.9883030694261343180371086320035
absolute error = 2.55081215e-23
relative error = 1.2829091244808154521516512712365e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1033.8MB, alloc=4.4MB, time=120.93
NO POLE
NO POLE
x[1] = 0.1532
y2[1] (analytic) = 0.84739857059959648523666380541004
y2[1] (numeric) = 0.84739857059959648523666776768615
absolute error = 3.96227611e-24
relative error = 4.6758116516486448260619943321594e-22 %
h = 0.0001
y1[1] (analytic) = 1.9882878142246587782626398237219
y1[1] (numeric) = 1.9882878142246587782626142679587
absolute error = 2.55557632e-23
relative error = 1.2853150845249020288106507866023e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1533
y2[1] (analytic) = 0.84729974258134588036063757876649
y2[1] (numeric) = 0.84729974258134588036064155105085
absolute error = 3.97228436e-24
relative error = 4.6881689682782321487557695268002e-22 %
h = 0.0001
y1[1] (analytic) = 1.9882725491403051044772895071528
y1[1] (numeric) = 1.9882725491403051044772639037495
absolute error = 2.56034033e-23
relative error = 1.2877210074177442005797430056012e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1037.6MB, alloc=4.4MB, time=121.54
NO POLE
NO POLE
x[1] = 0.1534
y2[1] (analytic) = 0.84720091609009784839865040378529
y2[1] (numeric) = 0.84720091609009784839865438608746
absolute error = 3.98230217e-24
relative error = 4.7005404436749823104700780759171e-22 %
h = 0.0001
y1[1] (analytic) = 1.9882572741732259475244927192347
y1[1] (numeric) = 1.9882572741732259475244670681931
absolute error = 2.56510416e-23
relative error = 1.2901268831352036327277049683207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1535
y2[1] (analytic) = 0.84710209112684065426235904599283
y2[1] (numeric) = 0.84710209112684065426236303832239
absolute error = 3.99232956e-24
relative error = 4.7129261063318628606510123425310e-22 %
h = 0.0001
y1[1] (analytic) = 1.9882419893235740570749137381034
y1[1] (numeric) = 1.9882419893235740570748880394253
absolute error = 2.56986781e-23
relative error = 1.2925327117119695567244748184497e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1041.4MB, alloc=4.4MB, time=122.15
NO POLE
NO POLE
x[1] = 0.1536
y2[1] (analytic) = 0.84700326769256254758351190539184
y2[1] (numeric) = 0.84700326769256254758351590775835
absolute error = 4.00236651e-24
relative error = 4.7253259375296084076875792875234e-22 %
h = 0.0001
y1[1] (analytic) = 1.9882266945915022816249440945076
y1[1] (numeric) = 1.9882266945915022816249183481947
absolute error = 2.57463129e-23
relative error = 1.2949384982123376137225445137961e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1537
y2[1] (analytic) = 0.84690444578825176270406652015208
y2[1] (numeric) = 0.8469044457882517627040705325651
absolute error = 4.01241302e-24
relative error = 4.7377399421554200714609875218707e-22 %
h = 0.0001
y1[1] (analytic) = 1.9882113899771635684951740868466
y1[1] (numeric) = 1.9882113899771635684951482929006
absolute error = 2.57939460e-23
relative error = 1.2973442426711108987942871968531e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1045.2MB, alloc=4.4MB, time=122.77
NO POLE
NO POLE
x[1] = 0.1538
y2[1] (analytic) = 0.84680562541489651866630722319901
y2[1] (numeric) = 0.84680562541489651866631124566812
absolute error = 4.02246911e-24
relative error = 4.7501681487167397736851915109634e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881960754807109638288633079651
y1[1] (numeric) = 1.9881960754807109638288374663878
absolute error = 2.58415773e-23
relative error = 1.2997499400934065084909652145247e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1539
y2[1] (analytic) = 0.84670680657348501920296295179922
y2[1] (numeric) = 0.84670680657348501920296698433398
absolute error = 4.03253476e-24
relative error = 4.7626105384922513589391621175932e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881807511022976125904101837226
y1[1] (numeric) = 1.9881807511022976125903842945157
absolute error = 2.58892069e-23
relative error = 1.3021555955436330403113547565835e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1049.0MB, alloc=4.4MB, time=123.38
NO POLE
NO POLE
x[1] = 0.154
y2[1] (analytic) = 0.84660798926500545272732521024132
y2[1] (numeric) = 0.8466079892650054527273292528513
absolute error = 4.04260998e-24
relative error = 4.7750671281872124808066028219096e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881654168420767585638205233501
y1[1] (numeric) = 1.9881654168420767585637945865155
absolute error = 2.59368346e-23
relative error = 1.3045611989970654102759123387951e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1541
y2[1] (analytic) = 0.84650917349044599232336618571131
y2[1] (numeric) = 0.84650917349044599232337023840606
absolute error = 4.05269475e-24
relative error = 4.7875378990748056835321891721080e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881500727002017443511750816119
y1[1] (numeric) = 1.9881500727002017443511490971512
absolute error = 2.59844607e-23
relative error = 1.3069667655776739528410707268739e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1052.8MB, alloc=4.4MB, time=124.00
NO POLE
NO POLE
x[1] = 0.1542
y2[1] (analytic) = 0.84641035925079479573585701746104
y2[1] (numeric) = 0.84641035925079479573586108025014
absolute error = 4.06278910e-24
relative error = 4.8000228914922569365680006390705e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881347186768260113710961327854
y1[1] (numeric) = 1.9881347186768260113710701007004
absolute error = 2.60320850e-23
relative error = 1.3093722852606926704084387370745e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1543
y2[1] (analytic) = 0.8463115465470400053604862193688
y2[1] (numeric) = 0.84631154654704000536049029226181
absolute error = 4.07289301e-24
relative error = 4.8125220867155201163776673197960e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881193547721030998572130564767
y1[1] (numeric) = 1.9881193547721030998571869767692
absolute error = 2.60797075e-23
relative error = 1.3117777580808019872342470399936e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1056.6MB, alloc=4.4MB, time=124.59
NO POLE
NO POLE
x[1] = 0.1544
y2[1] (analytic) = 0.84621273538016974823397825599061
y2[1] (numeric) = 0.8462127353801697482339823389971
absolute error = 4.08300649e-24
relative error = 4.8250355014636685516066478293486e-22 %
h = 0.0001
y1[1] (analytic) = 1.9881039809861866488566269352853
y1[1] (numeric) = 1.988103980986186648856600807957
absolute error = 2.61273283e-23
relative error = 1.3141831891025991934059670539380e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1545
y2[1] (analytic) = 0.84611392575117213602421227220124
y2[1] (numeric) = 0.84611392575117213602421636533077
absolute error = 4.09312953e-24
relative error = 4.8375631288258934768954216532794e-22 %
h = 0.0001
y1[1] (analytic) = 1.9880885973192303962283741643344
y1[1] (numeric) = 1.9880885973192303962283479893871
absolute error = 2.61749473e-23
relative error = 1.3165885733309222878993354156751e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1060.5MB, alloc=4.4MB, time=125.21
NO POLE
NO POLE
x[1] = 0.1546
y2[1] (analytic) = 0.84601511766103526502034097652364
y2[1] (numeric) = 0.84601511766103526502034507978578
absolute error = 4.10326214e-24
relative error = 4.8501049855281836122496852609550e-22 %
h = 0.0001
y1[1] (analytic) = 1.988073203771388178641889072682
y1[1] (numeric) = 1.9880732037713881786418628501175
absolute error = 2.62225645e-23
relative error = 1.3189939108004483723771110203793e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1547
y2[1] (analytic) = 0.84591631111074721612290967824566
y2[1] (numeric) = 0.84591631111074721612291379164997
absolute error = 4.11340431e-24
relative error = 4.8626610646611279542279874406799e-22 %
h = 0.0001
y1[1] (analytic) = 1.9880578003428139315754655566276
y1[1] (numeric) = 1.9880578003428139315754392864477
absolute error = 2.62701799e-23
relative error = 1.3213992015458534176105870695079e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1064.3MB, alloc=4.4MB, time=125.83
NO POLE
NO POLE
x[1] = 0.1548
y2[1] (analytic) = 0.84581750610129605483397547842282
y2[1] (numeric) = 0.84581750610129605483397960197887
absolute error = 4.12355605e-24
relative error = 4.8752313829576356563416946277048e-22 %
h = 0.0001
y1[1] (analytic) = 1.9880423870336616893147177249308
y1[1] (numeric) = 1.9880423870336616893146914071372
absolute error = 2.63177936e-23
relative error = 1.3238044506318861026726131224949e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1549
y2[1] (analytic) = 0.84571870263366983124722661486598
y2[1] (numeric) = 0.84571870263366983124723074858333
absolute error = 4.13371735e-24
relative error = 4.8878159335096961143534052283814e-22 %
h = 0.0001
y1[1] (analytic) = 1.9880269638440855849510395559561
y1[1] (numeric) = 1.9880269638440855849510131905505
absolute error = 2.63654056e-23
relative error = 1.3262096580933372104272447384758e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1068.1MB, alloc=4.4MB, time=126.44
NO POLE
NO POLE
x[1] = 0.155
y2[1] (analytic) = 0.84561990070885658003810196121268
y2[1] (numeric) = 0.84561990070885658003810610510089
absolute error = 4.14388821e-24
relative error = 4.9004147212314998499201239427794e-22 %
h = 0.0001
y1[1] (analytic) = 1.9880115307742398503800635667605
y1[1] (numeric) = 1.9880115307742398503800371537447
absolute error = 2.64130158e-23
relative error = 1.3286148189348446391430891952027e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1551
y2[1] (analytic) = 0.84552110032784432045391068018099
y2[1] (numeric) = 0.84552110032784432045391483424963
absolute error = 4.15406864e-24
relative error = 4.9130277628663456792644037816512e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879960878242788163001184941384
y1[1] (numeric) = 1.9879960878242788163000920335143
absolute error = 2.64606241e-23
relative error = 1.3310199281608890154438586922303e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1071.9MB, alloc=4.4MB, time=127.06
NO POLE
NO POLE
x[1] = 0.1552
y2[1] (analytic) = 0.84542230149162105630395203110468
y2[1] (numeric) = 0.84542230149162105630395619536331
absolute error = 4.16425863e-24
relative error = 4.9256550515083280971891212160471e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879806349943569122106859876398
y1[1] (numeric) = 1.987980634994356912210659479409
absolute error = 2.65082308e-23
relative error = 1.3334250008967137822952315989370e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1553
y2[1] (analytic) = 0.84532350420117477594963533184841
y2[1] (numeric) = 0.84532350420117477594963950630659
absolute error = 4.17445818e-24
relative error = 4.9382965920778884311205465894752e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879651722846286664108563145761
y1[1] (numeric) = 1.9879651722846286664108297587405
absolute error = 2.65558356e-23
relative error = 1.3358300220864153460440799229248e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1075.7MB, alloc=4.4MB, time=127.66
NO POLE
NO POLE
x[1] = 0.1554
y2[1] (analytic) = 0.8452247084574934522946000752019
y2[1] (numeric) = 0.84522470845749345229460425986919
absolute error = 4.18466729e-24
relative error = 4.9509523894975532343081538016463e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879496996952487059977830770315
y1[1] (numeric) = 1.9879496996952487059977564735928
absolute error = 2.66034387e-23
relative error = 1.3382350018251612948181118618179e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1555
y2[1] (analytic) = 0.84512591426156504277483619985176
y2[1] (numeric) = 0.84512591426156504277484039473773
absolute error = 4.19488597e-24
relative error = 4.9636224605244915952189979220732e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879342172263717568651369408918
y1[1] (numeric) = 1.9879342172263717568651102898518
absolute error = 2.66510400e-23
relative error = 1.3406399351173887372973939374064e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1079.5MB, alloc=4.4MB, time=128.27
NO POLE
NO POLE
x[1] = 0.1556
y2[1] (analytic) = 0.84502712161437748934880451602984
y2[1] (numeric) = 0.84502712161437748934880872114405
absolute error = 4.20511421e-24
relative error = 4.9763067982556137663400843080167e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879187248781526437015583769096
y1[1] (numeric) = 1.9879187248781526437015316782701
absolute error = 2.66986395e-23
relative error = 1.3430448219977637470821341687673e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1557
y2[1] (analytic) = 0.84492833051691871848755728593684
y2[1] (numeric) = 0.84492833051691871848756150128885
absolute error = 4.21535201e-24
relative error = 4.9890054076197086659003691222260e-22 %
h = 0.0001
y1[1] (analytic) = 1.9879032226507462899891094138189
y1[1] (numeric) = 1.9879032226507462899890826675816
absolute error = 2.67462373e-23
relative error = 1.3454496675313772495544934188042e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1083.3MB, alloc=4.4MB, time=128.90
NO POLE
NO POLE
x[1] = 0.1558
y2[1] (analytic) = 0.84482954097017664116485895904
y2[1] (numeric) = 0.84482954097017664116486318463938
absolute error = 4.22559938e-24
relative error = 5.0017183053843616008377379594621e-22 %
h = 0.0001
y1[1] (analytic) = 1.9878877105443077180017244035157
y1[1] (numeric) = 1.9878877105443077180016976096825
absolute error = 2.67938332e-23
relative error = 1.3478544616920803910790016699117e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1559
y2[1] (analytic) = 0.84473075297513915284730706234375
y2[1] (numeric) = 0.84473075297513915284731129820005
absolute error = 4.23585630e-24
relative error = 5.0144454728105102649850551441333e-22 %
h = 0.0001
y1[1] (analytic) = 1.9878721885589920488036597983204
y1[1] (numeric) = 1.9878721885589920488036329568931
absolute error = 2.68414273e-23
relative error = 1.3502592095449226326418494595664e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1087.2MB, alloc=4.4MB, time=129.52
NO POLE
NO POLE
x[1] = 0.156
y2[1] (analytic) = 0.84463196653279413348445324573189
y2[1] (numeric) = 0.84463196653279413348445749185467
absolute error = 4.24612278e-24
relative error = 5.0271869266685370720876377401672e-22 %
h = 0.0001
y1[1] (analytic) = 1.9878566566949545022479429403361
y1[1] (numeric) = 1.9878566566949545022479160513163
absolute error = 2.68890198e-23
relative error = 1.3526639211856531962854336029778e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1561
y2[1] (analytic) = 0.84453318164412944749892448248036
y2[1] (numeric) = 0.84453318164412944749892873887918
absolute error = 4.25639882e-24
relative error = 5.0399426718955930653074463486359e-22 %
h = 0.0001
y1[1] (analytic) = 1.9878411149523503969748198629195
y1[1] (numeric) = 1.9878411149523503969747929263091
absolute error = 2.69366104e-23
relative error = 1.3550685815574191300410369849344e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1091.0MB, alloc=4.4MB, time=130.14
NO POLE
NO POLE
x[1] = 0.1562
y2[1] (analytic) = 0.84443439831013294377654442503918
y2[1] (numeric) = 0.84443439831013294377654869172361
absolute error = 4.26668443e-24
relative error = 5.0527127252731683822925293866696e-22 %
h = 0.0001
y1[1] (analytic) = 1.9878255633313351504102021042804
y1[1] (numeric) = 1.9878255633313351504101751200811
absolute error = 2.69841993e-23
relative error = 1.3574732007560068855245373367448e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1563
y2[1] (analytic) = 0.84433561653179245565645491618245
y2[1] (numeric) = 0.84433561653179245565645919316205
absolute error = 4.27697960e-24
relative error = 5.0654970799031257124627976775831e-22 %
h = 0.0001
y1[1] (analytic) = 1.987810001832064278764112533223
y1[1] (numeric) = 1.9878100018320642787640855014367
absolute error = 2.70317863e-23
relative error = 1.3598777687548691858773021461982e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1094.8MB, alloc=4.4MB, time=130.74
NO POLE
NO POLE
x[1] = 0.1564
y2[1] (analytic) = 0.84423683631009580092123765562519
y2[1] (numeric) = 0.84423683631009580092124194290951
absolute error = 4.28728432e-24
relative error = 5.0782957288838813693233025996821e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877944304546933970291301870478
y1[1] (numeric) = 1.9877944304546933970291031076763
absolute error = 2.70793715e-23
relative error = 1.3622822906192463964021219661544e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1565
y2[1] (analytic) = 0.84413805764603078178703602220568
y2[1] (numeric) = 0.84413805764603078178704031980429
absolute error = 4.29759861e-24
relative error = 5.0911087008496135909050038574271e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877788491993782189788341216266
y1[1] (numeric) = 1.9877788491993782189788069946716
absolute error = 2.71269550e-23
relative error = 1.3646867714145353510859268757666e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1098.6MB, alloc=4.4MB, time=131.36
NO POLE
NO POLE
x[1] = 0.1566
y2[1] (analytic) = 0.84403928054058518489367705173236
y2[1] (numeric) = 0.84403928054058518489368135965481
absolute error = 4.30792245e-24
relative error = 5.1039359770565273054085906428408e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877632580662745571662462736679
y1[1] (numeric) = 1.9877632580662745571662190991313
absolute error = 2.71745366e-23
relative error = 1.3670912011139490717160148358080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1567
y2[1] (analytic) = 0.8439405049947467812947935705937
y2[1] (numeric) = 0.84394050499474678129479788884955
absolute error = 4.31825585e-24
relative error = 5.1167775742993631425045657633018e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877476570555383229222733351887
y1[1] (numeric) = 1.9877476570555383229222461130722
absolute error = 2.72221165e-23
relative error = 1.3694955898136624047809402761733e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1102.4MB, alloc=4.4MB, time=131.98
NO POLE
NO POLE
x[1] = 0.1568
y2[1] (analytic) = 0.84384173100950332644794648523016
y2[1] (numeric) = 0.84384173100950332644795081382897
absolute error = 4.32859881e-24
relative error = 5.1296334975299431100482650343425e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877320461673255263541476402058
y1[1] (numeric) = 1.9877320461673255263541203705112
absolute error = 2.72696946e-23
relative error = 1.3718999325175874946306897969639e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1569
y2[1] (analytic) = 0.84374295858584256020474722756679
y2[1] (numeric) = 0.84374295858584256020475156651812
absolute error = 4.33895133e-24
relative error = 5.1425037517021889458427597145657e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877164254017922763438670636654
y1[1] (numeric) = 1.9877164254017922763438397463946
absolute error = 2.73172708e-23
relative error = 1.3743042242294773900446317311055e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1106.2MB, alloc=4.4MB, time=132.59
NO POLE
NO POLE
x[1] = 0.157
y2[1] (analytic) = 0.84364418772475220680098035650535
y2[1] (numeric) = 0.84364418772475220680098470581876
absolute error = 4.34931341e-24
relative error = 5.1553883417721230886459092620811e-22 %
h = 0.0001
y1[1] (analytic) = 1.9877007947590947805466339326243
y1[1] (numeric) = 1.987700794759094780546606567779
absolute error = 2.73648453e-23
relative error = 1.3767084750457406026766735192453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1571
y2[1] (analytic) = 0.84354541842721997484672631557469
y2[1] (numeric) = 0.84354541842721997484673067525974
absolute error = 4.35968505e-24
relative error = 5.1682872726978696496901135181804e-22 %
h = 0.0001
y1[1] (analytic) = 1.9876851542393893453892929496991
y1[1] (numeric) = 1.9876851542393893453892655372811
absolute error = 2.74124180e-23
relative error = 1.3791126799701675078888616268214e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1110.1MB, alloc=4.4MB, time=133.19
NO POLE
NO POLE
x[1] = 0.1572
y2[1] (analytic) = 0.8434466506942335573164843468382
y2[1] (numeric) = 0.84344665069423355731648871690445
absolute error = 4.37006625e-24
relative error = 5.1812005494396553847150674126075e-22 %
h = 0.0001
y1[1] (analytic) = 1.9876695038428323760687681287989
y1[1] (numeric) = 1.9876695038428323760687406688101
absolute error = 2.74599888e-23
relative error = 1.3815168340063890813821039763568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1573
y2[1] (analytic) = 0.84334788452678063153929556115702
y2[1] (numeric) = 0.84334788452678063153929994161402
absolute error = 4.38045700e-24
relative error = 5.1941281651023077504886036805674e-22 %
h = 0.0001
y1[1] (analytic) = 1.9876538435695803765504987431578
y1[1] (numeric) = 1.9876538435695803765504712355999
absolute error = 2.75075579e-23
relative error = 1.3839209472510479712078443570689e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1113.9MB, alloc=4.4MB, time=133.79
NO POLE
NO POLE
x[1] = 0.1574
y2[1] (analytic) = 0.84324911992584885918886616490787
y2[1] (numeric) = 0.84324911992584885918887055576518
absolute error = 4.39085731e-24
relative error = 5.2070701365049870326641208633271e-22 %
h = 0.0001
y1[1] (analytic) = 1.9876381734197899495668742856814
y1[1] (numeric) = 1.9876381734197899495668467305562
absolute error = 2.75551252e-23
relative error = 1.3863250147078125632237548658450e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1575
y2[1] (analytic) = 0.84315035689242588627369084325421
y2[1] (numeric) = 0.84315035689242588627369524452139
absolute error = 4.40126718e-24
relative error = 5.2200264686142328479012331846743e-22 %
h = 0.0001
y1[1] (analytic) = 1.9876224933936177966156684416244
y1[1] (numeric) = 1.9876224933936177966156408389337
absolute error = 2.76026907e-23
relative error = 1.3887290364113280019072377647772e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1117.7MB, alloc=4.4MB, time=134.38
NO POLE
NO POLE
x[1] = 0.1576
y2[1] (analytic) = 0.84305159542749934312717630006955
y2[1] (numeric) = 0.84305159542749934312718071175616
absolute error = 4.41168661e-24
relative error = 5.2329971663986913502941472446801e-22 %
h = 0.0001
y1[1] (analytic) = 1.9876068034912207179584720736141
y1[1] (numeric) = 1.9876068034912207179584444233598
absolute error = 2.76502543e-23
relative error = 1.3911330073650621557801167119702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1121.5MB, alloc=4.4MB, time=134.95
x[1] = 0.1577
y2[1] (analytic) = 0.8429528355320568443977649546116
y2[1] (numeric) = 0.84295283553205684439776937672719
absolute error = 4.42211559e-24
relative error = 5.2459822229660562831868379611415e-22 %
h = 0.0001
y1[1] (analytic) = 1.9875911037127556126191252190359
y1[1] (numeric) = 1.9875911037127556126190975212198
absolute error = 2.76978161e-23
relative error = 1.3935369326347546695938992660864e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1578
y2[1] (analytic) = 0.84285407720708598903905879504604
y2[1] (numeric) = 0.84285407720708598903906322760017
absolute error = 4.43255413e-24
relative error = 5.2589816551494697018652561341817e-22 %
h = 0.0001
y1[1] (analytic) = 1.9875753940583794783821480997962
y1[1] (numeric) = 1.98757539405837947838212035442
absolute error = 2.77453762e-23
relative error = 1.3959408172863030036255702023169e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1125.3MB, alloc=4.4MB, time=135.52
x[1] = 0.1579
y2[1] (analytic) = 0.84275532045357436029994338891879
y2[1] (numeric) = 0.84275532045357436029994783192102
absolute error = 4.44300223e-24
relative error = 5.2719954679239023114469515225004e-22 %
h = 0.0001
y1[1] (analytic) = 1.9875596745282494117911711444781
y1[1] (numeric) = 1.9875596745282494117911433515438
absolute error = 2.77929343e-23
relative error = 1.3983446462605807845201406083179e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.158
y2[1] (analytic) = 0.84265656527250952571471205067536
y2[1] (numeric) = 0.84265656527250952571471650413523
absolute error = 4.45345987e-24
relative error = 5.2850236425319735256350515845027e-22 %
h = 0.0001
y1[1] (analytic) = 1.9875439451225226081473640229073
y1[1] (numeric) = 1.9875439451225226081473361824165
absolute error = 2.78404908e-23
relative error = 1.4007484397173299470404826832316e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1129.1MB, alloc=4.4MB, time=136.07
NO POLE
NO POLE
x[1] = 0.1581
y2[1] (analytic) = 0.84255781166487903709319016632611
y2[1] (numeric) = 0.84255781166487903709319463025319
absolute error = 4.46392708e-24
relative error = 5.2980662195503957336042958356309e-22 %
h = 0.0001
y1[1] (analytic) = 1.9875282058413563615078636931406
y1[1] (numeric) = 1.9875282058413563615078358050952
absolute error = 2.78880454e-23
relative error = 1.4031521825973025550136109612621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1582
y2[1] (analytic) = 0.8424590596316704305108596753563
y2[1] (numeric) = 0.84245905963167043051086414976014
absolute error = 4.47440384e-24
relative error = 5.3111231802246197156167185378002e-22 %
h = 0.0001
y1[1] (analytic) = 1.9875124566849080646842014608968
y1[1] (numeric) = 1.9875124566849080646841735252986
absolute error = 2.79355982e-23
relative error = 1.4055558799664314870823087001316e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1132.9MB, alloc=4.4MB, time=136.64
NO POLE
NO POLE
x[1] = 0.1583
y2[1] (analytic) = 0.84236030917387122629898370997942
y2[1] (numeric) = 0.84236030917387122629898819486958
absolute error = 4.48489016e-24
relative error = 5.3241945414052928341754366009562e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874966976533352092407290514421
y1[1] (numeric) = 1.987496697653335209240701068293
absolute error = 2.79831491e-23
relative error = 1.4079595268278981537031542001891e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1584
y2[1] (analytic) = 0.84226156029246892903473139183285
y2[1] (numeric) = 0.84226156029246892903473588721888
absolute error = 4.49538603e-24
relative error = 5.3372802962051495592541418734946e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874809287467953854930436939482
y1[1] (numeric) = 1.98748092874679538549301566325
absolute error = 2.80306982e-23
relative error = 1.4103631282477128374009102791572e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1136.8MB, alloc=4.4MB, time=137.20
NO POLE
NO POLE
x[1] = 0.1585
y2[1] (analytic) = 0.84216281298845102753130278621438
y2[1] (numeric) = 0.84216281298845102753130729210583
absolute error = 4.50589145e-24
relative error = 5.3503804496076596491913431016078e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874651499654462825064122183375
y1[1] (numeric) = 1.987465149965446282506384140092
absolute error = 2.80782455e-23
relative error = 1.4127666842605095947932925397485e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1586
y2[1] (analytic) = 0.8420640672628049948280540139584
y2[1] (numeric) = 0.84206406726280499482805853036483
absolute error = 4.51640643e-24
relative error = 5.3634950184739882973888375615194e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874493613094456880941941646318
y1[1] (numeric) = 1.9874493613094456880941660388408
absolute error = 2.81257910e-23
relative error = 1.4151701949009213952337221399512e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1140.6MB, alloc=4.4MB, time=137.81
NO POLE
NO POLE
x[1] = 0.1587
y2[1] (analytic) = 0.84196532311651828818062252105064
y2[1] (numeric) = 0.8419653231165182881806270479816
absolute error = 4.52693096e-24
relative error = 5.3766239959190397391278965085223e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874335627789514888162639048199
y1[1] (numeric) = 1.9874335627789514888162357314853
absolute error = 2.81733346e-23
relative error = 1.4175736551719653865828620132240e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1588
y2[1] (analytic) = 0.84186658055057834905105250607995
y2[1] (numeric) = 0.841866580550578349051057043545
absolute error = 4.53746505e-24
relative error = 5.3897673988109977756730230920082e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874177543741216699774317772605
y1[1] (numeric) = 1.987417754374121669977403556384
absolute error = 2.82208765e-23
relative error = 1.4199770751714618150216965045489e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1144.4MB, alloc=4.4MB, time=138.38
NO POLE
NO POLE
x[1] = 0.1589
y2[1] (analytic) = 0.84176783956597260309792050562615
y2[1] (numeric) = 0.84176783956597260309792505363484
absolute error = 4.54800869e-24
relative error = 5.4029252202662168336209430024142e-22 %
h = 0.0001
y1[1] (analytic) = 1.9874019360951143156258642336349
y1[1] (numeric) = 1.9874019360951143156258359652184
absolute error = 2.82684165e-23
