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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cos $eq_no = 1
> array_tmp1_g[1] := sin(array_x[1]);
> array_tmp1[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp3[1] := sin(array_x[1]);
> array_tmp3_g[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre cos $eq_no = 1
> array_tmp1_g[2] := (att(1,array_tmp1,array_x,1));
> array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp3[2] := att(1,array_tmp3_g,array_x,1);
> array_tmp3_g[2] := -att(1,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp2[2] + array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre cos $eq_no = 1
> array_tmp1_g[3] := (att(2,array_tmp1,array_x,1));
> array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp3[3] := att(2,array_tmp3_g,array_x,1);
> array_tmp3_g[3] := -att(2,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp2[3] + array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre cos $eq_no = 1
> array_tmp1_g[4] := (att(3,array_tmp1,array_x,1));
> array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp3[4] := att(3,array_tmp3_g,array_x,1);
> array_tmp3_g[4] := -att(3,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp2[4] + array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre cos $eq_no = 1
> array_tmp1_g[5] := (att(4,array_tmp1,array_x,1));
> array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1));
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp3[5] := att(4,array_tmp3_g,array_x,1);
> array_tmp3_g[5] := -att(4,array_tmp3,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp2[5] + array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit cos $eq_no = 1
> array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1));
> array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1));
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit sin $eq_no = 1
> array_tmp3[kkk] := att(kkk-1,array_tmp3_g,array_x,1);
> array_tmp3_g[kkk] := -att(kkk-1,array_tmp3,array_x,1);
> #emit add $eq_no = 1
> array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp4[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
array_tmp1_g[1] := sin(array_x[1]);
array_tmp1[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := sin(array_x[1]);
array_tmp3_g[1] := cos(array_x[1]);
array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
array_tmp3[2] := att(1, array_tmp3_g, array_x, 1);
array_tmp3_g[2] := -att(1, array_tmp3, array_x, 1);
array_tmp4[2] := array_tmp2[2] + array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
array_tmp3[3] := att(2, array_tmp3_g, array_x, 1);
array_tmp3_g[3] := -att(2, array_tmp3, array_x, 1);
array_tmp4[3] := array_tmp2[3] + array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
array_tmp3[4] := att(3, array_tmp3_g, array_x, 1);
array_tmp3_g[4] := -att(3, array_tmp3, array_x, 1);
array_tmp4[4] := array_tmp2[4] + array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
array_tmp3[5] := att(4, array_tmp3_g, array_x, 1);
array_tmp3_g[5] := -att(4, array_tmp3, array_x, 1);
array_tmp4[5] := array_tmp2[5] + array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
array_tmp3[kkk] := att(kkk - 1, array_tmp3_g, array_x, 1);
array_tmp3_g[kkk] := -att(kkk - 1, array_tmp3, array_x, 1);
array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp4[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 + sin(x) - cos(x);
> end;
exact_soln_y := proc(x) 2.0 + sin(x) - cos(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> INFO,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> ALWAYS,
> #Top Generate Globals Decl
> glob_start,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_dump_analytic,
> glob_initial_pass,
> glob_almost_1,
> glob_max_opt_iter,
> glob_normmax,
> glob_max_iter,
> glob_clock_sec,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_hmax,
> glob_optimal_done,
> days_in_year,
> glob_display_flag,
> glob_smallish_float,
> glob_last_good_h,
> glob_percent_done,
> glob_h,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_small_float,
> glob_log10_relerr,
> sec_in_min,
> glob_log10normmin,
> glob_subiter_method,
> glob_curr_iter_when_opt,
> glob_abserr,
> glob_disp_incr,
> years_in_century,
> min_in_hour,
> glob_warned,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_look_poles,
> glob_not_yet_finished,
> glob_html_log,
> MAX_UNCHANGED,
> glob_large_float,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_iter,
> glob_current_iter,
> glob_warned2,
> glob_hmin,
> glob_reached_optimal_h,
> centuries_in_millinium,
> djd_debug,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y_init,
> array_tmp1_g,
> array_1st_rel_error,
> array_y,
> array_x,
> array_m1,
> array_norms,
> array_tmp3_g,
> array_last_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_type_pole,
> array_pole,
> array_y_set_initial,
> array_real_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_complex_pole,
> array_y_higher,
> array_poles,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> glob_iolevel := 5;
> DEBUGL := 3;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_start := 0;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_initial_pass := true;
> glob_almost_1 := 0.9990;
> glob_max_opt_iter := 10;
> glob_normmax := 0.0;
> glob_max_iter := 1000;
> glob_clock_sec := 0.0;
> glob_log10abserr := 0.0;
> glob_orig_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_hmax := 1.0;
> glob_optimal_done := false;
> days_in_year := 365.0;
> glob_display_flag := true;
> glob_smallish_float := 0.1e-100;
> glob_last_good_h := 0.1;
> glob_percent_done := 0.0;
> glob_h := 0.1;
> glob_not_yet_start_msg := true;
> hours_in_day := 24.0;
> glob_max_sec := 10000.0;
> glob_small_float := 0.1e-50;
> glob_log10_relerr := 0.1e-10;
> sec_in_min := 60.0;
> glob_log10normmin := 0.1;
> glob_subiter_method := 3;
> glob_curr_iter_when_opt := 0;
> glob_abserr := 0.1e-10;
> glob_disp_incr := 0.1;
> years_in_century := 100.0;
> min_in_hour := 60.0;
> glob_warned := false;
> glob_max_trunc_err := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_not_yet_finished := true;
> glob_html_log := true;
> MAX_UNCHANGED := 10;
> glob_large_float := 9.0e100;
> glob_hmin_init := 0.001;
> glob_clock_start_sec := 0.0;
> djd_debug2 := true;
> glob_optimal_expect_sec := 0.1;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_iter := 0;
> glob_current_iter := 0;
> glob_warned2 := false;
> glob_hmin := 0.00000000001;
> glob_reached_optimal_h := false;
> centuries_in_millinium := 10.0;
> djd_debug := true;
> glob_dump := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/addpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0 + sin(x) - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> max_terms := 30;
> Digits := 32;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_tmp3_g:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= 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_type_pole:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[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_m1[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_tmp3_g[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_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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3_g[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_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 10.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T11:49:31-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"add")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"add diffeq.mxt")
> ;
> logitem_str(html_log_file,"add maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global INFO, glob_iolevel, DEBUGL, glob_max_terms, DEBUGMASSIVE, ALWAYS,
glob_start, glob_unchanged_h_cnt, glob_no_eqs, glob_max_rel_trunc_err,
glob_relerr, glob_dump_analytic, glob_initial_pass, glob_almost_1,
glob_max_opt_iter, glob_normmax, glob_max_iter, glob_clock_sec,
glob_log10abserr, glob_orig_start_sec, glob_optimal_start, glob_hmax,
glob_optimal_done, days_in_year, glob_display_flag, glob_smallish_float,
glob_last_good_h, glob_percent_done, glob_h, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_small_float, glob_log10_relerr, sec_in_min,
glob_log10normmin, glob_subiter_method, glob_curr_iter_when_opt,
glob_abserr, glob_disp_incr, years_in_century, min_in_hour, glob_warned,
glob_max_trunc_err, glob_log10_abserr, glob_look_poles,
glob_not_yet_finished, glob_html_log, MAX_UNCHANGED, glob_large_float,
glob_hmin_init, glob_clock_start_sec, djd_debug2, glob_optimal_expect_sec,
glob_max_minutes, glob_log10relerr, glob_iter, glob_current_iter,
glob_warned2, glob_hmin, glob_reached_optimal_h, centuries_in_millinium,
djd_debug, glob_dump, glob_optimal_clock_start_sec, glob_max_hours,
array_const_0D0, array_const_1, array_y_init, array_tmp1_g,
array_1st_rel_error, array_y, array_x, array_m1, array_norms, array_tmp3_g,
array_last_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_type_pole, array_pole, array_y_set_initial,
array_real_pole, array_y_higher_work, array_y_higher_work2,
array_complex_pole, array_y_higher, array_poles, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
glob_iolevel := 5;
DEBUGL := 3;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_start := 0;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_initial_pass := true;
glob_almost_1 := 0.9990;
glob_max_opt_iter := 10;
glob_normmax := 0.;
glob_max_iter := 1000;
glob_clock_sec := 0.;
glob_log10abserr := 0.;
glob_orig_start_sec := 0.;
glob_optimal_start := 0.;
glob_hmax := 1.0;
glob_optimal_done := false;
days_in_year := 365.0;
glob_display_flag := true;
glob_smallish_float := 0.1*10^(-100);
glob_last_good_h := 0.1;
glob_percent_done := 0.;
glob_h := 0.1;
glob_not_yet_start_msg := true;
hours_in_day := 24.0;
glob_max_sec := 10000.0;
glob_small_float := 0.1*10^(-50);
glob_log10_relerr := 0.1*10^(-10);
sec_in_min := 60.0;
glob_log10normmin := 0.1;
glob_subiter_method := 3;
glob_curr_iter_when_opt := 0;
glob_abserr := 0.1*10^(-10);
glob_disp_incr := 0.1;
years_in_century := 100.0;
min_in_hour := 60.0;
glob_warned := false;
glob_max_trunc_err := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_not_yet_finished := true;
glob_html_log := true;
MAX_UNCHANGED := 10;
glob_large_float := 0.90*10^101;
glob_hmin_init := 0.001;
glob_clock_start_sec := 0.;
djd_debug2 := true;
glob_optimal_expect_sec := 0.1;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_iter := 0;
glob_current_iter := 0;
glob_warned2 := false;
glob_hmin := 0.1*10^(-10);
glob_reached_optimal_h := false;
centuries_in_millinium := 10.0;
djd_debug := true;
glob_dump := false;
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/addpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0 + sin(x) - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
max_terms := 30;
Digits := 32;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_tmp3_g := Array(1 .. max_terms + 1, []);
array_last_rel_error := 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_type_pole := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_m1[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_tmp3_g[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_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_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_tmp3_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp3_g[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_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_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T11:49:31-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "add");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"add diffeq.mxt");
logitem_str(html_log_file,
"add maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/addpostode.ode#################
diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
max_terms := 30;
Digits := 32;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 + sin(x) - cos(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0001
y[1] (analytic) = 1.0001000049998333291667500013888
y[1] (numeric) = 1.000100004999833329166750049999
absolute error = 4.86102e-26
relative error = 4.8605339223059099067186492115008e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0002
y[1] (analytic) = 1.000200019998666600002666755553
y[1] (numeric) = 1.0002000199986666000026668527684
absolute error = 9.72154e-26
relative error = 9.7195958864437536295280861070034e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0003
y[1] (analytic) = 1.0003000449954996625202510124566
y[1] (numeric) = 1.0003000449954996625202511582724
absolute error = 1.458158e-25
relative error = 1.4577206182236653150737335276307e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0004
y[1] (analytic) = 1.0004000799893322667520056885638
y[1] (numeric) = 1.0004000799893322667520058829752
absolute error = 1.944114e-25
relative error = 1.9433365099498302674058493001738e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0005
y[1] (analytic) = 1.0005001249791640627604383665053
y[1] (numeric) = 1.0005001249791640627604386095075
absolute error = 2.430022e-25
relative error = 2.4288072928032932292935385826422e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0006
y[1] (analytic) = 1.0006001799639946006480647944453
y[1] (numeric) = 1.0006001799639946006480650860333
absolute error = 2.915880e-25
relative error = 2.9141309969631670966814256530008e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0007
y[1] (analytic) = 1.0007002449428233305674133850473
y[1] (numeric) = 1.0007002449428233305674137252163
absolute error = 3.401690e-25
relative error = 3.3993096506080711554056021922066e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0008
y[1] (analytic) = 1.0008003199146496027310307139413
y[1] (numeric) = 1.0008003199146496027310311026863
absolute error = 3.887450e-25
relative error = 3.8843412843148671972292457803534e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0009
y[1] (analytic) = 1.0009004048784726674214880175891
y[1] (numeric) = 1.0009004048784726674214884549055
absolute error = 4.373164e-25
relative error = 4.3692299240612065274300422517635e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 1.0010004998332916750013886904514
y[1] (numeric) = 1.0010004998332916750013891763341
absolute error = 4.858827e-25
relative error = 4.8539706032206750234944115171851e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.23
NO POLE
x[1] = 0.0011
y[1] (analytic) = 1.0011006047781056759233767813522
y[1] (numeric) = 1.0011006047781056759233773157964
absolute error = 5.344442e-25
relative error = 5.3385663483687511820148092736736e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0012
y[1] (analytic) = 1.0012007197119136207401464889448
y[1] (numeric) = 1.0012007197119136207401470719457
absolute error = 5.830009e-25
relative error = 5.8230171884789814555834535821231e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0013
y[1] (analytic) = 1.0013008446337143601144526561763
y[1] (numeric) = 1.001300844633714360114453287729
absolute error = 6.315527e-25
relative error = 6.3073221538230915315739893883306e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0014
y[1] (analytic) = 1.0014009795425066448291222636518
y[1] (numeric) = 1.0014009795425066448291229437514
absolute error = 6.800996e-25
relative error = 6.7914812736722681801974191064948e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0015
y[1] (analytic) = 1.0015011244372891257970669217975
y[1] (numeric) = 1.0015011244372891257970676504391
absolute error = 7.286416e-25
relative error = 7.2754945772966554719040381186675e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0016
y[1] (analytic) = 1.0016012793170603540712963617235
y[1] (numeric) = 1.0016012793170603540712971389023
absolute error = 7.771788e-25
relative error = 7.7593630923666318426960461702743e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0017
y[1] (analytic) = 1.0017014441808187808549329246854
y[1] (numeric) = 1.0017014441808187808549337503965
absolute error = 8.257111e-25
relative error = 8.2430858495492947160031721845095e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0018
y[1] (analytic) = 1.0018016190275627575112270500446
y[1] (numeric) = 1.0018016190275627575112279242831
absolute error = 8.742385e-25