relative error = 1.4223804448707708501630967114035e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.159
y2[1] (analytic) = 0.84166910016368846016646113768246
y2[1] (numeric) = 0.84166910016368846016646569624434
absolute error = 4.55856188e-24
relative error = 5.4160974652787506940637931014640e-22 %
h = 0.0001
y1[1] (analytic) = 1.9873861079420876085515029984672
y1[1] (numeric) = 1.9873861079420876085514746825125
absolute error = 2.83159547e-23
relative error = 1.4247837693361357819148343137212e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1148.2MB, alloc=4.4MB, time=138.94
NO POLE
NO POLE
x[1] = 0.1591
y2[1] (analytic) = 0.84157036234471331427869300321136
y2[1] (numeric) = 0.84157036234471331427869757233599
absolute error = 4.56912463e-24
relative error = 5.4292841507273202501896168498431e-22 %
h = 0.0001
y1[1] (analytic) = 1.9873702699151998302844832412257
y1[1] (numeric) = 1.9873702699151998302844548777347
absolute error = 2.83634910e-23
relative error = 1.4271870435704091032369913146249e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1592
y2[1] (analytic) = 0.84147162611003454362354474593269
y2[1] (numeric) = 0.84147162611003454362354932562962
absolute error = 4.57969693e-24
relative error = 5.4424852697304598327209003531751e-22 %
h = 0.0001
y1[1] (analytic) = 1.9873544220146093610935507610234
y1[1] (numeric) = 1.9873544220146093610935223499979
absolute error = 2.84110255e-23
relative error = 1.4295902726399119358948324747095e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1152.0MB, alloc=4.4MB, time=139.53
NO POLE
NO POLE
x[1] = 0.1593
y2[1] (analytic) = 0.84137289146063951054698127044256
y2[1] (numeric) = 0.84137289146063951054698586072134
absolute error = 4.59027878e-24
relative error = 5.4557008272885852240121975883258e-22 %
h = 0.0001
y1[1] (analytic) = 1.9873385642404746799844781839314
y1[1] (numeric) = 1.9873385642404746799844497253732
absolute error = 2.84585582e-23
relative error = 1.4319934565792695158454306568711e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1594
y2[1] (analytic) = 0.8412741583975155615421301187619
y2[1] (numeric) = 0.84127415839751556154213471963209
absolute error = 4.60087019e-24
relative error = 5.4689308402909659873168992864419e-22 %
h = 0.0001
y1[1] (analytic) = 1.9873226965929543646984801729226
y1[1] (numeric) = 1.9873226965929543646984516668335
absolute error = 2.85060891e-23
relative error = 1.4343965954231060007152604311779e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1155.8MB, alloc=4.4MB, time=140.08
NO POLE
NO POLE
x[1] = 0.1595
y2[1] (analytic) = 0.84117542692165002723940800541348
y2[1] (numeric) = 0.84117542692165002723941261688463
absolute error = 4.61147115e-24
relative error = 5.4821753018583224561663161374316e-22 %
h = 0.0001
y1[1] (analytic) = 1.987306819072207091710627650461
y1[1] (numeric) = 1.9873068190722070917105990968429
absolute error = 2.85536181e-23
relative error = 1.4367996841741088362033337740349e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1596
y2[1] (analytic) = 0.84107669703403022239664751112591
y2[1] (numeric) = 0.84107669703403022239665213320757
absolute error = 4.62208166e-24
relative error = 5.4954342169974412588313935843140e-22 %
h = 0.0001
y1[1] (analytic) = 1.9872909316783916362282610337524
y1[1] (numeric) = 1.9872909316783916362282324326071
absolute error = 2.86011453e-23
relative error = 1.4392027278987552057402242083522e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1159.6MB, alloc=4.4MB, time=140.65
NO POLE
NO POLE
x[1] = 0.1597
y2[1] (analytic) = 0.84097796873564344588922393526356
y2[1] (numeric) = 0.84097796873564344588922856796529
absolute error = 4.63270173e-24
relative error = 5.5087076026081522231045810951654e-22 %
h = 0.0001
y1[1] (analytic) = 1.987275034411666872189402482672
y1[1] (numeric) = 1.9872750344116668721893738340013
absolute error = 2.86486707e-23
relative error = 1.4416057266316659617368348993835e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1598
y2[1] (analytic) = 0.84087924202747698070018230708107
y2[1] (numeric) = 0.84087924202747698070018695041241
absolute error = 4.64333134e-24
relative error = 5.5219954399210537746522163488487e-22 %
h = 0.0001
y1[1] (analytic) = 1.9872591272721917722611671603856
y1[1] (numeric) = 1.9872591272721917722611384641914
absolute error = 2.86961942e-23
relative error = 1.4440086753754044876952114971756e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1163.5MB, alloc=4.4MB, time=141.21
NO POLE
NO POLE
x[1] = 0.1599
y2[1] (analytic) = 0.84078051691051809391036455590107
y2[1] (numeric) = 0.84078051691051809391036920987157
absolute error = 4.65397050e-24
relative error = 5.5352977458388334574971142656264e-22 %
h = 0.0001
y1[1] (analytic) = 1.9872432102601254078381735066802
y1[1] (numeric) = 1.9872432102601254078381447629642
absolute error = 2.87437160e-23
relative error = 1.4464115842286619747719055752070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.16
y2[1] (analytic) = 0.84068179338575403668853684031401
y2[1] (numeric) = 0.84068179338575403668854150493323
absolute error = 4.66461922e-24
relative error = 5.5486145372718920584719618014548e-22 %
h = 0.0001
y1[1] (analytic) = 1.9872272833756269490409525240183
y1[1] (numeric) = 1.9872272833756269490409237327825
absolute error = 2.87912358e-23
relative error = 1.4488144381297658808757579683485e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1167.3MB, alloc=4.4MB, time=141.77
NO POLE
NO POLE
x[1] = 0.1601
y2[1] (analytic) = 0.84058307145417204428151703649875
y2[1] (numeric) = 0.84058307145417204428152171177624
absolute error = 4.67527749e-24
relative error = 5.5619458073453393430224750693978e-22 %
h = 0.0001
y1[1] (analytic) = 1.9872113466188556647143560763349
y1[1] (numeric) = 1.9872113466188556647143272375811
absolute error = 2.88387538e-23
relative error = 1.4512172471774454058763531430237e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1602
y2[1] (analytic) = 0.84048435111675933600430238576258
y2[1] (numeric) = 0.84048435111675933600430707170789
absolute error = 4.68594531e-24
relative error = 5.5752915610787293043818457336894e-22 %
h = 0.0001
y1[1] (analytic) = 1.9871953999899709224259642005895
y1[1] (numeric) = 1.9871953999899709224259353143195
absolute error = 2.88862700e-23
relative error = 1.4536200114063158901523044717371e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1171.1MB, alloc=4.4MB, time=142.34
NO POLE
NO POLE
x[1] = 0.1603
y2[1] (analytic) = 0.84038563237450311523019730139948
y2[1] (numeric) = 0.84038563237450311523020199802215
absolute error = 4.69662267e-24
relative error = 5.5886517915944480284868266711867e-22 %
h = 0.0001
y1[1] (analytic) = 1.9871794434891321884644914310919
y1[1] (numeric) = 1.9871794434891321884644624973076
absolute error = 2.89337843e-23
relative error = 1.4560227258187334306407922850398e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1604
y2[1] (analytic) = 0.84028691522839056938094133496531
y2[1] (numeric) = 0.84028691522839056938094604227489
absolute error = 4.70730958e-24
relative error = 5.6020265158128161193208393225677e-22 %
h = 0.0001
y1[1] (analytic) = 1.9871634771164990278381921366167
y1[1] (numeric) = 1.9871634771164990278381631553199
absolute error = 2.89812968e-23
relative error = 1.4584253954814885414945031671743e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1174.9MB, alloc=4.4MB, time=142.90
NO POLE
NO POLE
x[1] = 0.1605
y2[1] (analytic) = 0.84018819967940886991683730206863
y2[1] (numeric) = 0.84018819967940886991684202007467
absolute error = 4.71800604e-24
relative error = 5.6154157387597831980689288624447e-22 %
h = 0.0001
y1[1] (analytic) = 1.9871475008722311042732648703217
y1[1] (numeric) = 1.9871475008722311042732358415142
absolute error = 2.90288075e-23
relative error = 1.4608280204291932846392717238880e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1606
y2[1] (analytic) = 0.8400894857285451723268795677759
y2[1] (numeric) = 0.84008948572854517232688429648795
absolute error = 4.72871205e-24
relative error = 5.6288194654634330443227116919029e-22 %
h = 0.0001
y1[1] (analytic) = 1.9871315147564881802122557324871
y1[1] (numeric) = 1.9871315147564881802122266561709
absolute error = 2.90763162e-23
relative error = 1.4632305906316995550713818896564e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1178.7MB, alloc=4.4MB, time=143.47
NO POLE
NO POLE
x[1] = 0.1607
y2[1] (analytic) = 0.83999077337678661611888249172978
y2[1] (numeric) = 0.83999077337678661611888723115739
absolute error = 4.73942761e-24
relative error = 5.6422377009539845853987313971725e-22 %
h = 0.0001
y1[1] (analytic) = 1.9871155187694301168124607460921
y1[1] (numeric) = 1.9871155187694301168124316222689
absolute error = 2.91238232e-23
relative error = 1.4656331212206344092044858288747e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1608
y2[1] (analytic) = 0.8398920626251203248096090330792
y2[1] (numeric) = 0.83989206262512032480961378323192
absolute error = 4.75015272e-24
relative error = 5.6556704502637928861804030490639e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870995129112168739443272452423
y1[1] (numeric) = 1.9870995129112168739442980739141
absolute error = 2.91713282e-23
relative error = 1.4680355971333463808636667489881e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1182.5MB, alloc=4.4MB, time=144.03
NO POLE
NO POLE
x[1] = 0.1609
y2[1] (analytic) = 0.83979335347453340591489951531993
y2[1] (numeric) = 0.83979335347453340591490427620732
absolute error = 4.76088739e-24
relative error = 5.6691177303350414288067935400735e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870834971820085101898542764675
y1[1] (numeric) = 1.9870834971820085101898250576361
absolute error = 2.92188314e-23
relative error = 1.4704380284692021500452398894822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.161
y2[1] (analytic) = 0.83969464592601295093980055114447
y2[1] (numeric) = 0.83969464592601295093980532277607
absolute error = 4.77163160e-24
relative error = 5.6825795223903777158436015900431e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870674715819651828409920129024
y1[1] (numeric) = 1.9870674715819651828409627465696
absolute error = 2.92663328e-23
relative error = 1.4728404152628082342735795319121e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1186.3MB, alloc=4.4MB, time=144.62
NO POLE
NO POLE
x[1] = 0.1611
y2[1] (analytic) = 0.83959593998054603536869412739974
y2[1] (numeric) = 0.83959593998054603536869890978509
absolute error = 4.78238535e-24
relative error = 5.6960558314643718604490291538549e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870514361112471478980401813684
y1[1] (numeric) = 1.9870514361112471478980108675362
absolute error = 2.93138322e-23
relative error = 1.4752427474836053775334581766523e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1612
y2[1] (analytic) = 0.83949723563911971865542685025152
y2[1] (numeric) = 0.83949723563911971865543164340017
absolute error = 4.79314865e-24
relative error = 5.7095466745056237567476178309725e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870353907700147600680455023727
y1[1] (numeric) = 1.9870353907700147600680161410428
absolute error = 2.93613299e-23
relative error = 1.4776450402638231364643761034370e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1190.2MB, alloc=4.4MB, time=145.20
NO POLE
NO POLE
x[1] = 0.1613
y2[1] (analytic) = 0.8393985329027210442134393506542
y2[1] (numeric) = 0.8393985329027210442134441545757
absolute error = 4.80392150e-24
relative error = 5.7230520565571831038380087470685e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870193355584284727631981430382
y1[1] (numeric) = 1.9870193355584284727631687342125
absolute error = 2.94088257e-23
relative error = 1.4800472835728593732164604735023e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1614
y2[1] (analytic) = 0.83929983177233703940589585022461
y2[1] (numeric) = 0.83929983177233703940590066492851
absolute error = 4.81470390e-24
relative error = 5.7365719826642416881057247361103e-22 %
h = 0.0001
y1[1] (analytic) = 1.9870032704766488380992271829836
y1[1] (numeric) = 1.987003270476648838099197726664
absolute error = 2.94563196e-23
relative error = 1.4824494774451942291141481998900e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1194.0MB, alloc=4.4MB, time=145.75
NO POLE
NO POLE
x[1] = 0.1615
y2[1] (analytic) = 0.8392011322489547155358138876186
y2[1] (numeric) = 0.83920113224895471553581871311444
absolute error = 4.82549584e-24
relative error = 5.7501064459580398724317573877755e-22 %
h = 0.0001
y1[1] (analytic) = 1.9869871955248365068937950931671
y1[1] (numeric) = 1.9869871955248365068937655893554
absolute error = 2.95038117e-23
relative error = 1.4848516269480517003820027153304e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1616
y2[1] (analytic) = 0.83910243433356106783619420550906
y2[1] (numeric) = 0.83910243433356106783619904180639
absolute error = 4.83629733e-24
relative error = 5.7636554634013478847660351909698e-22 %
h = 0.0001
y1[1] (analytic) = 1.9869711107031522286648912277113
y1[1] (numeric) = 1.9869711107031522286648616764094
absolute error = 2.95513019e-23
relative error = 1.4872537270832459296357105698362e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1197.8MB, alloc=4.4MB, time=146.32
NO POLE
NO POLE
x[1] = 0.1617
y2[1] (analytic) = 0.8390037380271430754601507982642
y2[1] (numeric) = 0.83900373802714307546015564537256
absolute error = 4.84710836e-24
relative error = 5.7772190281268907862359640003567e-22 %
h = 0.0001
y1[1] (analytic) = 1.9869550160117568516292243287246
y1[1] (numeric) = 1.9869550160117568516291947299344
absolute error = 2.95987902e-23
relative error = 1.4896557778852535119701906338940e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1618
y2[1] (analytic) = 0.83890504333068770147104112042456
y2[1] (numeric) = 0.83890504333068770147104597835351
absolute error = 4.85792895e-24
relative error = 5.7907971690248315678442839570205e-22 %
h = 0.0001
y1[1] (analytic) = 1.9869389114508113227006140441355
y1[1] (numeric) = 1.9869389114508113227005843978588
absolute error = 2.96462767e-23
relative error = 1.4920577844214172001079872497793e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1201.6MB, alloc=4.4MB, time=146.88
NO POLE
NO POLE
x[1] = 0.1619
y2[1] (analytic) = 0.83880635024518189283259645607774
y2[1] (numeric) = 0.83880635024518189283260132483681
absolute error = 4.86875907e-24
relative error = 5.8043898553901847649545257708259e-22 %
h = 0.0001
y1[1] (analytic) = 1.9869227970204766874883814585555
y1[1] (numeric) = 1.9869227970204766874883517647942
absolute error = 2.96937613e-23
relative error = 1.4944597416934254516509915753249e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.162
y2[1] (analytic) = 0.83870765877161258039905244922922
y2[1] (numeric) = 0.83870765877161258039905732882797
absolute error = 4.87959875e-24
relative error = 5.8179971280419144846741127678931e-22 %
h = 0.0001
y1[1] (analytic) = 1.9869066727209140902957386371875
y1[1] (numeric) = 1.9869066727209140902957088959435
absolute error = 2.97412440e-23
relative error = 1.4968616497357513254564038568950e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1205.4MB, alloc=4.4MB, time=147.50
NO POLE
NO POLE
x[1] = 0.1621
y2[1] (analytic) = 0.83860896891096667890527979526832
y2[1] (numeric) = 0.83860896891096667890528468571628
absolute error = 4.89044796e-24
relative error = 5.8316189562709153460481597954668e-22 %
h = 0.0001
y1[1] (analytic) = 1.986890538552284774118177182795
y1[1] (numeric) = 1.9868905385522847741181473940702
absolute error = 2.97887248e-23
relative error = 1.4992635085828666781937665449036e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1622
y2[1] (analytic) = 0.83851028066423108695691509362765
y2[1] (numeric) = 0.83851028066423108695691999493437
absolute error = 4.90130672e-24
relative error = 5.8452553689829535217143777630207e-22 %
h = 0.0001
y1[1] (analytic) = 1.9868743945147500806418558057484
y1[1] (numeric) = 1.9868743945147500806418259695446
absolute error = 2.98362038e-23
relative error = 1.5016653233022729537139913067103e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1209.2MB, alloc=4.4MB, time=148.06
NO POLE
NO POLE
x[1] = 0.1623
y2[1] (analytic) = 0.838411594032392687020491861735
y2[1] (numeric) = 0.83841159403239268702049677391003
absolute error = 4.91217503e-24
relative error = 5.8589063712425406650972131951135e-22 %
h = 0.0001
y1[1] (analytic) = 1.9868582406084714502419869071648
y1[1] (numeric) = 1.9868582406084714502419570234839
absolute error = 2.98836809e-23
relative error = 1.5040670888954906602488748047202e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1624
y2[1] (analytic) = 0.83831290901643834541357171035623
y2[1] (numeric) = 0.83831290901643834541357663340911
absolute error = 4.92305288e-24
relative error = 5.8725719561876204314994431065208e-22 %
h = 0.0001
y1[1] (analytic) = 1.9868420768336104219812221751574
y1[1] (numeric) = 1.9868420768336104219811922440012
absolute error = 2.99311562e-23
relative error = 1.5064688104301007863474569830096e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1213.1MB, alloc=4.4MB, time=148.63
NO POLE
NO POLE
x[1] = 0.1625
y2[1] (analytic) = 0.83821422561735491229487568042786
y2[1] (numeric) = 0.83821422561735491229488061436814
absolute error = 4.93394028e-24
relative error = 5.8862521408129208566735013723648e-22 %
h = 0.0001
y1[1] (analytic) = 1.98682590319032863360803719421
y1[1] (numeric) = 1.9868259031903286336080072155804
absolute error = 2.99786296e-23
relative error = 1.5088704829075397567416900734119e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1626
y2[1] (analytic) = 0.8381155438361292216544157414781
y2[1] (numeric) = 0.83811554383612922165442068631532
absolute error = 4.94483722e-24
relative error = 5.8999469182578827027369276713891e-22 %
h = 0.0001
y1[1] (analytic) = 1.9868097196787878215551150676937
y1[1] (numeric) = 1.9868097196787878215550850415927
absolute error = 3.00261010e-23
relative error = 1.5112721013290789637826476584717e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1216.9MB, alloc=4.4MB, time=149.24
NO POLE
NO POLE
x[1] = 0.1627
y2[1] (analytic) = 0.83801686367374809130362645173494
y2[1] (numeric) = 0.83801686367374809130363140747864
absolute error = 4.95574370e-24
relative error = 5.9136562935914159039626694522911e-22 %
h = 0.0001
y1[1] (analytic) = 1.9867935262991498209377290535417
y1[1] (numeric) = 1.9867935262991498209376989799711
absolute error = 3.00735706e-23
relative error = 1.5136736757955314531901754473500e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1628
y2[1] (analytic) = 0.83791818513119832286549678002003
y2[1] (numeric) = 0.83791818513119832286550174667976
absolute error = 4.96665973e-24
relative error = 5.9273802838189239773772720694957e-22 %
h = 0.0001
y1[1] (analytic) = 1.9867773230515765655521242130975
y1[1] (numeric) = 1.9867773230515765655520940920593
absolute error = 3.01210382e-23
relative error = 1.5160751962749305289193581473976e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1220.7MB, alloc=4.4MB, time=149.79
NO POLE
NO POLE
x[1] = 0.1629
y2[1] (analytic) = 0.83781950820946670176470208952703
y2[1] (numeric) = 0.83781950820946670176470706711233
absolute error = 4.97758530e-24
relative error = 5.9411188820820980728205589625291e-22 %
h = 0.0001
y1[1] (analytic) = 1.9867611099362300878738980731542
y1[1] (numeric) = 1.9867611099362300878738679046502
absolute error = 3.01685040e-23
relative error = 1.5184766728682509413496341210559e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.163
memory used=1224.5MB, alloc=4.4MB, time=150.39
y2[1] (analytic) = 0.83772083290953999721773628358307
y2[1] (numeric) = 0.83772083290953999721774127210348
absolute error = 4.98852041e-24
relative error = 5.9548720934563146361934665930855e-22 %
h = 0.0001
y1[1] (analytic) = 1.9867448869532725190563803011996
y1[1] (numeric) = 1.9867448869532725190563500852316
absolute error = 3.02159680e-23
relative error = 1.5208781056100771546606040456219e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1631
y2[1] (analytic) = 0.83762215923240496222304411349202
y2[1] (numeric) = 0.83762215923240496222304911295709
absolute error = 4.99946507e-24
relative error = 5.9686399349576644394781484300353e-22 %
h = 0.0001
y1[1] (analytic) = 1.986728654102866088929011393884
y1[1] (numeric) = 1.986728654102866088928981130454
absolute error = 3.02634300e-23
relative error = 1.5232794844681926035617324263449e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1228.3MB, alloc=4.4MB, time=150.96
x[1] = 0.1632
y2[1] (analytic) = 0.83752348717904833355115364855829
y2[1] (numeric) = 0.83752348717904833355115865897756
absolute error = 5.01041927e-24
relative error = 5.9824223997300952572918505644518e-22 %
h = 0.0001
y1[1] (analytic) = 1.9867124113851731259957203787281
y1[1] (numeric) = 1.9867124113851731259956900678378
absolute error = 3.03108903e-23
relative error = 1.5256808245772562134187271314558e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1633
y2[1] (analytic) = 0.83742481675045683173480890838975
y2[1] (numeric) = 0.83742481675045683173481392977276
absolute error = 5.02138301e-24
relative error = 5.9962194928554590589123281409754e-22 %
h = 0.0001
y1[1] (analytic) = 1.9866961588003560574333015290838
y1[1] (numeric) = 1.9866961588003560574332711707352
absolute error = 3.03583486e-23
relative error = 1.5280821108715257435498138750174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1232.1MB, alloc=4.4MB, time=151.52
NO POLE
NO POLE
x[1] = 0.1634
y2[1] (analytic) = 0.83732614794761716105910265757853
y2[1] (numeric) = 0.83732614794761716105910768993481
absolute error = 5.03235628e-24
relative error = 6.0100312074749903746836402400656e-22 %
h = 0.0001
y1[1] (analytic) = 1.9866798963485774090897900923686
y1[1] (numeric) = 1.9866798963485774090897596865637
absolute error = 3.04058049e-23
relative error = 1.5304833433853342227144884075859e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1635
y2[1] (analytic) = 0.83722748077151600955160936285829
y2[1] (numeric) = 0.83722748077151600955161440619739
absolute error = 5.04333910e-24
relative error = 6.0238575725590104179476145811737e-22 %
h = 0.0001
y1[1] (analytic) = 1.9866636240299998054828370315863
y1[1] (numeric) = 1.9866636240299998054828065783268
absolute error = 3.04532595e-23
relative error = 1.5328845372537076070481975646872e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1235.9MB, alloc=4.4MB, time=152.11
NO POLE
NO POLE
x[1] = 0.1636
y2[1] (analytic) = 0.83712881522314004897251831283674
y2[1] (numeric) = 0.8371288152231400489725233671682
absolute error = 5.05433146e-24
relative error = 6.0376985812544842849514982216713e-22 %
h = 0.0001
y1[1] (analytic) = 1.9866473418447859697980827801515
y1[1] (numeric) = 1.9866473418447859697980522794394
absolute error = 3.05007121e-23
relative error = 1.5352856774105295017691010325573e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1637
y2[1] (analytic) = 0.83703015130347593480476690040192
y2[1] (numeric) = 0.83703015130347593480477196573529
absolute error = 5.06533337e-24
relative error = 6.0515542505989117192240003905862e-22 %
h = 0.0001
y1[1] (analytic) = 1.9866310497930987238875300100351
y1[1] (numeric) = 1.9866310497930987238874994618723
absolute error = 3.05481628e-23
relative error = 1.5376867689237764378803956110553e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1239.8MB, alloc=4.4MB, time=152.67
NO POLE
NO POLE
x[1] = 0.1638
y2[1] (analytic) = 0.8369314890135103062441740679011
y2[1] (numeric) = 0.83693148901351030624417914424591
absolute error = 5.07634481e-24
relative error = 6.0654245617923622618879021393577e-22 %
h = 0.0001
y1[1] (analytic) = 1.9866147478751009882679154132452
y1[1] (numeric) = 1.9866147478751009882678848176336
absolute error = 3.05956116e-23
relative error = 1.5400878118279002354803485989757e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1639
y2[1] (analytic) = 0.83683282835422978618957391519076
y2[1] (numeric) = 0.83683282835422978618957900255655
absolute error = 5.08736579e-24
relative error = 6.0793095318752570308386479953639e-22 %
h = 0.0001
y1[1] (analytic) = 1.9865984360909557821190804966614
y1[1] (numeric) = 1.9865984360909557821190498536029
absolute error = 3.06430585e-23
relative error = 1.5424888061573515324291896015502e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1243.6MB, alloc=4.4MB, time=153.26
NO POLE
NO POLE
x[1] = 0.164
y2[1] (analytic) = 0.8367341693266209812329494706565
y2[1] (numeric) = 0.83673416932662098123295456905282
absolute error = 5.09839632e-24
relative error = 6.0932091778958175179506201256851e-22 %
h = 0.0001
y1[1] (analytic) = 1.9865821144408262232823413902376
y1[1] (numeric) = 1.986582114440826223282310699734
absolute error = 3.06905036e-23
relative error = 1.5448897569803510689630509938767e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1641
y2[1] (analytic) = 0.83663551193167048164956662530143
y2[1] (numeric) = 0.83663551193167048164957173473782
absolute error = 5.10943639e-24
relative error = 6.1071234930047970600411640788146e-22 %
h = 0.0001
y1[1] (analytic) = 1.98656578292487552825885766859
y1[1] (numeric) = 1.9865657829248755282588269306433
absolute error = 3.07379467e-23
relative error = 1.5472906542638459373039437493097e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1247.4MB, alloc=4.4MB, time=153.83
NO POLE
NO POLE
x[1] = 0.1642
y2[1] (analytic) = 0.83653685617036486138810823000175
y2[1] (numeric) = 0.83653685617036486138811335048774
absolute error = 5.12048599e-24
relative error = 6.1210524703494806262780767087526e-22 %
h = 0.0001
y1[1] (analytic) = 1.9865494415432670122080001859874
y1[1] (numeric) = 1.9865494415432670122079694005995
absolute error = 3.07853879e-23
relative error = 1.5496915030760131618993364886504e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1643
y2[1] (analytic) = 0.83643820204369067806080835602809
y2[1] (numeric) = 0.83643820204369067806081348757322
absolute error = 5.13154513e-24
relative error = 6.1349961269845944450437833354966e-22 %
h = 0.0001
y1[1] (analytic) = 1.9865330902961640889457179247582
y1[1] (numeric) = 1.986533090296164088945687091931
absolute error = 3.08328272e-23
relative error = 1.5520923034512986627314047745781e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1251.2MB, alloc=4.4MB, time=154.41
NO POLE
NO POLE
x[1] = 0.1644
y2[1] (analytic) = 0.83633954955263447293358671893144
y2[1] (numeric) = 0.83633954955263447293359186154525
absolute error = 5.14261381e-24
relative error = 6.1489544680158080010580258127052e-22 %
h = 0.0001
y1[1] (analytic) = 1.9865167291837302709429038571329
y1[1] (numeric) = 1.9865167291837302709428729768683
absolute error = 3.08802646e-23
relative error = 1.5544930554241471830807114112590e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1645
y2[1] (analytic) = 0.83624089869818277091618326589215
y2[1] (numeric) = 0.83624089869818277091618841958419
absolute error = 5.15369204e-24
relative error = 6.1629275105092386832258048344334e-22 %
h = 0.0001
y1[1] (analytic) = 1.986500358206129169323759820536
y1[1] (numeric) = 1.9865003582061291693237288928359
absolute error = 3.09277001e-23
relative error = 1.5568937590290022906333681450642e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1255.0MB, alloc=4.4MB, time=155.01
NO POLE
NO POLE
x[1] = 0.1646
y2[1] (analytic) = 0.83614224948132208055229292663078
y2[1] (numeric) = 0.83614224948132208055229809141057
absolute error = 5.16477979e-24
relative error = 6.1769152237000696195337817550392e-22 %
h = 0.0001
y1[1] (analytic) = 1.9864839773635244938641604063456
y1[1] (numeric) = 1.9864839773635244938641294312119
absolute error = 3.09751337e-23
relative error = 1.5592944143003063785881564547374e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1647
y2[1] (analytic) = 0.83604360190303889400970052797932
y2[1] (numeric) = 0.83604360190303889400970570385641
absolute error = 5.17587709e-24
relative error = 6.1909176485753170350805781229510e-22 %
h = 0.0001
y1[1] (analytic) = 1.9864675866560800529900158621361
y1[1] (numeric) = 1.9864675866560800529899848395707
absolute error = 3.10225654e-23
relative error = 1.5616950212725006667636074951293e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1258.8MB, alloc=4.4MB, time=155.58
NO POLE
NO POLE
x[1] = 0.1648
y2[1] (analytic) = 0.83594495596431968707041587221161
y2[1] (numeric) = 0.83594495596431968707042105919554
absolute error = 5.18698393e-24
relative error = 6.2049347782910649138447399242394e-22 %
h = 0.0001