relative error = 8.7266628781116684412229736514124e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0019
y[1] (analytic) = 1.0019018038562905355735737616272
y[1] (numeric) = 1.0019018038562905355735746843883
absolute error = 9.227611e-25
relative error = 9.2100952054215263687533231570253e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 1.0020019986660002667555301523823
y[1] (numeric) = 1.0020019986660002667555311236612
absolute error = 9.712789e-25
relative error = 9.6933828604443605402676771631850e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0021
y[1] (analytic) = 1.0021022034556900029608338672377
y[1] (numeric) = 1.0021022034556900029608348870294
absolute error = 1.0197917e-24
relative error = 1.0176523876340245711104895044408e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0022
y[1] (analytic) = 1.0022024182243576962934225840542
y[1] (numeric) = 1.0022024182243576962934236523538
absolute error = 1.0682996e-24
relative error = 1.0659519280473792281987468207424e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0023
y[1] (analytic) = 1.0023026429710011990674544925777
y[1] (numeric) = 1.0023026429710011990674556093804
absolute error = 1.1168027e-24
relative error = 1.1142370099809380002244610889870e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0024
y[1] (analytic) = 1.0024028776946182638173297712897
y[1] (numeric) = 1.0024028776946182638173309365906
absolute error = 1.1653009e-24
relative error = 1.1625075365705490021980496132884e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0025
y[1] (analytic) = 1.0025031223942065433077130620547
y[1] (numeric) = 1.0025031223942065433077142758489
absolute error = 1.2137942e-24
relative error = 1.2107635107421731317732662563235e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=0.49
NO POLE
x[1] = 0.0026
y[1] (analytic) = 1.0026033770687635905435569424651
y[1] (numeric) = 1.0026033770687635905435582047478
absolute error = 1.2622827e-24
relative error = 1.2590050351620013476873054939724e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0027
y[1] (analytic) = 1.0027036417172868587801263957835
y[1] (numeric) = 1.0027036417172868587801277065498
absolute error = 1.3107663e-24
relative error = 1.3072320129954925093382021648242e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0028
y[1] (analytic) = 1.0028039163387737015330242783816
y[1] (numeric) = 1.0028039163387737015330256376267
absolute error = 1.3592451e-24
relative error = 1.3554445468886771216276043790605e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0029
y[1] (analytic) = 1.0029042009322213725882177845759
y[1] (numeric) = 1.0029042009322213725882191922949
absolute error = 1.4077190e-24
relative error = 1.4036425400267487410193833735232e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 1.0030044954966270260120659087596
y[1] (numeric) = 1.0030044954966270260120673649476
absolute error = 1.4561880e-24
relative error = 1.4518259953351295535816189303175e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0031
y[1] (analytic) = 1.0031048000309877161613479047306
y[1] (numeric) = 1.0031048000309877161613494093827
absolute error = 1.5046521e-24
relative error = 1.4999949157391317271212447784043e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0032
y[1] (analytic) = 1.0032051145343003976932927421156
y[1] (numeric) = 1.0032051145343003976932942952269
absolute error = 1.5531113e-24
relative error = 1.5481493041639570540472776304482e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0033
y[1] (analytic) = 1.003305439005561925575609559789
y[1] (numeric) = 1.0033054390055619255756111613546
absolute error = 1.6015656e-24
relative error = 1.5962891635346965944986449733833e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0034
y[1] (analytic) = 1.0034057734437690550965191161878
y[1] (numeric) = 1.003405773443769055096520766203
absolute error = 1.6500152e-24
relative error = 1.6444146960974876154374968698825e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0035
y[1] (analytic) = 1.0035061178479184418747862364213
y[1] (numeric) = 1.003506117847918441874787934881
absolute error = 1.6984597e-24
relative error = 1.6925255061149531687624729494435e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0036
y[1] (analytic) = 1.0036064722170066418697532560743
y[1] (numeric) = 1.0036064722170066418697550029737
absolute error = 1.7468994e-24
relative error = 1.7406218954935889330274981202086e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0037
y[1] (analytic) = 1.0037068365500301113913744616058
y[1] (numeric) = 1.0037068365500301113913762569401
absolute error = 1.7953343e-24
relative error = 1.7887038671281491727504004429417e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0038
y[1] (analytic) = 1.0038072108459852071102515272413
y[1] (numeric) = 1.0038072108459852071102533710056
absolute error = 1.8437643e-24
relative error = 1.8367713242925587581744792475737e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0039
y[1] (analytic) = 1.0039075951038681860676699482581
y[1] (numeric) = 1.0039075951038681860676718404474
absolute error = 1.8921893e-24
relative error = 1.8848241703004814226695714615256e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 1.004007989322675205685636470564
y[1] (numeric) = 1.0040079893226752056856384111735
absolute error = 1.9406095e-24
relative error = 1.9328626073077125291927415782765e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0041
y[1] (analytic) = 1.0041083935014023237769175164691
y[1] (numeric) = 1.004108393501402323776919505494
absolute error = 1.9890249e-24
relative error = 1.9808866382085692181477237270246e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.76
NO POLE
x[1] = 0.0042
y[1] (analytic) = 1.0042088076390454985550786065498
y[1] (numeric) = 1.0042088076390454985550806439851
absolute error = 2.0374353e-24
relative error = 2.0288960667354942860171291229854e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0043
y[1] (analytic) = 1.0043092317346005886445247775044
y[1] (numeric) = 1.0043092317346005886445268633453
absolute error = 2.0858409e-24
relative error = 2.0768910949841847854866986032764e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0044
y[1] (analytic) = 1.0044096657870633530905419959013
y[1] (numeric) = 1.0044096657870633530905441301429
absolute error = 2.1342416e-24
relative error = 2.1248716262876576490600407654745e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0045
y[1] (analytic) = 1.0045101097954294513693395677172
y[1] (numeric) = 1.0045101097954294513693417503546
absolute error = 2.1826374e-24
relative error = 2.1728376635696564496715787124016e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0046
y[1] (analytic) = 1.0046105637586944433980935435669
y[1] (numeric) = 1.0046105637586944433980957745952
absolute error = 2.2310283e-24
relative error = 2.2207892097538094138089821713690e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0047
y[1] (analytic) = 1.004711027675853789544991119523
y[1] (numeric) = 1.0047110276758537895449933989374
absolute error = 2.2794144e-24
relative error = 2.2687263672947352723970966863840e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0048
y[1] (analytic) = 1.004811501545902850639276033426
y[1] (numeric) = 1.0048115015459028506392783612216
absolute error = 2.3277956e-24
relative error = 2.3166490395648195167013957747722e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0049
y[1] (analytic) = 1.0049119853678368879812949565833
y[1] (numeric) = 1.0049119853678368879812973327551
absolute error = 2.3761718e-24
relative error = 2.3645571299761428000638217703796e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 1.005012479140651063352544880757
y[1] (numeric) = 1.0050124791406510633525473053002
absolute error = 2.4245432e-24
relative error = 2.4124508404842266878958354583017e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0051
y[1] (analytic) = 1.0051129828633404390257215003412
y[1] (numeric) = 1.0051129828633404390257239732509
absolute error = 2.4729097e-24
relative error = 2.4603300744909665820441893652441e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0052
y[1] (analytic) = 1.0052134965348999777747685896263
y[1] (numeric) = 1.0052134965348999777747711108976
absolute error = 2.5212713e-24
relative error = 2.5081948349192942377157261531945e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0053
y[1] (analytic) = 1.0053140201543245428849283750511
y[1] (numeric) = 1.0053140201543245428849309446792
absolute error = 2.5696281e-24
relative error = 2.5560452241634305360505907423823e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0054
y[1] (analytic) = 1.0054145537206088981627929023424
y[1] (numeric) = 1.0054145537206088981627955203223
absolute error = 2.6179799e-24
relative error = 2.6038810461933110176053496012684e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0055
y[1] (analytic) = 1.0055150972327477079463563984402
y[1] (numeric) = 1.0055150972327477079463590647671
absolute error = 2.6663269e-24
relative error = 2.6517025028643824731183508198138e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0056
y[1] (analytic) = 1.0056156506897355371150686281098
y[1] (numeric) = 1.0056156506897355371150713427788
absolute error = 2.7146690e-24
relative error = 2.6995094976276993767017544823160e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=4.1MB, time=1.04
x[1] = 0.0057
y[1] (analytic) = 1.0057162140905668510998892451388
y[1] (numeric) = 1.0057162140905668510998920081449
absolute error = 2.7630061e-24
relative error = 2.7473019339739763953127846515709e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0058
y[1] (analytic) = 1.0058167874342360158933431380187
y[1] (numeric) = 1.0058167874342360158933459493572
absolute error = 2.8113385e-24
relative error = 2.7950801131203187480464252104891e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0059
y[1] (analytic) = 1.0059173707197372980595767700121
y[1] (numeric) = 1.0059173707197372980595796296781
absolute error = 2.8596660e-24
relative error = 2.8428438391056904171331251484060e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 1.0060179639460648647444155135024
y[1] (numeric) = 1.0060179639460648647444184214908
absolute error = 2.9079884e-24
relative error = 2.8905929160484698063462300079470e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0061
y[1] (analytic) = 1.0061185671122127836854219785267
y[1] (numeric) = 1.0061185671122127836854249348327
absolute error = 2.9563060e-24
relative error = 2.9383276451057503201437819000168e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0062
y[1] (analytic) = 1.0062191802171750232219553353926
y[1] (numeric) = 1.0062191802171750232219583400114
absolute error = 3.0046188e-24
relative error = 2.9860480291694548596492164640963e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0063
y[1] (analytic) = 1.006319803259945452305231631276
y[1] (numeric) = 1.0063198032599454523052346842026
absolute error = 3.0529266e-24
relative error = 3.0337538723874138820455128576675e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0064
y[1] (analytic) = 1.0064204362395178405083851007001
y[1] (numeric) = 1.0064204362395178405083882019297
absolute error = 3.1012296e-24
relative error = 3.0814453764350417639887143332797e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0065
y[1] (analytic) = 1.0065210791548858580365304697964
y[1] (numeric) = 1.006521079154885858036533619324
absolute error = 3.1495276e-24
relative error = 3.1291223454996745285410979083873e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0066
y[1] (analytic) = 1.0066217320050430757368262542443
y[1] (numeric) = 1.0066217320050430757368294520651
absolute error = 3.1978208e-24
relative error = 3.1767849812167369666325779523033e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0067
y[1] (analytic) = 1.0067223947889829651085390507921
y[1] (numeric) = 1.0067223947889829651085422969011
absolute error = 3.2461090e-24
relative error = 3.2244330878130612256780379932068e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0068
y[1] (analytic) = 1.0068230675056988983131088222552
y[1] (numeric) = 1.0068230675056988983131121166475
absolute error = 3.2943923e-24
relative error = 3.2720667675617720431479513956361e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0069
y[1] (analytic) = 1.0069237501541841481842151758934
y[1] (numeric) = 1.0069237501541841481842185185642
absolute error = 3.3426708e-24
relative error = 3.3196861226961396261962593352700e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 1.0070244427334318882378446350663
y[1] (numeric) = 1.0070244427334318882378480260106
absolute error = 3.3909443e-24
relative error = 3.3672909575022226072174373499894e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0071
y[1] (analytic) = 1.0071251452424351926823589040641
y[1] (numeric) = 1.0071251452424351926823623432772
absolute error = 3.4392131e-24
relative error = 3.4148815728080272764005401538998e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0072
y[1] (analytic) = 1.0072258576801870364285641260168
y[1] (numeric) = 1.0072258576801870364285676134936
absolute error = 3.4874768e-24
relative error = 3.4624575743441038803149483019611e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.32
NO POLE
x[1] = 0.0073
y[1] (analytic) = 1.0073265800456802950997811337764
y[1] (numeric) = 1.0073265800456802950997846695121
absolute error = 3.5357357e-24
relative error = 3.5100192629084217000056000082211e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0074
y[1] (analytic) = 1.0074273123379077450419166936762
y[1] (numeric) = 1.007427312337907745041920277666
absolute error = 3.5839898e-24
relative error = 3.5575666413914641599185324174869e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0075
y[1] (analytic) = 1.0075280545558620633335357420632
y[1] (numeric) = 1.0075280545558620633335393743022
absolute error = 3.6322390e-24
relative error = 3.6050996134307758842370029276822e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0076
y[1] (analytic) = 1.0076288066985358277959346145041
y[1] (numeric) = 1.0076288066985358277959382949872
absolute error = 3.6804831e-24
relative error = 3.6526179834605834733361562064693e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0077
y[1] (analytic) = 1.0077295687649215170032152675632
y[1] (numeric) = 1.0077295687649215170032189962856
absolute error = 3.7287224e-24
relative error = 3.7001220521592326908535343503408e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0078
y[1] (analytic) = 1.0078303407540115102923604930541
y[1] (numeric) = 1.007830340754011510292364270011
absolute error = 3.7769569e-24
relative error = 3.7476118224167150492711572825662e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0079
y[1] (analytic) = 1.007931122664798087773310124661
y[1] (numeric) = 1.0079311226647980877733139498473
absolute error = 3.8251863e-24
relative error = 3.7950869994835157196485590419871e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 1.0080319144962734303390382368304
y[1] (numeric) = 1.0080319144962734303390421102414
absolute error = 3.8734110e-24
relative error = 3.8425479831514992402899781298343e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0081
y[1] (analytic) = 1.0081327162474296196756313358339
y[1] (numeric) = 1.0081327162474296196756352574646
absolute error = 3.9216307e-24
relative error = 3.8899944787006596317967226908494e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0082
y[1] (analytic) = 1.0082335279172586382723675428982
y[1] (numeric) = 1.0082335279172586382723715127437
absolute error = 3.9698455e-24
relative error = 3.9374265882633770512891511645463e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0083
y[1] (analytic) = 1.0083343495047523694317967693042
y[1] (numeric) = 1.0083343495047523694318007873596
absolute error = 4.0180554e-24
relative error = 3.9848443147587749094012900671788e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0084
y[1] (analytic) = 1.008435181008902597279821883353
y[1] (numeric) = 1.0084351810089025972798259496135
absolute error = 4.0662605e-24
relative error = 4.0322477602693856453802734652284e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0085
y[1] (analytic) = 1.008536022428701006775780869099
y[1] (numeric) = 1.0085360224287010067757849835595
absolute error = 4.1144605e-24