y1[1] (analytic) = 1.9864511860839597537756340074202
y1[1] (numeric) = 1.986451186083959753775602937425
absolute error = 3.10699952e-23
relative error = 1.5640955799800252027050412586172e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1649
y2[1] (analytic) = 0.83584631166615091912080897923145
y2[1] (numeric) = 0.83584631166615091912081417733175
absolute error = 5.19810030e-24
relative error = 6.2189666059999272754241186379989e-22 %
h = 0.0001
y1[1] (analytic) = 1.9864347756473276019420811629075
y1[1] (numeric) = 1.9864347756473276019420500454844
absolute error = 3.11174231e-23
relative error = 1.5664960904573188627915650183223e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1262.6MB, alloc=4.4MB, time=156.15
NO POLE
NO POLE
x[1] = 0.165
y2[1] (analytic) = 0.83574766900951903314174549271711
y2[1] (numeric) = 0.83574766900951903314175070194332
absolute error = 5.20922621e-24
relative error = 6.2330131487817140908637238854042e-22 %
h = 0.0001
y1[1] (analytic) = 1.9864183553463477018555420932949
y1[1] (numeric) = 1.9864183553463477018555109284459
absolute error = 3.11648490e-23
relative error = 1.5688965477046330888607835412587e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1651
y2[1] (analytic) = 0.83564902799541045569872225032089
y2[1] (numeric) = 0.83564902799541045569872747068255
absolute error = 5.22036166e-24
relative error = 6.2470744117573140105012350122966e-22 %
h = 0.0001
y1[1] (analytic) = 1.9864019251811842565256789636065
y1[1] (numeric) = 1.9864019251811842565256477513334
absolute error = 3.12122731e-23
relative error = 1.5712969618247353078812220605528e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1266.5MB, alloc=4.4MB, time=156.72
NO POLE
NO POLE
x[1] = 0.1652
y2[1] (analytic) = 0.8355503886248115969320030180224
y2[1] (numeric) = 0.83555038862481159693200824952905
absolute error = 5.23150665e-24
relative error = 6.2611504000497940285959614016517e-22 %
h = 0.0001
y1[1] (analytic) = 1.9863854851520015676039893090978
y1[1] (numeric) = 1.9863854851520015676039580494026
absolute error = 3.12596952e-23
relative error = 1.5736973227836466696708089092378e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1653
y2[1] (analytic) = 0.83545175089870885054675438873412
y2[1] (numeric) = 0.83545175089870885054675963139529
absolute error = 5.24266117e-24
relative error = 6.2752411068148283584189066903531e-22 %
h = 0.0001
y1[1] (analytic) = 1.9863690352589640353821630187426
y1[1] (numeric) = 1.9863690352589640353821317116272
absolute error = 3.13071154e-23
relative error = 1.5760976356499875644284764750890e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1270.3MB, alloc=4.4MB, time=157.33
NO POLE
NO POLE
x[1] = 0.1654
y2[1] (analytic) = 0.83535311481808859380318184525794
y2[1] (numeric) = 0.83535311481808859380318709908317
absolute error = 5.25382523e-24
relative error = 6.2893465491465891939774016676974e-22 %
h = 0.0001
y1[1] (analytic) = 1.9863525755022361587904383323172
y1[1] (numeric) = 1.9863525755022361587904069777835
absolute error = 3.13545337e-23
relative error = 1.5784979004581909522357109681369e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1655
y2[1] (analytic) = 0.83525448038393718750666598769137
y2[1] (numeric) = 0.83525448038393718750667125269019
absolute error = 5.26499882e-24
relative error = 6.3034667202022845970292390280531e-22 %
h = 0.0001
y1[1] (analytic) = 1.9863361058819825353959568510995
y1[1] (numeric) = 1.9863361058819825353959254491495
absolute error = 3.14019500e-23
relative error = 1.5808981122082939104567336303899e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1274.1MB, alloc=4.4MB, time=157.94
NO POLE
NO POLE
x[1] = 0.1656
y2[1] (analytic) = 0.83515584759724097599789892538191
y2[1] (numeric) = 0.83515584759724097599790420156386
absolute error = 5.27618195e-24
relative error = 6.3176016370832753474124459918695e-22 %
h = 0.0001
y1[1] (analytic) = 1.9863196263983678614011175621989
y1[1] (numeric) = 1.9863196263983678614010861128345
absolute error = 3.14493644e-23
relative error = 1.5832982759690382537871262940042e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1657
y2[1] (analytic) = 0.83505721645898628714302083352837
y2[1] (numeric) = 0.83505721645898628714302612090298
absolute error = 5.28737461e-24
relative error = 6.3317512929483061708392390205937e-22 %
h = 0.0001
y1[1] (analytic) = 1.9863031370515569316419298765338
y1[1] (numeric) = 1.9863031370515569316418983797569
absolute error = 3.14967769e-23
relative error = 1.5856983917748533749662732089618e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1277.9MB, alloc=4.4MB, time=158.52
NO POLE
NO POLE
x[1] = 0.1658
y2[1] (analytic) = 0.83495858697015943232375667452769
y2[1] (numeric) = 0.83495858697015943232376197310449
absolute error = 5.29857680e-24
relative error = 6.3459156929292898292003445564470e-22 %
h = 0.0001
y1[1] (analytic) = 1.9862866378417146395863656804727
y1[1] (numeric) = 1.9862866378417146395863341362851
absolute error = 3.15441876e-23
relative error = 1.5880984646946876042250946992015e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1659
y2[1] (analytic) = 0.83485995913174670642755308416587
y2[1] (numeric) = 0.83485995913174670642755839395441
absolute error = 5.30978854e-24
relative error = 6.3600948661164362403232352616432e-22 %
h = 0.0001
y1[1] (analytic) = 1.9862701287690059773327104011558
y1[1] (numeric) = 1.9862701287690059773326788095595
absolute error = 3.15915963e-23
relative error = 1.5904984846939696604709341560218e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1281.7MB, alloc=4.4MB, time=159.10
NO POLE
NO POLE
x[1] = 0.166
y2[1] (analytic) = 0.83476133294473438783771542275181
y2[1] (numeric) = 0.83476133294473438783772074376161
absolute error = 5.32100980e-24
relative error = 6.3742887817161015669861214373622e-22 %
h = 0.0001
y1[1] (analytic) = 1.9862536098335960356079130855139
y1[1] (numeric) = 1.9862536098335960356078814465109
absolute error = 3.16390030e-23
relative error = 1.5928984518069999214524787642481e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1661
y2[1] (analytic) = 0.83466270841010873842354499129237
y2[1] (numeric) = 0.83466270841010873842355032353298
absolute error = 5.33224061e-24
relative error = 6.3884974808051701738721940434879e-22 %
h = 0.0001
y1[1] (analytic) = 1.9862370810356500037659354929999
y1[1] (numeric) = 1.9862370810356500037659038065921
absolute error = 3.16864078e-23
relative error = 1.5952983711027231633192921754576e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1285.5MB, alloc=4.4MB, time=159.71
NO POLE
NO POLE
x[1] = 0.1662
y2[1] (analytic) = 0.83456408552885600353047641280766
y2[1] (numeric) = 0.83456408552885600353048175628861
absolute error = 5.34348095e-24
relative error = 6.4027209445681844666665627758341e-22 %
h = 0.0001
y1[1] (analytic) = 1.9862205423753331697861002020508
y1[1] (numeric) = 1.9862205423753331697860684682401
absolute error = 3.17338107e-23
relative error = 1.5976982426155629067285212953771e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1663
y2[1] (analytic) = 0.83446546430196241197021517888487
y2[1] (numeric) = 0.83446546430196241197022053361569
absolute error = 5.35473082e-24
relative error = 6.4169591781479880742578266958381e-22 %
h = 0.0001
y1[1] (analytic) = 1.9862039938528109202714377302955
y1[1] (numeric) = 1.9862039938528109202714059490839
absolute error = 3.17812116e-23
relative error = 1.6000980613452119365362923146564e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1289.3MB, alloc=4.4MB, time=160.32
NO POLE
NO POLE
x[1] = 0.1664
y2[1] (analytic) = 0.83436684473041417601087536156943
y2[1] (numeric) = 0.83436684473041417601088072755965
absolute error = 5.36599022e-24
relative error = 6.4312121866896132918579949969931e-22 %
h = 0.0001
y1[1] (analytic) = 1.9861874354682487404470326685266
y1[1] (numeric) = 1.9861874354682487404470008399159
absolute error = 3.18286107e-23
relative error = 1.6024978373955086500033463903259e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1665
y2[1] (analytic) = 0.83426822681519749136711749069211
y2[1] (numeric) = 0.83426822681519749136712286795127
absolute error = 5.37725916e-24
relative error = 6.4454799873268347195500216742013e-22 %
h = 0.0001
y1[1] (analytic) = 1.98617086722181221415836882845
y1[1] (numeric) = 1.9861708672218122141583369524422
absolute error = 3.18760078e-23
relative error = 1.6048975607313719190489008360342e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1293.2MB, alloc=4.4MB, time=160.94
NO POLE
NO POLE
x[1] = 0.1666
y2[1] (analytic) = 0.83416961055729853719028659673062
y2[1] (numeric) = 0.83416961055729853719029198526826
absolute error = 5.38853764e-24
relative error = 6.4597625852133162231408487752235e-22 %
h = 0.0001
y1[1] (analytic) = 1.9861542891136670238696734042321
y1[1] (numeric) = 1.9861542891136670238696414808292
absolute error = 3.19234029e-23
relative error = 1.6072972313870945739171943778080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1667
y2[1] (analytic) = 0.8340709959577034760585504193044
y2[1] (numeric) = 0.83407099595770347605855581913004
absolute error = 5.39982564e-24
relative error = 6.4740599615261411537694455216239e-22 %
h = 0.0001
y1[1] (analytic) = 1.9861377011439789506622601478587
y1[1] (numeric) = 1.9861377011439789506622281770626
absolute error = 3.19707961e-23
relative error = 1.6096968544318657672037005673220e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1297.0MB, alloc=4.4MB, time=161.58
NO POLE
NO POLE
x[1] = 0.1668
y2[1] (analytic) = 0.83397238301739845396703778140112
y2[1] (numeric) = 0.83397238301739845396704319252429
absolute error = 5.41112317e-24
relative error = 6.4883721334056602161080565398082e-22 %
h = 0.0001
y1[1] (analytic) = 1.9861211033129138742328715583233
y1[1] (numeric) = 1.9861211033129138742328395401359
absolute error = 3.20181874e-23
relative error = 1.6120964299001019478533672569834e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1669
y2[1] (analytic) = 0.83387377173736960031797712943364
y2[1] (numeric) = 0.83387377173736960031798255186387
absolute error = 5.42243023e-24
relative error = 6.5026991060078652590392043903121e-22 %
h = 0.0001
y1[1] (analytic) = 1.9861044956206377728920200846608
y1[1] (numeric) = 1.9861044956206377728919880190841
absolute error = 3.20655767e-23
relative error = 1.6144959527912366098927070364533e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1300.8MB, alloc=4.4MB, time=162.22
NO POLE
NO POLE
x[1] = 0.167
y2[1] (analytic) = 0.83377516211860302791083523922592
y2[1] (numeric) = 0.83377516211860302791084067297276
absolute error = 5.43374684e-24
relative error = 6.5170409084782249908707427261749e-22 %
h = 0.0001
y1[1] (analytic) = 1.9860878780673167235623283428443
y1[1] (numeric) = 1.9860878780673167235622962298802
absolute error = 3.21129641e-23
relative error = 1.6168954281745814559734094393427e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1671
y2[1] (analytic) = 0.83367655416208483293245608802662
y2[1] (numeric) = 0.83367655416208483293246153309959
absolute error = 5.44507297e-24
relative error = 6.5313975100004545956993731473113e-22 %
h = 0.0001
y1[1] (analytic) = 1.9860712506531169017768683465597
y1[1] (numeric) = 1.9860712506531169017768361862101
absolute error = 3.21603496e-23
relative error = 1.6192948560845494140911808552933e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1304.6MB, alloc=4.4MB, time=162.85
NO POLE
NO POLE
x[1] = 0.1672
y2[1] (analytic) = 0.8335779478688010949471998926488
y2[1] (numeric) = 0.83357794786880109494720534905744
absolute error = 5.45640864e-24
relative error = 6.5457689397258355947063248522371e-22 %
h = 0.0001
y1[1] (analytic) = 1.9860546133782045816774997518767
y1[1] (numeric) = 1.9860546133782045816774675441435
absolute error = 3.22077332e-23
relative error = 1.6216942365555522665049166142626e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1673
y2[1] (analytic) = 0.83347934323973787688708231383461
y2[1] (numeric) = 0.83347934323973787688708778158844
absolute error = 5.46775383e-24
relative error = 6.5601551788276081191109632866036e-22 %
h = 0.0001
y1[1] (analytic) = 1.9860379662427461360132071158313
y1[1] (numeric) = 1.9860379662427461360131748607165
absolute error = 3.22551148e-23
relative error = 1.6240935645868501804222941478568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1308.4MB, alloc=4.4MB, time=163.48
NO POLE
NO POLE
x[1] = 0.1674
y2[1] (analytic) = 0.8333807402758812250419138269433
y2[1] (numeric) = 0.83338074027588122504191930605186
absolute error = 5.47910856e-24
relative error = 6.5745562564671261371589536085133e-22 %
h = 0.0001
y1[1] (analytic) = 1.9860213092469080361384361689377
y1[1] (numeric) = 1.9860213092469080361384038664433
absolute error = 3.23024944e-23
relative error = 1.6264928402127259587373584286745e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1675
y2[1] (analytic) = 0.83328213897821716904943925906137
y2[1] (numeric) = 0.83328213897821716904944474953418
absolute error = 5.49047281e-24
relative error = 6.5889721538163515905679741090349e-22 %
h = 0.0001
y1[1] (analytic) = 1.986004642390856852011429101645
y1[1] (numeric) = 1.986004642390856852011396751773
absolute error = 3.23498720e-23
relative error = 1.6288920634674611076798818348672e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1312.2MB, alloc=4.4MB, time=164.11
NO POLE
NO POLE
x[1] = 0.1676
y2[1] (analytic) = 0.83318353934773172188547749263329
y2[1] (numeric) = 0.83318353934773172188548299447989
absolute error = 5.50184660e-24
relative error = 6.6034029000467174847332159137294e-22 %
h = 0.0001
y1[1] (analytic) = 1.9859879656747592521925588647563
y1[1] (numeric) = 1.9859879656747592521925264675086
absolute error = 3.23972477e-23
relative error = 1.6312912394206130766659880629527e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1677
y2[1] (analytic) = 0.83308494138541087985406133571157
y2[1] (numeric) = 0.83308494138541087985406684894149
absolute error = 5.51322992e-24
relative error = 6.6178484883324870847364247206259e-22 %
h = 0.0001
y1[1] (analytic) = 1.9859712790987820038426624838262
y1[1] (numeric) = 1.9859712790987820038426300392047
absolute error = 3.24446215e-23
relative error = 1.6336903681065877044740355309364e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1316.1MB, alloc=4.4MB, time=164.70
NO POLE
NO POLE
x[1] = 0.1678
y2[1] (analytic) = 0.83298634509224062257757755892466
y2[1] (numeric) = 0.83298634509224062257758308354742
absolute error = 5.52462276e-24
relative error = 6.6323089118444452974131915778094e-22 %
h = 0.0001
y1[1] (analytic) = 1.9859545826630919727213733875537
y1[1] (numeric) = 1.9859545826630919727213408955605
absolute error = 3.24919932e-23
relative error = 1.6360894394890659317306528501394e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1679
y2[1] (analytic) = 0.83288775046920691298690709926123
y2[1] (numeric) = 0.83288775046920691298691263528637
absolute error = 5.53602514e-24
relative error = 6.6467841997691560529449072357494e-22 %
h = 0.0001
y1[1] (analytic) = 1.9859378763678561231854527501879
y1[1] (numeric) = 1.9859378763678561231854202108248
absolute error = 3.25393631e-23
relative error = 1.6384884687084098818088382794456e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1319.9MB, alloc=4.4MB, time=165.31
NO POLE
NO POLE
x[1] = 0.168
y2[1] (analytic) = 0.83278915751729569731156543076966
y2[1] (numeric) = 0.8327891575172956973115709782067
absolute error = 5.54743704e-24
relative error = 6.6612743332753928360581099194123e-22 %
h = 0.0001
y1[1] (analytic) = 1.985921160213241518187119847961
y1[1] (numeric) = 1.98592116021324151818708726123
absolute error = 3.25867310e-23
relative error = 1.6408874457282557329207980857880e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1681
y2[1] (analytic) = 0.83269056623749290506984310227104
y2[1] (numeric) = 0.83269056623749290506984866112951
absolute error = 5.55885847e-24
relative error = 6.6757793295505521236082190624430e-22 %
h = 0.0001
y1[1] (analytic) = 1.9859044341994153192723814295679
y1[1] (numeric) = 1.985904434199415319272348795471
absolute error = 3.26340969e-23
relative error = 1.6432863705828774657714786004735e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1323.7MB, alloc=4.4MB, time=165.92
NO POLE
NO POLE
x[1] = 0.1682
y2[1] (analytic) = 0.83259197663078444905894644218451
y2[1] (numeric) = 0.83259197663078444905895201247394
absolute error = 5.57028943e-24
relative error = 6.6902991937792387624601000417988e-22 %
h = 0.0001
y1[1] (analytic) = 1.9858876983265447865793601007075
y1[1] (numeric) = 1.9858876983265447865793274192466
absolute error = 3.26814609e-23
relative error = 1.6456852483420792416849618391748e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1683
y2[1] (analytic) = 0.83249338869815622534513843056341
y2[1] (numeric) = 0.83249338869815622534514401229333
absolute error = 5.58172992e-24
relative error = 6.7048339311482657097854584240547e-22 %
h = 0.0001
y1[1] (analytic) = 1.9858709525947972788366217227028
y1[1] (numeric) = 1.9858709525947972788365889938799
absolute error = 3.27288229e-23
relative error = 1.6480840740046859185279222107589e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1327.5MB, alloc=4.4MB, time=166.55
NO POLE
NO POLE
x[1] = 0.1684
y2[1] (analytic) = 0.83239480244059411325387973844085
y2[1] (numeric) = 0.83239480244059411325388533162079
absolute error = 5.59317994e-24
relative error = 6.7193835468466550618421434215702e-22 %
h = 0.0001
y1[1] (analytic) = 1.9858541970043402533615018252166
y1[1] (numeric) = 1.9858541970043402533614690490337
absolute error = 3.27761829e-23
relative error = 1.6504828476049676905220355582170e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1331.3MB, alloc=4.4MB, time=167.19
x[1] = 0.1685
y2[1] (analytic) = 0.83229621785908397535996993458336
y2[1] (numeric) = 0.83229621785908397535997553922284
absolute error = 5.60463948e-24
relative error = 6.7339480340506860107959405480075e-22 %
h = 0.0001
y1[1] (analytic) = 1.9858374315553412660584310330798
y1[1] (numeric) = 1.9858374315553412660583982095388
absolute error = 3.28235410e-23
relative error = 1.6528815742128523983552518794709e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1686
y2[1] (analytic) = 0.83219763495461165747768885975104
y2[1] (numeric) = 0.83219763495461165747769447585959
absolute error = 5.61610855e-24
relative error = 6.7485274099659084871164502999995e-22 %
h = 0.0001
y1[1] (analytic) = 1.9858206562479679714172595072481
y1[1] (numeric) = 1.9858206562479679714172266363509
absolute error = 3.28708972e-23
relative error = 1.6552802538627352828394646310497e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1335.1MB, alloc=4.4MB, time=167.83
x[1] = 0.1687
y2[1] (analytic) = 0.83209905372816298865093816856304
y2[1] (numeric) = 0.8320990537281629886509437961502
absolute error = 5.62758716e-24
relative error = 6.7631216918057772339331289755041e-22 %
h = 0.0001
y1[1] (analytic) = 1.9858038710823881225115803999051
y1[1] (numeric) = 1.9858038710823881225115474816538
absolute error = 3.29182513e-23
relative error = 1.6576788765175223840807063308014e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1688
y2[1] (analytic) = 0.83200047418072378114338303906675
y2[1] (numeric) = 0.83200047418072378114338867814204
absolute error = 5.63907529e-24
relative error = 6.7777308607339842107781759382091e-22 %
h = 0.0001
y1[1] (analytic) = 1.9857870760587695709970523237278
y1[1] (numeric) = 1.9857870760587695709970193581244
absolute error = 3.29656034e-23
relative error = 1.6600774472471377694691996037604e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1338.9MB, alloc=4.4MB, time=168.46
NO POLE
NO POLE
x[1] = 0.1689
y2[1] (analytic) = 0.83190189631327983042859405010933
y2[1] (numeric) = 0.83190189631327983042859970068227
absolute error = 5.65057294e-24
relative error = 6.7923549219463399345850564696801e-22 %
h = 0.0001
y1[1] (analytic) = 1.9857702711772802671097208353316
y1[1] (numeric) = 1.9857702711772802671096878223779
absolute error = 3.30129537e-23
relative error = 1.6624759761575037774766363412098e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.169
y2[1] (analytic) = 0.83180332012681691518018922661023
y2[1] (numeric) = 0.83180332012681691518019488869036
absolute error = 5.66208013e-24
relative error = 6.8069939046850137979222005704297e-22 %
h = 0.0001
y1[1] (analytic) = 1.9857534564380882596643389329105
y1[1] (numeric) = 1.9857534564380882596643058726085
absolute error = 3.30603020e-23
relative error = 1.6648744532113950646615427869535e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1342.8MB, alloc=4.4MB, time=169.10
NO POLE
NO POLE
x[1] = 0.1691
y2[1] (analytic) = 0.83170474562232079726197625283327
y2[1] (numeric) = 0.8317047456223207972619819264301
absolute error = 5.67359683e-24
relative error = 6.8216477780883006938955240092412e-22 %
h = 0.0001
y1[1] (analytic) = 1.9857366318413616960526865680918
y1[1] (numeric) = 1.9857366318413616960526534604436
absolute error = 3.31076482e-23
relative error = 1.6672728734071585283897182215202e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1692
y2[1] (analytic) = 0.8316061728007772217180948537567
y2[1] (numeric) = 0.83160617280077722171810053887976
absolute error = 5.68512306e-24
relative error = 6.8363165714042264337181371234164e-22 %
h = 0.0001
y1[1] (analytic) = 1.9857197973872688222418891720196
y1[1] (numeric) = 1.985719797387268822241856017027
absolute error = 3.31549926e-23
relative error = 1.6696712518867979945665310132517e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1346.6MB, alloc=4.4MB, time=169.73
NO POLE
NO POLE
x[1] = 0.1693
y2[1] (analytic) = 0.83150760166317191676315934464008
y2[1] (numeric) = 0.8315076016631719167631650412989
absolute error = 5.69665882e-24
relative error = 6.8510002898417389284222475396732e-22 %
h = 0.0001
y1[1] (analytic) = 1.9857029530759779827727351956842
y1[1] (numeric) = 1.9857029530759779827727019933493
absolute error = 3.32023349e-23
relative error = 1.6720695735768287024066106750137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1694
y2[1] (analytic) = 0.83140903221049059377240134888634
y2[1] (numeric) = 0.83140903221049059377240705709044
absolute error = 5.70820410e-24
relative error = 6.8656989265842314740222193552531e-22 %
h = 0.0001
y1[1] (analytic) = 1.9856860989076576207579926645165
y1[1] (numeric) = 1.9856860989076576207579594148413
absolute error = 3.32496752e-23
relative error = 1.6744678435474228218573042061966e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1350.4MB, alloc=4.4MB, time=170.35
NO POLE
NO POLE
x[1] = 0.1695
y2[1] (analytic) = 0.83131046444371894727181268429765
y2[1] (numeric) = 0.83131046444371894727181840405656
absolute error = 5.71975891e-24
relative error = 6.8804124988700137536168141111919e-22 %
h = 0.0001
y1[1] (analytic) = 1.9856692348824762778807247472614
y1[1] (numeric) = 1.9856692348824762778806914502478
absolute error = 3.32970136e-23
relative error = 1.6768660668689221755877913091291e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1696
y2[1] (analytic) = 0.83121189836384265492828841782374
y2[1] (numeric) = 0.83121189836384265492829414914698
absolute error = 5.73132324e-24
relative error = 6.8951409998840675792363208330799e-22 %
h = 0.0001
y1[1] (analytic) = 1.9856523610006025943926043391484
y1[1] (numeric) = 1.9856523610006025943925709947984
absolute error = 3.33443500e-23
relative error = 1.6792642385395819468854926376153e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1354.2MB, alloc=4.4MB, time=170.98
NO POLE
NO POLE
x[1] = 0.1697
y2[1] (analytic) = 0.83111333397184737753977008890116
y2[1] (numeric) = 0.83111333397184737753977583179825
absolute error = 5.74289709e-24
relative error = 6.9098844348399437034394494081524e-22 %
h = 0.0001
y1[1] (analytic) = 1.9856354772622053091122276593764
y1[1] (numeric) = 1.985635477262205309112194267692
absolute error = 3.33916844e-23
relative error = 1.6816623585936560104292257213630e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1698
y2[1] (analytic) = 0.83101477126871875902538910148207
y2[1] (numeric) = 0.83101477126871875902539485596254
absolute error = 5.75448047e-24
relative error = 6.9246428209868950385363630927231e-22 %
h = 0.0001
y1[1] (analytic) = 1.9856185836674532594234268629293
y1[1] (numeric) = 1.9856185836674532594233934239125
absolute error = 3.34390168e-23
relative error = 1.6840604270653969694889748939110e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1358.0MB, alloc=4.4MB, time=171.60
NO POLE
NO POLE
x[1] = 0.1699
y2[1] (analytic) = 0.83091621025544242641561028485114
y2[1] (numeric) = 0.83091621025544242641561605092452
absolute error = 5.76607338e-24
relative error = 6.9394161635471989375147681972219e-22 %
h = 0.0001
y1[1] (analytic) = 1.9856016802165153812735816667389
y1[1] (numeric) = 1.9856016802165153812735481803916
absolute error = 3.34863473e-23
relative error = 1.6864584490253129751115194308152e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.17
y2[1] (analytic) = 0.83081765093300398984237562332915
y2[1] (numeric) = 0.83081765093300398984238140100495
absolute error = 5.77767580e-24
relative error = 6.9542044436726873916000756005725e-22 %
h = 0.0001
y1[1] (analytic) = 1.9855847669095607091719299902125
y1[1] (numeric) = 1.9855847669095607091718964565367
absolute error = 3.35336758e-23
relative error = 1.6888564194714830711064950751606e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1361.8MB, alloc=4.4MB, time=172.23
NO POLE
NO POLE
x[1] = 0.1701
y2[1] (analytic) = 0.83071909330238904252924815496171
y2[1] (numeric) = 0.83071909330238904252925394424947
absolute error = 5.78928776e-24
relative error = 6.9690077026948126656373363397623e-22 %
h = 0.0001
y1[1] (analytic) = 1.9855678437467583761878776101421
y1[1] (numeric) = 1.9855678437467583761878440291398
absolute error = 3.35810023e-23
relative error = 1.6912543384381561302850024694249e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1702
y2[1] (analytic) = 0.83062053736458316078155603929193
y2[1] (numeric) = 0.83062053736458316078156184020116
absolute error = 5.80090923e-24
relative error = 6.9838259097292397857997913882342e-22 %
h = 0.0001
y1[1] (analytic) = 1.9855509107282776139493068300115
y1[1] (numeric) = 1.9855509107282776139492732016847
absolute error = 3.36283268e-23
relative error = 1.6936522059595797584378117367236e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1365.6MB, alloc=4.4MB, time=172.85
NO POLE
NO POLE
x[1] = 0.1703
y2[1] (analytic) = 0.83052198312057190397653679431528
y2[1] (numeric) = 0.83052198312057190397654260685551
absolute error = 5.81254023e-24
relative error = 6.9986590940798232281638372517811e-22 %
h = 0.0001
y1[1] (analytic) = 1.9855339678542877526408841637193
y1[1] (numeric) = 1.9855339678542877526408504880699
absolute error = 3.36756494e-23
relative error = 1.6960500271064288642193438827178e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1704
y2[1] (analytic) = 0.83042343057134081455348170271546
y2[1] (numeric) = 0.83042343057134081455348752689621
absolute error = 5.82418075e-24
relative error = 7.0135072489379268303099977744473e-22 %
h = 0.0001
y1[1] (analytic) = 1.9855170151249582210023670337329
y1[1] (numeric) = 1.9855170151249582210023333107631
absolute error = 3.37229698e-23
relative error = 1.6984477868036628163046020207416e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1369.5MB, alloc=4.4MB, time=173.48
NO POLE
NO POLE
x[1] = 0.1705
y2[1] (analytic) = 0.83032487971787541800388038747972
y2[1] (numeric) = 0.83032487971787541800388622331051
absolute error = 5.83583079e-24
relative error = 7.0283703795349069335850735589460e-22 %
h = 0.0001
y1[1] (analytic) = 1.9855000525404585463269094836934
y1[1] (numeric) = 1.985500052540458546326875713405
absolute error = 3.37702884e-23
relative error = 1.7008455052313257308925115937857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1706
y2[1] (analytic) = 0.83022633056116122286156555699212
y2[1] (numeric) = 0.83022633056116122286157140448247
absolute error = 5.84749035e-24
relative error = 7.0432484911043498991582290238862e-22 %
h = 0.0001
y1[1] (analytic) = 1.9854830801009583544593669054844
y1[1] (numeric) = 1.9854830801009583544593330878795
absolute error = 3.38176049e-23
relative error = 1.7032431673142454442793809333983e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1373.3MB, alloc=4.4MB, time=174.14
NO POLE
NO POLE
x[1] = 0.1707
y2[1] (analytic) = 0.83012778310218372069285791970346
y2[1] (numeric) = 0.8301277831021837206928637788629
absolute error = 5.85915944e-24