relative error = 4.0796366302234623299789758463700e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0086
y[1] (analytic) = 1.0086368737631391837225299767469
y[1] (numeric) = 1.0086368737631391837225341394027
absolute error = 4.1626558e-24
relative error = 4.1270113241740627371017876885884e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0087
y[1] (analytic) = 1.0087377350112086147765278646163
y[1] (numeric) = 1.0087377350112086147765320754623
absolute error = 4.2108460e-24
relative error = 4.1743714484451313586481840846821e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0088
y[1] (analytic) = 1.0088386061719006874579207325672
y[1] (numeric) = 1.0088386061719006874579249915986
absolute error = 4.2590314e-24
relative error = 4.2217173033862701853173339487744e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=1.59
NO POLE
x[1] = 0.0089
y[1] (analytic) = 1.0089394872442066901606284467914
y[1] (numeric) = 1.0089394872442066901606327540032
absolute error = 4.3072118e-24
relative error = 4.2690486936581457718159360419483e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 1.0090403782271178121624316558638
y[1] (numeric) = 1.0090403782271178121624360112513
absolute error = 4.3553875e-24
relative error = 4.3163659195208899914468367421745e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0091
y[1] (analytic) = 1.0091412791196251436350598979574
y[1] (numeric) = 1.0091412791196251436350643015155
absolute error = 4.4035581e-24
relative error = 4.3636685874565195726670050447588e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0092
y[1] (analytic) = 1.0092421899207196756542806991162
y[1] (numeric) = 1.0092421899207196756542851508401
absolute error = 4.4517239e-24
relative error = 4.4109569976951737436306478597600e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0093
y[1] (analytic) = 1.0093431106293923002099896624904
y[1] (numeric) = 1.0093431106293923002099941623751
absolute error = 4.4998847e-24
relative error = 4.4582309549762753761504382608126e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0094
y[1] (analytic) = 1.009444041244633810216301548428
y[1] (numeric) = 1.0094440412446338102163060964687
absolute error = 4.5480407e-24
relative error = 4.5054906603760957293701385697042e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0095
y[1] (analytic) = 1.0095449817654348995216423453262
y[1] (numeric) = 1.0095449817654348995216469415179
absolute error = 4.5961917e-24
relative error = 4.5527359186734216843594385783790e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0096
y[1] (analytic) = 1.0096459321907861629188423311378
y[1] (numeric) = 1.0096459321907861629188469754757
absolute error = 4.6443379e-24
relative error = 4.5999669309046351505521057590580e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0097
y[1] (analytic) = 1.0097468925196780961552301254352
y[1] (numeric) = 1.0097468925196780961552348179143
absolute error = 4.6924791e-24
relative error = 4.6471835018878775863119096310582e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0098
y[1] (analytic) = 1.0098478627511010959427277319283
y[1] (numeric) = 1.0098478627511010959427324725438
absolute error = 4.7406155e-24
relative error = 4.6943858326196482617709079858280e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0099
y[1] (analytic) = 1.009948842884045459967946571337
y[1] (numeric) = 1.009948842884045459967951360084
absolute error = 4.7887470e-24
relative error = 4.7415738269723499372676662674370e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 1.0100498329175013869022845045169
y[1] (numeric) = 1.0100498329175013869022893413903
absolute error = 4.8368734e-24
relative error = 4.7887472898528413596483444004998e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0101
y[1] (analytic) = 1.0101508328504589764120238457363
y[1] (numeric) = 1.0101508328504589764120287307313
absolute error = 4.8849950e-24
relative error = 4.8359065212226245930932180017549e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0102
y[1] (analytic) = 1.0102518426819082291684303660054
y[1] (numeric) = 1.0102518426819082291684352991172
absolute error = 4.9331118e-24
relative error = 4.8830515239686214621644333826998e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0103
y[1] (analytic) = 1.0103528624108390468578532863555
y[1] (numeric) = 1.0103528624108390468578582675791
absolute error = 4.9812236e-24
relative error = 4.9301821030269805718200149664149e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0104
y[1] (analytic) = 1.0104538920362412321918262609664
y[1] (numeric) = 1.0104538920362412321918312902969
absolute error = 5.0293305e-24
relative error = 4.9772983603091674512903349146570e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=1.86
NO POLE
x[1] = 0.0105
y[1] (analytic) = 1.0105549315571044889171693500432
y[1] (numeric) = 1.0105549315571044889171744274756
absolute error = 5.0774324e-24
relative error = 5.0244001997758636384196159123735e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0106
y[1] (analytic) = 1.0106559809724184218260919823391
y[1] (numeric) = 1.0106559809724184218260971078687
absolute error = 5.1255296e-24
relative error = 5.0714879212097391630207714429519e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0107
y[1] (analytic) = 1.0107570402811725367662969072259
y[1] (numeric) = 1.0107570402811725367663020808476
absolute error = 5.1736217e-24
relative error = 5.1185611317243965790232673483226e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0108
y[1] (analytic) = 1.0108581094823562406510851362074
y[1] (numeric) = 1.0108581094823562406510903579163
absolute error = 5.2217089e-24
relative error = 5.1656200321466985834525079925402e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0109
y[1] (analytic) = 1.0109591885749588414694618737786
y[1] (numeric) = 1.0109591885749588414694671435698
absolute error = 5.2697912e-24
relative error = 5.2126646253923085033731270961752e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 1.0110602775579695482962434375271
y[1] (numeric) = 1.0110602775579695482962487553958
absolute error = 5.3178687e-24
relative error = 5.2596950132828236404569762027071e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0111
y[1] (analytic) = 1.0111613764303774713021651673767
y[1] (numeric) = 1.0111613764303774713021705333179
absolute error = 5.3659412e-24
relative error = 5.3067110009116004234088580311839e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0112
y[1] (analytic) = 1.0112624851911716217639903238713
y[1] (numeric) = 1.01126248519117162176399573788
absolute error = 5.4140087e-24
relative error = 5.3537125912235556542745653970402e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0113
y[1] (analytic) = 1.0113636038393409120746199753988
y[1] (numeric) = 1.0113636038393409120746254374702
absolute error = 5.4620714e-24
relative error = 5.4006999849162769888793256568268e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0114
y[1] (analytic) = 1.0114647323738741557532038742542
y[1] (numeric) = 1.0114647323738741557532093843834
absolute error = 5.5101292e-24
relative error = 5.4476730860085547937316521083312e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0115
y[1] (analytic) = 1.0115658707937600674552523214391
y[1] (numeric) = 1.0115658707937600674552578796212
absolute error = 5.5581821e-24
relative error = 5.4946318974152228114081307306712e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0116
y[1] (analytic) = 1.0116670190979872629827490200985
y[1] (numeric) = 1.0116670190979872629827546263285
absolute error = 5.6062300e-24
relative error = 5.5415763232042223010130692898020e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0117
y[1] (analytic) = 1.0117681772855442592942649174923
y[1] (numeric) = 1.0117681772855442592942705717653
absolute error = 5.6542730e-24
relative error = 5.5885064651566265469186034300878e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0118
y[1] (analytic) = 1.0118693453554194745150730354014
y[1] (numeric) = 1.0118693453554194745150787377125
absolute error = 5.7023111e-24
relative error = 5.6354223261868469373940371248968e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0119
y[1] (analytic) = 1.0119705233066012279472642888665
y[1] (numeric) = 1.0119705233066012279472700392107
absolute error = 5.7503442e-24
relative error = 5.6823238103920469056387926472532e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.2MB, time=2.15
x[1] = 0.012
y[1] (analytic) = 1.0120717111380777400798642931584
y[1] (numeric) = 1.0120717111380777400798700915309
absolute error = 5.7983725e-24
relative error = 5.7292111183304514637703368159672e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0121
y[1] (analytic) = 1.0121729088488371325989511588799
y[1] (numeric) = 1.0121729088488371325989570052757
absolute error = 5.8463958e-24
relative error = 5.7760840552917124441110422873197e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0122
y[1] (analytic) = 1.0122741164378674283977742750962
y[1] (numeric) = 1.0122741164378674283977801695104
absolute error = 5.8944142e-24
relative error = 5.8229427230067819339257778151707e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0123
y[1] (analytic) = 1.012375333904156551586874080394
y[1] (numeric) = 1.0123753339041565515868800228217
absolute error = 5.9424277e-24
relative error = 5.8697871243893627296261671090703e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0124
y[1] (analytic) = 1.0124765612466923275042028217678
y[1] (numeric) = 1.012476561246692327504208812204
absolute error = 5.9904362e-24
relative error = 5.9166171635852970041879600113046e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0125
y[1] (analytic) = 1.0125777984644624827252463012317
y[1] (numeric) = 1.0125777984644624827252523396716
absolute error = 6.0384399e-24
relative error = 5.9634330410533147836079769207139e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0126
y[1] (analytic) = 1.0126790455564546450731466100564
y[1] (numeric) = 1.0126790455564546450731526964952
absolute error = 6.0864388e-24
relative error = 6.0102347596770672291314262773740e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0127
y[1] (analytic) = 1.0127803025216563436288258505295
y[1] (numeric) = 1.0127803025216563436288319849621
absolute error = 6.1344326e-24
relative error = 6.0570220261257767201044603560046e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0128
y[1] (analytic) = 1.0128815693590550087411108451371
y[1] (numeric) = 1.0128815693590550087411170275585
absolute error = 6.1824214e-24
relative error = 6.1037949420998911015927227674090e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0129
y[1] (analytic) = 1.0129828460676379720368588330676
y[1] (numeric) = 1.012982846067637972036865063473
absolute error = 6.2304054e-24
relative error = 6.1505537079785742198921172924969e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 1.0130841326463924664310841539349
y[1] (numeric) = 1.0130841326463924664310904323194
absolute error = 6.2783845e-24
relative error = 6.1972982279364268171512392370201e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0131
y[1] (analytic) = 1.0131854290943056261370859186194
y[1] (numeric) = 1.013185429094305626137092244978
absolute error = 6.3263586e-24
relative error = 6.2440284061873860520518282296673e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0132
y[1] (analytic) = 1.0132867354103644866765766671269
y[1] (numeric) = 1.0132867354103644866765830414545
absolute error = 6.3743276e-24
relative error = 6.2907441469847150493970872422234e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0133
y[1] (analytic) = 1.0133880515935559848898120133623
y[1] (numeric) = 1.0133880515935559848898184356543
absolute error = 6.4222920e-24
relative error = 6.3374459466942846649214406230784e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0134
y[1] (analytic) = 1.01348937764286695894572127672
y[1] (numeric) = 1.0134893776428669589457277469712
absolute error = 6.4702512e-24
relative error = 6.3841332161253148426884317351696e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0135
y[1] (analytic) = 1.0135907135572841483520391003845
y[1] (numeric) = 1.0135907135572841483520456185902
absolute error = 6.5182057e-24
relative error = 6.4308064515743185419434750826425e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.2MB, time=2.43
NO POLE
x[1] = 0.0136
y[1] (analytic) = 1.0136920593357941939654380562461
y[1] (numeric) = 1.0136920593357941939654446224013
absolute error = 6.5661552e-24
relative error = 6.4774653599460669549527016239849e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0137
y[1] (analytic) = 1.0137934149773836380016622363247
y[1] (numeric) = 1.0137934149773836380016688504244
absolute error = 6.6140997e-24
relative error = 6.5241099441818248861032218609441e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0138
y[1] (analytic) = 1.0138947804810389240456618306043
y[1] (numeric) = 1.0138947804810389240456684926436
absolute error = 6.6620393e-24
relative error = 6.5707403058522681743063732744354e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0139
y[1] (analytic) = 1.0139961558457463970617286911751
y[1] (numeric) = 1.0139961558457463970617354011491
absolute error = 6.7099740e-24
relative error = 6.6173564478687738477092996836127e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 1.0140975410704923034036328825821
y[1] (numeric) = 1.0140975410704923034036396404859
absolute error = 6.7579038e-24
relative error = 6.6639583731425715235919836022964e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0141
y[1] (analytic) = 1.0141989361542627908247602182789
y[1] (numeric) = 1.0141989361542627908247670241075
absolute error = 6.8058286e-24
relative error = 6.7105459859847579728126425144147e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0142
y[1] (analytic) = 1.0143003410960439084882507830851
y[1] (numeric) = 1.0143003410960439084882576368337
absolute error = 6.8537486e-24
relative error = 6.7571194865160947770921355453026e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0143
y[1] (analytic) = 1.0144017558948216069771384415473
y[1] (numeric) = 1.0144017558948216069771453432109
absolute error = 6.9016636e-24
relative error = 6.8036786804572526688867413975130e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0144
y[1] (analytic) = 1.0145031805495817383044913320994
y[1] (numeric) = 1.0145031805495817383044982816731
absolute error = 6.9495737e-24
relative error = 6.8502236693188504032497711726939e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0145
y[1] (analytic) = 1.0146046150593100559235533469241
y[1] (numeric) = 1.0146046150593100559235603444028
absolute error = 6.9974787e-24
relative error = 6.8967542588902506807681083871758e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0146
y[1] (analytic) = 1.0147060594229922147378865974112
y[1] (numeric) = 1.0147060594229922147378936427901
absolute error = 7.0453789e-24
relative error = 6.9432707477930320793188870866909e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0147
y[1] (analytic) = 1.0148075136396137711115148651146
y[1] (numeric) = 1.0148075136396137711115219583888
absolute error = 7.0932742e-24
relative error = 6.9897730403669615978072571392523e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0148
y[1] (analytic) = 1.014908977708160182879068038103
y[1] (numeric) = 1.0149089777081601828790751792676
absolute error = 7.1411646e-24
relative error = 7.0362611395220716671729370856257e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0149
y[1] (analytic) = 1.0150104516276168093559275326052
y[1] (numeric) = 1.0150104516276168093559347216551
absolute error = 7.1890499e-24
relative error = 7.0827348511259383586606126191982e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 1.0151119353969689113483726998476
y[1] (numeric) = 1.015111935396968911348379936778
absolute error = 7.2369304e-24
relative error = 7.1291944736813004085031265928695e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0151
y[1] (analytic) = 1.0152134290152016511637282179834
y[1] (numeric) = 1.0152134290152016511637355027894
absolute error = 7.2848060e-24
relative error = 7.1756399115667316741018375026521e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.2MB, time=2.70
NO POLE
x[1] = 0.0152
y[1] (analytic) = 1.0153149324813000926205124690109