relative error = 7.0581416009284113191042181648462e-22 %
h = 0.0001
y1[1] (analytic) = 1.9854660978066273697945997807856
y1[1] (numeric) = 1.9854660978066273697945659158662
absolute error = 3.38649194e-23
relative error = 1.7056407781231348143881810227869e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1708
y2[1] (analytic) = 0.8300292373419283860867112684763
y2[1] (numeric) = 0.83002923734192838608671713931434
absolute error = 5.87083804e-24
relative error = 7.0730496901538945847211953359216e-22 %
h = 0.0001
y1[1] (analytic) = 1.9854491056576354152757764371253
y1[1] (numeric) = 1.9854491056576354152757425248933
absolute error = 3.39122320e-23
relative error = 1.7080383427288777040560531265684e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1377.1MB, alloc=4.4MB, time=174.80
NO POLE
NO POLE
x[1] = 0.1709
y2[1] (analytic) = 0.82993069328138067664485773470356
y2[1] (numeric) = 0.82993069328138067664486361722973
absolute error = 5.88252617e-24
relative error = 7.0879727881151895425077490475179e-22 %
h = 0.0001
y1[1] (analytic) = 1.9854321036541524123926748184502
y1[1] (numeric) = 1.9854321036541524123926408589076
absolute error = 3.39595426e-23
relative error = 1.7104358561291553058312681991985e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.171
y2[1] (analytic) = 0.8298321509215260329719532122995
y2[1] (numeric) = 0.82983215092152603297195910652332
absolute error = 5.89422382e-24
relative error = 7.1029108880084758186583345104030e-22 %
h = 0.0001
y1[1] (analytic) = 1.9854150917963483811799832702289
y1[1] (numeric) = 1.9854150917963483811799492633778
absolute error = 3.40068511e-23
relative error = 1.7128333133214750827666073402574e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1380.9MB, alloc=4.4MB, time=175.46
NO POLE
NO POLE
x[1] = 0.1711
y2[1] (analytic) = 0.82973361026334987866572295166131
y2[1] (numeric) = 0.8297336102633498786657288575923
absolute error = 5.90593099e-24
relative error = 7.1178639950785064383940736120106e-22 %
h = 0.0001
y1[1] (analytic) = 1.9853980700843934402156003391068
y1[1] (numeric) = 1.9853980700843934402155662849491
absolute error = 3.40541577e-23
relative error = 1.7152307244134904283468197561584e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1712
y2[1] (analytic) = 0.82963507130783762030710732370011
y2[1] (numeric) = 0.82963507130783762030711324134778
absolute error = 5.91764767e-24
relative error = 7.1328321025187783310458415949204e-22 %
h = 0.0001
y1[1] (analytic) = 1.9853810385184578066189335871281
y1[1] (numeric) = 1.9853810385184578066188994856658
absolute error = 3.41014623e-23
relative error = 1.7176280844027494488307236410506e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1384.7MB, alloc=4.4MB, time=176.11
NO POLE
NO POLE
x[1] = 0.1713
y2[1] (analytic) = 0.82953653405597464745040775403971
y2[1] (numeric) = 0.82953653405597464745041368341359
absolute error = 5.92937388e-24
relative error = 7.1478152396840710597539906813923e-22 %
h = 0.0001
y1[1] (analytic) = 1.9853639970987117960491974205433
y1[1] (numeric) = 1.9853639970987117960491632717785
absolute error = 3.41487648e-23
relative error = 1.7200253882866262154103164947861e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1714
y2[1] (analytic) = 0.82943799850874633261343282748187
y2[1] (numeric) = 0.82943799850874633261343876859148
absolute error = 5.94110961e-24
relative error = 7.1628133997737886993582496722198e-22 %
h = 0.0001
y1[1] (analytic) = 1.9853469458253258227037099332187
y1[1] (numeric) = 1.9853469458253258227036757371534
absolute error = 3.41960653e-23
relative error = 1.7224226411361265205265316706558e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1388.5MB, alloc=4.4MB, time=176.76
NO POLE
NO POLE
x[1] = 0.1715
y2[1] (analytic) = 0.82933946466713803126764456283637
y2[1] (numeric) = 0.82933946466713803126765051569123
absolute error = 5.95285486e-24
relative error = 7.1778265880416356278366476021861e-22 %
h = 0.0001
y1[1] (analytic) = 1.9853298846984703993161887646644
y1[1] (numeric) = 1.9853298846984703993161545213005
absolute error = 3.42433639e-23
relative error = 1.7248198480224278898746918644557e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1716
y2[1] (analytic) = 0.82924093253213508182830485821463
y2[1] (numeric) = 0.82924093253213508182831082282426
absolute error = 5.96460963e-24
relative error = 7.1928548097435566738738799941161e-22 %
h = 0.0001
y1[1] (analytic) = 1.9853128137183161371550459726983
y1[1] (numeric) = 1.9853128137183161371550116820379
absolute error = 3.42906604e-23
relative error = 1.7272169989059110340398406122141e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1392.3MB, alloc=4.4MB, time=177.44
NO POLE
NO POLE
x[1] = 0.1717
y2[1] (analytic) = 0.8291424021047228056446221068853
y2[1] (numeric) = 0.82914240210472280564462808325922
absolute error = 5.97637392e-24
relative error = 7.2078980701377381629732631657538e-22 %
h = 0.0001
y1[1] (analytic) = 1.9852957328850337460216819207642
y1[1] (numeric) = 1.9852957328850337460216475828092
absolute error = 3.43379550e-23
relative error = 1.7296141038947406302378043667546e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1718
y2[1] (analytic) = 0.82904387338588650698989798379038
y2[1] (numeric) = 0.8290438733858865069899039719381
absolute error = 5.98814772e-24
relative error = 7.2229563624225211530684741896203e-22 %
h = 0.0001
y1[1] (analytic) = 1.9852786421987940342487781799182
y1[1] (numeric) = 1.9852786421987940342487437946707
absolute error = 3.43852475e-23
relative error = 1.7320111529491216455354212837487e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1396.2MB, alloc=4.4MB, time=178.10
NO POLE
NO POLE
x[1] = 0.1719
y2[1] (analytic) = 0.82894534637661147305167440282041
y2[1] (numeric) = 0.82894534637661147305168040275145
absolute error = 5.99993104e-24
relative error = 7.2380297039197985571596295915248e-22 %
h = 0.0001
y1[1] (analytic) = 1.9852615416597679086985894455042
y1[1] (numeric) = 1.9852615416597679086985550129662
absolute error = 3.44325380e-23
relative error = 1.7344081511402699163517403141747e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.172
y2[1] (analytic) = 0.82884682107788297392188064494727
y2[1] (numeric) = 0.82884682107788297392188665667116
absolute error = 6.01172389e-24
relative error = 7.2531181119594420103759348289507e-22 %
h = 0.0001
y1[1] (analytic) = 1.9852444312681263747612344685321
y1[1] (numeric) = 1.9852444312681263747611999887057
absolute error = 3.44798264e-23
relative error = 1.7368050934652473263239776024898e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1400.0MB, alloc=4.4MB, time=178.76
NO POLE
NO POLE
x[1] = 0.1721
y2[1] (analytic) = 0.82874829749068626258698065731312
y2[1] (numeric) = 0.82874829749068626258698668083936
absolute error = 6.02352624e-24
relative error = 7.2682215556137468952431041362942e-22 %
h = 0.0001
y1[1] (analytic) = 1.9852273110240405363529860017787
y1[1] (numeric) = 1.9852273110240405363529514746658
absolute error = 3.45271129e-23
relative error = 1.7392019900325603828716602993561e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1722
y2[1] (analytic) = 0.82864977561600657491812052337391
y2[1] (numeric) = 0.82864977561600657491812655871202
absolute error = 6.03533811e-24
relative error = 7.2833400642791638156656333209056e-22 %
h = 0.0001
y1[1] (analytic) = 1.9852101809276815959145597606257
y1[1] (numeric) = 1.9852101809276815959145251862283
absolute error = 3.45743974e-23
relative error = 1.7415988358393118921673310005697e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1403.8MB, alloc=4.4MB, time=179.42
NO POLE
NO POLE
x[1] = 0.1723
y2[1] (analytic) = 0.82855125545482912966127610419618
y2[1] (numeric) = 0.82855125545482912966128215135569
absolute error = 6.04715951e-24
relative error = 7.2984736552966075460300781607425e-22 %
h = 0.0001
y1[1] (analytic) = 1.9851930409792208544094023986544
y1[1] (numeric) = 1.9851930409792208544093677769745
absolute error = 3.46216799e-23
relative error = 1.7439956309197231057210053186722e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1724
y2[1] (analytic) = 0.82845273700813912842740085100552
y2[1] (numeric) = 0.82845273700813912842740690999594
absolute error = 6.05899042e-24
relative error = 7.3136223098028988571631819622895e-22 %
h = 0.0001
y1[1] (analytic) = 1.9851758911788297113219784980125
y1[1] (numeric) = 1.9851758911788297113219438290523
absolute error = 3.46689602e-23
relative error = 1.7463923652333400000324780135722e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1407.6MB, alloc=4.4MB, time=180.09
NO POLE
NO POLE
x[1] = 0.1725
y2[1] (analytic) = 0.8283542202769217556825737890852
y2[1] (numeric) = 0.82835422027692175568257985991604
absolute error = 6.07083084e-24
relative error = 7.3287860330698860986069001398176e-22 %
h = 0.0001
y1[1] (analytic) = 1.9851587315266796646560565745712
y1[1] (numeric) = 1.9851587315266796646560218583326
absolute error = 3.47162386e-23
relative error = 1.7487890539262617622509572600596e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1726
y2[1] (analytic) = 0.82825570526216217873814767312361
y2[1] (numeric) = 0.82825570526216217873815375580439
absolute error = 6.08268078e-24
relative error = 7.3439648424452327513134369249484e-22 %
h = 0.0001
y1[1] (analytic) = 1.9851415620229423109329940978885
y1[1] (numeric) = 1.9851415620229423109329593343735
absolute error = 3.47635150e-23
relative error = 1.7511856919954123419601401789272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1411.4MB, alloc=4.4MB, time=180.75
NO POLE
NO POLE
x[1] = 0.1727
y2[1] (analytic) = 0.82815719196484554774089731410896
y2[1] (numeric) = 0.8281571919648455477409034086492
absolute error = 6.09454024e-24
relative error = 7.3591587432095949179480407467699e-22 %
h = 0.0001
y1[1] (analytic) = 1.9851243826677893451900215259972
y1[1] (numeric) = 1.9851243826677893451899867152078
absolute error = 3.48107894e-23
relative error = 1.7535822794750079483193608357053e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1728
y2[1] (analytic) = 0.82805868038595699566316807786973
y2[1] (numeric) = 0.82805868038595699566317418427894
absolute error = 6.10640921e-24
relative error = 7.3743677285694429126277824810171e-22 %
h = 0.0001
y1[1] (analytic) = 1.9851071934613925609785253550341
y1[1] (numeric) = 1.9851071934613925609784904969724
absolute error = 3.48580617e-23
relative error = 1.7559788113617522110312429216242e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1415.2MB, alloc=4.4MB, time=181.41
NO POLE
NO POLE
x[1] = 0.1729
y2[1] (analytic) = 0.82796017052648163829302455535941
y2[1] (numeric) = 0.82796017052648163829303067364711
absolute error = 6.11828770e-24
relative error = 7.3895918158835051140889131831261e-22 %
h = 0.0001
y1[1] (analytic) = 1.9850899944039238503623301837276
y1[1] (numeric) = 1.9850899944039238503622952783956
absolute error = 3.49053320e-23
relative error = 1.7583752927272829129879773314049e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.173
y2[1] (analytic) = 0.82786166238740457422439940478408
y2[1] (numeric) = 0.82786166238740457422440553495978
absolute error = 6.13017570e-24
relative error = 7.4048309983598861229507617291874e-22 %
h = 0.0001
y1[1] (analytic) = 1.9850727854955552039159797927608
y1[1] (numeric) = 1.9850727854955552039159448401605
absolute error = 3.49526003e-23
relative error = 1.7607717236058124737522057102316e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1419.1MB, alloc=4.4MB, time=182.07
NO POLE
NO POLE
x[1] = 0.1731
y2[1] (analytic) = 0.82776315596971088484724236567129
y2[1] (numeric) = 0.82776315596971088484724850774451
absolute error = 6.14207322e-24
relative error = 7.4200852933646974472176274705450e-22 %
h = 0.0001
y1[1] (analytic) = 1.9850555667364587107230172390276
y1[1] (numeric) = 1.985055566736458710722982239161
absolute error = 3.49998666e-23
relative error = 1.7631681040315520776293354516066e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1732
y2[1] (analytic) = 0.82766465127438563433766944497877
y2[1] (numeric) = 0.82766465127438563433767559895902
absolute error = 6.15398025e-24
relative error = 7.4353546941076809207980730996538e-22 %
h = 0.0001
y1[1] (analytic) = 1.9850383381268065583742639647983
y1[1] (numeric) = 1.9850383381268065583742289176676
absolute error = 3.50471307e-23
relative error = 1.7655644239633395190421602104017e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1422.9MB, alloc=4.4MB, time=182.73
NO POLE
NO POLE
x[1] = 0.1733
y2[1] (analytic) = 0.82756614830241386964811227534147
y2[1] (numeric) = 0.82756614830241386964811844123827
absolute error = 6.16589680e-24
relative error = 7.4506392179623366647713878415239e-22 %
h = 0.0001
y1[1] (analytic) = 1.9850210996667710329660979218137
y1[1] (numeric) = 1.9850210996667710329660628274207
absolute error = 3.50943930e-23
relative error = 1.7679607035860403292501560595702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1734
y2[1] (analytic) = 0.82746764705478062049746764555549
y2[1] (numeric) = 0.82746764705478062049747382337835
absolute error = 6.17782286e-24
relative error = 7.4659388581400466969011698042795e-22 %
h = 0.0001
y1[1] (analytic) = 1.9850038513565245190987307103216
y1[1] (numeric) = 1.9850038513565245190986955686685
absolute error = 3.51416531e-23
relative error = 1.7703569227830300816235904936174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1426.7MB, alloc=4.4MB, time=183.38
NO POLE
NO POLE
x[1] = 0.1735
y2[1] (analytic) = 0.82736914753247089936124720339725
y2[1] (numeric) = 0.82736914753247089936125339315569
absolute error = 6.18975844e-24
relative error = 7.4812536320217052403669162571220e-22 %
h = 0.0001
y1[1] (analytic) = 1.9849865931962394998744837330771
y1[1] (numeric) = 1.9849865931962394998744485441659
absolute error = 3.51889112e-23
relative error = 1.7727530916638870315487989752453e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1736
y2[1] (analytic) = 0.82727064973646970146172733087667
y2[1] (numeric) = 0.82727064973646970146173353258019
absolute error = 6.20170352e-24
relative error = 7.4965835207323950066833668707763e-22 %
h = 0.0001
y1[1] (analytic) = 1.9849693251860885568960633643204
y1[1] (numeric) = 1.9849693251860885568960281281531
absolute error = 3.52361673e-23
relative error = 1.7751492102628160489014136313908e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1430.5MB, alloc=4.4MB, time=184.05
NO POLE
NO POLE
x[1] = 0.1737
y2[1] (analytic) = 0.82717215366776200475809919202253
y2[1] (numeric) = 0.82717215366776200475810540568065
absolute error = 6.21365812e-24
relative error = 7.5119285537454735004253871954290e-22 %
h = 0.0001
y1[1] (analytic) = 1.9849520473262443702648351337511
y1[1] (numeric) = 1.9849520473262443702647998503298
absolute error = 3.52834213e-23
relative error = 1.7775452735761156962624226293713e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1738
y2[1] (analytic) = 0.82707365932733276993661895329883
y2[1] (numeric) = 0.82707365932733276993662517892106
absolute error = 6.22562223e-24
relative error = 7.5272887242756110212067404738281e-22 %
h = 0.0001
y1[1] (analytic) = 1.9849347596168797185790969255162
y1[1] (numeric) = 1.9849347596168797185790615948429
absolute error = 3.53306733e-23
relative error = 1.7799412866758057109463481811572e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1434.3MB, alloc=4.4MB, time=184.70
NO POLE
NO POLE
x[1] = 0.1739
y2[1] (analytic) = 0.82697516671616694040075817675039
y2[1] (numeric) = 0.82697516671616694040076441434625
absolute error = 6.23759586e-24
relative error = 7.5426640497185055313285015137317e-22 %
h = 0.0001
y1[1] (analytic) = 1.9849174620581674789323511922283
y1[1] (numeric) = 1.9849174620581674789323158143051
absolute error = 3.53779232e-23
relative error = 1.7823372445580943435101999080682e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.174
y2[1] (analytic) = 0.82687667583524944226135438597639
y2[1] (numeric) = 0.82687667583524944226136063555539
absolute error = 6.24957900e-24
relative error = 7.5580545232904763879580021941401e-22 %
h = 0.0001
y1[1] (analytic) = 1.9849001546502806269115761840325
y1[1] (numeric) = 1.9849001546502806269115407588614
absolute error = 3.54251711e-23
relative error = 1.7847331522950864796273664810338e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1438.1MB, alloc=4.4MB, time=185.35
NO POLE
NO POLE
x[1] = 0.1741
y2[1] (analytic) = 0.82677818668556518432676180503015
y2[1] (numeric) = 0.8267781866855651843267680666018
absolute error = 6.26157165e-24
relative error = 7.5734601502994896336906320181227e-22 %
h = 0.0001
y1[1] (analytic) = 1.9848828373933922365954961927374
y1[1] (numeric) = 1.9848828373933922365954607203204
absolute error = 3.54724170e-23
relative error = 1.7871290099209807020475993450137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1441.9MB, alloc=4.4MB, time=185.96
x[1] = 0.1742
y2[1] (analytic) = 0.82667969926809905809300227034384
y2[1] (numeric) = 0.82667969926809905809300854391766
absolute error = 6.27357382e-24
relative error = 7.5888809481523607196025048306540e-22 %
h = 0.0001
y1[1] (analytic) = 1.9848655102876754805528508110299
y1[1] (numeric) = 1.984865510287675480552815291369
absolute error = 3.55196609e-23
relative error = 1.7895248174699743702902432370557e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1743
y2[1] (analytic) = 0.82658121358383593773391631577645
y2[1] (numeric) = 0.82658121358383593773392260136194
absolute error = 6.28558549e-24
relative error = 7.6043168979698628996639189940778e-22 %
h = 0.0001
y1[1] (analytic) = 1.9848481733333036298406632067887
y1[1] (numeric) = 1.984848173333303629840627639886
absolute error = 3.55669027e-23
relative error = 1.7919205699380948920839614136508e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1445.8MB, alloc=4.4MB, time=186.59
x[1] = 0.1744
y2[1] (analytic) = 0.82648272963376068009131443088358
y2[1] (numeric) = 0.82648272963376068009132072849025
absolute error = 6.29760667e-24
relative error = 7.6197680171619056776507960249029e-22 %
h = 0.0001
y1[1] (analytic) = 1.984830826530450054002507412516
y1[1] (numeric) = 1.9848308265304500540024717983736
absolute error = 3.56141424e-23
relative error = 1.7943162673594050876966912054383e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1745
y2[1] (analytic) = 0.82638424741885812466512849250757
y2[1] (numeric) = 0.82638424741885812466513480214493
absolute error = 6.30963736e-24
relative error = 7.6352343110455251394653303141207e-22 %
h = 0.0001
y1[1] (analytic) = 1.9848134698792882210667746299031
y1[1] (numeric) = 1.984813469879288221066738968523
absolute error = 3.56613801e-23
relative error = 1.7967119148062232223095406906335e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1449.6MB, alloc=4.4MB, time=187.22
NO POLE
NO POLE
x[1] = 0.1746
y2[1] (analytic) = 0.82628576694011309360356336978635
y2[1] (numeric) = 0.82628576694011309360356969146392
absolute error = 6.32167757e-24
relative error = 7.6507157970423780769337830833187e-22 %
h = 0.0001
y1[1] (analytic) = 1.9847961033799916975449385495476
y1[1] (numeric) = 1.9847961033799916975449028409318
absolute error = 3.57086158e-23
relative error = 1.7991075123127416188454849456607e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1747
y2[1] (analytic) = 0.82618728819851039169324870267965
y2[1] (numeric) = 0.82618728819851039169325503640693
absolute error = 6.33372728e-24
relative error = 7.6662124562707834382729264868765e-22 %
h = 0.0001
y1[1] (analytic) = 1.9847787270327341484298196858404
y1[1] (numeric) = 1.984778727032734148429783929991
absolute error = 3.57558494e-23
relative error = 1.8015030548748063700931406091815e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1453.4MB, alloc=4.4MB, time=187.85
NO POLE
NO POLE
x[1] = 0.1748
y2[1] (analytic) = 0.82608881119503480634939085411086
y2[1] (numeric) = 0.82608881119503480634939719989737
absolute error = 6.34578651e-24
relative error = 7.6817243182607352675529835000684e-22 %
h = 0.0001
y1[1] (analytic) = 1.9847613408376893371938487270389
y1[1] (numeric) = 1.984761340837689337193812923958
absolute error = 3.58030809e-23
relative error = 1.8038985425264749592240886001359e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1749
y2[1] (analytic) = 0.82599033593067110760592503582321
y2[1] (numeric) = 0.82599033593067110760593139367845
absolute error = 6.35785524e-24
relative error = 7.6972513641293279145022211308246e-22 %
h = 0.0001
y1[1] (analytic) = 1.9847439447950311257873289005443
y1[1] (numeric) = 1.9847439447950311257872930502339
absolute error = 3.58503104e-23
relative error = 1.8062939803402368075482215425404e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1457.2MB, alloc=4.4MB, time=188.48
NO POLE
NO POLE
x[1] = 0.175
y2[1] (analytic) = 0.82589186240640404810566760804859
y2[1] (numeric) = 0.82589186240640404810567397798208
absolute error = 6.36993349e-24
relative error = 7.7127936234168747012545355197391e-22 %
h = 0.0001
y1[1] (analytic) = 1.9847265389049334746366973533995
y1[1] (numeric) = 1.9847265389049334746366614558617
absolute error = 3.58975378e-23
relative error = 1.8086893633118017238502886336145e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1751
y2[1] (analytic) = 0.82579339062321836309046855308763
y2[1] (numeric) = 0.82579339062321836309047493510887
absolute error = 6.38202124e-24
relative error = 7.7283510772392470860713684472033e-22 %
h = 0.0001
y1[1] (analytic) = 1.9847091231675704426427855480269
y1[1] (numeric) = 1.9847091231675704426427496032637
absolute error = 3.59447632e-23
relative error = 1.8110846965137448686689071283672e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1461.0MB, alloc=4.4MB, time=189.10
NO POLE
NO POLE
x[1] = 0.1752
y2[1] (analytic) = 0.82569492058209877039136412289937
y2[1] (numeric) = 0.82569492058209877039137051701788
absolute error = 6.39411851e-24
relative error = 7.7439237551470844753706454068628e-22 %
h = 0.0001
y1[1] (analytic) = 1.9846916975831161871790786732209
y1[1] (numeric) = 1.9846916975831161871790426812344
absolute error = 3.59919865e-23
relative error = 1.8134799749416850971420139170233e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1753
y2[1] (analytic) = 0.82559645228402997041872966079915
y2[1] (numeric) = 0.82559645228402997041873606702443
absolute error = 6.40622528e-24
relative error = 7.7595116382550371460688317865974e-22 %
h = 0.0001
y1[1] (analytic) = 1.9846742621517449640899740704148
y1[1] (numeric) = 1.9846742621517449640899380312071
absolute error = 3.60392077e-23
relative error = 1.8158751986296732068932658466159e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1464.8MB, alloc=4.4MB, time=189.73
NO POLE
NO POLE
x[1] = 0.1754
y2[1] (analytic) = 0.825497985729996646152432597363
y2[1] (numeric) = 0.82549798572999664615243901570456
absolute error = 6.41834156e-24
relative error = 7.7751147440101774608477583727736e-22 %
h = 0.0001
y1[1] (analytic) = 1.9846568168736311276890386752383
y1[1] (numeric) = 1.9846568168736311276890025888114
absolute error = 3.60864269e-23
relative error = 1.8182703726504131301146076790166e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1755
y2[1] (analytic) = 0.82539952092098346313198562063723
y2[1] (numeric) = 0.82539952092098346313199205110457
absolute error = 6.43046734e-24
relative error = 7.7907330656369459493662105351379e-22 %
h = 0.0001
y1[1] (analytic) = 1.9846393617489491307572654743832
y1[1] (numeric) = 1.9846393617489491307572293407392
absolute error = 3.61336440e-23
relative error = 1.8206654919993870676675095821830e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1468.6MB, alloc=4.4MB, time=190.34
NO POLE
NO POLE
x[1] = 0.1756
y2[1] (analytic) = 0.82530105785797506944670002075146
y2[1] (numeric) = 0.8253010578579750694467064633541
absolute error = 6.44260264e-24
relative error = 7.8063666327066536716880843913068e-22 %
h = 0.0001
y1[1] (analytic) = 1.9846218967778735245413289777949
y1[1] (numeric) = 1.9846218967778735245412927969358
absolute error = 3.61808591e-23
relative error = 1.8230605617493849596123325277893e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1757
y2[1] (analytic) = 0.82520259654195609572583920903376
y2[1] (numeric) = 0.8252025965419560957258456637812
absolute error = 6.45474744e-24
relative error = 7.8220154263315127268917216263733e-22 %
h = 0.0001
y1[1] (analytic) = 1.9846044219605789587518397062072
y1[1] (numeric) = 1.9846044219605789587518034781351
absolute error = 3.62280721e-23
relative error = 1.8254555768957978062962783675174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1472.5MB, alloc=4.4MB, time=190.96
NO POLE
NO POLE
x[1] = 0.1758
y2[1] (analytic) = 0.82510413697391115512877241172618
y2[1] (numeric) = 0.82510413697391115512877887862793
absolute error = 6.46690175e-24
relative error = 7.8376794639734984187650616487483e-22 %
h = 0.0001
y1[1] (analytic) = 1.9845869372972401815615976940376
y1[1] (numeric) = 1.9845869372972401815615614187546
absolute error = 3.62752830e-23
relative error = 1.8278505374726697469812881847887e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1759
y2[1] (analytic) = 0.82500567915482484333512853839929
y2[1] (numeric) = 0.82500567915482484333513501746486
absolute error = 6.47906557e-24
relative error = 7.8533587509815250153262577164149e-22 %
h = 0.0001
y1[1] (analytic) = 1.9845694427880320396038450076606
y1[1] (numeric) = 1.9845694427880320396038086851689
absolute error = 3.63224917e-23
relative error = 1.8302454384751672267977914116163e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1476.3MB, alloc=4.4MB, time=191.58
NO POLE
NO POLE
x[1] = 0.176
y2[1] (analytic) = 0.82490722308568173853495022516409
y2[1] (numeric) = 0.82490722308568173853495671640298
absolute error = 6.49123889e-24
relative error = 7.8690532805842164801791180974218e-22 %
h = 0.0001
y1[1] (analytic) = 1.9845519384331294779705172790773
y1[1] (numeric) = 1.9845519384331294779704809093788
absolute error = 3.63696985e-23
relative error = 1.8326402950539606717491428308406e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1761
y2[1] (analytic) = 0.82480876876746640141884805277977
y2[1] (numeric) = 0.82480876876746640141885455620148
absolute error = 6.50342171e-24
relative error = 7.8847630581307172400671509334502e-22 %
h = 0.0001
y1[1] (analytic) = 1.9845344242327075402104942549967
y1[1] (numeric) = 1.9845344242327075402104578380935
absolute error = 3.64169032e-23
relative error = 1.8350350971654263913835280015981e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1480.1MB, alloc=4.4MB, time=192.20
NO POLE
NO POLE
x[1] = 0.1762
y2[1] (analytic) = 0.82471031620116337516815493975583
y2[1] (numeric) = 0.82471031620116337516816145536987
absolute error = 6.51561404e-24
relative error = 7.9004881010979267877950173975785e-22 %
h = 0.0001
y1[1] (analytic) = 1.9845169001869413683278493613489
y1[1] (numeric) = 1.984516900186941368327812897243
absolute error = 3.64641059e-23
relative error = 1.8374298498826129168547314961648e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1763
y2[1] (analytic) = 0.82461186538775718544508071054695
y2[1] (numeric) = 0.82461186538775718544508723836283
absolute error = 6.52781588e-24
relative error = 7.9162284148439042294398164084774e-22 %
h = 0.0001
y1[1] (analytic) = 1.9844993662960062027800982832456
y1[1] (numeric) = 1.9844993662960062027800617719392
absolute error = 3.65113064e-23
relative error = 1.8398245431615827098213902186570e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1483.9MB, alloc=4.4MB, time=192.83
NO POLE
NO POLE
x[1] = 0.1764
y2[1] (analytic) = 0.82451341632823234038286683893909
y2[1] (numeric) = 0.82451341632823234038287337896632
absolute error = 6.54002723e-24
relative error = 7.9319840047289980376114780718782e-22 %
h = 0.0001
y1[1] (analytic) = 1.9844818225600773824764465604067
y1[1] (numeric) = 1.9844818225600773824764100019018
absolute error = 3.65585049e-23
relative error = 1.8422191871144359112870017537423e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1765
y2[1] (analytic) = 0.8244149690235733305759413667253
y2[1] (numeric) = 0.82441496902357333057594791897338
absolute error = 6.55224808e-24
relative error = 7.9477548639860334065024859105339e-22 %
h = 0.0001
y1[1] (analytic) = 1.9844642689793303447760361980694
y1[1] (numeric) = 1.984464268979330344775999592368
absolute error = 3.66057014e-23
relative error = 1.8446137817753409652802714690348e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1487.7MB, alloc=4.4MB, time=193.45
NO POLE
NO POLE
x[1] = 0.1766
y2[1] (analytic) = 0.82431652347476462907007399776962
y2[1] (numeric) = 0.82431652347476462907008056224804
absolute error = 6.56447842e-24
relative error = 7.9635409858443325389600179797775e-22 %
h = 0.0001
y1[1] (analytic) = 1.9844467055539406254861912933981
y1[1] (numeric) = 1.9844467055539406254861546405024
absolute error = 3.66528957e-23
relative error = 1.8470083171000891442672324471727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1767
y2[1] (analytic) = 0.82421807968279069135253136755757
y2[1] (numeric) = 0.82421807968279069135253794427585
absolute error = 6.57671828e-24
relative error = 7.9793424120605576742397525097562e-22 %
h = 0.0001
y1[1] (analytic) = 1.9844291322840838588606626774131
y1[1] (numeric) = 1.9844291322840838588606259773252
absolute error = 3.67000879e-23
relative error = 1.8494027981618113619340301824154e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1491.5MB, alloc=4.4MB, time=194.08
NO POLE
NO POLE
x[1] = 0.1768
y2[1] (analytic) = 0.82411963764863595534223248833174
y2[1] (numeric) = 0.82411963764863595534223907729939
absolute error = 6.58896765e-24
relative error = 7.9951591358744098410421983513732e-22 %
h = 0.0001
y1[1] (analytic) = 1.9844115491699357775978715724544
y1[1] (numeric) = 1.9844115491699357775978348251763
absolute error = 3.67472781e-23
relative error = 1.8517972300338156305300856131855e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1769
y2[1] (analytic) = 0.82402119737328484137990436991079
y2[1] (numeric) = 0.8240211973732848413799109711373
absolute error = 6.60122651e-24
relative error = 8.0109911383864782347481091979755e-22 %
h = 0.0001
y1[1] (analytic) = 1.9843939562116722128391522651986
y1[1] (numeric) = 1.9843939562116722128391154707324
absolute error = 3.67944662e-23
relative error = 1.8541916077109434409948582092511e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1495.3MB, alloc=4.4MB, time=194.71
NO POLE
NO POLE
x[1] = 0.177
y2[1] (analytic) = 0.82392275885772175221823781629032
y2[1] (numeric) = 0.8239227588577217522182444297852
absolute error = 6.61349488e-24
relative error = 8.0268384492362887985044923530225e-22 %
h = 0.0001
y1[1] (analytic) = 1.9843763534094690941669937952475
y1[1] (numeric) = 1.9843763534094690941669569535953
absolute error = 3.68416522e-23
relative error = 1.8565859312272229241270364958148e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1771
y2[1] (analytic) = 0.82382432210293107301204339812426
y2[1] (numeric) = 0.82382432210293107301205002389701
absolute error = 6.62577275e-24
relative error = 8.0427010616617315042175428299056e-22 %
h = 0.0001
y1[1] (analytic) = 1.9843587407635024496032806593043
y1[1] (numeric) = 1.9843587407635024496032437704682
absolute error = 3.68888361e-23
relative error = 1.8589802006166808644011445474404e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1499.2MB, alloc=4.4MB, time=195.33
NO POLE
NO POLE
x[1] = 0.1772
y2[1] (analytic) = 0.82372588710989717130840760118491
y2[1] (numeric) = 0.82372588710989717130841423924503
absolute error = 6.63806012e-24
relative error = 8.0585789810371529154317171972026e-22 %
h = 0.0001
y1[1] (analytic) = 1.9843411182739484056075325309565
y1[1] (numeric) = 1.9843411182739484056074955949386
absolute error = 3.69360179e-23
relative error = 1.8613744159133427010516080224020e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1773
y2[1] (analytic) = 0.82362745387960439703684915090027
y2[1] (numeric) = 0.82362745387960439703685580125727
absolute error = 6.65035700e-24
relative error = 8.0744722248806084020163259469408e-22 %
h = 0.0001
y1[1] (analytic) = 1.984323485940983187075142996082
y1[1] (numeric) = 1.9843234859409831870751060128843
absolute error = 3.69831977e-23
relative error = 1.8637685821907334325379125659613e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1503.0MB, alloc=4.4MB, time=195.95
NO POLE
NO POLE
x[1] = 0.1774
y2[1] (analytic) = 0.8235290224130370824994755130671
y2[1] (numeric) = 0.82352902241303708249948217573048
absolute error = 6.66266338e-24
relative error = 8.0903807864325305145859149966519e-22 %
h = 0.0001
y1[1] (analytic) = 1.9843058437647831173356173038966
y1[1] (numeric) = 1.9843058437647831173355802735213
absolute error = 3.70303753e-23
relative error = 1.8661626894039188095775070548670e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1775
y2[1] (analytic) = 0.82343059271117954236113957083801
y2[1] (numeric) = 0.82343059271117954236114624581727
absolute error = 6.67497926e-24
relative error = 8.1063046710741613469050101739238e-22 %
h = 0.0001
y1[1] (analytic) = 1.9842881917455246181508091336608
y1[1] (numeric) = 1.9842881917455246181507720561099
absolute error = 3.70775509e-23
relative error = 1.8685567476659669060154237477295e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1506.8MB, alloc=4.4MB, time=196.57
NO POLE
NO POLE
x[1] = 0.1776
y2[1] (analytic) = 0.82333216477501607363959647808116
y2[1] (numeric) = 0.8233321647750160736396031653858
absolute error = 6.68730464e-24
relative error = 8.1222438841890433369885720399194e-22 %
h = 0.0001
y1[1] (analytic) = 1.9842705298833842097131563770622
y1[1] (numeric) = 1.9842705298833842097131192523378
absolute error = 3.71247244e-23
relative error = 1.8709507519713969649737774448062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1777
y2[1] (analytic) = 0.8232337386055309556956606892109
y2[1] (numeric) = 0.82323373860553095569566738885042
absolute error = 6.69963952e-24
relative error = 8.1381984311630203454282261206239e-22 %
h = 0.0001
y1[1] (analytic) = 1.9842528581785385106439159362927
y1[1] (numeric) = 1.984252858178538510643878764397
absolute error = 3.71718957e-23
relative error = 1.8733446973145475130865519866718e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1510.6MB, alloc=4.4MB, time=197.17
NO POLE
NO POLE
x[1] = 0.1778
y2[1] (analytic) = 0.8231353142037084502233631655878
y2[1] (numeric) = 0.82313531420370845022336987757171
absolute error = 6.71198391e-24
relative error = 8.1541683295329095876093355327697e-22 %
h = 0.0001
y1[1] (analytic) = 1.9842351766311642379913975378379
y1[1] (numeric) = 1.9842351766311642379913603187729
absolute error = 3.72190650e-23
relative error = 1.8757385938087516697504830974279e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1779
y2[1] (analytic) = 0.82303689157053280124010875858659
y2[1] (numeric) = 0.82303689157053280124011548292439
absolute error = 6.72433780e-24
relative error = 8.1701535725433957439642086473368e-22 %
h = 0.0001
y1[1] (analytic) = 1.9842174852414382072291965619948
y1[1] (numeric) = 1.9842174852414382072291592957626
absolute error = 3.72662322e-23
relative error = 1.8781324364483901680792303533086e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1514.4MB, alloc=4.4MB, time=197.79
NO POLE
NO POLE
x[1] = 0.178
y2[1] (analytic) = 0.82293847070698823507683376943031
y2[1] (numeric) = 0.82293847070698823507684050613149
absolute error = 6.73670118e-24
relative error = 8.1861541534356576172646688328469e-22 %
h = 0.0001
y1[1] (analytic) = 1.9841997840095373322544258881378
y1[1] (numeric) = 1.9841997840095373322543885747405
absolute error = 3.73133973e-23
relative error = 1.8805262252674778018101340143939e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1781
y2[1] (analytic) = 0.82284005161405896036816368588909
y2[1] (numeric) = 0.82284005161405896036817043496316
absolute error = 6.74907407e-24
relative error = 8.2021701019064566103145191453229e-22 %
h = 0.0001
y1[1] (analytic) = 1.9841820729356386253859467557488
y1[1] (numeric) = 1.9841820729356386253859093951885
absolute error = 3.73605603e-23
relative error = 1.8829199603000280291984819109316e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1518.2MB, alloc=4.4MB, time=198.41
NO POLE
NO POLE
x[1] = 0.1782
y2[1] (analytic) = 0.82274163429272916804257109594217
y2[1] (numeric) = 0.82274163429272916804257785739863
absolute error = 6.76145646e-24
relative error = 8.2182014112030372077806520708358e-22 %
h = 0.0001
y1[1] (analytic) = 1.9841643520199191973625986412301
y1[1] (numeric) = 1.984164352019919197362561233509
absolute error = 3.74077211e-23
relative error = 1.8853136365401478927403682297450e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1783
y2[1] (analytic) = 0.82264321874398303131253377850133
y2[1] (numeric) = 0.82264321874398303131254055234968
absolute error = 6.77384835e-24
relative error = 8.2342480867250754480283660915207e-22 %
h = 0.0001
y1[1] (analytic) = 1.9841466212625562573414281505177
y1[1] (numeric) = 1.9841466212625562573413906956378
absolute error = 3.74548799e-23
relative error = 1.8877072641016133080324680009021e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1522.0MB, alloc=4.4MB, time=199.03
NO POLE
NO POLE
x[1] = 0.1784
y2[1] (analytic) = 0.82254480496880470566469297129434
y2[1] (numeric) = 0.82254480496880470566469975754407
absolute error = 6.78624973e-24
relative error = 8.2503101217171639089064937754944e-22 %
h = 0.0001
y1[1] (analytic) = 1.9841288806637271128959169275118
y1[1] (numeric) = 1.9841288806637271128958794254753
absolute error = 3.75020365e-23
relative error = 1.8901008329385784813895302507910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1785
y2[1] (analytic) = 0.82244639296817832885001181600672
y2[1] (numeric) = 0.82244639296817832885001861466734
absolute error = 6.79866062e-24
relative error = 8.2663875458969278573805963477331e-22 %
h = 0.0001
y1[1] (analytic) = 1.9841111302236091700142085783442
y1[1] (numeric) = 1.9841111302236091700141710291531
absolute error = 3.75491911e-23
relative error = 1.8924943531649968156935839247609e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1525.9MB, alloc=4.4MB, time=199.65
NO POLE
NO POLE
x[1] = 0.1786
y2[1] (analytic) = 0.82234798274308802087393398078034
y2[1] (numeric) = 0.82234798274308802087394079186134
absolute error = 6.81108100e-24
relative error = 8.2824803403547332787867583478269e-22 %
h = 0.0001
y1[1] (analytic) = 1.9840933699423799330973346114976
y1[1] (numeric) = 1.984093369942379933097297015154
absolute error = 3.75963436e-23
relative error = 1.8948878197749249890132322416952e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1787
y2[1] (analytic) = 0.82224957429451788398654246016717
y2[1] (numeric) = 0.82224957429451788398654928367805
absolute error = 6.82351088e-24
relative error = 8.2985885226568901429824094292182e-22 %
h = 0.0001
y1[1] (analytic) = 1.9840755998202170049574393937972
y1[1] (numeric) = 1.9840755998202170049574017503033
absolute error = 3.76434939e-23
relative error = 1.8972812277622379417221408923411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1529.7MB, alloc=4.4MB, time=200.26
NO POLE
NO POLE
x[1] = 0.1788
y2[1] (analytic) = 0.82215116762345200267271855263664
y2[1] (numeric) = 0.8221511676234520026727253885869
absolute error = 6.83595026e-24
relative error = 8.3147120982146292942268701450680e-22 %
h = 0.0001
y1[1] (analytic) = 1.9840578198572980868160041222907
y1[1] (numeric) = 1.9840578198572980868159664316486
absolute error = 3.76906421e-23
relative error = 1.8996745822009800083886103126702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1789
y2[1] (analytic) = 0.82205276273087444364230101573505
y2[1] (numeric) = 0.82205276273087444364230786413418
absolute error = 6.84839913e-24
relative error = 8.3308510602768266913910092405587e-22 %
h = 0.0001
y1[1] (analytic) = 1.9840400300538009783020698120348
y1[1] (numeric) = 1.9840400300538009783020320742466
absolute error = 3.77377882e-23
relative error = 1.9020678831251539249895677429966e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1533.5MB, alloc=4.4MB, time=200.88
NO POLE
NO POLE
x[1] = 0.179
y2[1] (analytic) = 0.82195435961776925582024539899536
y2[1] (numeric) = 0.82195435961776925582025225985287
absolute error = 6.86085751e-24
relative error = 8.3470054385872253302040445153869e-22 %
h = 0.0001
y1[1] (analytic) = 1.9840222304099035774504592998064
y1[1] (numeric) = 1.9840222304099035774504215148742
absolute error = 3.77849322e-23
relative error = 1.9044611305687611017667471158037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1791
y2[1] (analytic) = 0.82185595828512047033678355469587
y2[1] (numeric) = 0.82185595828512047033679042802125
absolute error = 6.87332538e-24
relative error = 8.3631752142332069695951482802634e-22 %
h = 0.0001
y1[1] (analytic) = 1.9840044209257838806999982637559
y1[1] (numeric) = 1.9840044209257838806999604316818
absolute error = 3.78320741e-23
relative error = 1.9068543245658016243098380499095e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1537.3MB, alloc=4.4MB, time=201.49
NO POLE
NO POLE
x[1] = 0.1792
y2[1] (analytic) = 0.82175755873391210051758332656606
y2[1] (numeric) = 0.82175755873391210051759021236881
absolute error = 6.88580275e-24
relative error = 8.3793604047999349271812994324985e-22 %
h = 0.0001
y1[1] (analytic) = 1.9839866016016199828917352590203
y1[1] (numeric) = 1.9839866016016199828916973798064
absolute error = 3.78792139e-23
relative error = 1.9092474651502742546395872019093e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1793
y2[1] (analytic) = 0.82165916096512814187390841653814
y2[1] (numeric) = 0.82165916096512814187391531482775
absolute error = 6.89828961e-24
relative error = 8.3955610035397254120122740077545e-22 %
h = 0.0001
y1[1] (analytic) = 1.9839687724375900772671607693142
y1[1] (numeric) = 1.9839687724375900772671228429626
absolute error = 3.79263516e-23
relative error = 1.9116405523561764322908520371351e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1541.1MB, alloc=4.4MB, time=202.10
NO POLE
NO POLE
x[1] = 0.1794
y2[1] (analytic) = 0.82156076497975257209277842964259
y2[1] (numeric) = 0.82156076497975257209278534042856
absolute error = 6.91078597e-24
relative error = 8.4117770280452923636719306753978e-22 %
h = 0.0001
y1[1] (analytic) = 1.9839509334338724554664252745165
y1[1] (numeric) = 1.9839509334338724554663873010294
absolute error = 3.79734871e-23
relative error = 1.9140335811770570387838895380451e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1795
y2[1] (analytic) = 0.82146237077876935102712909714619
y2[1] (numeric) = 0.82146237077876935102713602043802
absolute error = 6.92329183e-24
relative error = 8.4280084837440883660483169693841e-22 %
h = 0.0001
y1[1] (analytic) = 1.9839330845906455075265563342702
y1[1] (numeric) = 1.9839330845906455075265183136498
absolute error = 3.80206204e-23
relative error = 1.9164265516467748298133741167032e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1544.9MB, alloc=4.4MB, time=202.72
NO POLE
NO POLE
x[1] = 0.1796
y2[1] (analytic) = 0.82136397836316242068597267803085
y2[1] (numeric) = 0.82136397836316242068597961383803
absolute error = 6.93580718e-24
relative error = 8.4442553638910176082239011499359e-22 %
h = 0.0001
y1[1] (analytic) = 1.983915225908087721879674687614
y1[1] (numeric) = 1.9839152259080877218796366198623
absolute error = 3.80677517e-23
relative error = 1.9188194738802630012911544761211e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1797
y2[1] (analytic) = 0.82126558773391570522455853891168
y2[1] (numeric) = 0.82126558773391570522456548724371
absolute error = 6.94833203e-24
relative error = 8.4605176860901310307165120520562e-22 %
h = 0.0001
y1[1] (analytic) = 1.983897357386377685351209368662
y1[1] (numeric) = 1.9838973573863776853511712537811
absolute error = 3.81148809e-23
relative error = 1.9212123428710663995774975655883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1548.8MB, alloc=4.4MB, time=203.34
NO POLE
NO POLE
x[1] = 0.1798
y2[1] (analytic) = 0.82116719889201311093453391249271
y2[1] (numeric) = 0.82116719889201311093454087335908
absolute error = 6.96086637e-24
relative error = 8.4767954435980616527261852754546e-22 %
h = 0.0001
y1[1] (analytic) = 1.9838794790256940831581118383514
y1[1] (numeric) = 1.9838794790256940831580736763434
absolute error = 3.81620080e-23
relative error = 1.9236051586531757905693788292503e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1552.6MB, alloc=4.4MB, time=203.95
x[1] = 0.1799
y2[1] (analytic) = 0.8210688118384385262341048346586
y2[1] (numeric) = 0.82106881183843852623411180806881
absolute error = 6.97341021e-24
relative error = 8.4930886540264251563959199172777e-22 %
h = 0.0001
y1[1] (analytic) = 1.983861590826215698907069132274
y1[1] (numeric) = 1.9838615908262156989070309231412
absolute error = 3.82091328e-23
relative error = 1.9259979111792321609097212487566e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.18
y2[1] (analytic) = 0.82097042657417582165819726030079
y2[1] (numeric) = 0.82097042657417582165820424626434
absolute error = 6.98596355e-24
relative error = 8.5093973228142931915516274291699e-22 %
h = 0.0001
y1[1] (analytic) = 1.9838436927881214145927160246115
y1[1] (numeric) = 1.9838436927881214145926777683559
absolute error = 3.82562556e-23
relative error = 1.9283906156051099111199443689050e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1556.4MB, alloc=4.4MB, time=204.57
NO POLE
NO POLE
x[1] = 0.1801
y2[1] (analytic) = 0.82087204310020884984861835797645
y2[1] (numeric) = 0.82087204310020884984862535650282
absolute error = 6.99852637e-24
relative error = 8.5257214310387316495147004362159e-22 %
h = 0.0001
y1[1] (analytic) = 1.98382578491159021059584620819
y1[1] (numeric) = 1.9838257849115902105958079048137
absolute error = 3.83033763e-23
relative error = 1.9307832669241670039155326647333e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1802
y2[1] (analytic) = 0.82077366141752144554421798349857
y2[1] (numeric) = 0.82077366141752144554422499459727
absolute error = 7.01109870e-24
relative error = 8.5420610206855874420127565679008e-22 %
h = 0.0001
y1[1] (analytic) = 1.9838078671968011656816224906737
y1[1] (numeric) = 1.9838078671968011656815841401789
absolute error = 3.83504948e-23
relative error = 1.9331758601295781318014734075108e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1560.2MB, alloc=4.4MB, time=205.18
NO POLE
NO POLE
x[1] = 0.1803
y2[1] (analytic) = 0.82067528152709742557105033255572
y2[1] (numeric) = 0.82067528152709742557105735623623
absolute error = 7.02368051e-24
relative error = 8.5584160606500355010271548847413e-22 %
h = 0.0001
y1[1] (analytic) = 1.9837899396439334569977860069151
y1[1] (numeric) = 1.9837899396439334569977476093039
absolute error = 3.83976112e-23
relative error = 1.9355684002960470446975545116558e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1804
y2[1] (analytic) = 0.82057690342992058883253577245962
y2[1] (numeric) = 0.82057690342992058883254280873144
absolute error = 7.03627182e-24
relative error = 8.5747865807447942561611096257915e-22 %
h = 0.0001
y1[1] (analytic) = 1.9837720022531663600728644474786
y1[1] (numeric) = 1.9837720022531663600728260027532
absolute error = 3.84447254e-23
relative error = 1.9379608824166546017393480191722e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1564.0MB, alloc=4.4MB, time=205.81
NO POLE
NO POLE
x[1] = 0.1805
y2[1] (analytic) = 0.82047852712697471629962285311924
y2[1] (numeric) = 0.82047852712697471629962990199186
absolute error = 7.04887262e-24
relative error = 8.5911725742325713536994475128816e-22 %
h = 0.0001
y1[1] (analytic) = 1.9837540550246792488143793033572
y1[1] (numeric) = 1.9837540550246792488143408115197
absolute error = 3.84918375e-23
relative error = 1.9403533115661928856579214802003e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1806
y2[1] (analytic) = 0.82038015261924357100095049733942
y2[1] (numeric) = 0.82038015261924357100095755882234
absolute error = 7.06148292e-24
relative error = 8.6075740587515031716705573078214e-22 %
h = 0.0001
y1[1] (analytic) = 1.9837360979586515955070521268983
y1[1] (numeric) = 1.9837360979586515955070135879508
absolute error = 3.85389475e-23
relative error = 1.9427456877786419323026310649695e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1567.8MB, alloc=4.4MB, time=206.42
NO POLE
NO POLE
x[1] = 0.1807
y2[1] (analytic) = 0.82028177990771089801301037054274
y2[1] (numeric) = 0.82028177990771089801301744464544
absolute error = 7.07410270e-24
relative error = 8.6239910153751073031913929960725e-22 %
h = 0.0001
y1[1] (analytic) = 1.9837181310552629708110098089584
y1[1] (numeric) = 1.9837181310552629708109712229031
absolute error = 3.85860553e-23
relative error = 1.9451380060469417039110795118014e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1808
y2[1] (analytic) = 0.82018340899336042445030943001277
y2[1] (numeric) = 0.82018340899336042445031651674474
absolute error = 7.08673197e-24
relative error = 8.6404234617447239101072489785915e-22 %
h = 0.0001
y1[1] (analytic) = 1.9837001543146930437599888723031
y1[1] (numeric) = 1.983700154314693043759950239142
absolute error = 3.86331611e-23
relative error = 1.9475302764871014722306370042508e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1571.6MB, alloc=4.4MB, time=207.03
NO POLE
NO POLE
x[1] = 0.1809
y2[1] (analytic) = 0.82008503987717585945553265375719
y2[1] (numeric) = 0.82008503987717585945553975312793
absolute error = 7.09937074e-24
relative error = 8.6568714155098754044019226523395e-22 %
h = 0.0001
y1[1] (analytic) = 1.9836821677371215817595387812711
y1[1] (numeric) = 1.9836821677371215817595001010065
absolute error = 3.86802646e-23
relative error = 1.9499224840098439289332860532105e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.181
y2[1] (analytic) = 0.81998667256014089418970594908918
y2[1] (numeric) = 0.81998667256014089418971306110818
absolute error = 7.11201900e-24
relative error = 8.6733348699376304622990003005029e-22 %
h = 0.0001
y1[1] (analytic) = 1.9836641713227284505852242677207
y1[1] (numeric) = 1.9836641713227284505851855403546
absolute error = 3.87273661e-23
relative error = 1.9523146437723971574221119532630e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1575.5MB, alloc=4.4MB, time=207.65
NO POLE
NO POLE
x[1] = 0.1811
y2[1] (analytic) = 0.81988830704323920182235924102532
y2[1] (numeric) = 0.81988830704323920182236636570208
absolute error = 7.12467676e-24
relative error = 8.6898138426851102603386773528217e-22 %
h = 0.0001
y1[1] (analytic) = 1.983646165071693614380826673275
y1[1] (numeric) = 1.9836461650716936143807878988096
absolute error = 3.87744654e-23
relative error = 1.9547067457264284874839504550533e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1812
y2[1] (analytic) = 0.81978994332745443752168974059851
y2[1] (numeric) = 0.81978994332745443752169687794251
absolute error = 7.13734400e-24
relative error = 8.7063083148228871452247871852891e-22 %
h = 0.0001
y1[1] (analytic) = 1.9836281489841971356565443078861
y1[1] (numeric) = 1.9836281489841971356565054863236
absolute error = 3.88215625e-23
relative error = 1.9570987899057726906070550111290e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1579.3MB, alloc=4.4MB, time=208.27
NO POLE
NO POLE
x[1] = 0.1813
y2[1] (analytic) = 0.81969158141377023844472539318417
y2[1] (numeric) = 0.81969158141377023844473254320491
absolute error = 7.15002074e-24
relative error = 8.7228183162110059361355743999459e-22 %
h = 0.0001
y1[1] (analytic) = 1.9836101230604191752871918247345
y1[1] (numeric) = 1.983610123060419175287152956077
absolute error = 3.88686575e-23
relative error = 1.9594907813855763343499676160518e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1814
y2[1] (analytic) = 0.81959322130317022372748850693819
y2[1] (numeric) = 0.81959322130317022372749566964515
absolute error = 7.16270696e-24
relative error = 8.7393438279188636388909228077896e-22 %
h = 0.0001
y1[1] (analytic) = 1.9835920873005399925103986114822
y1[1] (numeric) = 1.9835920873005399925103596957318
absolute error = 3.89157504e-23
relative error = 1.9618827201998087936337230460422e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1583.1MB, alloc=4.4MB, time=208.87
NO POLE
NO POLE
x[1] = 0.1815
y2[1] (analytic) = 0.81949486299663799447515956144487
y2[1] (numeric) = 0.81949486299663799447516673684754
absolute error = 7.17540267e-24
relative error = 8.7558848676144017919240897190998e-22 %
h = 0.0001
y1[1] (analytic) = 1.9835740417047399449248061978982
y1[1] (numeric) = 1.9835740417047399449247672350571
absolute error = 3.89628411e-23
relative error = 1.9642746013410331909227302790825e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1816
y2[1] (analytic) = 0.81939650649515713375224119667334
y2[1] (numeric) = 0.81939650649515713375224838478121
absolute error = 7.18810787e-24
relative error = 8.7724414407696571752029357476687e-22 %
h = 0.0001
y1[1] (analytic) = 1.9835559862731994884882646798735
y1[1] (numeric) = 1.9835559862731994884882256699438
absolute error = 3.90099297e-23
relative error = 1.9666664298845294792342225788563e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1586.9MB, alloc=4.4MB, time=209.47
NO POLE
NO POLE
x[1] = 0.1817
y2[1] (analytic) = 0.81929815179971120657272238234072
y2[1] (numeric) = 0.81929815179971120657272958316328
absolute error = 7.20082256e-24
relative error = 8.7890135528590096464884025683867e-22 %
h = 0.0001
y1[1] (analytic) = 1.983537921006099177516028159844
y1[1] (numeric) = 1.9835379210060991775159891028279
absolute error = 3.90570161e-23
relative error = 1.9690582008227663041960017676338e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1818
y2[1] (analytic) = 0.81919979891128375989024276778042
y2[1] (numeric) = 0.81919979891128375989024998132716
absolute error = 7.21354674e-24
relative error = 8.8056012093591832426710323979577e-22 %
h = 0.0001
y1[1] (analytic) = 1.9835198459036196646789492036398
y1[1] (numeric) = 1.9835198459036196646789100995394
absolute error = 3.91041004e-23
relative error = 1.9714499192311126511835027771621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1590.7MB, alloc=4.4MB, time=210.08
NO POLE
NO POLE
x[1] = 0.1819
y2[1] (analytic) = 0.81910144783085832258825721241394
y2[1] (numeric) = 0.81910144783085832258826443869435
absolute error = 7.22628041e-24
relative error = 8.8222044157492472816982639927024e-22 %
h = 0.0001
y1[1] (analytic) = 1.9835017609659417010016723137775
y1[1] (numeric) = 1.983501760965941701001633162595
absolute error = 3.91511825e-23
relative error = 1.9738415801019425899619574518446e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.182
y2[1] (analytic) = 0.81900309855941840547020049692454
y2[1] (numeric) = 0.81900309855941840547020773594811
absolute error = 7.23902357e-24
relative error = 8.8388231775106174650928603164075e-22 %
h = 0.0001
y1[1] (analytic) = 1.983483666193246135860826419216
y1[1] (numeric) = 1.9834836661932461358607872209536
absolute error = 3.91982624e-23
relative error = 1.9762331834690795854200196591126e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1594.5MB, alloc=4.4MB, time=210.69
NO POLE
NO POLE
x[1] = 0.1821
y2[1] (analytic) = 0.81890475109794750124965221523106
y2[1] (numeric) = 0.81890475109794750124965946700728
absolute error = 7.25177622e-24
relative error = 8.8554575001270569810628232689653e-22 %
h = 0.0001
y1[1] (analytic) = 1.9834655615857139169832163815915
y1[1] (numeric) = 1.9834655615857139169831771362513
absolute error = 3.92453402e-23
relative error = 1.9786247344080263345545421859053e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1822
y2[1] (analytic) = 0.81880640544742908454050184736032
y2[1] (numeric) = 0.81880640544742908454050911189868
absolute error = 7.26453836e-24
relative error = 8.8721073890846776082031511044994e-22 %
h = 0.0001
y1[1] (analytic) = 1.9834474471435260904440135179505
y1[1] (numeric) = 1.9834474471435260904439742255347
absolute error = 3.92924158e-23
relative error = 1.9810162279110148188876038270154e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1598.3MB, alloc=4.4MB, time=211.29
NO POLE
NO POLE
x[1] = 0.1823
y2[1] (analytic) = 0.81870806160884661184711401331646
y2[1] (numeric) = 0.81870806160884661184712129062644
absolute error = 7.27730998e-24
relative error = 8.8887728376575747118648785677894e-22 %
h = 0.0001
y1[1] (analytic) = 1.9834293228668638006649451400003
y1[1] (numeric) = 1.9834293228668638006649058005111
absolute error = 3.93394892e-23
relative error = 1.9834076640118642423229713808737e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1824
y2[1] (analytic) = 0.81860971958318352155449390804544
y2[1] (numeric) = 0.81860971958318352155450119813653
absolute error = 7.29009109e-24
relative error = 8.9054538635479919763999388468124e-22 %
h = 0.0001
y1[1] (analytic) = 1.9834111887559082904124831098928
y1[1] (numeric) = 1.9834111887559082904124437233323
absolute error = 3.93865605e-23
relative error = 1.9857990477862112556991325175850e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1602.2MB, alloc=4.4MB, time=211.91
NO POLE
NO POLE
x[1] = 0.1825