y[1] (numeric) = 1.0153149324813000926205198016875
absolute error = 7.3326766e-24
relative error = 7.2220710692000504583164075809004e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0153
y[1] (analytic) = 1.0154164457942492010585869005792
y[1] (numeric) = 1.0154164457942492010585942811216
absolute error = 7.3805424e-24
relative error = 7.2684881464835928442655833010796e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0154
y[1] (analytic) = 1.0155179689530338433493063725821
y[1] (numeric) = 1.0155179689530338433493138009852
absolute error = 7.4284031e-24
relative error = 7.3148908508811943135446496186245e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0155
y[1] (analytic) = 1.0156195019566387879056704884352
y[1] (numeric) = 1.0156195019566387879056779646941
absolute error = 7.4762589e-24
relative error = 7.3612793822850341412416835399136e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0156
y[1] (analytic) = 1.0157210448040487046924759109381
y[1] (numeric) = 1.0157210448040487046924834350478
absolute error = 7.5241097e-24
relative error = 7.4076536451516954903272454516157e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0157
y[1] (analytic) = 1.0158225974942481652364696626172
y[1] (numeric) = 1.0158225974942481652364772345729
absolute error = 7.5719557e-24
relative error = 7.4540138393041352438792795835754e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0158
y[1] (analytic) = 1.015924160026221642636503410451
y[1] (numeric) = 1.0159241600262216426365110302476
absolute error = 7.6197966e-24
relative error = 7.5003596723236981085547627581159e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0159
y[1] (analytic) = 1.0160257323989535115736887348718
y[1] (numeric) = 1.0160257323989535115736964025044
absolute error = 7.6676326e-24
relative error = 7.5466913440231856131171187942134e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 1.0161273146114280483215533829469
y[1] (numeric) = 1.0161273146114280483215610984106
absolute error = 7.7154637e-24
relative error = 7.5930088573107891217322359992633e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0161
y[1] (analytic) = 1.0162289066626294307561985056346
y[1] (numeric) = 1.0162289066626294307562062689245
absolute error = 7.7632899e-24
relative error = 7.6393122150945457317497592265212e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0162
y[1] (analytic) = 1.016330508551541738366456879015
y[1] (numeric) = 1.0163305085515417383664646901261
absolute error = 7.8111111e-24
relative error = 7.6856013218891487674733069920540e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0163
y[1] (analytic) = 1.0164321202771489522640521093928
y[1] (numeric) = 1.0164321202771489522640599683201
absolute error = 7.8589273e-24
relative error = 7.7318761806318346349606760931793e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0164
y[1] (analytic) = 1.0165337418384349551937588221717
y[1] (numeric) = 1.0165337418384349551937667289104
absolute error = 7.9067387e-24
relative error = 7.7781369910067137264402598024600e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0165
y[1] (analytic) = 1.0166353732343835315435638343986
y[1] (numeric) = 1.0166353732343835315435717889436
absolute error = 7.9545450e-24
relative error = 7.8243834608006437843142933282545e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0166
y[1] (analytic) = 1.0167370144639783673548283108745
y[1] (numeric) = 1.016737014463978367354836313221
absolute error = 8.0023465e-24
relative error = 7.8706158880414326001802900162067e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0167
y[1] (analytic) = 1.0168386655262030503324509037332
y[1] (numeric) = 1.0168386655262030503324589538763
absolute error = 8.0501431e-24
relative error = 7.9168341772626611390197169386694e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.2MB, time=2.98
NO POLE
x[1] = 0.0168
y[1] (analytic) = 1.0169403264200410698550318753835
y[1] (numeric) = 1.0169403264200410698550399733182
absolute error = 8.0979347e-24
relative error = 7.9630382330370847161179251977604e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0169
y[1] (analytic) = 1.0170419971444758169850382047146
y[1] (numeric) = 1.0170419971444758169850463504359
absolute error = 8.1457213e-24
relative error = 8.0092280583009791215706059384227e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 1.017143677698490584478969676463
y[1] (numeric) = 1.017143677698490584478977869966
absolute error = 8.1935030e-24
relative error = 8.0554037543049843128911520168645e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0171
y[1] (analytic) = 1.0172453680810685667975259536392
y[1] (numeric) = 1.017245368081068566797534194919
absolute error = 8.2412798e-24
relative error = 8.1015653239555647800898989245632e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0172
y[1] (analytic) = 1.0173470682911928601157746329124
y[1] (numeric) = 1.017347068291192860115782921964
absolute error = 8.2890516e-24
relative error = 8.1477126718641550591054897631010e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0173
y[1] (analytic) = 1.0174487783278464623333202828506
y[1] (numeric) = 1.0174487783278464623333286196691
absolute error = 8.3368185e-24
relative error = 8.1938458992514280743733281328847e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0174
y[1] (analytic) = 1.017550498190012273084474464917
y[1] (numeric) = 1.0175504981900122730844828494974
absolute error = 8.3845804e-24
relative error = 8.2399649107481499529200124966481e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0175
y[1] (analytic) = 1.0176522278766730937484267371178
y[1] (numeric) = 1.0176522278766730937484351694552
absolute error = 8.4323374e-24
relative error = 8.2860698075550180531323215647922e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0176
y[1] (analytic) = 1.017753967386811627459416640202
y[1] (numeric) = 1.0177539673868116274594251202915
absolute error = 8.4800895e-24
relative error = 8.3321605925776984968822067931473e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0177
y[1] (analytic) = 1.0178557167194104791169066663106
y[1] (numeric) = 1.0178557167194104791169151941472
absolute error = 8.5278366e-24
relative error = 8.3782371704759463010500233182592e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0178
y[1] (analytic) = 1.0179574758734521553957562099735
y[1] (numeric) = 1.0179574758734521553957647855522
absolute error = 8.5755787e-24
relative error = 8.4242995441845715661476913743461e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0179
y[1] (analytic) = 1.018059244847919064756396501352
y[1] (numeric) = 1.018059244847919064756405124668
absolute error = 8.6233160e-24
relative error = 8.4703479130904394787569550158006e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 1.0181610236417935174550065216268
y[1] (numeric) = 1.0181610236417935174550151926751
absolute error = 8.6710483e-24
relative error = 8.5163820836365302372728068187144e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0181
y[1] (analytic) = 1.0182628122540577255536899004273
y[1] (numeric) = 1.0182628122540577255536986192028
absolute error = 8.7187755e-24
relative error = 8.5624019605506870191249184299763e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0182
y[1] (analytic) = 1.0183646106836938029306527952017
y[1] (numeric) = 1.0183646106836938029306615616995
absolute error = 8.7664978e-24
relative error = 8.6084077431898237045775491896484e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0183
y[1] (analytic) = 1.0184664189296837652903827524271
y[1] (numeric) = 1.0184664189296837652903915666423
absolute error = 8.8142152e-24
memory used=45.7MB, alloc=4.2MB, time=3.25
relative error = 8.6543994344584716071077063748379e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0184
y[1] (analytic) = 1.0185682369910095301738285505558
y[1] (numeric) = 1.0185682369910095301738374124835
absolute error = 8.8619277e-24
relative error = 8.7003770372610003911105761061644e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0185
y[1] (analytic) = 1.0186700648666529169685810245975
y[1] (numeric) = 1.0186700648666529169685899342328
absolute error = 8.9096353e-24
relative error = 8.7463405545016177540685799037688e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0186
y[1] (analytic) = 1.0187719025555956469190548722349
y[1] (numeric) = 1.0187719025555956469190638295727
absolute error = 8.9573378e-24
relative error = 8.7922897927695713624877603834518e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0187
y[1] (analytic) = 1.0188737500568193431366714413706
y[1] (numeric) = 1.018873750056819343136680446406
absolute error = 9.0050354e-24
relative error = 8.8382249513227893679385686243575e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0188
y[1] (analytic) = 1.018975607369305530610042499005
y[1] (numeric) = 1.0189756073693055306100515517331
absolute error = 9.0527281e-24
relative error = 8.8841460330649855637239325341478e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0189
y[1] (analytic) = 1.0190774744920356362151549813417
y[1] (numeric) = 1.0190774744920356362151640817575
absolute error = 9.1004158e-24
relative error = 8.9300529427717442794425733978619e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 1.0191793514239909887255567250185
y[1] (numeric) = 1.0191793514239909887255658731171
absolute error = 9.1480986e-24
relative error = 8.9759457814940364439912534558794e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0191
y[1] (analytic) = 1.0192812381641528188225431793642
y[1] (numeric) = 1.0192812381641528188225523751406
absolute error = 9.1957764e-24
relative error = 9.0218244540267325954148095749108e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0192
y[1] (analytic) = 1.0193831347115022591053450995768
y[1] (numeric) = 1.0193831347115022591053543430259
absolute error = 9.2434491e-24
relative error = 9.0676888652037663471319873360501e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0193
y[1] (analytic) = 1.0194850410650203441013172207221
y[1] (numeric) = 1.0194850410650203441013265118393
absolute error = 9.2911172e-24
relative error = 9.1135395084305455004522195215984e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0194
y[1] (analytic) = 1.0195869572236880102761279124532
y[1] (numeric) = 1.0195869572236880102761372512334
absolute error = 9.3387802e-24
relative error = 9.1593758961268836929857384725675e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0195
y[1] (analytic) = 1.0196888831864860960439498143438
y[1] (numeric) = 1.019688883186486096043959200782
absolute error = 9.3864382e-24
relative error = 9.2051981293232933456933933772398e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0196
y[1] (analytic) = 1.0197908189523953417776514517387
y[1] (numeric) = 1.0197908189523953417776608858299
absolute error = 9.4340912e-24
relative error = 9.2510062109515725978360404017753e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0197
y[1] (analytic) = 1.0198927645203963898189898320166
y[1] (numeric) = 1.0198927645203963898189993137558
absolute error = 9.4817392e-24
relative error = 9.2968001439433477226074493812211e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0198
y[1] (analytic) = 1.0199947198894697844888040211637
y[1] (numeric) = 1.019994719889469784488813550546
absolute error = 9.5293823e-24
relative error = 9.3425800292697960084203045568078e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=49.5MB, alloc=4.2MB, time=3.53
x[1] = 0.0199
y[1] (analytic) = 1.0200966850585959720972097005572
y[1] (numeric) = 1.0200966850585959720972192775777
absolute error = 9.5770205e-24
relative error = 9.3883458698327999638311963712576e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 1.0201986600267553009537947038555
y[1] (numeric) = 1.0201986600267553009538043285093
absolute error = 9.6246538e-24
relative error = 9.4340976685340753904253097732977e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0201
y[1] (analytic) = 1.0203006447929280213778155338939
y[1] (numeric) = 1.0203006447929280213778252061759
absolute error = 9.6722820e-24
relative error = 9.4798352322545167444790142267013e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0202
y[1] (analytic) = 1.0204026393560942857083948594832
y[1] (numeric) = 1.0204026393560942857084045793885
absolute error = 9.7199053e-24
relative error = 9.5255587599553463693074175236787e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0203
y[1] (analytic) = 1.0205046437152341483147199920105
y[1] (numeric) = 1.0205046437152341483147297595341
absolute error = 9.7675236e-24
relative error = 9.5712681565470370640540827855969e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0204
y[1] (analytic) = 1.0206066578693275656062423417382
y[1] (numeric) = 1.0206066578693275656062521568753
absolute error = 9.8151371e-24
relative error = 9.6169636209218929549860629571541e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0205
y[1] (analytic) = 1.020708681817354396042877853702
y[1] (numeric) = 1.0207086818173543960428877164474
absolute error = 9.8627454e-24
relative error = 9.6626447640668148923966019854134e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0206
y[1] (analytic) = 1.0208107155582944001452084231018
y[1] (numeric) = 1.0208107155582944001452183334506
absolute error = 9.9103488e-24
relative error = 9.7083118828547012664723406726445e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0207
y[1] (analytic) = 1.0209127590911272405046842900886
y[1] (numeric) = 1.0209127590911272405046942480359
absolute error = 9.9579473e-24
relative error = 9.7539649801860768862977010118351e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0208
y[1] (analytic) = 1.0210148124148324817938274138409
y[1] (numeric) = 1.0210148124148324817938374193818
absolute error = 1.00055409e-23
relative error = 9.7996040589612973485679661140164e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0209
y[1] (analytic) = 1.0211168755283895907764358258313
y[1] (numeric) = 1.0211168755283895907764458789608
absolute error = 1.00531295e-23
relative error = 9.8452290241485662107286695002099e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 1.0212189484307779363177889621797
y[1] (numeric) = 1.0212189484307779363177990628929
absolute error = 1.01007132e-23
relative error = 9.8908399765994592243219882807946e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0211
y[1] (analytic) = 1.0213210311209767893948539749922
y[1] (numeric) = 1.0213210311209767893948641232841
absolute error = 1.01482919e-23
relative error = 9.9364368213014128907467359214348e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0212
y[1] (analytic) = 1.0214231235979653231064930225829
y[1] (numeric) = 1.0214231235979653231065032184485
absolute error = 1.01958656e-23
relative error = 9.9820195611834591763413595022067e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0213
y[1] (analytic) = 1.0215252258607226126836715384766
y[1] (numeric) = 1.021525225860722612683681781911
absolute error = 1.02434344e-23
relative error = 1.0027588297067287792165910923546e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0214
y[1] (analytic) = 1.021627337908227635499667479091
y[1] (numeric) = 1.0216273379082276354996777700891
absolute error = 1.02909981e-23
relative error = 1.0073142836086122957701440209579e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.2MB, time=3.81
NO POLE
x[1] = 0.0215
y[1] (analytic) = 1.0217294597394592710802815499949
y[1] (numeric) = 1.0217294597394592710802918885519
absolute error = 1.03385570e-23
relative error = 1.0118683474817618715072473224764e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0216
y[1] (analytic) = 1.0218315913533963011140484106423
y[1] (numeric) = 1.0218315913533963011140587967531
absolute error = 1.03861108e-23
relative error = 1.0164209922540950106158265882345e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0217
y[1] (analytic) = 1.0219337327490174094624488574779
y[1] (numeric) = 1.0219337327490174094624592911376
absolute error = 1.04336597e-23
relative error = 1.0209722377921017870030349423392e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0218
y[1] (analytic) = 1.0220358839253011821701229853144
y[1] (numeric) = 1.022035883925301182170133466518
absolute error = 1.04812036e-23
relative error = 1.0255220746012527351056849230889e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0219