y2[1] (analytic) = 0.8185113793714232339184529175932
y2[1] (numeric) = 0.81851137937142323391846022047489
absolute error = 7.30288169e-24
relative error = 8.9221504722490926031343421452724e-22 %
h = 0.0001
y1[1] (analytic) = 1.9833930448108409007960314125614
y1[1] (numeric) = 1.9833930448108409007959919789317
absolute error = 3.94336297e-23
relative error = 1.9881903792680105426044455737112e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1826
y2[1] (analytic) = 0.81841304097454915105577441655576
y2[1] (numeric) = 0.81841304097454915105578173223754
absolute error = 7.31568178e-24
relative error = 8.9388626692563928041420610079123e-22 %
h = 0.0001
y1[1] (analytic) = 1.9833748910318430712661127446283
y1[1] (numeric) = 1.9833748910318430712660732639316
absolute error = 3.94806967e-23
relative error = 1.9905816534493043385755947133446e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1606.0MB, alloc=4.4MB, time=212.52
NO POLE
NO POLE
x[1] = 0.1827
y2[1] (analytic) = 0.81831470439354465693437974691956
y2[1] (numeric) = 0.81831470439354465693438707541091
absolute error = 7.32849135e-24
relative error = 8.9555904478475254546532470939472e-22 %
h = 0.0001
y1[1] (analytic) = 1.9833567274190963396125541199012
y1[1] (numeric) = 1.9833567274190963396125145921397
absolute error = 3.95277615e-23
relative error = 1.9929728703639062329322271017997e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1828
y2[1] (analytic) = 0.81821636962939311736349437839046
y2[1] (numeric) = 0.81821636962939311736350171970086
absolute error = 7.34131040e-24
relative error = 8.9723338135183101562758164911661e-22 %
h = 0.0001
y1[1] (analytic) = 1.9833385539727823419626714914761
y1[1] (numeric) = 1.983338553972782341962631916652
absolute error = 3.95748241e-23
relative error = 1.9953640300456283752701998857614e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1609.8MB, alloc=4.4MB, time=213.13
NO POLE
NO POLE
x[1] = 0.1829
y2[1] (analytic) = 0.81811803668307787998381425030963
y2[1] (numeric) = 0.81811803668307787998382160444858
absolute error = 7.35413895e-24
relative error = 8.9890927962132710514951438965982e-22 %
h = 0.0001
y1[1] (analytic) = 1.983320370693082812779453390466
y1[1] (numeric) = 1.9833203706930828127794137685814
absolute error = 3.96218846e-23
relative error = 1.9977551375703312370094554936588e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.183
y2[1] (analytic) = 0.81801970555558227425767229525488
y2[1] (numeric) = 0.81801970555558227425767966223185
absolute error = 7.36697697e-24
relative error = 9.0058673647678202664070841908699e-22 %
h = 0.0001
y1[1] (analytic) = 1.9833021775801795848597435813723
y1[1] (numeric) = 1.9833021775801795848597039124294
absolute error = 3.96689429e-23
relative error = 2.0001461879298668339171853751480e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1613.6MB, alloc=4.4MB, time=213.73
NO POLE
NO POLE
x[1] = 0.1831
y2[1] (analytic) = 0.81792137624788961145920514442542
y2[1] (numeric) = 0.81792137624788961145921252424991
absolute error = 7.37982449e-24
relative error = 9.0226575613587789675096019030369e-22 %
h = 0.0001
y1[1] (analytic) = 1.9832839746342545893324227341179
y1[1] (numeric) = 1.9832839746342545893323830181189
absolute error = 3.97159990e-23
relative error = 2.0025371811580430803913196734523e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1832
y2[1] (analytic) = 0.81782304876098318466452001490877
y2[1] (numeric) = 0.81782304876098318466452740759025
absolute error = 7.39268148e-24
relative error = 9.0394633548174597160445684127773e-22 %
h = 0.0001
y1[1] (analytic) = 1.9832657618554898556565891127601
y1[1] (numeric) = 1.9832657618554898556565493497071
absolute error = 3.97630530e-23
relative error = 2.0049281223308550477342408858330e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1617.4MB, alloc=4.4MB, time=214.34
NO POLE
NO POLE
x[1] = 0.1833
y2[1] (analytic) = 0.81772472309584626874186177892782
y2[1] (numeric) = 0.81772472309584626874186918447578
absolute error = 7.40554796e-24
relative error = 9.0562847751051656727791499450677e-22 %
h = 0.0001
y1[1] (analytic) = 1.9832475392440675116197382809008
y1[1] (numeric) = 1.9832475392440675116196984707961
absolute error = 3.98101047e-23
relative error = 2.0073190013977769248611313354919e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1834
y2[1] (analytic) = 0.81762639925346212034178021516662
y2[1] (numeric) = 0.81762639925346212034178763359055
absolute error = 7.41842393e-24
relative error = 9.0731218277362731085480471215702e-22 %
h = 0.0001
y1[1] (analytic) = 1.9832293068001697833359418238134
y1[1] (numeric) = 1.9832293068001697833359019666592
absolute error = 3.98571542e-23
relative error = 2.0097098234347546122909594115309e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1621.2MB, alloc=4.4MB, time=214.95
NO POLE
NO POLE
x[1] = 0.1835
y2[1] (analytic) = 0.81752807723481397788729744227307
y2[1] (numeric) = 0.81752807723481397788730487358245
absolute error = 7.43130938e-24
relative error = 9.0899745059955254935581486887031e-22 %
h = 0.0001
y1[1] (analytic) = 1.9832110645239789952440250873036
y1[1] (numeric) = 1.9832110645239789952439851831019
absolute error = 3.99042017e-23
relative error = 2.0121005985602456028031220371725e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1836
y2[1] (analytic) = 0.81742975704088506156407553463686
y2[1] (numeric) = 0.81742975704088506156408297884117
absolute error = 7.44420431e-24
relative error = 9.1068428153976124101854902835473e-22 %
h = 0.0001
y1[1] (analytic) = 1.9831928124156775701057439333222
y1[1] (numeric) = 1.9831928124156775701057039820752
absolute error = 3.99512470e-23
relative error = 2.0144913167235809568198562383137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1625.1MB, alloc=4.4MB, time=215.56
NO POLE
NO POLE
x[1] = 0.1837
y2[1] (analytic) = 0.81733143867265857331058432054108
y2[1] (numeric) = 0.8173314386726585733105917776498
absolute error = 7.45710872e-24
relative error = 9.1237267614595866962858665161197e-22 %
h = 0.0001
y1[1] (analytic) = 1.9831745504754480290039605123495
y1[1] (numeric) = 1.9831745504754480290039205140595
absolute error = 3.99982900e-23
relative error = 2.0168819729161396515719718843761e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1838
y2[1] (analytic) = 0.81723312213111769680826936278569
y2[1] (numeric) = 0.81723312213111769680827683280831
absolute error = 7.47002262e-24
relative error = 9.1406263619372761105953241269115e-22 %
h = 0.0001
y1[1] (analytic) = 1.9831562787034729913408180525683
y1[1] (numeric) = 1.9831562787034729913407780072374
absolute error = 4.00453309e-23
relative error = 2.0192725772565142643513224875753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1628.9MB, alloc=4.4MB, time=216.18
NO POLE
NO POLE
x[1] = 0.1839
y2[1] (analytic) = 0.81713480741724559747172012188127
y2[1] (numeric) = 0.81713480741724559747172760482727
absolute error = 7.48294600e-24
relative error = 9.1575416101189972678691205225681e-22 %
h = 0.0001
y1[1] (analytic) = 1.9831379970999351748359146658435
y1[1] (numeric) = 1.9831379970999351748358745734739
absolute error = 4.00923696e-23
relative error = 2.0216631247361273478590776827537e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.184
y2[1] (analytic) = 0.81703649453202542243883830191132
y2[1] (numeric) = 0.81703649453202542243884579779019
absolute error = 7.49587887e-24
relative error = 9.1744725237682557908957720796523e-22 %
h = 0.0001
y1[1] (analytic) = 1.9831197056650173955244761705281
y1[1] (numeric) = 1.983119705665017395524436031122
absolute error = 4.01394061e-23
relative error = 2.0240536153887740913210570172835e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1632.7MB, alloc=4.4MB, time=216.79
NO POLE
NO POLE
x[1] = 0.1841
y2[1] (analytic) = 0.81693818347644030056100637916143
y2[1] (numeric) = 0.81693818347644030056101388798265
absolute error = 7.50882122e-24
relative error = 9.1914190961751600772418947318936e-22 %
h = 0.0001
y1[1] (analytic) = 1.9831014043989025677555279311122
y1[1] (numeric) = 1.9831014043989025677554877446718
absolute error = 4.01864404e-23
relative error = 2.0264440492482482581823457120172e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1842
y2[1] (analytic) = 0.81683987425147334239325631361366
y2[1] (numeric) = 0.8168398742514733423932638353867
absolute error = 7.52177304e-24
relative error = 9.2083813206262964230251051785957e-22 %
h = 0.0001
y1[1] (analytic) = 1.9830830933017737041900657147343
y1[1] (numeric) = 1.9830830933017737041900254812618
absolute error = 4.02334725e-23
relative error = 2.0288344263483421871786053891763e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1636.5MB, alloc=4.4MB, time=217.40
NO POLE
NO POLE
x[1] = 0.1843
y2[1] (analytic) = 0.81674156685810764018443844340437
y2[1] (numeric) = 0.81674156685810764018444597813873
absolute error = 7.53473436e-24
relative error = 9.2253592393798269760670791083521e-22 %
h = 0.0001
y1[1] (analytic) = 1.9830647723738139157992255645731
y1[1] (numeric) = 1.9830647723738139157991852840707
absolute error = 4.02805024e-23
relative error = 2.0312247467228467934073322720680e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1844
y2[1] (analytic) = 0.81664326129732626786739056234398
y2[1] (numeric) = 0.81664326129732626786739811004913
absolute error = 7.54770515e-24
relative error = 9.2423528212424760697882336132252e-22 %
h = 0.0001
y1[1] (analytic) = 1.9830464416152064118624526901374
y1[1] (numeric) = 1.9830464416152064118624123626072
absolute error = 4.03275302e-23
relative error = 2.0336150154482978158535453098208e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1640.3MB, alloc=4.4MB, time=218.00
NO POLE
NO POLE
x[1] = 0.1845
y2[1] (analytic) = 0.81654495757011228104910718059673
y2[1] (numeric) = 0.81654495757011228104911474128215
absolute error = 7.56068542e-24
relative error = 9.2593620839925461216649149882764e-22 %
h = 0.0001
y1[1] (analytic) = 1.9830281010261344999656693744732
y1[1] (numeric) = 1.9830281010261344999656289999174
absolute error = 4.03745558e-23
relative error = 2.0360052275158303575907746879458e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1846
y2[1] (analytic) = 0.81644665567744871700090896861895
y2[1] (numeric) = 0.81644665567744871700091654229411
absolute error = 7.57367516e-24
relative error = 9.2763870209202137208507726824413e-22 %
h = 0.0001
y1[1] (analytic) = 1.9830097506067815859994418983061
y1[1] (numeric) = 1.9830097506067815859994014767269
absolute error = 4.04215792e-23
relative error = 2.0383953829592311468130996246046e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1644.1MB, alloc=4.4MB, time=218.60
NO POLE
NO POLE
x[1] = 0.1847
y2[1] (analytic) = 0.81634835562031859464861238445401
y2[1] (numeric) = 0.81634835562031859464861997112841
absolute error = 7.58667440e-24
relative error = 9.2934276743108204163686832893123e-22 %
h = 0.0001
y1[1] (analytic) = 1.9829913903573311741571464811372
y1[1] (numeric) = 1.9829913903573311741571060125368
absolute error = 4.04686004e-23
relative error = 2.0407854818122854923647238428844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1647.9MB, alloc=4.4MB, time=219.20
x[1] = 0.1848
y2[1] (analytic) = 0.81625005739970491456269948448242
y2[1] (numeric) = 0.81625005739970491456270708416553
absolute error = 7.59968311e-24
relative error = 9.3104840129628974507517683822721e-22 %
h = 0.0001
y1[1] (analytic) = 1.9829730202779668669331342393107
y1[1] (numeric) = 1.9829730202779668669330937236913
absolute error = 4.05156194e-23
relative error = 2.0431755241087772848109747335754e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1849
y2[1] (analytic) = 0.81615176101659065894848791772512
y2[1] (numeric) = 0.81615176101659065894849553042642
absolute error = 7.61270130e-24
relative error = 9.3275560546701432635566709639740e-22 %
h = 0.0001
y1[1] (analytic) = 1.9829546403688723651208951610722
y1[1] (numeric) = 1.9829546403688723651208545984359
absolute error = 4.05626363e-23
relative error = 2.0455655149254686988199087549084e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1651.8MB, alloc=4.4MB, time=219.81
x[1] = 0.185
y2[1] (analytic) = 0.81605346647195879163630110379855
y2[1] (numeric) = 0.81605346647195879163630872952753
absolute error = 7.62572898e-24
relative error = 9.3446438172345354584234515169441e-22 %
h = 0.0001
y1[1] (analytic) = 1.9829362506302314678112210986348
y1[1] (numeric) = 1.982936250630231467811180488984
absolute error = 4.06096508e-23
relative error = 2.0479554391672016876799143496279e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1851
y2[1] (analytic) = 0.8159551737667922580716385946196
y2[1] (numeric) = 0.81595517376679225807164623338572
absolute error = 7.63876612e-24
relative error = 9.3617472694440343621266704920669e-22 %
h = 0.0001
y1[1] (analytic) = 1.9829178510622280723903677772735
y1[1] (numeric) = 1.9829178510622280723903271206103
absolute error = 4.06566632e-23
relative error = 2.0503453119966949974771387833190e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1655.6MB, alloc=4.4MB, time=220.42
NO POLE
NO POLE
x[1] = 0.1852
y2[1] (analytic) = 0.81585688290207398530534661995876
y2[1] (numeric) = 0.81585688290207398530535427177151
absolute error = 7.65181275e-24
relative error = 9.3788664536135745442448568940587e-22 %
h = 0.0001
y1[1] (analytic) = 1.9828994416650461745382158214633
y1[1] (numeric) = 1.98289944166504617453817511779
absolute error = 4.07036733e-23
relative error = 2.0527351233616270704612687304239e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1853
y2[1] (analytic) = 0.81575859387878688198378881693991
y2[1] (numeric) = 0.81575859387878688198379648180877
absolute error = 7.66486886e-24
relative error = 9.3960013630440755394593399351850e-22 %
h = 0.0001
y1[1] (analytic) = 1.9828810224388698682264307980828
y1[1] (numeric) = 1.9828810224388698682263900474015
absolute error = 4.07506813e-23
relative error = 2.0551248833819680448993155591616e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1659.4MB, alloc=4.4MB, time=221.04
NO POLE
NO POLE
x[1] = 0.1854
y2[1] (analytic) = 0.81566030669791383833901714358485
y2[1] (numeric) = 0.81566030669791383833902482151929
absolute error = 7.67793444e-24
relative error = 9.4131519910329324804358502251967e-22 %
h = 0.0001
y1[1] (analytic) = 1.9828625933838833457166222766984
y1[1] (numeric) = 1.9828625933838833457165814790113
absolute error = 4.07976871e-23
relative error = 2.0575145870484200598680102503411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1855
y2[1] (analytic) = 0.81556202136043772617894297650095
y2[1] (numeric) = 0.81556202136043772617895066751046
absolute error = 7.69100951e-24
relative error = 9.4303183676584634516933473668426e-22 %
h = 0.0001
y1[1] (analytic) = 1.9828441545002708975585019069499
y1[1] (numeric) = 1.9828441545002708975584610622592
absolute error = 4.08446907e-23
relative error = 2.0599042343947571079631990918730e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1663.2MB, alloc=4.4MB, time=221.67
NO POLE
NO POLE
x[1] = 0.1856
y2[1] (analytic) = 0.81546373786734139887750839281027
y2[1] (numeric) = 0.81546373786734139887751609690432
absolute error = 7.70409405e-24
relative error = 9.4475004739613476190890891830242e-22 %
h = 0.0001
y1[1] (analytic) = 1.9828257057882169125880405130552
y1[1] (numeric) = 1.9828257057882169125879996213631
absolute error = 4.08916921e-23
relative error = 2.0622938254547517720679721787766e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1857
y2[1] (analytic) = 0.81536545621960769136485763641828
y2[1] (numeric) = 0.81536545621960769136486535360635
absolute error = 7.71718807e-24
relative error = 9.4646983277661439838756775470345e-22 %
h = 0.0001
y1[1] (analytic) = 1.9828072472479058779256242054518
y1[1] (numeric) = 1.9828072472479058779255832667606
absolute error = 4.09386912e-23
relative error = 2.0646833552188206523062273481293e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1667.0MB, alloc=4.4MB, time=222.27
NO POLE
NO POLE
x[1] = 0.1858
y2[1] (analytic) = 0.81526717641821942011750876872065
y2[1] (numeric) = 0.81526717641821942011751649901222
absolute error = 7.73029157e-24
relative error = 9.4819119346397925986040927446027e-22 %
h = 0.0001
y1[1] (analytic) = 1.9827887788795223789742095095947
y1[1] (numeric) = 1.9827887788795223789741685239066
absolute error = 4.09856881e-23
relative error = 2.0670728287639941384278618646616e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1859
y2[1] (analytic) = 0.81516889846415938314852550384624
y2[1] (numeric) = 0.81516889846415938314853324725078
absolute error = 7.74340454e-24
relative error = 9.4991412878842249933031277228460e-22 %
h = 0.0001
y1[1] (analytic) = 1.9827703006832510994174775119283
y1[1] (numeric) = 1.9827703006832510994174364792454
absolute error = 4.10326829e-23
relative error = 2.0694622511674890640064787697799e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1670.8MB, alloc=4.4MB, time=222.87
NO POLE
NO POLE
x[1] = 0.186
y2[1] (analytic) = 0.81507062235841035999768922853466
y2[1] (numeric) = 0.81507062235841035999769698506165
absolute error = 7.75652699e-24
relative error = 9.5163864053355962111790519610892e-22 %
h = 0.0001
y1[1] (analytic) = 1.9827518126592768212179870230509
y1[1] (numeric) = 1.9827518126592768212179459433755
absolute error = 4.10796754e-23
relative error = 2.0718516123762222313668187867629e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1861
y2[1] (analytic) = 0.81497234810195511172167120674663
y2[1] (numeric) = 0.81497234810195511172167897640555
absolute error = 7.76965892e-24
relative error = 9.5336472925680122893828786515617e-22 %
h = 0.0001
y1[1] (analytic) = 1.982733314807784424615326758091
y1[1] (numeric) = 1.9827333148077844246152856314254
absolute error = 4.11266656e-23
relative error = 2.0742409124238180314572329677601e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1674.6MB, alloc=4.4MB, time=223.47
NO POLE
NO POLE
x[1] = 0.1862
y2[1] (analytic) = 0.81487407569577638088420496910549
y2[1] (numeric) = 0.8148740756957763808842127519058
absolute error = 7.78280031e-24
relative error = 9.5509239306143010052894811646961e-22 %
h = 0.0001
y1[1] (analytic) = 1.982714807128958888124266534313
y1[1] (numeric) = 1.9827148071289588881242253606593
absolute error = 4.11736537e-23
relative error = 2.0766301614310787175840826646578e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1863
y2[1] (analytic) = 0.814775805140856891546258887268
y2[1] (numeric) = 0.81477580514085689154626668321918
absolute error = 7.79595118e-24
relative error = 9.5682163495911010604377300662393e-22 %
h = 0.0001
y1[1] (analytic) = 1.9826962896229852885329074859705
y1[1] (numeric) = 1.982696289622985288532866265331
absolute error = 4.12206395e-23
relative error = 2.0790193493446345633337871499710e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1678.5MB, alloc=4.4MB, time=224.07
NO POLE
NO POLE
x[1] = 0.1864
y2[1] (analytic) = 0.81467753643817934925620893332291
y2[1] (numeric) = 0.81467753643817934925621674243444
absolute error = 7.80911153e-24
relative error = 9.5855245550796936276094498591122e-22 %
h = 0.0001
y1[1] (analytic) = 1.9826777622900488009008312964275
y1[1] (numeric) = 1.9826777622900488009007900288043
absolute error = 4.12676232e-23
relative error = 2.0814084862854733347072685312846e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1865
y2[1] (analytic) = 0.81457926958872644104001162431534
y2[1] (numeric) = 0.81457926958872644104001944659669
absolute error = 7.82228135e-24
relative error = 9.6028485403874784284148158154513e-22 %
h = 0.0001
y1[1] (analytic) = 1.9826592251303346985572484475635
y1[1] (numeric) = 1.9826592251303346985572071329589
absolute error = 4.13146046e-23
relative error = 2.0837975622000340844636724626438e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1682.3MB, alloc=4.4MB, time=224.68
NO POLE
NO POLE
x[1] = 0.1866
y2[1] (analytic) = 0.81448100459348083539137715199543
y2[1] (numeric) = 0.81448100459348083539138498745608
absolute error = 7.83546065e-24
relative error = 9.6201883233738408922078690769240e-22 %
h = 0.0001
y1[1] (analytic) = 1.9826406781440283530991454864836
y1[1] (numeric) = 1.9826406781440283530991041248998
absolute error = 4.13615838e-23
relative error = 2.0861865821657120172902743910579e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1867
y2[1] (analytic) = 0.81438274145342518226194269788942
y2[1] (numeric) = 0.81438274145342518226195054653884
absolute error = 7.84864942e-24
relative error = 9.6375438973480098613576893837649e-22 %
h = 0.0001
y1[1] (analytic) = 1.9826221213313152343894313095496
y1[1] (numeric) = 1.9826221213313152343893899009888
absolute error = 4.14085608e-23
relative error = 2.0885755462162641245771331363571e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1686.1MB, alloc=4.4MB, time=225.28
NO POLE
NO POLE
x[1] = 0.1868
y2[1] (analytic) = 0.81428448016954211305144593379147
y2[1] (numeric) = 0.81428448016954211305145379563913
absolute error = 7.86184766e-24
relative error = 9.6549152678964055217510423520574e-22 %
h = 0.0001
y1[1] (analytic) = 1.9826035546923809105550824637527
y1[1] (numeric) = 1.9826035546923809105550410082171
absolute error = 4.14555356e-23
relative error = 2.0909644543854460008368842590227e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1869
y2[1] (analytic) = 0.81418622074281424059789870777445
y2[1] (numeric) = 0.81418622074281424059790658282983
absolute error = 7.87505538e-24
relative error = 9.6723024528900476829775948419007e-22 %
h = 0.0001
y1[1] (analytic) = 1.9825849782274110479852874654453
y1[1] (numeric) = 1.9825849782274110479852459629372
absolute error = 4.15025081e-23
relative error = 2.0933533016630918565677413655676e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1689.9MB, alloc=4.4MB, time=225.90
NO POLE
NO POLE
x[1] = 0.187
y2[1] (analytic) = 0.81408796317422415916776091581804
y2[1] (numeric) = 0.81408796317422415916776880409062
absolute error = 7.88827258e-24
relative error = 9.6897054579245992536679024057615e-22 %
h = 0.0001
y1[1] (analytic) = 1.9825663919365914113295901364508
y1[1] (numeric) = 1.9825663919365914113295485869724
absolute error = 4.15494784e-23
relative error = 2.0957420931267799118135862104750e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1871
y2[1] (analytic) = 0.81398970746475444444611455915232
y2[1] (numeric) = 0.81398970746475444444612246065156
absolute error = 7.90149924e-24
relative error = 9.7071242640277893041003356566278e-22 %
h = 0.0001
y1[1] (analytic) = 1.9825477958201078634960319575693
y1[1] (numeric) = 1.9825477958201078634959903611228
absolute error = 4.15964465e-23
relative error = 2.0981308288102614992186141303864e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1693.7MB, alloc=4.4MB, time=226.52
NO POLE
NO POLE
x[1] = 0.1872
y2[1] (analytic) = 0.81389145361538765352683798741509
y2[1] (numeric) = 0.81389145361538765352684590215048
absolute error = 7.91473539e-24
relative error = 9.7245589136511383275881744358848e-22 %
h = 0.0001
y1[1] (analytic) = 1.9825291898781463656492934394991
y1[1] (numeric) = 1.9825291898781463656492517960867
absolute error = 4.16434124e-23
relative error = 2.1005195087472865588251024071983e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1873
y2[1] (analytic) = 0.81379320162710632490278032772136
y2[1] (numeric) = 0.81379320162710632490278825570235
absolute error = 7.92798099e-24
relative error = 9.7420093632494286604935345140574e-22 %
h = 0.0001
y1[1] (analytic) = 1.9825105741108929772088345111912
y1[1] (numeric) = 1.9825105741108929772087928208152
absolute error = 4.16903760e-23
relative error = 2.1029081279274943513605004965039e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1697.5MB, alloc=4.4MB, time=227.12
NO POLE
NO POLE
x[1] = 0.1874
y2[1] (analytic) = 0.81369495150089297845593609974295
y2[1] (numeric) = 0.81369495150089297845594404097902
absolute error = 7.94123607e-24
relative error = 9.7594756552834345544032775572312e-22 %
h = 0.0001
y1[1] (analytic) = 1.9824919485185338558470339256566
y1[1] (numeric) = 1.9824919485185338558469921883192
absolute error = 4.17373374e-23
relative error = 2.1052966914286465434317621395904e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1875
y2[1] (analytic) = 0.81359670323773011544762001689679
y2[1] (numeric) = 0.81359670323773011544762797139742
absolute error = 7.95450063e-24
relative error = 9.7769577953608333324113293657624e-22 %
h = 0.0001
y1[1] (analytic) = 1.9824733131012552574873276832436
y1[1] (numeric) = 1.9824733131012552574872858989471
absolute error = 4.17842965e-23
relative error = 2.1076851942402847331317249902761e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1701.3MB, alloc=4.4MB, time=227.73
NO POLE
NO POLE
x[1] = 0.1876
y2[1] (analytic) = 0.81349845683860021850864197373998
y2[1] (numeric) = 0.81349845683860021850864994151463
absolute error = 7.96777465e-24
relative error = 9.7944557645065367594398855249225e-22 %
h = 0.0001
y1[1] (analytic) = 1.9824546678592435363023464724054
y1[1] (numeric) = 1.982454667859243536302304641152
absolute error = 4.18312534e-23
relative error = 2.1100736414402624332344944622608e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1877
y2[1] (analytic) = 0.81340021230448575162948221966981
y2[1] (numeric) = 0.81340021230448575162949020072795
absolute error = 7.98105814e-24
relative error = 9.8119695806182001182953366402274e-22 %
h = 0.0001
y1[1] (analytic) = 1.982436012792685144712052127975
y1[1] (numeric) = 1.9824360127926851447120102497669
absolute error = 4.18782081e-23
relative error = 2.1124620330623224814699729420034e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1705.2MB, alloc=4.4MB, time=228.34
NO POLE
NO POLE
x[1] = 0.1878
y2[1] (analytic) = 0.8133019696363691601504667190272
y2[1] (numeric) = 0.8133019696363691601504747133783
absolute error = 7.99435110e-24
relative error = 9.8294992493062682085051327543207e-22 %
h = 0.0001
y1[1] (analytic) = 1.9824173479017666333818731069675
y1[1] (numeric) = 1.982417347901766633381831181807
absolute error = 4.19251605e-23
relative error = 2.1148503640958598346359445513729e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1879
y2[1] (analytic) = 0.8132037288352328707519426977016
y2[1] (numeric) = 0.81320372883523287075195070535514
absolute error = 8.00765354e-24
relative error = 9.8470447884806358301573872931313e-22 %
h = 0.0001
y1[1] (analytic) = 1.982398673186674651220838981927
y1[1] (numeric) = 1.9823986731866746512207970098163
absolute error = 4.19721107e-23
relative error = 2.1172386396188660157551793255378e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1709.0MB, alloc=4.4MB, time=228.94
NO POLE
NO POLE
x[1] = 0.188
y2[1] (analytic) = 0.81310548990205929144445437633573
y2[1] (numeric) = 0.81310548990205929144446239730117
absolute error = 8.02096544e-24
relative error = 9.8646061791639686491462906364010e-22 %
h = 0.0001
y1[1] (analytic) = 1.9823799886475959453797139518383
y1[1] (numeric) = 1.9823799886475959453796719327796
absolute error = 4.20190587e-23
relative error = 2.1196268596650796295079218094501e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1881
y2[1] (analytic) = 0.81300725283783081155891889022829
y2[1] (numeric) = 0.81300725283783081155892692451511
absolute error = 8.03428682e-24
relative error = 9.8821834515695097622541248933836e-22 %
h = 0.0001
y1[1] (analytic) = 1.9823612942847173612491293706202
y1[1] (numeric) = 1.9823612942847173612490873046158
absolute error = 4.20660044e-23
relative error = 2.1220150192237487679658023609857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1712.8MB, alloc=4.4MB, time=229.55
NO POLE
NO POLE
x[1] = 0.1882
y2[1] (analytic) = 0.81290901764352980173680239603301
y2[1] (numeric) = 0.81290901764352980173681044365067
absolute error = 8.04761766e-24
relative error = 9.8997765867188046407291965089714e-22 %
h = 0.0001
y1[1] (analytic) = 1.9823425900982258424577152932213
y1[1] (numeric) = 1.9823425900982258424576731802735
absolute error = 4.21129478e-23
relative error = 2.1244031183284664806512525925921e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1883
y2[1] (analytic) = 0.81281078432013861392029636535215
y2[1] (numeric) = 0.81281078432013861392030442631013
absolute error = 8.06095798e-24
relative error = 9.9173856148358655580452533002611e-22 %
h = 0.0001
y1[1] (analytic) = 1.9823238760883084308702310393351
y1[1] (numeric) = 1.9823238760883084308701888794461
absolute error = 4.21598890e-23
relative error = 2.1267911620574086298751894721271e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1716.6MB, alloc=4.4MB, time=230.17