y[1] (analytic) = 1.0221380448812261074750843268771
y[1] (numeric) = 1.0221380448812261074750948556196
absolute error = 1.05287425e-23
relative error = 1.0300705029743271939489920545317e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 1.0222402156157705758189349704154
y[1] (numeric) = 1.0222402156157705758189455466919
absolute error = 1.05762765e-23
relative error = 1.0346175329865231001115747775839e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0221
y[1] (analytic) = 1.0223423961279128798570816552785
y[1] (numeric) = 1.022342396127912879857092279084
absolute error = 1.06238055e-23
relative error = 1.0391631551461919888763756596659e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0222
y[1] (analytic) = 1.0224445864166312144689528453525
y[1] (numeric) = 1.022444586416631214468963516682
absolute error = 1.06713295e-23
relative error = 1.0437073697460596959848372030869e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0223
y[1] (analytic) = 1.0225467864809036767682167802575
y[1] (numeric) = 1.0225467864809036767682274991062
absolute error = 1.07188487e-23
relative error = 1.0482501966378412989934877049665e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0224
y[1] (analytic) = 1.0226489963197082661130005042031
y[1] (numeric) = 1.0226489963197082661130112705659
absolute error = 1.07663628e-23
relative error = 1.0527916067727834749865178147914e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0225
y[1] (analytic) = 1.0227512159320228841161098723978
y[1] (numeric) = 1.0227512159320228841161206862697
absolute error = 1.08138719e-23
relative error = 1.0573316102240394240664483116812e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0226
y[1] (analytic) = 1.0228534453168253346552505349128
y[1] (numeric) = 1.0228534453168253346552613962889
absolute error = 1.08613761e-23
relative error = 1.0618702170608347641819376184260e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0227
y[1] (analytic) = 1.0229556844730933238832498978965
y[1] (numeric) = 1.0229556844730933238832608067718
absolute error = 1.09088753e-23
relative error = 1.0664074177972794470542591785902e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0228
y[1] (analytic) = 1.0230579333998044602382800620375
y[1] (numeric) = 1.023057933399804460238291018407
absolute error = 1.09563695e-23
relative error = 1.0709432127259914682566030577880e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0229
y[1] (analytic) = 1.0231601920959362544540817381744
y[1] (numeric) = 1.0231601920959362544540927420332
absolute error = 1.10038588e-23
relative error = 1.0754776119132112463615335774598e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 1.0232624605604661195701891399502
y[1] (numeric) = 1.0232624605604661195702001912932
absolute error = 1.10513430e-23
relative error = 1.0800105961032623556886057476781e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.2MB, time=4.09
NO POLE
x[1] = 0.0231
y[1] (analytic) = 1.0233647387923713709421558534077
y[1] (numeric) = 1.02336473879237137094216695223
absolute error = 1.10988223e-23
relative error = 1.0845421851350127542893397416667e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0232
y[1] (analytic) = 1.0234670267906292262517816834262
y[1] (numeric) = 1.023467026790629226251792829723
absolute error = 1.11462968e-23
relative error = 1.0890723890687881718803558869278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0233
y[1] (analytic) = 1.0235693245542168055173404768949
y[1] (numeric) = 1.023569324554216805517351670661
absolute error = 1.11937661e-23
relative error = 1.0936011691123207728571403970393e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0234
y[1] (analytic) = 1.0236716320821111311038089225209
y[1] (numeric) = 1.0236716320821111311038201637514
absolute error = 1.12412305e-23
relative error = 1.0981285548702510320831207594031e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0235
y[1] (analytic) = 1.0237739493732891277330963271718
y[1] (numeric) = 1.0237739493732891277331076158617
absolute error = 1.12886899e-23
relative error = 1.1026545368643591552679389992966e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0236
y[1] (analytic) = 1.0238762764267276224942753686475
y[1] (numeric) = 1.0238762764267276224942867047919
absolute error = 1.13361444e-23
relative error = 1.1071791251539224884313804554791e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0237
y[1] (analytic) = 1.0239786132414033448538138247812
y[1] (numeric) = 1.0239786132414033448538252083752
absolute error = 1.13835940e-23
relative error = 1.1117023200284665920687380407238e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0238
y[1] (analytic) = 1.0240809598162929266658072787665
y[1] (numeric) = 1.0240809598162929266658187098049
absolute error = 1.14310384e-23
relative error = 1.1162240924829402757523743312888e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0239
y[1] (analytic) = 1.024183316150372902182212800607
y[1] (numeric) = 1.0241833161503729021822242790849
absolute error = 1.14784779e-23
relative error = 1.1207444721072476454249925774980e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 1.0242856822426197080630836045889
y[1] (numeric) = 1.0242856822426197080630951305015
absolute error = 1.15259126e-23
relative error = 1.1252634689537609934768040294905e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0241
y[1] (analytic) = 1.0243880580920096833868046826723
y[1] (numeric) = 1.0243880580920096833868162560144
absolute error = 1.15733421e-23
relative error = 1.1297810442613039557916281913024e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0242
y[1] (analytic) = 1.0244904436975190696603294136978
y[1] (numeric) = 1.0244904436975190696603410344644
absolute error = 1.16207666e-23
relative error = 1.1342972178499922423258499959025e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0243
y[1] (analytic) = 1.0245928390581240108294171483089
y[1] (numeric) = 1.0245928390581240108294288164952
absolute error = 1.16681863e-23
relative error = 1.1388120095321178390797682297622e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0244
y[1] (analytic) = 1.0246952441728005532888717694864
y[1] (numeric) = 1.0246952441728005532888834850874
absolute error = 1.17156010e-23
relative error = 1.1433254000761544846963492215763e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0245
y[1] (analytic) = 1.0247976590405246458927812285911
y[1] (numeric) = 1.0247976590405246458927929916017
absolute error = 1.17630106e-23
relative error = 1.1478373800163845774674415551732e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0246
y[1] (analytic) = 1.0249000836602721399647580568145
y[1] (numeric) = 1.0249000836602721399647698672298
absolute error = 1.18104153e-23
relative error = 1.1523479691621185481134212777331e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.2MB, time=4.36
NO POLE
x[1] = 0.0247
y[1] (analytic) = 1.0250025180310187893081808519346
y[1] (numeric) = 1.0250025180310187893081927097496
absolute error = 1.18578150e-23
relative error = 1.1568571580466260781955374952407e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0248
y[1] (analytic) = 1.025104962151740250216436740273
y[1] (numeric) = 1.0251049621517402502164486454828
absolute error = 1.19052098e-23
relative error = 1.1613649567172558383100699246071e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0249
y[1] (analytic) = 1.025207416021412081483164813753
y[1] (numeric) = 1.0252074160214120814831767663525
absolute error = 1.19525995e-23
relative error = 1.1658713459550669771408706546039e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 1.0253098796390097444125005419541
y[1] (numeric) = 1.0253098796390097444125125419384
absolute error = 1.19999843e-23
relative error = 1.1703763455614944977588702116615e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0251
y[1] (analytic) = 1.0254123530035086028293211590628
y[1] (numeric) = 1.0254123530035086028293332064269
absolute error = 1.20473641e-23
relative error = 1.1748799460736336700803265611922e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0252
y[1] (analytic) = 1.0255148361138839230894920256147
y[1] (numeric) = 1.0255148361138839230895041203536
absolute error = 1.20947389e-23
relative error = 1.1793821477836594986020132073682e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0253
y[1] (analytic) = 1.0256173289691108740901139649276
y[1] (numeric) = 1.0256173289691108740901261070363
absolute error = 1.21421087e-23
relative error = 1.1838829509837280738218726155111e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0254
y[1] (analytic) = 1.0257198315681645272797715741219
y[1] (numeric) = 1.0257198315681645272797837635955
absolute error = 1.21894736e-23
relative error = 1.1883823657152274507947884002712e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0255
y[1] (analytic) = 1.0258223439100198566687825096263
y[1] (numeric) = 1.0258223439100198566687947464597
absolute error = 1.22368334e-23
relative error = 1.1928803727707997233085349023289e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0256
y[1] (analytic) = 1.0259248659936517388394477470656
y[1] (numeric) = 1.0259248659936517388394600312539
absolute error = 1.22841883e-23
relative error = 1.1973769919400718198914110791610e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0257
y[1] (analytic) = 1.02602739781803495295630281543
y[1] (numeric) = 1.0260273978180349529563151469682
absolute error = 1.23315382e-23
relative error = 1.2018722137658732714644522667927e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0258
y[1] (analytic) = 1.0261299393821441807763700054205
y[1] (numeric) = 1.0261299393821441807763823843036
absolute error = 1.23788831e-23
relative error = 1.2063660385402654531509536761920e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0259
y[1] (analytic) = 1.0262324906849540066594115518703
y[1] (numeric) = 1.0262324906849540066594239780934
absolute error = 1.24262231e-23
relative error = 1.2108584762996712715274002279270e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 1.0263350517254389175781837901389
y[1] (numeric) = 1.0263350517254389175781962636969
absolute error = 1.24735580e-23
relative error = 1.2153495078463788805637746047534e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0261
y[1] (analytic) = 1.0264376225025733031286922863756
y[1] (numeric) = 1.0264376225025733031287048072636
absolute error = 1.25208880e-23
relative error = 1.2198391529601799880354504643572e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0262
memory used=64.8MB, alloc=4.2MB, time=4.64
y[1] (analytic) = 1.0265402030153314555404479415512
y[1] (numeric) = 1.0265402030153314555404605097641
absolute error = 1.25682129e-23
relative error = 1.2243273924472194091123607915054e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0263
y[1] (analytic) = 1.0266427932626875696867240691541
y[1] (numeric) = 1.026642793262687569686736684687
absolute error = 1.26155329e-23
relative error = 1.2288142460833558611460872137723e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0264
y[1] (analytic) = 1.0267453932436157430948144464493
y[1] (numeric) = 1.0267453932436157430948271092972
absolute error = 1.26628479e-23
relative error = 1.2332997044181027808610472914094e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0265
y[1] (analytic) = 1.0268480029570899759562923391966
y[1] (numeric) = 1.0268480029570899759563050493545
absolute error = 1.27101579e-23
relative error = 1.2377837677433875588252761290699e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0266
y[1] (analytic) = 1.0269506224020841711372704997266
y[1] (numeric) = 1.0269506224020841711372832571895
absolute error = 1.27574629e-23
relative error = 1.2422664363511182815254284020857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0267
y[1] (analytic) = 1.0270532515775721341886621382709
y[1] (numeric) = 1.0270532515775721341886749430338
absolute error = 1.28047629e-23
relative error = 1.2467477105331837015260280041137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0268
y[1] (analytic) = 1.0271558904825275733564428674442
y[1] (numeric) = 1.0271558904825275733564557195022
absolute error = 1.28520580e-23
relative error = 1.2512276003170737620970047822352e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0269
y[1] (analytic) = 1.0272585391159240995919136197766
y[1] (numeric) = 1.0272585391159240995919265191246
absolute error = 1.28993480e-23
relative error = 1.2557060865224245194303538023358e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 1.0273611974767352265619645381911
y[1] (numeric) = 1.0273611974767352265619774848243
absolute error = 1.29466332e-23
relative error = 1.2601831986450100249254303720137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0271
y[1] (analytic) = 1.0274638655639343706593398393274
y[1] (numeric) = 1.0274638655639343706593528332406
absolute error = 1.29939132e-23
relative error = 1.2646588980399961610670177052588e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0272
y[1] (analytic) = 1.0275665433764948510129036496045
y[1] (numeric) = 1.0275665433764948510129166907928
absolute error = 1.30411883e-23
relative error = 1.2691332142001998595668253665638e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0273
y[1] (analytic) = 1.0276692309133898894979068139245
y[1] (numeric) = 1.0276692309133898894979199023829
absolute error = 1.30884584e-23
relative error = 1.2736061376837185546921672628202e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0274
y[1] (analytic) = 1.0277719281735926107462546769114
y[1] (numeric) = 1.0277719281735926107462678126348
absolute error = 1.31357234e-23
relative error = 1.2780776590525200279926418565691e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0275
y[1] (analytic) = 1.0278746351560760421567758365828
y[1] (numeric) = 1.0278746351560760421567890195664
absolute error = 1.31829836e-23
relative error = 1.2825478077876929167375042849664e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0276
y[1] (analytic) = 1.0279773518598131139054918703543
y[1] (numeric) = 1.0279773518598131139055051005929
absolute error = 1.32302386e-23
relative error = 1.2870165452637548398368190568659e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0277
y[1] (analytic) = 1.0280800782837766589558880332692
y[1] (numeric) = 1.028080078283776658955901310758
absolute error = 1.32774888e-23
relative error = 1.2914839106857073158170131122482e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.2MB, time=4.92
x[1] = 0.0278
y[1] (analytic) = 1.0281828144269394130691849283565
y[1] (numeric) = 1.0281828144269394130691982530905
absolute error = 1.33247340e-23
relative error = 1.2959498848875992949430981114398e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0279
y[1] (analytic) = 1.0282855602882740148146111490094
y[1] (numeric) = 1.0282855602882740148146245209835
absolute error = 1.33719741e-23
relative error = 1.3004144584361607714725077491929e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 1.0283883158667530055796768932843
y[1] (numeric) = 1.0283883158667530055796903124935
absolute error = 1.34192092e-23
relative error = 1.3048776413498955231188701143953e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0281
y[1] (analytic) = 1.0284910811613488295804485500176
y[1] (numeric) = 1.0284910811613488295804620164569
absolute error = 1.34664393e-23
relative error = 1.3093394339204188148068280323195e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0282
y[1] (analytic) = 1.0285938561710338338718242566562
y[1] (numeric) = 1.0285938561710338338718377703207
absolute error = 1.35136645e-23
relative error = 1.3137998461613363704272541657967e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0283
y[1] (analytic) = 1.0286966408947802683578104287003
y[1] (numeric) = 1.0286966408947802683578239895849
absolute error = 1.35608846e-23
relative error = 1.3182588589192319948193751637737e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0284
y[1] (analytic) = 1.0287994353315602858017992606542
y[1] (numeric) = 1.0287994353315602858018128687539
absolute error = 1.36080997e-23
relative error = 1.3227164822086432669202930807078e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0285
y[1] (analytic) = 1.0289022394803459418368471983842
y[1] (numeric) = 1.0289022394803459418368608536941
absolute error = 1.36553099e-23