NO POLE
NO POLE
x[1] = 0.1884
y2[1] (analytic) = 0.81271255286863958134249406532279
y2[1] (numeric) = 0.81271255286863958134250213963055
absolute error = 8.07430776e-24
relative error = 9.9350105169411196985314805897386e-22 %
h = 0.0001
y1[1] (analytic) = 1.9823051522551522665856947747538
y1[1] (numeric) = 1.9823051522551522665856525679258
absolute error = 4.22068280e-23
relative error = 2.1291791504443081393944390901231e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1885
y2[1] (analytic) = 0.81261432329001501851756722629406
y2[1] (numeric) = 0.81261432329001501851757531396107
absolute error = 8.08766701e-24
relative error = 9.9526513109633949262201981761573e-22 %
h = 0.0001
y1[1] (analytic) = 1.9822864185989445879355121103798
y1[1] (numeric) = 1.9822864185989445879354698566151
absolute error = 4.22537647e-23
relative error = 2.1315670784782168822406576086255e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1720.4MB, alloc=4.4MB, time=230.80
NO POLE
NO POLE
x[1] = 0.1886
y2[1] (analytic) = 0.81251609558524722123094289669363
y2[1] (numeric) = 0.81251609558524722123095099772936
absolute error = 8.10103573e-24
relative error = 9.9703080025324359226401036435860e-22 %
h = 0.0001
y1[1] (analytic) = 1.9822676751198727314816037189134
y1[1] (numeric) = 1.9822676751198727314815614182142
absolute error = 4.23006992e-23
relative error = 2.1339549512374492971220319590644e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1887
y2[1] (analytic) = 0.81241786975531846652948048518162
y2[1] (numeric) = 0.81241786975531846652948859959554
absolute error = 8.11441392e-24
relative error = 9.9879805972804049827416584358070e-22 %
h = 0.0001
y1[1] (analytic) = 1.9822489218181241320145319692347
y1[1] (numeric) = 1.9822489218181241320144896216033
absolute error = 4.23476314e-23
relative error = 2.1363427637109589985512446663633e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1724.2MB, alloc=4.4MB, time=231.41
NO POLE
NO POLE
x[1] = 0.1888
y2[1] (analytic) = 0.81231964580121101271164899019019
y2[1] (numeric) = 0.81231964580121101271165711799176
absolute error = 8.12780157e-24
relative error = 1.0005669088531458249689466070835e-21 %
h = 0.0001
y1[1] (analytic) = 1.9822301586938863225516265784999
y1[1] (numeric) = 1.9822301586938863225515841839385
absolute error = 4.23945614e-23
relative error = 2.1387305209771529184202024010301e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1889
y2[1] (analytic) = 0.81222142372390709931770441694703
y2[1] (numeric) = 0.81222142372390709931771255814572
absolute error = 8.14119869e-24
relative error = 1.0023373494230044174067501112295e-21 %
h = 0.0001
y1[1] (analytic) = 1.9822113857473469343351092819695
y1[1] (numeric) = 1.9822113857473469343350668404804
absolute error = 4.24414891e-23
relative error = 2.1411182180248863133787565695692e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1728.0MB, alloc=4.4MB, time=232.02
NO POLE
NO POLE
x[1] = 0.189
y2[1] (analytic) = 0.81212320352438894711986738208099
y2[1] (numeric) = 0.81212320352438894711987553668627
absolute error = 8.15460528e-24
relative error = 1.0041093820015583748553753469190e-21 %
h = 0.0001
y1[1] (analytic) = 1.9821926029786936968302175205875
y1[1] (numeric) = 1.9821926029786936968301750321729
absolute error = 4.24884146e-23
relative error = 2.1435058599326587163628571596183e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1891
y2[1] (analytic) = 0.81202498520363875811250090590807
y2[1] (numeric) = 0.8120249852036387581125090739294
absolute error = 8.16802133e-24
relative error = 1.0058830059215028141870237798431e-21 %
h = 0.0001
y1[1] (analytic) = 1.9821738103881144377233271463308
y1[1] (numeric) = 1.982173810388114437723284610993
absolute error = 4.25353378e-23
relative error = 2.1458934416892269268074984720083e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1731.9MB, alloc=4.4MB, time=232.62
NO POLE
NO POLE
x[1] = 0.1892
y2[1] (analytic) = 0.81192676876263871550228839249594
y2[1] (numeric) = 0.81192676876263871550229657394279
absolute error = 8.18144685e-24
relative error = 1.0076582229784556470767719332339e-21 %
h = 0.0001
y1[1] (analytic) = 1.9821550079757970829200741453468
y1[1] (numeric) = 1.9821550079757970829200315630881
absolute error = 4.25822587e-23
relative error = 2.1482809633281690682083199175052e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1893
y2[1] (analytic) = 0.81182855420237098369841179760535
y2[1] (numeric) = 0.81182855420237098369841999248718
absolute error = 8.19488183e-24
relative error = 1.0094350325052986981931956215969e-21 %
h = 0.0001
y1[1] (analytic) = 1.9821361957419296565434753788989
y1[1] (numeric) = 1.9821361957419296565434327497215
absolute error = 4.26291774e-23
relative error = 2.1506684299281237384621452362693e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1735.7MB, alloc=4.4MB, time=233.23
NO POLE
NO POLE
x[1] = 0.1894
y2[1] (analytic) = 0.81173034152381770830272998460643
y2[1] (numeric) = 0.81173034152381770830273819293271
absolute error = 8.20832628e-24
relative error = 1.0112134362984326283711333991023e-21 %
h = 0.0001
y1[1] (analytic) = 1.9821173736867002809320483421375
y1[1] (numeric) = 1.9821173736867002809320056660437
absolute error = 4.26760938e-23
relative error = 2.1530558364776998260175065792127e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1895
y2[1] (analytic) = 0.81163213072796101609995726846832
y2[1] (numeric) = 0.81163213072796101609996549024852
absolute error = 8.22178020e-24
relative error = 1.0129934349230115739884010704313e-21 %
h = 0.0001
y1[1] (analytic) = 1.9820985418102971766379299407167
y1[1] (numeric) = 1.9820985418102971766378872177087
absolute error = 4.27230080e-23
relative error = 2.1554431880556287994942151101109e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1739.5MB, alloc=4.4MB, time=233.83
NO POLE
NO POLE
x[1] = 0.1896
y2[1] (analytic) = 0.81153392181578301504784214792023
y2[1] (numeric) = 0.81153392181578301504785038316381
absolute error = 8.23524358e-24
relative error = 1.0147750277121980811171606961423e-21 %
h = 0.0001
y1[1] (analytic) = 1.9820797001129086624249942852743
y1[1] (numeric) = 1.9820797001129086624249515153544
absolute error = 4.27699199e-23
relative error = 2.1578304796504208417062074408935e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1743.3MB, alloc=4.5MB, time=234.45
x[1] = 0.1897
y2[1] (analytic) = 0.8114357147882657942673462258821
y2[1] (numeric) = 0.81143571478826579426735447459852
absolute error = 8.24871642e-24
relative error = 1.0165582152311845754570699051524e-21 %
h = 0.0001
y1[1] (analytic) = 1.9820608485947231552669695037949
y1[1] (numeric) = 1.9820608485947231552669266869654
absolute error = 4.28168295e-23
relative error = 2.1602177112956466141117488323531e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1898
y2[1] (analytic) = 0.81133750964639142403282331826317
y2[1] (numeric) = 0.8113375096463914240328315804619
absolute error = 8.26219873e-24
relative error = 1.0183429992779389896823772365585e-21 %
h = 0.0001
y1[1] (analytic) = 1.9820419872559291703455535718738
y1[1] (numeric) = 1.982041987255929170345510708137
absolute error = 4.28637368e-23
relative error = 2.1626048830248752578530521028883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1747.1MB, alloc=4.5MB, time=235.08
x[1] = 0.1899
y2[1] (analytic) = 0.81123930639114195576219875122667
y2[1] (numeric) = 0.81123930639114195576220702691717
absolute error = 8.27569050e-24
relative error = 1.0201293791859052247337080866836e-21 %
h = 0.0001
y1[1] (analytic) = 1.9820231160967153210485291609021
y1[1] (numeric) = 1.9820231160967153210484862502602
absolute error = 4.29106419e-23
relative error = 2.1649919999170242289245469038309e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.19
y2[1] (analytic) = 0.81114110502349942200714884701869
y2[1] (numeric) = 0.81114110502349942200715713621043
absolute error = 8.28919174e-24
relative error = 1.0219173567538357370968292046377e-21 %
h = 0.0001
y1[1] (analytic) = 1.9820042351172703189678775041899
y1[1] (numeric) = 1.9820042351172703189678345466452
absolute error = 4.29575447e-23
relative error = 2.1673790569604059229802582393164e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1750.9MB, alloc=4.5MB, time=235.70
NO POLE
NO POLE
x[1] = 0.1901
y2[1] (analytic) = 0.81104290554444583644328059845967
y2[1] (numeric) = 0.81104290554444583644328890116211
absolute error = 8.30270244e-24
relative error = 1.0237069313153624388184784086037e-21 %
h = 0.0001
y1[1] (analytic) = 1.9819853443177829738978912810484
y1[1] (numeric) = 1.9819853443177829738978482766031
absolute error = 4.30044453e-23
relative error = 2.1697660592340309904097360987309e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1902
y2[1] (analytic) = 0.81094470795496319386031153219644
y2[1] (numeric) = 0.81094470795496319386031984841904
absolute error = 8.31622260e-24
relative error = 1.0254981034368932083605206182222e-21 %
h = 0.0001
y1[1] (analytic) = 1.9819664436984421938332865188484
y1[1] (numeric) = 1.9819664436984421938332434675048
absolute error = 4.30513436e-23
relative error = 2.1721530017261128230579508158118e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1754.8MB, alloc=4.5MB, time=236.32
NO POLE
NO POLE
x[1] = 0.1903
y2[1] (analytic) = 0.81084651225603347015224976081327
y2[1] (numeric) = 0.8108465122560334701522580905655
absolute error = 8.32975223e-24
relative error = 1.0272908749183583494762717251328e-21 %
h = 0.0001
y1[1] (analytic) = 1.9819475332594369849673135130749
y1[1] (numeric) = 1.9819475332594369849672704148353
absolute error = 4.30982396e-23
relative error = 2.1745398844702131318639087567933e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1904
y2[1] (analytic) = 0.81074831844863862230757422389997
y2[1] (numeric) = 0.81074831844863862230758256719129
absolute error = 8.34329132e-24
relative error = 1.0290852450936723539451394564842e-21 %
h = 0.0001
y1[1] (analytic) = 1.9819286130009564516898667653959
y1[1] (numeric) = 1.9819286130009564516898236202626
absolute error = 4.31451333e-23
relative error = 2.1769267074998921138093966427241e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1758.6MB, alloc=4.5MB, time=236.95
NO POLE
NO POLE
x[1] = 0.1905
y2[1] (analytic) = 0.81065012653376058839941511817529
y2[1] (numeric) = 0.81065012653376058839942347501516
absolute error = 8.35683987e-24
relative error = 1.0308812145299737316793774670037e-21 %
h = 0.0001
y1[1] (analytic) = 1.9819096829231897965855939397653
y1[1] (numeric) = 1.9819096829231897965855507477406
absolute error = 4.31920247e-23
relative error = 2.1793134708487084529772916942915e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1906
y2[1] (analytic) = 0.81055193651238128757573451676377
y2[1] (numeric) = 0.81055193651238128757574288716165
absolute error = 8.37039788e-24
relative error = 1.0326787837946447334216920150832e-21 %
h = 0.0001
y1[1] (analytic) = 1.9818907430263263204320038365778
y1[1] (numeric) = 1.981890743026326320431960597664
absolute error = 4.32389138e-23
relative error = 2.1817001745502193216098150090613e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1762.4MB, alloc=4.5MB, time=237.58
NO POLE
NO POLE
x[1] = 0.1907
y2[1] (analytic) = 0.81045374838548262004950717772432
y2[1] (numeric) = 0.81045374838548262004951556168968
absolute error = 8.38396536e-24
relative error = 1.0344779546891881702334435678502e-21 %
h = 0.0001
y1[1] (analytic) = 1.9818717933105554221975733848956
y1[1] (numeric) = 1.9818717933105554221975300990948
absolute error = 4.32858008e-23
relative error = 2.1840868287294505093083820612182e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1908
y2[1] (analytic) = 0.81035556215404646708890154192867
y2[1] (numeric) = 0.81035556215404646708890993947097
absolute error = 8.39754230e-24
relative error = 1.0362787265478964198877315456451e-21 %
h = 0.0001
y1[1] (analytic) = 1.9818528337760665990398536527648
y1[1] (numeric) = 1.9818528337760665990398103200794
absolute error = 4.33326854e-23
relative error = 2.1864734182828957867338021937406e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1766.2MB, alloc=4.5MB, time=238.20
NO POLE
NO POLE
x[1] = 0.1909
y2[1] (analytic) = 0.81025737781905469100746092038786
y2[1] (numeric) = 0.81025737781905469100746933151655
absolute error = 8.41112869e-24
relative error = 1.0380810987047080059596049114403e-21 %
h = 0.0001
y1[1] (analytic) = 1.9818338644230494463035748756419
y1[1] (numeric) = 1.9818338644230494463035314960743
absolute error = 4.33795676e-23
relative error = 2.1888599432439630635832989772945e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.191
y2[1] (analytic) = 0.81015919538148913515428487112495
y2[1] (numeric) = 0.8101591953814891351542932958495
absolute error = 8.42472455e-24
relative error = 1.0398850741961833098556002615815e-21 %
h = 0.0001
y1[1] (analytic) = 1.9818148852516936575187505029481
y1[1] (numeric) = 1.9818148852516936575187070765005
absolute error = 4.34264476e-23
relative error = 2.1912464137378184923671532748853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1770.0MB, alloc=4.5MB, time=238.82
NO POLE
NO POLE
x[1] = 0.1911
y2[1] (analytic) = 0.81006101484233162390421076569227
y2[1] (numeric) = 0.81006101484233162390421920402214
absolute error = 8.43832987e-24
relative error = 1.0416906523568989103262494042651e-21 %
h = 0.0001
y1[1] (analytic) = 1.9817958962621890243987802627704
y1[1] (numeric) = 1.981795896262189024398736789445
absolute error = 4.34733254e-23
relative error = 2.1936328297981567464433207653400e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1912
y2[1] (analytic) = 0.80996283620256396264799554543119
y2[1] (numeric) = 0.80996283620256396264800399737583
absolute error = 8.45194464e-24
relative error = 1.0434978325210774782139956732080e-21 %
h = 0.0001
y1[1] (analytic) = 1.9817768974547254368385522447291
y1[1] (numeric) = 1.9817768974547254368385087245283
absolute error = 4.35202008e-23
relative error = 2.1960191813667177988336289294391e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1773.8MB, alloc=4.5MB, time=239.44
NO POLE
NO POLE
x[1] = 0.1913
y2[1] (analytic) = 0.80986465946316793778249766757273
y2[1] (numeric) = 0.80986465946316793778250613314161
absolute error = 8.46556888e-24
relative error = 1.0453066177269102065077633916088e-21 %
h = 0.0001
y1[1] (analytic) = 1.9817578888294928829125440010313
y1[1] (numeric) = 1.9817578888294928829125004339573
absolute error = 4.35670740e-23
relative error = 2.1984054785689533744755342678773e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1914
y2[1] (analytic) = 0.80976648462512531670085924127719
y2[1] (numeric) = 0.80976648462512531670086772047976
absolute error = 8.47920257e-24
relative error = 1.0471170060743346966616686655235e-21 %
h = 0.0001
y1[1] (analytic) = 1.9817388703866814488729226657266
y1[1] (numeric) = 1.9817388703866814488728790517818
absolute error = 4.36139448e-23
relative error = 2.2007917113464069422976259059689e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1777.6MB, alloc=4.5MB, time=240.08
NO POLE
NO POLE
x[1] = 0.1915
y2[1] (analytic) = 0.80966831168941784778268835371085
y2[1] (numeric) = 0.80966831168941784778269684655658
absolute error = 8.49284573e-24
relative error = 1.0489290006026302614277421436445e-21 %
h = 0.0001
y1[1] (analytic) = 1.9817198421264813191476440921881
y1[1] (numeric) = 1.9817198421264813191476004313746
absolute error = 4.36608135e-23
relative error = 2.2031778948708427745256467341862e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1916
y2[1] (analytic) = 0.80957014065702726038424158625815
y2[1] (numeric) = 0.80957014065702726038425009275649
absolute error = 8.50649834e-24
relative error = 1.0507425994116253701495995983216e-21 %
h = 0.0001
y1[1] (analytic) = 1.9817008040490827763385510088334
y1[1] (numeric) = 1.9817008040490827763385073011536
absolute error = 4.37076798e-23
relative error = 2.2055640140375826354050550982800e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1781.5MB, alloc=4.5MB, time=240.69
NO POLE
NO POLE
x[1] = 0.1917
y2[1] (analytic) = 0.80947197152893526482860672096723
y2[1] (numeric) = 0.80947197152893526482861524112764
absolute error = 8.52016041e-24
relative error = 1.0525578043063149607583169652571e-21 %
h = 0.0001
y1[1] (analytic) = 1.9816817561546762012194701931086
y1[1] (numeric) = 1.9816817561546762012194264385648
absolute error = 4.37545438e-23
relative error = 2.2079500739262407934701906246727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1918
y2[1] (analytic) = 0.80937380430612355239588563732728
y2[1] (numeric) = 0.80937380430612355239589417115922
absolute error = 8.53383194e-24
relative error = 1.0543746158570151808839654784894e-21 %
h = 0.0001
y1[1] (analytic) = 1.9816626984434520727343086637512
y1[1] (numeric) = 1.9816626984434520727342648623457
absolute error = 4.38014055e-23
relative error = 2.2103360745703565169960927242526e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1785.3MB, alloc=4.5MB, time=241.30
NO POLE
NO POLE
x[1] = 0.1919
y2[1] (analytic) = 0.80927563898957379531337739947569
y2[1] (numeric) = 0.80927563898957379531338594698861
absolute error = 8.54751292e-24
relative error = 1.0561930333986144920331634686203e-21 %
h = 0.0001
y1[1] (analytic) = 1.9816436309156009679951488913527
y1[1] (numeric) = 1.9816436309156009679951050430877
absolute error = 4.38482650e-23
relative error = 2.2127220210497835958641241252680e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.192
y2[1] (analytic) = 0.80917747558026764674576153393323
y2[1] (numeric) = 0.80917747558026764674577009513659
absolute error = 8.56120336e-24
relative error = 1.0580130587372927702667773224646e-21 %
h = 0.0001
y1[1] (analytic) = 1.9816245535713135622803430272392
y1[1] (numeric) = 1.9816245535713135622802991321171
absolute error = 4.38951221e-23
relative error = 2.2151079033054748453791526758050e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1789.1MB, alloc=4.5MB, time=241.92
NO POLE
NO POLE
x[1] = 0.1921
y2[1] (analytic) = 0.80907931407918674078528149796545
y2[1] (numeric) = 0.8090793140791867407852900728687
absolute error = 8.57490325e-24
relative error = 1.0598346912081293738676070013545e-21 %
h = 0.0001
y1[1] (analytic) = 1.9816054664107806290326061506898
y1[1] (numeric) = 1.9816054664107806290325622087129
absolute error = 4.39419769e-23
relative error = 2.2174937264172325068599055730479e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1922
y2[1] (analytic) = 0.80898115448731269244192833866841
y2[1] (numeric) = 0.80898115448731269244193692728101
absolute error = 8.58861260e-24
relative error = 1.0616579326180948516923607635913e-21 %
h = 0.0001
y1[1] (analytic) = 1.9815863694341930398571085345109
y1[1] (numeric) = 1.9815863694341930398570645456814
absolute error = 4.39888295e-23
relative error = 2.2198794954650517046161437442406e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1792.9MB, alloc=4.5MB, time=242.55
NO POLE
NO POLE
x[1] = 0.1923
y2[1] (analytic) = 0.80888299680562709763362454287696
y2[1] (numeric) = 0.80888299680562709763363314520838
absolute error = 8.60233142e-24
relative error = 1.0634827847750052724787256015117e-21 %
h = 0.0001
y1[1] (analytic) = 1.9815672626417417645195669289858
y1[1] (numeric) = 1.9815672626417417645195228933061
absolute error = 4.40356797e-23
relative error = 2.2222652003895892023833587297471e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1924
y2[1] (analytic) = 0.80878484103511153317640807799371
y2[1] (numeric) = 0.8087848410351115331764166940534
absolute error = 8.61605969e-24
relative error = 1.0653092457782543417795370814567e-21 %
h = 0.0001
y1[1] (analytic) = 1.9815481460336178709443348642197
y1[1] (numeric) = 1.9815481460336178709442907816921
absolute error = 4.40825276e-23
relative error = 2.2246508462707885044514398048901e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1796.7MB, alloc=4.5MB, time=243.17
NO POLE
NO POLE
x[1] = 0.1925
y2[1] (analytic) = 0.8086866871767475567746166238368
y2[1] (numeric) = 0.80868668717674755677462525363421
absolute error = 8.62979741e-24
relative error = 1.0671373161994270428971829438846e-21 %
h = 0.0001
y1[1] (analytic) = 1.9815290196100125252124919708972
y1[1] (numeric) = 1.981529019610012525212447841524
absolute error = 4.41293732e-23
relative error = 2.2270364331421784147379769966856e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1926
y2[1] (analytic) = 0.80858853523151670701107199560471
y2[1] (numeric) = 0.80858853523151670701108063914929
absolute error = 8.64354458e-24
relative error = 1.0689669966103542156224797721223e-21 %
h = 0.0001
y1[1] (analytic) = 1.9815098833711169915599323194734
y1[1] (numeric) = 1.9815098833711169915598881432569
absolute error = 4.41762165e-23
relative error = 2.2294219610372862464810616741555e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1800.5MB, alloc=4.5MB, time=243.79
NO POLE
NO POLE
x[1] = 0.1927
y2[1] (analytic) = 0.80849038520040050333726475805624
y2[1] (numeric) = 0.80849038520040050333727341535745
absolute error = 8.65730121e-24
relative error = 1.0707982888199857614234868744320e-21 %
h = 0.0001
y1[1] (analytic) = 1.9814907373171226323754517778166
y1[1] (numeric) = 1.981490737317122632375407554759
absolute error = 4.42230576e-23
relative error = 2.2318074350363432212432137919176e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1928
y2[1] (analytic) = 0.80839223708438044606353903100376
y2[1] (numeric) = 0.80839223708438044606354770207106
absolute error = 8.67106730e-24
relative error = 1.0726311934010950941864987162303e-21 %
h = 0.0001
y1[1] (analytic) = 1.9814715814482209081988343873215
y1[1] (numeric) = 1.9814715814482209081987901174252
absolute error = 4.42698963e-23
relative error = 2.2341928450795116671860677989849e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1804.3MB, alloc=4.5MB, time=244.42
NO POLE
NO POLE
x[1] = 0.1929
y2[1] (analytic) = 0.80829409088443801634927748621797
y2[1] (numeric) = 0.80829409088443801634928617106081
absolute error = 8.68484284e-24
relative error = 1.0744657096895285713234333957528e-21 %
h = 0.0001
y1[1] (analytic) = 1.9814524157646033777189377575136
y1[1] (numeric) = 1.9814524157646033777188934407809
absolute error = 4.43167327e-23
relative error = 2.2365781962469710667349216576768e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.193
y2[1] (analytic) = 0.80819594660155467619308653584224
y2[1] (numeric) = 0.80819594660155467619309523447007
absolute error = 8.69862783e-24
relative error = 1.0763018382581018244808465781756e-21 %
h = 0.0001
y1[1] (analytic) = 1.9814332402664616977717774791618
y1[1] (numeric) = 1.981433240266461697771733115595
absolute error = 4.43635668e-23
relative error = 2.2389634885722427809811136934082e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1808.2MB, alloc=4.5MB, time=245.04
NO POLE
NO POLE
x[1] = 0.1931
y2[1] (analytic) = 0.80809780423671186842298171241472
y2[1] (numeric) = 0.808097804236711868422990424837
absolute error = 8.71242228e-24
relative error = 1.0781395809173508970212266402794e-21 %
h = 0.0001
y1[1] (analytic) = 1.9814140549539876233386105559198
y1[1] (numeric) = 1.9814140549539876233385661455213
absolute error = 4.44103985e-23
relative error = 2.2413487170419459760004861820634e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1932
y2[1] (analytic) = 0.80799966379089101668657324059638
y2[1] (numeric) = 0.80799966379089101668658196682256
absolute error = 8.72622618e-24
relative error = 1.0799789370034110528005103863895e-21 %
h = 0.0001
y1[1] (analytic) = 1.9813948598273730075440178545155
y1[1] (numeric) = 1.9813948598273730075439733972876
absolute error = 4.44572279e-23
relative error = 2.2437338867364019672176177746186e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1812.0MB, alloc=4.5MB, time=245.66
NO POLE
NO POLE
x[1] = 0.1933
y2[1] (analytic) = 0.80790152526507352544125180070307
y2[1] (numeric) = 0.8079015252650735254412605407426
absolute error = 8.74003953e-24
relative error = 1.0818199070898376919577782072822e-21 %
h = 0.0001
y1[1] (analytic) = 1.9813756548868098016539855735063
y1[1] (numeric) = 1.9813756548868098016539410694513
absolute error = 4.45040550e-23
relative error = 2.2461189976891275848734416142814e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1934
y2[1] (analytic) = 0.80780338866024077994437448413979
y2[1] (numeric) = 0.80780338866024077994438323800213
absolute error = 8.75386234e-24
relative error = 1.0836624929883579919237739984372e-21 %
h = 0.0001
y1[1] (analytic) = 1.9813564401324900550739857306214
y1[1] (numeric) = 1.9813564401324900550739411797415
absolute error = 4.45508799e-23
relative error = 2.2485040549806856427718420618647e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1815.8MB, alloc=4.5MB, time=246.28
NO POLE
NO POLE
x[1] = 0.1935
y2[1] (analytic) = 0.80770525397737414624345094083532
y2[1] (numeric) = 0.80770525397737414624345970852992
absolute error = 8.76769460e-24
relative error = 1.0855066940353968722741525394586e-21 %
h = 0.0001
y1[1] (analytic) = 1.981337215564605915347055668708
y1[1] (numeric) = 1.9813372155646059153470110710056
absolute error = 4.45977024e-23
relative error = 2.2508890485505440467883488731539e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1936
y2[1] (analytic) = 0.80760712121745497116632971877527
y2[1] (numeric) = 0.80760712121745497116633850031159
absolute error = 8.78153632e-24
relative error = 1.0873525120434763858972333828985e-21 %
h = 0.0001
y1[1] (analytic) = 1.9813179811833496281518765803031
y1[1] (numeric) = 1.9813179811833496281518319357806
absolute error = 4.46445225e-23
relative error = 2.2532739784320682717965908939910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1819.6MB, alloc=4.5MB, time=246.92
NO POLE
NO POLE
x[1] = 0.1937
y2[1] (analytic) = 0.80750899038146458231138479573182
y2[1] (numeric) = 0.80750899038146458231139359111929
absolute error = 8.79538747e-24
relative error = 1.0891999438724623961859636617722e-21 %
h = 0.0001
y1[1] (analytic) = 1.9812987369889135373008510508482
y1[1] (numeric) = 1.9812987369889135373008063595079
absolute error = 4.46913403e-23
relative error = 2.2556588497058166134081923464530e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1938
y2[1] (analytic) = 0.80741086147038428803770230328808
y2[1] (numeric) = 0.80741086147038428803771111253617
absolute error = 8.80924809e-24
relative error = 1.0910489950503498308143152542606e-21 %
h = 0.0001
y1[1] (analytic) = 1.9812794829814900847381796205666
y1[1] (numeric) = 1.9812794829814900847381348824108
absolute error = 4.47381558e-23
relative error = 2.2580436624052984234373221023435e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1823.4MB, alloc=4.5MB, time=247.58
NO POLE
NO POLE
x[1] = 0.1939
y2[1] (analytic) = 0.80731273448519537745526744325549
y2[1] (numeric) = 0.80731273448519537745527626637365
absolute error = 8.82311816e-24
relative error = 1.0928996636757251188882172513536e-21 %
h = 0.0001
y1[1] (analytic) = 1.9812602191612718105379363650231
y1[1] (numeric) = 1.9812602191612718105378915800542
absolute error = 4.47849689e-23
relative error = 2.2604284115167289983745974693021e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.194
y2[1] (analytic) = 0.8072146094268791204151515965821
y2[1] (numeric) = 0.80721460942687912041516043357977
absolute error = 8.83699767e-24
relative error = 1.0947519490850459210430404543651e-21 %
h = 0.0001
y1[1] (analytic) = 1.9812409455284513529021434943852
y1[1] (numeric) = 1.9812409455284513529020986626054
absolute error = 4.48317798e-23
relative error = 2.2628131071681507935685670468301e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1827.2MB, alloc=4.5MB, time=248.23
NO POLE
NO POLE
x[1] = 0.1941
y2[1] (analytic) = 0.80711648629641676749969962485003
y2[1] (numeric) = 0.80711648629641676749970847573667
absolute error = 8.85088664e-24
relative error = 1.0966058543313506762366573092015e-21 %
h = 0.0001
y1[1] (analytic) = 1.9812216620832214481588449714039
y1[1] (numeric) = 1.9812216620832214481588000928156
absolute error = 4.48785883e-23
relative error = 2.2651977392984344241282793489707e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1942
y2[1] (analytic) = 0.80701836509478955001271736446023
y2[1] (numeric) = 0.80701836509478955001272622924528
absolute error = 8.86478505e-24
relative error = 1.0984613775126137808762625701878e-21 %
h = 0.0001
y1[1] (analytic) = 1.9812023688257749307601791481354
y1[1] (numeric) = 1.9812023688257749307601342227409
absolute error = 4.49253945e-23
relative error = 2.2675823129883758409171339422397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1831.0MB, alloc=4.5MB, time=248.88
NO POLE
NO POLE
x[1] = 0.1943
y2[1] (analytic) = 0.80692024582297867996965931360256
y2[1] (numeric) = 0.80692024582297867996966819229547
absolute error = 8.87869291e-24
relative error = 1.1003185204436918254530618528823e-21 %
h = 0.0001
y1[1] (analytic) = 1.9811830657563047332804504214209
y1[1] (numeric) = 1.9811830657563047332804054492226
absolute error = 4.49721983e-23
relative error = 2.2699668232239878081161119502114e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1944
y2[1] (analytic) = 0.80682212848196535008781651210945
y2[1] (numeric) = 0.80682212848196535008782540471968
absolute error = 8.89261023e-24
relative error = 1.1021772849402919933362475594370e-21 %
h = 0.0001
y1[1] (analytic) = 1.9811637528750038864141999071457
y1[1] (numeric) = 1.9811637528750038864141548881459
absolute error = 4.50189998e-23
relative error = 2.2723512750861614810128759271521e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1834.9MB, alloc=4.5MB, time=249.51
NO POLE
NO POLE
x[1] = 0.1945
y2[1] (analytic) = 0.80672401307273073377650461429116
y2[1] (numeric) = 0.80672401307273073377651352082815
absolute error = 8.90653699e-24
relative error = 1.1040376691002286183458860021718e-21 %
h = 0.0001
y1[1] (analytic) = 1.9811444301820655189742751332948
y1[1] (numeric) = 1.9811444301820655189742300674957
absolute error = 4.50657991e-23
relative error = 2.2747356736559833091252847443147e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1838.7MB, alloc=4.5MB, time=250.09
x[1] = 0.1946
y2[1] (analytic) = 0.80662589959625598512725215485079
y2[1] (numeric) = 0.80662589959625598512726107532399
absolute error = 8.92047320e-24
relative error = 1.1058996747395544511102528157638e-21 %
h = 0.0001
y1[1] (analytic) = 1.9811250976776828578898987518262
y1[1] (numeric) = 1.9811250976776828578898536392303
absolute error = 4.51125959e-23
relative error = 2.2771200038241879927333872476897e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1947
y2[1] (analytic) = 0.80652778805352223890398900797719
y2[1] (numeric) = 0.80652778805352223890399794239604
absolute error = 8.93441885e-24
relative error = 1.1077633011954078238707230385254e-21 %
h = 0.0001
y1[1] (analytic) = 1.9811057553620492282047362693806
y1[1] (numeric) = 1.9811057553620492282046911099902
absolute error = 4.51593904e-23
relative error = 2.2795042757193480750281368413494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1842.5MB, alloc=4.5MB, time=250.68
x[1] = 0.1948
y2[1] (analytic) = 0.8064296784455106105332350397138
y2[1] (numeric) = 0.80642967844551061053324398808776
absolute error = 8.94837396e-24
relative error = 1.1096285515246733101322364016623e-21 %
h = 0.0001
y1[1] (analytic) = 1.9810864032353580530749627968462
y1[1] (numeric) = 1.9810864032353580530749175906636
absolute error = 4.52061826e-23
relative error = 2.2818884893749579522032295560397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1949
y2[1] (analytic) = 0.80633157077320219609428895370167
y2[1] (numeric) = 0.80633157077320219609429791604019
absolute error = 8.96233852e-24
relative error = 1.1114954250651370333805494705803e-21 %
h = 0.0001
y1[1] (analytic) = 1.9810670412978028537673288177981
y1[1] (numeric) = 1.9810670412978028537672835648257
absolute error = 4.52529724e-23
relative error = 2.2842726397767258039461076210887e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1846.3MB, alloc=4.5MB, time=251.28
NO POLE
NO POLE
x[1] = 0.195
y2[1] (analytic) = 0.80623346503757807230941733039465
y2[1] (numeric) = 0.80623346503757807230942630670717
absolute error = 8.97631252e-24
relative error = 1.1133639211542303445121444031948e-21 %
h = 0.0001
y1[1] (analytic) = 1.9810476695495772496572249758333
y1[1] (numeric) = 1.9810476695495772496571796760734
absolute error = 4.52997599e-23
relative error = 2.2866567320058291249093906897485e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1951
y2[1] (analytic) = 0.80613536123961929653404385984484
y2[1] (numeric) = 0.80613536123961929653405285014081
absolute error = 8.99029597e-24
relative error = 1.1152340416100025210016715755353e-21 %
h = 0.0001
y1[1] (analytic) = 1.9810282879908749582267458808176
y1[1] (numeric) = 1.9810282879908749582267005342725
absolute error = 4.53465451e-23
relative error = 2.2890407660957578373617375632104e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1850.1MB, alloc=4.5MB, time=251.85
NO POLE
NO POLE
x[1] = 0.1952
y2[1] (analytic) = 0.8060372593803069067469387681566
y2[1] (numeric) = 0.80603725938030690674694777244547
absolute error = 9.00428887e-24
relative error = 1.1171057870107180164891722726929e-21 %
h = 0.0001
y1[1] (analytic) = 1.9810088966218897950627529340667
y1[1] (numeric) = 1.9810088966218897950627075407387
absolute error = 4.53933280e-23
relative error = 2.2914247420800004003344703060221e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1953
y2[1] (analytic) = 0.80593915946062192154040843770698
y2[1] (numeric) = 0.80593915946062192154041745599819
absolute error = 9.01829121e-24
relative error = 1.1189791566941018567381672733486e-21 %
h = 0.0001
y1[1] (analytic) = 1.9809894954428156738549361724789
y1[1] (numeric) = 1.9809894954428156738548907323705
absolute error = 4.54401084e-23
relative error = 2.2938086498960791192898205435407e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1853.9MB, alloc=4.5MB, time=252.42
NO POLE
NO POLE
x[1] = 0.1954
y2[1] (analytic) = 0.80584106148154534011048522123086
y2[1] (numeric) = 0.80584106148154534011049425353385
absolute error = 9.03230299e-24
relative error = 1.1208541512384635194552649440870e-21 %
h = 0.0001
y1[1] (analytic) = 1.9809700844538466063938751316403
y1[1] (numeric) = 1.9809700844538466063938296447538
absolute error = 4.54868865e-23
relative error = 2.2961924996732463660951620431768e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1955
y2[1] (analytic) = 0.80574296544405814224711744986875
y2[1] (numeric) = 0.80574296544405814224712649619298
absolute error = 9.04632423e-24
relative error = 1.1227307737045426867426536598782e-21 %
h = 0.0001
y1[1] (analytic) = 1.98095066365517670256909872792
y1[1] (numeric) = 1.9809506636551767025690531942578
absolute error = 4.55336622e-23
relative error = 2.2985762863969047613150735167289e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1857.8MB, alloc=4.5MB, time=252.98
NO POLE
NO POLE
x[1] = 0.1956
y2[1] (analytic) = 0.80564487134914128832435963527556
y2[1] (numeric) = 0.80564487134914128832436869563047
absolute error = 9.06035491e-24
relative error = 1.1246090221895703685694227538700e-21 %
h = 0.0001
y1[1] (analytic) = 1.9809312330470001703671441595771
y1[1] (numeric) = 1.9809312330470001703670985791414
absolute error = 4.55804357e-23
relative error = 2.3009600201966498485930884360235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1957
y2[1] (analytic) = 0.80554677919777571929056286588816
y2[1] (numeric) = 0.80554677919777571929057194028319
absolute error = 9.07439503e-24
relative error = 1.1264888972726037652855884722442e-21 %
h = 0.0001
y1[1] (analytic) = 1.9809117926295113158696148268962
y1[1] (numeric) = 1.9809117926295113158695691996895
absolute error = 4.56272067e-23
relative error = 2.3033436859615701077871937577078e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1861.6MB, alloc=4.5MB, time=253.55
NO POLE
NO POLE
x[1] = 0.1958
y2[1] (analytic) = 0.80544868899094235665856539745007
y2[1] (numeric) = 0.80544868899094235665857448589467
absolute error = 9.08844460e-24
relative error = 1.1283704007744935030209565403784e-21 %
h = 0.0001
y1[1] (analytic) = 1.9808923424029045432512372713737
y1[1] (numeric) = 1.9808923424029045432511915973983
absolute error = 4.56739754e-23
relative error = 2.3057272938213075275854717465025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1959
y2[1] (analytic) = 0.80535060072962210249588343789127
y2[1] (numeric) = 0.80535060072962210249589254039488
absolute error = 9.10250361e-24
relative error = 1.1302535320335541335714903439312e-21 %
h = 0.0001
y1[1] (analytic) = 1.9808728823673743547779171339717
y1[1] (numeric) = 1.9808728823673743547778714132299
absolute error = 4.57207418e-23
relative error = 2.3081108438093400422448863784833e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1865.4MB, alloc=4.5MB, time=254.14
NO POLE
NO POLE
x[1] = 0.196
y2[1] (analytic) = 0.80525251441479583941490212666118
y2[1] (numeric) = 0.80525251441479583941491124323325
absolute error = 9.11657207e-24
relative error = 1.1321382928714380225761549884489e-21 %
h = 0.0001
y1[1] (analytic) = 1.9808534125231153508047941324606
y1[1] (numeric) = 1.9808534125231153508047483649548
absolute error = 4.57675058e-23
relative error = 2.3104943309108149934888270850480e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1961
y2[1] (analytic) = 0.805154430047444430563066708613
y2[1] (numeric) = 0.80515443004744443056307583926297
absolute error = 9.13064997e-24
relative error = 1.1340246826266569069095425764640e-21 %
h = 0.0001
y1[1] (analytic) = 1.9808339328703222297742960578696
y1[1] (numeric) = 1.9808339328703222297742502436022
absolute error = 4.58142674e-23
relative error = 2.3128777551590584701951682108626e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1869.2MB, alloc=4.5MB, time=254.71
NO POLE
NO POLE
x[1] = 0.1962
y2[1] (analytic) = 0.80505634762854871961307390253742
y2[1] (numeric) = 0.80505634762854871961308304727474
absolute error = 9.14473732e-24
relative error = 1.1359127031216655010865362624126e-21 %
h = 0.0001
y1[1] (analytic) = 1.9808144434091897882141917900638
y1[1] (numeric) = 1.9808144434091897882141459290371
absolute error = 4.58610267e-23
relative error = 2.3152611216358234076028924040561e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1963
y2[1] (analytic) = 0.80495826715908953075306346444386
y2[1] (numeric) = 0.80495826715908953075307262327796
absolute error = 9.15883410e-24
relative error = 1.1378023524528726377544499005925e-21 %
h = 0.0001
y1[1] (analytic) = 1.9807949441399129207356433324682
y1[1] (numeric) = 1.9807949441399129207355974246846
absolute error = 4.59077836e-23
relative error = 2.3176444253261036187428511640809e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1873.0MB, alloc=4.5MB, time=255.28
NO POLE
NO POLE
x[1] = 0.1964
y2[1] (analytic) = 0.80486018864004766867680994568719
y2[1] (numeric) = 0.80486018864004766867681911862752
absolute error = 9.17294033e-24
relative error = 1.1396936336855336504155327352348e-21 %
h = 0.0001
y1[1] (analytic) = 1.9807754350626866200312568659576
y1[1] (numeric) = 1.9807754350626866200312109114195
absolute error = 4.59545381e-23
relative error = 2.3200276662632204479166281088411e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1965
y2[1] (analytic) = 0.80476211207240391857391464603821
y2[1] (numeric) = 0.80476211207240391857392383309421
absolute error = 9.18705600e-24
relative error = 1.1415865461585555616550440803492e-21 %
h = 0.0001
y1[1] (analytic) = 1.9807559161777059768731328219326
y1[1] (numeric) = 1.9807559161777059768730868206422
absolute error = 4.60012904e-23
relative error = 2.3224108545776488850262314167723e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1876.8MB, alloc=4.5MB, time=255.84
NO POLE
NO POLE
x[1] = 0.1966
y2[1] (analytic) = 0.80466403745713904611999776179577
y2[1] (numeric) = 0.80466403745713904612000696297689
absolute error = 9.20118112e-24
relative error = 1.1434810916959995125093891690548e-21 %
h = 0.0001
y1[1] (analytic) = 1.9807363874851661801109149745994
y1[1] (numeric) = 1.9807363874851661801108689265592
absolute error = 4.60480402e-23
relative error = 2.3247939751571235145528474708396e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1967
y2[1] (analytic) = 0.80456596479523379746689072903878
y2[1] (numeric) = 0.80456596479523379746689994435446
absolute error = 9.21531568e-24
relative error = 1.1453772696369707286478413936912e-21 %
h = 0.0001
y1[1] (analytic) = 1.9807168489852625166698385524758
y1[1] (numeric) = 1.9807168489852625166697924576882
absolute error = 4.60947876e-23
relative error = 2.3271770330834888216429780529310e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1880.6MB, alloc=4.5MB, time=256.41
NO POLE
NO POLE
x[1] = 0.1968
y2[1] (analytic) = 0.80446789408766889923282876211604
y2[1] (numeric) = 0.80446789408766889923283799157572
absolute error = 9.22945968e-24
relative error = 1.1472750805632768441716862132787e-21 %
h = 0.0001
y1[1] (analytic) = 1.9806973006781903715487773691401
y1[1] (numeric) = 1.9806973006781903715487312276074
absolute error = 4.61415327e-23
relative error = 2.3295600334387868430865064130156e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1969
y2[1] (analytic) = 0.80436982533542505849264358747206
y2[1] (numeric) = 0.80436982533542505849265283108518
absolute error = 9.24361312e-24
relative error = 1.1491745250569762083187392582317e-21 %
h = 0.0001
y1[1] (analytic) = 1.9806777425641452278182899732442
y1[1] (numeric) = 1.9806777425641452278182437849687
absolute error = 4.61882755e-23
relative error = 2.3319429762564805448298548190420e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1884.5MB, alloc=4.5MB, time=256.97
NO POLE
NO POLE
x[1] = 0.197
y2[1] (analytic) = 0.80427175853948296276795637290694
y2[1] (numeric) = 0.80427175853948296276796563068294
absolute error = 9.25777600e-24
relative error = 1.1510756037003780045025602752197e-21 %
h = 0.0001
y1[1] (analytic) = 1.980658174643322666618664817809
y1[1] (numeric) = 1.9806581746433226666186185827932
absolute error = 4.62350158e-23
relative error = 2.3343258514723779230337321858276e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1971
y2[1] (analytic) = 0.80417369370082328001737085236831
y2[1] (numeric) = 0.80417369370082328001738012431662
absolute error = 9.27194831e-24
relative error = 1.1529783158325299195149650773259e-21 %
h = 0.0001
y1[1] (analytic) = 1.9806385969159183671579644488242
y1[1] (numeric) = 1.9806385969159183671579181670704
absolute error = 4.62817538e-23
relative error = 2.3367086692173929600463795945544e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1888.3MB, alloc=4.5MB, time=257.53
NO POLE
NO POLE
x[1] = 0.1972
y2[1] (analytic) = 0.80407563082042665862666664637345
y2[1] (numeric) = 0.80407563082042665862667593250352
absolute error = 9.28613007e-24
relative error = 1.1548826645231164068974929587315e-21 %
h = 0.0001
y1[1] (analytic) = 1.9806190093821281067100687131685
y1[1] (numeric) = 1.980619009382128106710022384679
absolute error = 4.63284895e-23
relative error = 2.3390914295249841362165123454095e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1973
y2[1] (analytic) = 0.80397756989927372739899277815972
y2[1] (numeric) = 0.80397756989927372739900207848099
absolute error = 9.30032127e-24
relative error = 1.1567886491118390390072573662998e-21 %
h = 0.0001
y1[1] (analytic) = 1.9805994120421477606127169858724
y1[1] (numeric) = 1.9805994120421477606126706106497
absolute error = 4.63752227e-23
relative error = 2.3414741223306553769749053776837e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1892.1MB, alloc=4.5MB, time=258.12
NO POLE
NO POLE
x[1] = 0.1974
y2[1] (analytic) = 0.80387951093834509554506138566118
y2[1] (numeric) = 0.80387951093834509554507070018309
absolute error = 9.31452191e-24
relative error = 1.1586962701820115276334809568984e-21 %
h = 0.0001
y1[1] (analytic) = 1.9805798048961733022655494167433
y1[1] (numeric) = 1.9805798048961733022655029947897
absolute error = 4.64219536e-23
relative error = 2.3438567577656154618426900078315e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1975
y2[1] (analytic) = 0.80378145393862135267334162940968
y2[1] (numeric) = 0.80378145393862135267335095814167
absolute error = 9.32873199e-24
relative error = 1.1606055283171990149053020737436e-21 %
h = 0.0001
y1[1] (analytic) = 1.9805601879444008031281471963696
y1[1] (numeric) = 1.9805601879444008031281007276875
absolute error = 4.64686821e-23
relative error = 2.3462393308142418454300593113375e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1895.9MB, alloc=4.5MB, time=258.71
NO POLE
NO POLE
x[1] = 0.1976
y2[1] (analytic) = 0.80368339890108306878025379645833
y2[1] (numeric) = 0.80368339890108306878026313940984
absolute error = 9.34295151e-24
relative error = 1.1625164241012181927185054468646e-21 %
h = 0.0001
y1[1] (analytic) = 1.9805405611870264327180718415273
y1[1] (numeric) = 1.9805405611870264327180253261191
absolute error = 4.65154082e-23
relative error = 2.3486218415098369879730357536735e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1977
y2[1] (analytic) = 0.80358534582671079424036360042546
y2[1] (numeric) = 0.80358534582671079424037295760592
absolute error = 9.35718046e-24
relative error = 1.1644289568737145302549704492803e-21 %
h = 0.0001
y1[1] (analytic) = 1.9805209246242464586089035000058
y1[1] (numeric) = 1.9805209246242464586088569378738
absolute error = 4.65621320e-23
relative error = 2.3510042949348784030885502891545e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1899.7MB, alloc=4.5MB, time=259.29
NO POLE
NO POLE
x[1] = 0.1978
y2[1] (analytic) = 0.80348729471648505979657667775713
y2[1] (numeric) = 0.80348729471648505979658604917599
absolute error = 9.37141886e-24
relative error = 1.1663431297077021020920471098834e-21 %
h = 0.0001
y1[1] (analytic) = 1.9805012782562572464282782748736
y1[1] (numeric) = 1.9805012782562572464282316660203
absolute error = 4.66088533e-23
relative error = 2.3533866810243621611738803966636e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1979
y2[1] (analytic) = 0.80338924557138637655033328030629
y2[1] (numeric) = 0.80338924557138637655034266597298
absolute error = 9.38566669e-24
relative error = 1.1682589406987552553079143496335e-21 %
h = 0.0001
y1[1] (analytic) = 1.9804816220832552598559245682038
y1[1] (numeric) = 1.9804816220832552598558779126316
absolute error = 4.66555722e-23
relative error = 2.3557690048607125319438023802854e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1903.5MB, alloc=4.5MB, time=259.88
NO POLE
NO POLE
x[1] = 0.198
y2[1] (analytic) = 0.80329119839239523595180316432647
y2[1] (numeric) = 0.80329119839239523595181256425043
absolute error = 9.39992396e-24
relative error = 1.1701763916761208663001171293331e-21 %
h = 0.0001
y1[1] (analytic) = 1.9804619561054370606216984442784
y1[1] (numeric) = 1.9804619561054370606216517419896
absolute error = 4.67022888e-23
relative error = 2.3581512715265525966149483587436e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1981
y2[1] (analytic) = 0.80319315318049210979008067597833
y2[1] (numeric) = 0.80319315318049210979009009016899
absolute error = 9.41419066e-24
relative error = 1.1720954819798445338366030292615e-21 %
h = 0.0001
y1[1] (analytic) = 1.9804422803229993085036180122911
y1[1] (numeric) = 1.9804422803229993085035712632881
absolute error = 4.67490030e-23
relative error = 2.3605334760059502060067291142889e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1907.3MB, alloc=4.5MB, time=260.43
NO POLE
NO POLE
x[1] = 0.1982
y2[1] (analytic) = 0.80309510993665745018338003344683
y2[1] (numeric) = 0.80309510993665745018338946191364
absolute error = 9.42846681e-24
relative error = 1.1740162146851637293174585324849e-21 %
h = 0.0001
y1[1] (analytic) = 1.9804225947361387613258968285692
y1[1] (numeric) = 1.9804225947361387613258500328544
absolute error = 4.67957148e-23
relative error = 2.3629156183321983568539916935467e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1983
y2[1] (analytic) = 0.8029970686618716895692308057673
y2[1] (numeric) = 0.80299706866187168956924024851969
absolute error = 9.44275239e-24
relative error = 1.1759385878874461095856462475104e-21 %
h = 0.0001
y1[1] (analytic) = 1.9804028993450522749569763183328
y1[1] (numeric) = 1.9804028993450522749569294759085
absolute error = 4.68424243e-23
relative error = 2.3652977035880660193006645223243e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1911.2MB, alloc=4.5MB, time=261.00
NO POLE
NO POLE
x[1] = 0.1984
y2[1] (analytic) = 0.8028990293571152406946735884583
y2[1] (numeric) = 0.8028990293571152406946830455057
absolute error = 9.45704740e-24
relative error = 1.1778626021720687786758639812042e-21 %
h = 0.0001
y1[1] (analytic) = 1.980383194149936803307557217012
y1[1] (numeric) = 1.9803831941499368033075103278807
absolute error = 4.68891313e-23
relative error = 2.3676797217079381412236853537947e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1985
y2[1] (analytic) = 0.80280099202336849660645587605935
y2[1] (numeric) = 0.80280099202336849660646534741121
absolute error = 9.47135186e-24
relative error = 1.1797882606159387033187173188232e-21 %
h = 0.0001
y1[1] (analytic) = 1.9803634791509893983286300311418
y1[1] (numeric) = 1.9803634791509893983285830953059
absolute error = 4.69358359e-23
relative error = 2.3700616777745303054394895991080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1915.0MB, alloc=4.5MB, time=261.56
NO POLE
NO POLE
x[1] = 0.1986
y2[1] (analytic) = 0.80270295666161183064122813167169
y2[1] (numeric) = 0.80270295666161183064123761733744
absolute error = 9.48566575e-24
relative error = 1.1817155613142690409896036226004e-21 %
h = 0.0001
y1[1] (analytic) = 1.9803437543484072100095045188536
y1[1] (numeric) = 1.9803437543484072100094575363155
absolute error = 4.69825381e-23
relative error = 2.3724435718211291685861609421703e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1987
y2[1] (analytic) = 0.8026049232728255964157400535999
y2[1] (numeric) = 0.80260492327282559641574955358897
absolute error = 9.49998907e-24
relative error = 1.1836445048531947293067050195280e-21 %
h = 0.0001
y1[1] (analytic) = 1.980324019742387486375838189984
y1[1] (numeric) = 1.980324019742387486375791160746
absolute error = 4.70292380e-23
relative error = 2.3748254089306984939834064162846e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1918.8MB, alloc=4.5MB, time=262.13
NO POLE
NO POLE
x[1] = 0.1988
y2[1] (analytic) = 0.80250689185799012781703703919257
y2[1] (numeric) = 0.8025068918579901278170465535144
absolute error = 9.51432183e-24
relative error = 1.1855750930651987066417534084823e-21 %
h = 0.0001
y1[1] (analytic) = 1.9803042753331275734876638258194
y1[1] (numeric) = 1.980304275333127573487616749884
absolute error = 4.70759354e-23
relative error = 2.3772071790372147435625155271164e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1989
y2[1] (analytic) = 0.80240886241808573899265684598005
y2[1] (numeric) = 0.80240886241808573899266637464407
absolute error = 9.52866402e-24
relative error = 1.1875073252911308478874504485529e-21 %
h = 0.0001
y1[1] (analytic) = 1.9802845211208249154374160184979
y1[1] (numeric) = 1.9802845211208249154373688958674
absolute error = 4.71226305e-23
relative error = 2.3795888922733676073183101465862e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1922.6MB, alloc=4.5MB, time=262.69
NO POLE
NO POLE
x[1] = 0.199
y2[1] (analytic) = 0.8023108349540927243408264502072
y2[1] (numeric) = 0.80231083495409272434083599322285
absolute error = 9.54301565e-24
relative error = 1.1894412033642846231825141931009e-21 %
h = 0.0001
y1[1] (analytic) = 1.9802647571056770543479567300861
y1[1] (numeric) = 1.9802647571056770543479095607629
absolute error = 4.71693232e-23
relative error = 2.3819705436227588074003913004856e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1991
y2[1] (analytic) = 0.80221280946699135850065910285933
y2[1] (numeric) = 0.80221280946699135850066866023604
absolute error = 9.55737671e-24
relative error = 1.1913767266257118115238053750647e-21 %
h = 0.0001
y1[1] (analytic) = 1.9802449832878816303705998713523
y1[1] (numeric) = 1.9802449832878816303705526553389
absolute error = 4.72160134e-23
relative error = 2.3843521280687869426072664217014e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1926.4MB, alloc=4.5MB, time=263.26
NO POLE
NO POLE
x[1] = 0.1992
y2[1] (analytic) = 0.80211478595776189634235158327921
y2[1] (numeric) = 0.80211478595776189634236115502641
absolute error = 9.57174720e-24
relative error = 1.1933138956628126738223700181487e-21 %
h = 0.0001
y1[1] (analytic) = 1.9802251996676363816831349002554
y1[1] (numeric) = 1.9802251996676363816830876375541
absolute error = 4.72627013e-23
relative error = 2.3867336557444392858862016917721e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1993
y2[1] (analytic) = 0.80201676442738457295738165047327
y2[1] (numeric) = 0.80201676442738457295739123660039
absolute error = 9.58612712e-24
relative error = 1.1952527110632408557810197202670e-21 %
h = 0.0001
y1[1] (analytic) = 1.9802054062451391444878494401679
y1[1] (numeric) = 1.9802054062451391444878021307811
absolute error = 4.73093868e-23
relative error = 2.3891151216331617079727649134135e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1930.2MB, alloc=4.5MB, time=263.82
NO POLE
NO POLE
x[1] = 0.1994
y2[1] (analytic) = 0.80191874487683960364870569220501
y2[1] (numeric) = 0.80191874487683960364871529272148
absolute error = 9.60051647e-24
relative error = 1.1971931734149035083932890676439e-21 %
h = 0.0001
y1[1] (analytic) = 1.9801856030205878530095509178552
y1[1] (numeric) = 1.9801856030205878530095035617854
absolute error = 4.73560698e-23
relative error = 2.3914965207181966473263977801880e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1934.0MB, alloc=4.5MB, time=264.39
x[1] = 0.1995
y2[1] (analytic) = 0.80182072730710718392095657197357
y2[1] (numeric) = 0.80182072730710718392096618688884
absolute error = 9.61491527e-24
relative error = 1.1991352858002845556742800281406e-21 %
h = 0.0001
y1[1] (analytic) = 1.9801657899941805394935872212292
y1[1] (numeric) = 1.9801657899941805394935398184787
absolute error = 4.74027505e-23
relative error = 2.3938778631328294373178103012800e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1996
y2[1] (analytic) = 0.80172271171916748947064167397563
y2[1] (numeric) = 0.80172271171916748947065130329912
absolute error = 9.62932349e-24
relative error = 1.2010790450667712199854775625014e-21 %
h = 0.0001
y1[1] (analytic) = 1.9801459671661153342038663768962
y1[1] (numeric) = 1.9801459671661153342038189274674
absolute error = 4.74494288e-23
relative error = 2.3962591438603498726205608365586e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=1937.9MB, alloc=4.5MB, time=264.96
x[1] = 0.1997
y2[1] (analytic) = 0.80162469811400067617634114614844
y2[1] (numeric) = 0.80162469811400067617635078988958
absolute error = 9.64374114e-24
relative error = 1.2030244530500411289668402140156e-21 %
h = 0.0001
y1[1] (analytic) = 1.9801261345365904654208752475195
y1[1] (numeric) = 1.9801261345365904654208277514148
absolute error = 4.74961047e-23
relative error = 2.3986403629340273387230255855670e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1998
y2[1] (analytic) = 0.80152668649258688008890634139222
y2[1] (numeric) = 0.80152668649258688008891599956044
absolute error = 9.65816822e-24
relative error = 1.2049715103390167637239296878800e-21 %
h = 0.0001
y1[1] (analytic) = 1.9801062921058042594396972490164
y1[1] (numeric) = 1.9801062921058042594396497062383
absolute error = 4.75427781e-23
relative error = 2.4010215153368957107838936450576e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=1941.7MB, alloc=4.5MB, time=265.53
NO POLE
NO POLE
x[1] = 0.1999
y2[1] (analytic) = 0.8014286768559062174216584570698
y2[1] (numeric) = 0.80142867685590621742166812967454
absolute error = 9.67260474e-24
relative error = 1.2069202187706463860326050322573e-21 %
h = 0.0001
y1[1] (analytic) = 1.9800864398739551405680290876088
y1[1] (numeric) = 1.9800864398739551405679814981597
absolute error = 4.75894491e-23
relative error = 2.4034026061523539061511405518448e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.2
y2[1] (analytic) = 0.80133066920493878454058737288161
y2[1] (numeric) = 0.80133066920493878454059705993229
absolute error = 9.68705068e-24
relative error = 1.2088705764389700818972626294584e-21 %
h = 0.0001
y1[1] (analytic) = 1.9800665778412416311241965167482
y1[1] (numeric) = 1.9800665778412416311241488806304
absolute error = 4.76361178e-23
relative error = 2.4057836404640017547067335902454e-21 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y2 , x , 1 ) = m1 * y1 + 1.0;
diff ( y1 , x , 1 ) = y2 - 1.0;
Iterations = 1000
Total Elapsed Time = 4 Minutes 25 Seconds
Elapsed Time(since restart) = 4 Minutes 25 Seconds
Expected Time Remaining = 13 Minutes 16 Seconds
Optimized Time Remaining = 13 Minutes 16 Seconds
Time to Timeout = 10 Minutes 34 Seconds
Percent Done = 25.02 %
> quit
memory used=1943.9MB, alloc=4.5MB, time=265.84