relative error = 1.3271727260402025103670154845183e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0286
y[1] (analytic) = 1.0290050533401091949759543827795
y[1] (numeric) = 1.0290050533401091949759680852945
absolute error = 1.37025150e-23
relative error = 1.3316275712662620119600581818641e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0287
y[1] (analytic) = 1.0291078769098219066223450646132
y[1] (numeric) = 1.0291078769098219066223588143285
absolute error = 1.37497153e-23
relative error = 1.3360810473326940062343752555270e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0288
y[1] (analytic) = 1.0292107101884558410797489905024
y[1] (numeric) = 1.0292107101884558410797627874128
absolute error = 1.37969104e-23
relative error = 1.3405331156604158386507267302032e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0289
y[1] (analytic) = 1.0293135531749826655626837598611
y[1] (numeric) = 1.0293135531749826655626976039617
absolute error = 1.38441006e-23
relative error = 1.3449838056923468378165913797846e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 1.0294164058683739502067381527475
y[1] (numeric) = 1.0294164058683739502067520440333
absolute error = 1.38912858e-23
relative error = 1.3494331080027692403676812939450e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0291
y[1] (analytic) = 1.0295192682676011680788564284991
y[1] (numeric) = 1.029519268267601168078870366965
absolute error = 1.39384659e-23
relative error = 1.3538810131698281721095174077625e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0292
y[1] (analytic) = 1.0296221403716356951876235950546
y[1] (numeric) = 1.0296221403716356951876375806956
absolute error = 1.39856410e-23
relative error = 1.3583275312001323161620731542600e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0293
y[1] (analytic) = 1.0297250221794488104935516488596
y[1] (numeric) = 1.0297250221794488104935656816708
absolute error = 1.40328112e-23
relative error = 1.3627726720963881413956591640389e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.3MB, time=5.20
NO POLE
x[1] = 0.0294
y[1] (analytic) = 1.029827913690011695919366785253
y[1] (numeric) = 1.0298279136900116959193808652294
absolute error = 1.40799764e-23
relative error = 1.3672164264366804698423530962425e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0295
y[1] (analytic) = 1.0299308149022954363602975792312
y[1] (numeric) = 1.0299308149022954363603117063677
absolute error = 1.41271365e-23
relative error = 1.3716587848029552577584905347988e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0296
y[1] (analytic) = 1.0300337258152710196943641364868
y[1] (numeric) = 1.0300337258152710196943783107785
absolute error = 1.41742917e-23
relative error = 1.3760997669062784714482446161819e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0297
y[1] (analytic) = 1.0301366464279093367926682146204
y[1] (numeric) = 1.0301366464279093367926824360622
absolute error = 1.42214418e-23
relative error = 1.3805393536201354793626368730781e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0298
y[1] (analytic) = 1.0302395767391811815296843144206
y[1] (numeric) = 1.0302395767391811815296985830075
absolute error = 1.42685869e-23
relative error = 1.3849775549451913644438758876414e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0299
y[1] (analytic) = 1.0303425167480572507935517411109
y[1] (numeric) = 1.030342516748057250793566056838
absolute error = 1.43157271e-23
relative error = 1.3894143808782112782650817887744e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 1.0304454664535081444963676354597
y[1] (numeric) = 1.0304454664535081444963819983219
absolute error = 1.43628622e-23
relative error = 1.3938498122984392440598350973899e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0301
y[1] (analytic) = 1.0305484258545043655844809746505
y[1] (numeric) = 1.0305484258545043655844953846429
absolute error = 1.44099924e-23
relative error = 1.3982838689071407097560603863009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0302
y[1] (analytic) = 1.0306513949500163200487875428104
y[1] (numeric) = 1.0306513949500163200488019999279
absolute error = 1.44571175e-23
relative error = 1.4027165315873976323266309482376e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0303
y[1] (analytic) = 1.0307543737390143169350258710918
y[1] (numeric) = 1.0307543737390143169350403753294
absolute error = 1.45042376e-23
relative error = 1.4071478103349241110798748171065e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0304
y[1] (analytic) = 1.030857362220468568354074147207
y[1] (numeric) = 1.0308573622204685683540886985598
absolute error = 1.45513528e-23
relative error = 1.4115777151415362177160552858863e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0305
y[1] (analytic) = 1.0309603603933491894922480943109
y[1] (numeric) = 1.0309603603933491894922626927738
absolute error = 1.45984629e-23
relative error = 1.4160062268960710558594649518526e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0306
y[1] (analytic) = 1.0310633682566261986215998191285
y[1] (numeric) = 1.0310633682566261986216144646966
absolute error = 1.46455681e-23
relative error = 1.4204333652899979519690796882331e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0307
y[1] (analytic) = 1.0311663858092695171102176292269
y[1] (numeric) = 1.0311663858092695171102323218951
absolute error = 1.46926682e-23
relative error = 1.4248591112159896049328084104666e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0308
y[1] (analytic) = 1.031269413050248969432526819325
y[1] (numeric) = 1.0312694130502489694325415590882
absolute error = 1.47397632e-23
relative error = 1.4292834649680238105330151535648e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0309
y[1] (analytic) = 1.0313724499785342831795914265408
y[1] (numeric) = 1.031372449978534283179606213394
absolute error = 1.47868532e-23
relative error = 1.4337064365358756057234960871036e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=5.48
NO POLE
x[1] = 0.031
y[1] (analytic) = 1.0314754965930950890694169544723
y[1] (numeric) = 1.0314754965930950890694317884107
absolute error = 1.48339384e-23
relative error = 1.4381280456002740744715460698740e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0311
y[1] (analytic) = 1.0315785528929009209572540660092
y[1] (numeric) = 1.0315785528929009209572689470277
absolute error = 1.48810185e-23
relative error = 1.4425482633647731434380448170780e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0312
y[1] (analytic) = 1.0316816188769212158459032447712
y[1] (numeric) = 1.0316816188769212158459181728647
absolute error = 1.49280935e-23
relative error = 1.4469670901232669438141487708941e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0313
y[1] (analytic) = 1.0317846945441253138960204250715
y[1] (numeric) = 1.0317846945441253138960354002351
absolute error = 1.49751636e-23
relative error = 1.4513845455535173199292094098398e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0314
y[1] (analytic) = 1.0318877798934824584364235903022
y[1] (numeric) = 1.0318877798934824584364386125308
absolute error = 1.50222286e-23
relative error = 1.4558006105616138821256092605842e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0315
y[1] (analytic) = 1.0319908749239617959744003396368
y[1] (numeric) = 1.0319908749239617959744154089255
absolute error = 1.50692887e-23
relative error = 1.4602153048214037253665766142519e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0316
y[1] (analytic) = 1.0320939796345323762060164229494
y[1] (numeric) = 1.0320939796345323762060315392931
absolute error = 1.51163437e-23
relative error = 1.4646286092428078473635277632750e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0317
y[1] (analytic) = 1.0321970940241631520264252438448
y[1] (numeric) = 1.0321970940241631520264404072386
absolute error = 1.51633938e-23
relative error = 1.4690405434957592992550409196530e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0318
y[1] (analytic) = 1.0323002180918229795401783306991
y[1] (numeric) = 1.0323002180918229795401935411378
absolute error = 1.52104387e-23
relative error = 1.4734510788069051165668356589554e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0319
y[1] (analytic) = 1.0324033518364806180715367756048
y[1] (numeric) = 1.0324033518364806180715520330835
absolute error = 1.52574787e-23
relative error = 1.4778602445313048477610972457122e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 1.0325064952571047301747836411203
y[1] (numeric) = 1.0325064952571047301747989456339
absolute error = 1.53045136e-23
relative error = 1.4822680215865391532120894575582e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0321
y[1] (analytic) = 1.032609648352663881644537334718
y[1] (numeric) = 1.0326096483526638816445526862615
absolute error = 1.53515435e-23
relative error = 1.4866744199505132149594354879031e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0322
y[1] (analytic) = 1.0327128111221265415260659508296
y[1] (numeric) = 1.0327128111221265415260813493981
absolute error = 1.53985685e-23
relative error = 1.4910794495972410510554797202729e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0323
y[1] (analytic) = 1.0328159835644610821256025803852
y[1] (numeric) = 1.0328159835644610821256180259737
absolute error = 1.54455885e-23
relative error = 1.4954831011323127349727534106434e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0324
y[1] (analytic) = 1.0329191656786357790206615877419
y[1] (numeric) = 1.0329191656786357790206770803453
absolute error = 1.54926034e-23
relative error = 1.4998853651651667502649615235805e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0325
y[1] (analytic) = 1.0330223574636188110703558549003
y[1] (numeric) = 1.0330223574636188110703713945136
absolute error = 1.55396133e-23
relative error = 1.5042862516697541295240200503780e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.76
NO POLE
x[1] = 0.0326
y[1] (analytic) = 1.0331255589183782604257149929048
y[1] (numeric) = 1.0331255589183782604257305795229
absolute error = 1.55866181e-23
relative error = 1.5086857512574050599870663397157e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0327
y[1] (analytic) = 1.0332287700418821125400045203243
y[1] (numeric) = 1.0332287700418821125400201539423
absolute error = 1.56336180e-23
relative error = 1.5130838835784923512200482820400e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0328
y[1] (analytic) = 1.0333319908330982561790460087115
y[1] (numeric) = 1.0333319908330982561790616893244
absolute error = 1.56806129e-23
relative error = 1.5174806392433370089131876450478e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0329
y[1] (analytic) = 1.033435221290994483431538194936
y[1] (numeric) = 1.0334352212909944834315539225387
absolute error = 1.57276027e-23
relative error = 1.5218760088661062549107336533740e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 1.0335384614145384897193790602884
y[1] (numeric) = 1.0335384614145384897193948348758
absolute error = 1.57745874e-23
relative error = 1.5262699927403111342030877551577e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0331
y[1] (analytic) = 1.0336417112026978738079888762527
y[1] (numeric) = 1.0336417112026978738080046978199
absolute error = 1.58215672e-23
relative error = 1.5306626105085052467784363391290e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0332
y[1] (analytic) = 1.0337449706544401378166342168439
y[1] (numeric) = 1.0337449706544401378166500853859
absolute error = 1.58685420e-23
relative error = 1.5350538527847919250601678285941e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0333
y[1] (analytic) = 1.0338482397687326872287529374064
y[1] (numeric) = 1.0338482397687326872287688529182
absolute error = 1.59155118e-23
relative error = 1.5394437198597184943261397439043e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0334
y[1] (analytic) = 1.0339515185445428309022801197714
y[1] (numeric) = 1.0339515185445428309022960822478
absolute error = 1.59624764e-23
relative error = 1.5438321926805442799878572605533e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0335
y[1] (analytic) = 1.0340548069808377810799749836681
y[1] (numeric) = 1.0340548069808377810799909931043
absolute error = 1.60094362e-23
relative error = 1.5482193102262396013974192846999e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0336
y[1] (analytic) = 1.0341581050765846533997487642886
y[1] (numeric) = 1.0341581050765846533997648206795
absolute error = 1.60563909e-23
relative error = 1.5526050437723874734376229123002e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0337
y[1] (analytic) = 1.0342614128307504669049935558994
y[1] (numeric) = 1.03426141283075046690500965924
absolute error = 1.61033406e-23
relative error = 1.5569894032810829901271739609233e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0338
y[1] (analytic) = 1.0343647302423021440549121213991
y[1] (numeric) = 1.0343647302423021440549282716844
absolute error = 1.61502853e-23
relative error = 1.5613723890427664934657983753618e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0339
y[1] (analytic) = 1.0344680573102065107348486677179
y[1] (numeric) = 1.0344680573102065107348648649428
absolute error = 1.61972249e-23
relative error = 1.5657539916810528617138917841727e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 1.0345713940334302962666205869552
y[1] (numeric) = 1.0345713940334302962666368311148
absolute error = 1.62441596e-23
relative error = 1.5701342308209132133468736117670e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0341
y[1] (analytic) = 1.0346747404109401334188511631534
y[1] (numeric) = 1.0346747404109401334188674542425
absolute error = 1.62910891e-23
relative error = 1.5745130777552077725967765893931e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=6.04
NO POLE
x[1] = 0.0342
y[1] (analytic) = 1.0347780964417025584173032446024
y[1] (numeric) = 1.034778096441702558417319582616
absolute error = 1.63380136e-23
relative error = 1.5788905521078985070370418694779e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0343
y[1] (analytic) = 1.0348814621246840109552138815736
y[1] (numeric) = 1.0348814621246840109552302665068
absolute error = 1.63849332e-23
relative error = 1.5832666638322602032866577089826e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0344
y[1] (analytic) = 1.0349848374588508342036299293793
y[1] (numeric) = 1.034984837458850834203646361227
absolute error = 1.64318477e-23
relative error = 1.5876413938917536257553452816254e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0345
y[1] (analytic) = 1.0350882224431692748217446166531
y[1] (numeric) = 1.0350882224431692748217610954102
absolute error = 1.64787571e-23
relative error = 1.5920147425795634075193722502868e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0346
y[1] (analytic) = 1.0351916170766054829672350787494
y[1] (numeric) = 1.035191617076605482967251604411
absolute error = 1.65256616e-23
relative error = 1.5963867295089465775527839113898e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0347
y[1] (analytic) = 1.0352950213581255123066008561585
y[1] (numeric) = 1.0352950213581255123066174287195
absolute error = 1.65725610e-23
relative error = 1.6007573356490893034944099004223e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0348
y[1] (analytic) = 1.0353984352866953200255033578324
y[1] (numeric) = 1.0353984352866953200255199772878
absolute error = 1.66194554e-23
relative error = 1.6051265709512277986586863293505e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0349
y[1] (analytic) = 1.0355018588612807668391062893198
y[1] (numeric) = 1.0355018588612807668391229556646
absolute error = 1.66663448e-23
relative error = 1.6094944357055643237602350155742e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 1.035605292080847617002417045606
y[1] (numeric) = 1.0356052920808476170024337588351
absolute error = 1.67132291e-23
relative error = 1.6138609205460908270450605639829e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0351
y[1] (analytic) = 1.035708734944361538320629068554
y[1] (numeric) = 1.0357087349443615383206458286624
absolute error = 1.67601084e-23
relative error = 1.6182260354210835223479468898272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0352
y[1] (analytic) = 1.0358121874507881021594651688438
y[1] (numeric) = 1.0358121874507881021594819758266
absolute error = 1.68069828e-23
relative error = 1.6225897902749389333634434880353e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0353
y[1] (analytic) = 1.0359156495990927834555218123074
y[1] (numeric) = 1.0359156495990927834555386661593
absolute error = 1.68538519e-23
relative error = 1.6269521467816968076670271206542e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0354
y[1] (analytic) = 1.0360191213882409607266143705527
y[1] (numeric) = 1.0360191213882409607266312712689
absolute error = 1.69007162e-23
relative error = 1.6313131535017850447940757961063e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0355
y[1] (analytic) = 1.0361226028171979160821233357783
y[1] (numeric) = 1.0361226028171979160821402833537
absolute error = 1.69475754e-23
relative error = 1.6356727817653876556869816278365e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0356
y[1] (analytic) = 1.0362260938849288352333414996702
y[1] (numeric) = 1.0362260938849288352333584940997
absolute error = 1.69944295e-23
relative error = 1.6400310318654456515647459210659e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.3MB, time=6.31
x[1] = 0.0357
y[1] (analytic) = 1.0363295945903988075038220962801
y[1] (numeric) = 1.0363295945903988075038391375588
absolute error = 1.70412787e-23
relative error = 1.6443879233937570357125587250242e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0358
y[1] (analytic) = 1.036433104932572825839727908782
y[1] (numeric) = 1.0364331049325728258397449969048
absolute error = 1.70881228e-23
relative error = 1.6487434373404833598934129254161e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0359
y[1] (analytic) = 1.0365366249104157868201813400013
y[1] (numeric) = 1.0365366249104157868201984749632
absolute error = 1.71349619e-23
relative error = 1.6530975836460110093460396145673e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 1.0366401545228924906676154466153
y[1] (numeric) = 1.0366401545228924906676326284112
absolute error = 1.71817959e-23
relative error = 1.6574503529537518346854374219903e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0361
y[1] (analytic) = 1.0367436937689676412581259369198
y[1] (numeric) = 1.0367436937689676412581431655448
absolute error = 1.72286250e-23
relative error = 1.6618017648477059186184687192227e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0362
y[1] (analytic) = 1.0368472426476058461318241320603
y[1] (numeric) = 1.0368472426476058461318414075092
absolute error = 1.72754489e-23
relative error = 1.6661517906810329923334605341591e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0363
y[1] (analytic) = 1.0369508011577716165031908906212
y[1] (numeric) = 1.0369508011577716165032082128891
absolute error = 1.73222679e-23
relative error = 1.6705004596803840475618691876837e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0364
y[1] (analytic) = 1.0370543692984293672714314964735
y[1] (numeric) = 1.0370543692984293672714488655553
absolute error = 1.73690818e-23
relative error = 1.6748477528473497466570979130188e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0365
y[1] (analytic) = 1.0371579470685434170308315097732
y[1] (numeric) = 1.0371579470685434170308489256639
absolute error = 1.74158907e-23
relative error = 1.6791936801164021040936446352851e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0366
y[1] (analytic) = 1.0372615344670779880811135810104
y[1] (numeric) = 1.0372615344670779880811310437049
absolute error = 1.74626945e-23
relative error = 1.6835382321365985887181301521602e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0367
y[1] (analytic) = 1.037365131492997206437795228003
y[1] (numeric) = 1.0373651314929972064378127374963
absolute error = 1.75094933e-23
relative error = 1.6878814188404402573980489447255e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0368
y[1] (analytic) = 1.0374687381452651018425475757333
y[1] (numeric) = 1.0374687381452651018425651320204
absolute error = 1.75562871e-23
relative error = 1.6922232405177099597827775524796e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0369
y[1] (analytic) = 1.0375723544228456077735550589224
y[1] (numeric) = 1.0375723544228456077735726619982
absolute error = 1.76030758e-23
relative error = 1.6965636878202862142730984381206e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 1.0376759803247025614558760872396
y[1] (numeric) = 1.0376759803247025614558937370992
absolute error = 1.76498596e-23
relative error = 1.7009027803146339673820117342879e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0371
y[1] (analytic) = 1.0377796158497997038718046730438
y[1] (numeric) = 1.037779615849799703871822369682
absolute error = 1.76966382e-23
relative error = 1.7052404893797101006796236548852e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0372
y[1] (analytic) = 1.0378832609971006797712330215512
y[1] (numeric) = 1.0378832609971006797712507649629
absolute error = 1.77434117e-23
relative error = 1.7095768249459768584428466799352e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=6.59
NO POLE
x[1] = 0.0373
y[1] (analytic) = 1.0379869157655690376820150833279
y[1] (numeric) = 1.0379869157655690376820328735082
absolute error = 1.77901803e-23
relative error = 1.7139118065740570415275949581285e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0374
y[1] (analytic) = 1.0380905801541682299203310690031
y[1] (numeric) = 1.038090580154168229920348905947
absolute error = 1.78369439e-23
relative error = 1.7182454249176417189641968012142e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0375
y[1] (analytic) = 1.0381942541618616126010529260984
y[1] (numeric) = 1.0381942541618616126010708098008
absolute error = 1.78837024e-23
relative error = 1.7225776706342479915137106974581e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0376
y[1] (analytic) = 1.0382979377876124456481107778703
y[1] (numeric) = 1.0382979377876124456481287083262
absolute error = 1.79304559e-23
relative error = 1.7269085536475118033977578001719e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0377
y[1] (analytic) = 1.0384016310303838928048603240627
y[1] (numeric) = 1.038401631030383892804878301267
absolute error = 1.79772043e-23
relative error = 1.7312380646168286384605923520062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0378
y[1] (analytic) = 1.038505333889139021644451203464
y[1] (numeric) = 1.0385053338891390216444692274117
absolute error = 1.80239477e-23
relative error = 1.7355662134638651441201353868471e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0379
y[1] (analytic) = 1.0386090463628408035801963181678
y[1] (numeric) = 1.0386090463628408035802143888539
absolute error = 1.80706861e-23
relative error = 1.7398930004781566533389761589457e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 1.0387127684504521138759421194306
y[1] (numeric) = 1.0387127684504521138759602368499
absolute error = 1.81174193e-23
relative error = 1.7442184066946148597290401486659e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0381
y[1] (analytic) = 1.0388165001509357316564398550246
y[1] (numeric) = 1.0388165001509357316564580191721
absolute error = 1.81641475e-23
relative error = 1.7485424516611764115473476023247e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0382
y[1] (analytic) = 1.0389202414632543399177177779819
y[1] (numeric) = 1.0389202414632543399177359888527
absolute error = 1.82108708e-23
relative error = 1.7528651452926862497740691949678e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0383
y[1] (analytic) = 1.0390239923863705255374543166255
y[1] (numeric) = 1.0390239923863705255374725742145
absolute error = 1.82575890e-23
relative error = 1.7571864686268716503798808513516e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0384
y[1] (analytic) = 1.0391277529192467792853522057837
y[1] (numeric) = 1.0391277529192467792853705100858
absolute error = 1.83043021e-23
relative error = 1.7615064219560376970149939027026e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0385
y[1] (analytic) = 1.0392315230608454958335135790846
y[1] (numeric) = 1.0392315230608454958335319300947
absolute error = 1.83510101e-23
relative error = 1.7658250055724661673688726407541e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0386
y[1] (analytic) = 1.0393353028101289737668160222261
y[1] (numeric) = 1.0393353028101289737668344199393
absolute error = 1.83977132e-23
relative error = 1.7701422390114835957802699834120e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0387
y[1] (analytic) = 1.0394390921660594155932895871192
y[1] (numeric) = 1.0394390921660594155933080315303
absolute error = 1.84444111e-23
relative error = 1.7744580936978407638778260094695e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0388
y[1] (analytic) = 1.0395428911275989277544947667979
y[1] (numeric) = 1.039542891127598927754513257902
absolute error = 1.84911041e-23
relative error = 1.7787725987854699529429016255055e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.3MB, time=6.87
NO POLE
x[1] = 0.0389
y[1] (analytic) = 1.0396466996937095206359014309964
y[1] (numeric) = 1.0396466996937095206359199687883
absolute error = 1.85377919e-23
relative error = 1.7830857257048400977691912524745e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 1.0397505178633531085772687222844
y[1] (numeric) = 1.0397505178633531085772873067591
absolute error = 1.85844747e-23
relative error = 1.7873974939863817517136539566786e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0391
y[1] (analytic) = 1.0398543456354915098830259126617
y[1] (numeric) = 1.0398543456354915098830445438142
absolute error = 1.86311525e-23
relative error = 1.7917079039193559737147003514942e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0392
y[1] (analytic) = 1.0399581830090864468326542205048
y[1] (numeric) = 1.0399581830090864468326728983301
absolute error = 1.86778253e-23
relative error = 1.7960169557930009455203656120386e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0393
y[1] (analytic) = 1.040062029983099545691069587764
y[1] (numeric) = 1.040062029983099545691088312257
absolute error = 1.87244930e-23
relative error = 1.8003246402817207972916026966741e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0394
y[1] (analytic) = 1.0401658865564923367190064173048
y[1] (numeric) = 1.0401658865564923367190251884604
absolute error = 1.87711556e-23
relative error = 1.8046309576775878818299764402753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0395
y[1] (analytic) = 1.0402697527282262541834022702924
y[1] (numeric) = 1.0402697527282262541834210881057
absolute error = 1.88178133e-23
relative error = 1.8089359274984334692642656477940e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0396
y[1] (analytic) = 1.0403736284972626363677835235138
y[1] (numeric) = 1.0403736284972626363678023879797
absolute error = 1.88644659e-23
relative error = 1.8132395308066610571032245472986e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0397
y[1] (analytic) = 1.0404775138625627255826519865337
y[1] (numeric) = 1.040477513862562725582670897647
absolute error = 1.89111133e-23
relative error = 1.8175417582833010511346536013664e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0398
y[1] (analytic) = 1.0405814088230876681758724785803
y[1] (numeric) = 1.0405814088230876681758914363361
absolute error = 1.89577558e-23
relative error = 1.8218426390532472308387476286987e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0399
y[1] (analytic) = 1.040685313377798514543061365059
y[1] (numeric) = 1.0406853133777985145430803694522
absolute error = 1.90043932e-23
relative error = 1.8261421541845918284854233111085e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 1.0407892275256562191379760535868
y[1] (numeric) = 1.0407892275256562191379951046124
absolute error = 1.90510256e-23
relative error = 1.8304403135773595640870270813679e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0401
y[1] (analytic) = 1.0408931512656216404829054494465
y[1] (numeric) = 1.0408931512656216404829245470994
absolute error = 1.90976529e-23
relative error = 1.8347371079134462664373596948991e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0402
y[1] (analytic) = 1.0409970845966555411790613703548
y[1] (numeric) = 1.04099708459665554117908051463
absolute error = 1.91442752e-23
relative error = 1.8390325470909110062113918749430e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0403
y[1] (analytic) = 1.0411010275177185879169709204418
y[1] (numeric) = 1.0411010275177185879169901113343
absolute error = 1.91908925e-23
relative error = 1.8433266313987370020359216568641e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0404
y[1] (analytic) = 1.0412049800277713514868698233371
y[1] (numeric) = 1.0412049800277713514868890608417
absolute error = 1.92375046e-23
relative error = 1.8476193419173706927925696080515e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.3MB, time=7.14
NO POLE
x[1] = 0.0405
y[1] (analytic) = 1.0413089421257743067890967142584
y[1] (numeric) = 1.0413089421257743067891159983701
absolute error = 1.92841117e-23
relative error = 1.8519106981480979308685422299162e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0406
y[1] (analytic) = 1.0414129138106878328444883909999
y[1] (numeric) = 1.0414129138106878328445077217137
absolute error = 1.93307138e-23
relative error = 1.8562007003798316421342979513031e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0407
y[1] (analytic) = 1.041516895081472212804776023715
y[1] (numeric) = 1.0415168950814722128047954010258
absolute error = 1.93773108e-23
relative error = 1.8604893393000809810459451625593e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0408
y[1] (analytic) = 1.0416208859370876339629823233904
y[1] (numeric) = 1.0416208859370876339630017472931
absolute error = 1.94239027e-23
relative error = 1.8647766152005879699620100085744e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0409
y[1] (analytic) = 1.0417248863764941877638196689072
y[1] (numeric) = 1.0417248863764941877638391393968
absolute error = 1.94704896e-23
relative error = 1.8690625379725341589720334228120e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 1.0418288963986518698140891925851
y[1] (numeric) = 1.0418288963986518698141087096566
absolute error = 1.95170715e-23
relative error = 1.8733471079047385844661383387473e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0411
y[1] (analytic) = 1.0419329160025205798930808241058
y[1] (numeric) = 1.0419329160025205798931003877541
absolute error = 1.95636483e-23
relative error = 1.8776303156884500256824947956838e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0412
y[1] (analytic) = 1.0420369451870601219629742927114
y[1] (numeric) = 1.0420369451870601219629939029314
absolute error = 1.96102200e-23
relative error = 1.8819121616153151667042232909378e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0413
y[1] (analytic) = 1.0421409839512302041792410875737
y[1] (numeric) = 1.0421409839512302041792607443604
absolute error = 1.96567867e-23
relative error = 1.8861926555725873176972091174546e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0414
y[1] (analytic) = 1.0422450322939904389010473762312
y[1] (numeric) = 1.0422450322939904389010670795795
absolute error = 1.97033483e-23
relative error = 1.8904717882543184616888296335012e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0415
y[1] (analytic) = 1.0423490902143003427016578809887
y[1] (numeric) = 1.0423490902143003427016776308935
absolute error = 1.97499048e-23
relative error = 1.8947495599520833466343344473621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0416
y[1] (analytic) = 1.0424531577111193363788407131755
y[1] (numeric) = 1.0424531577111193363788605096318
absolute error = 1.97964563e-23
relative error = 1.8990259805501897529818424170930e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0417
y[1] (analytic) = 1.0425572347834067449652731651598
y[1] (numeric) = 1.0425572347834067449652930081625
absolute error = 1.98430027e-23
relative error = 1.9033010407454917021664036461661e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0418
y[1] (analytic) = 1.0426613214301217977389484600126
y[1] (numeric) = 1.0426613214301217977389683495567
absolute error = 1.98895441e-23
relative error = 1.9075747504203337749284171511009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0419
y[1] (analytic) = 1.0427654176502236282335834587195
y[1] (numeric) = 1.0427654176502236282336033948
absolute error = 1.99360805e-23
relative error = 1.9118471098633220549131236568974e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 1.0428695234426712742490273248348
y[1] (numeric) = 1.0428695234426712742490473074465
absolute error = 1.99826117e-23
relative error = 1.9161181001851844882990208757716e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.3MB, time=7.42
NO POLE
x[1] = 0.0421
y[1] (analytic) = 1.0429736388064236778616711464741
y[1] (numeric) = 1.042973638806423677861691175612
absolute error = 2.00291379e-23
relative error = 1.9203877408561632840602122390532e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0422
y[1] (analytic) = 1.043077763740439685434858515542
y[1] (numeric) = 1.043077763740439685434878591201
absolute error = 2.00756590e-23
relative error = 1.9246560225777800423420613143124e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0423
y[1] (analytic) = 1.0431818982436780476292970640898
y[1] (numeric) = 1.0431818982436780476293171862648
absolute error = 2.01221750e-23
relative error = 1.9289229456414166252899711339589e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0424
y[1] (analytic) = 1.0432860423150974194134709576996
y[1] (numeric) = 1.0432860423150974194134911263857
absolute error = 2.01686861e-23
relative error = 1.9331885295086285484035149139458e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0425
y[1] (analytic) = 1.0433901959536563600740543457916
y[1] (numeric) = 1.0433901959536563600740745609835
absolute error = 2.02151919e-23
relative error = 1.9374527361284393475139329294665e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0426
y[1] (analytic) = 1.0434943591583133332263257687473
y[1] (numeric) = 1.0434943591583133332263460304401
absolute error = 2.02616928e-23
relative error = 1.9417156041306405668193070199897e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0427
y[1] (analytic) = 1.0435985319280267068245835217493
y[1] (numeric) = 1.0435985319280267068246038299379
absolute error = 2.03081886e-23
relative error = 1.9459771146363191524538967433188e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0428
y[1] (analytic) = 1.0437027142617547531725619752291
y[1] (numeric) = 1.0437027142617547531725823299084
absolute error = 2.03546793e-23
relative error = 1.9502372679367355993128979814601e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0429
y[1] (analytic) = 1.0438069061584556489338488518209
y[1] (numeric) = 1.0438069061584556489338692529859
absolute error = 2.04011650e-23
relative error = 1.9544960739034419228789527726852e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 1.0439111076170874751423034597174
y[1] (numeric) = 1.0439111076170874751423239073631
absolute error = 2.04476457e-23
relative error = 1.9587535328247807674711224375526e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0431
y[1] (analytic) = 1.0440153186366082172124758823224
y[1] (numeric) = 1.0440153186366082172124963764437
absolute error = 2.04941213e-23
relative error = 1.9630096354106673515592065194704e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0432
y[1] (analytic) = 1.0441195392159757649500271240966
y[1] (numeric) = 1.0441195392159757649500476646884
absolute error = 2.05405918e-23
relative error = 1.9672643819522647303403420843470e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0433
y[1] (analytic) = 1.0442237693541479125621502124922
y[1] (numeric) = 1.0442237693541479125621707995494
absolute error = 2.05870572e-23
relative error = 1.9715177727407113792720968150628e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0434
y[1] (analytic) = 1.0443280090500823586679922558726
y[1] (numeric) = 1.04432800905008235866801288939
absolute error = 2.06335174e-23
relative error = 1.9757697984915855956005079486805e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0435
y[1] (analytic) = 1.0444322583027367063090774573116
y[1] (numeric) = 1.0444322583027367063090981372843
absolute error = 2.06799727e-23
relative error = 1.9800204882225833348121306575766e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.3MB, time=7.69
x[1] = 0.0436
y[1] (analytic) = 1.0445365171110684629597310841704
y[1] (numeric) = 1.0445365171110684629597518105933
absolute error = 2.07264229e-23
relative error = 1.9842698230717865851826787974405e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0437
y[1] (analytic) = 1.0446407854740350405375043933448
y[1] (numeric) = 1.0446407854740350405375251662129
absolute error = 2.07728681e-23
relative error = 1.9885178129029041097136775810989e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0438
y[1] (analytic) = 1.0447450633905937554136005120815
y[1] (numeric) = 1.0447450633905937554136213313897
absolute error = 2.08193082e-23
relative error = 1.9927644484323719177336639807279e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0439
y[1] (analytic) = 1.0448493508597018284233012742574
y[1] (numeric) = 1.0448493508597018284233221400006
absolute error = 2.08657432e-23
relative error = 1.9970097299511810805852982641651e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 1.0449536478803163848763950120176
y[1] (numeric) = 1.0449536478803163848764159241908
absolute error = 2.09121732e-23
relative error = 2.0012536673201003779683842119062e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0441
y[1] (analytic) = 1.0450579544513944545676053026694
y[1] (numeric) = 1.0450579544513944545676262612675
absolute error = 2.09585981e-23
relative error = 2.0054962512583585517840631849622e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0442
y[1] (analytic) = 1.045162270571892971787020670726
y[1] (numeric) = 1.045162270571892971787041675744
absolute error = 2.10050180e-23
relative error = 2.0097374916247648830673160878688e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0443
y[1] (analytic) = 1.0452665962407687753305252449973
y[1] (numeric) = 1.04526659624076877533054629643
absolute error = 2.10514327e-23
relative error = 2.0139773695734720821255465536685e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0444
y[1] (analytic) = 1.0453709314569786085102303706217
y[1] (numeric) = 1.0453709314569786085102514684641
absolute error = 2.10978424e-23
relative error = 2.0182159045301772450707103693046e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0445
y[1] (analytic) = 1.045475276219479119164907175937
y[1] (numeric) = 1.045475276219479119164928320184
absolute error = 2.11442470e-23
relative error = 2.0224530872178308479339718955977e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0446
y[1] (analytic) = 1.0455796305272268596704200940838
y[1] (numeric) = 1.0455796305272268596704412847302
absolute error = 2.11906464e-23
relative error = 2.0266889083631776293449883473705e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0447
y[1] (analytic) = 1.0456839943791782869501613392377
y[1] (numeric) = 1.0456839943791782869501825762786
absolute error = 2.12370409e-23
relative error = 2.0309233969492297167338955675496e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0448
y[1] (analytic) = 1.0457883677742897624854863373674
y[1] (numeric) = 1.0457883677742897624855076207976
absolute error = 2.12834302e-23
relative error = 2.0351565245745357750440485215262e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0449
y[1] (analytic) = 1.0458927507115175523261501114119
y[1] (numeric) = 1.0458927507115175523261714412264
absolute error = 2.13298145e-23
relative error = 2.0393883106551215896277181819584e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 1.0459971431898178271007446207744
y[1] (numeric) = 1.0459971431898178271007659969682
absolute error = 2.13761938e-23
relative error = 2.0436187554788423818980528497146e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0451
y[1] (analytic) = 1.0461015452081466620271370550281
y[1] (numeric) = 1.046101545208146662027158477596
absolute error = 2.14225679e-23
relative error = 2.0478478402149260832224286731853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.3MB, time=7.96
NO POLE
x[1] = 0.0452
y[1] (analytic) = 1.0462059567654600369229090817279
y[1] (numeric) = 1.0462059567654600369229305506649
absolute error = 2.14689370e-23
relative error = 2.0520755842735979869467799683832e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0453
y[1] (analytic) = 1.046310377860713836215797048227
y[1] (numeric) = 1.0463103778607138362158185635279
absolute error = 2.15153009e-23
relative error = 2.0563019688278523534055353081166e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0454
y[1] (analytic) = 1.0464148084928638489541331373898
y[1] (numeric) = 1.0464148084928638489541546990496
absolute error = 2.15616598e-23
relative error = 2.0605270132840481796382030875322e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0455
y[1] (analytic) = 1.0465192486608657688172874771006
y[1] (numeric) = 1.0465192486608657688173090851143
absolute error = 2.16080137e-23
relative error = 2.0647507179299170705546345382584e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0456
y[1] (analytic) = 1.0466236983636751941261112034611
y[1] (numeric) = 1.0466236983636751941261328578235
absolute error = 2.16543624e-23
relative error = 2.0689730639441013491445268743300e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0457
y[1] (analytic) = 1.0467281576002476278533804775726
y[1] (numeric) = 1.0467281576002476278534021782787
absolute error = 2.17007061e-23
relative error = 2.0731940707271622358452781712187e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0458
y[1] (analytic) = 1.0468326263695384776342414558004
y[1] (numeric) = 1.0468326263695384776342632028451
absolute error = 2.17470447e-23
relative error = 2.0774137290141315228396838462527e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0459
y[1] (analytic) = 1.046937104670503055776656213413
y[1] (numeric) = 1.0469371046705030557766780067912
absolute error = 2.17933782e-23
relative error = 2.0816320390955017263232598149844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 1.0470415925020965792718496214939
y[1] (numeric) = 1.0470415925020965792718714612006
absolute error = 2.18397067e-23
relative error = 2.0858490108124590592132781595448e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0461
y[1] (analytic) = 1.0471460898632741698047571770209
y[1] (numeric) = 1.047146089863274169804779063051
absolute error = 2.18860301e-23
relative error = 2.0900646349028203145645181145421e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0462
y[1] (analytic) = 1.0472505967529908537644737860077
y[1] (numeric) = 1.0472505967529908537644957183561
absolute error = 2.19323484e-23
relative error = 2.0942789116570024222649960412007e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0463
y[1] (analytic) = 1.0473551131702015622547034996046
y[1] (numeric) = 1.0473551131702015622547254782662
absolute error = 2.19786616e-23
relative error = 2.0984918413653969627595258689502e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0464
y[1] (analytic) = 1.0474596391138611311042102030524
y[1] (numeric) = 1.0474596391138611311042322280221
absolute error = 2.20249697e-23
relative error = 2.1027034243183701417352791392645e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0465
y[1] (analytic) = 1.0475641745829243008772692573861
y[1] (numeric) = 1.0475641745829243008772913286589
absolute error = 2.20712728e-23
relative error = 2.1069136703522173159972654588490e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0466
y[1] (analytic) = 1.0476687195763457168841200937839
y[1] (numeric) = 1.0476687195763457168841422113547
absolute error = 2.21175708e-23
relative error = 2.1111225702093941671292951565702e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0467
y[1] (analytic) = 1.0477732740930799291914197604554
y[1] (numeric) = 1.0477732740930799291914419243191
absolute error = 2.21638637e-23
relative error = 2.1153301241801909349186460151270e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.3MB, time=8.25
NO POLE
x[1] = 0.0468
y[1] (analytic) = 1.0478778381320813926326974219668
y[1] (numeric) = 1.0478778381320813926327196321183
absolute error = 2.22101515e-23
relative error = 2.1195363325548723833784834428845e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0469
y[1] (analytic) = 1.0479824116923044668188098108967
y[1] (numeric) = 1.0479824116923044668188320673309
absolute error = 2.22564342e-23
relative error = 2.1237411956236777755448493818883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 1.0480869947727034161483976317188
y[1] (numeric) = 1.0480869947727034161484199344307
absolute error = 2.23027119e-23
relative error = 2.1279447232180135640481809556465e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0471
y[1] (analytic) = 1.048191587372232409818342916807
y[1] (numeric) = 1.0481915873722324098183652657915
absolute error = 2.23489845e-23
relative error = 2.1321469060849711046777053829033e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0472
y[1] (analytic) = 1.0482961894898455218342273344576
y[1] (numeric) = 1.0482961894898455218342497297096
absolute error = 2.23952520e-23
relative error = 2.1363477445147133166472054005152e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0473
y[1] (analytic) = 1.048400801124496731020791448825
y[1] (numeric) = 1.0484008011244967310208138903394
absolute error = 2.24415144e-23
relative error = 2.1405472387973775176218556220945e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0474
y[1] (analytic) = 1.0485054222751399210323949316653
y[1] (numeric) = 1.048505422275139921032417419437
absolute error = 2.24877717e-23
relative error = 2.1447453892230753986263791615582e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0475
y[1] (analytic) = 1.0486100529407288803634777257841
y[1] (numeric) = 1.0486100529407288803635002598081
absolute error = 2.25340240e-23
relative error = 2.1489422056183264634038139211621e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0476
y[1] (analytic) = 1.0487146931202173023590221600837
y[1] (numeric) = 1.0487146931202173023590447403548
absolute error = 2.25802711e-23
relative error = 2.1531376691993726055302429030780e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0477
y[1] (analytic) = 1.048819342812558785225016016104
y[1] (numeric) = 1.0488193428125587852250386426171
absolute error = 2.26265131e-23
relative error = 2.1573317897936335937233082431036e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0478
y[1] (analytic) = 1.0489240020167068320389165459543
y[1] (numeric) = 1.0489240020167068320389392187043
absolute error = 2.26727500e-23
relative error = 2.1615245676911183619760402693735e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0479
y[1] (analytic) = 1.0490286707316148507601154415298
y[1] (numeric) = 1.0490286707316148507601381605117
absolute error = 2.27189819e-23
relative error = 2.1657160127144380168076189512212e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 1.0491333489562361542404047549093
y[1] (numeric) = 1.0491333489562361542404275201179
absolute error = 2.27652086e-23
relative error = 2.1699061060873429885981161347032e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0481
y[1] (analytic) = 1.0492380366895239602344437698279
y[1] (numeric) = 1.0492380366895239602344665812582
absolute error = 2.28114303e-23
relative error = 2.1740948671640698100537156072313e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0482
y[1] (analytic) = 1.0493427339304313914102268241225
y[1] (numeric) = 1.0493427339304313914102496817694
absolute error = 2.28576469e-23
relative error = 2.1782822867018966443823494590428e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0483
y[1] (analytic) = 1.0494474406779114753595520830424
y[1] (numeric) = 1.0494474406779114753595749869009
absolute error = 2.29038585e-23
relative error = 2.1824683745195277662537377435909e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=8.53
NO POLE
x[1] = 0.0484
y[1] (analytic) = 1.0495521569309171446084912633233
y[1] (numeric) = 1.0495521569309171446085142133881
absolute error = 2.29500648e-23
relative error = 2.1866531023203454195359158123357e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0485
y[1] (analytic) = 1.0496568826884012366278603079168
y[1] (numeric) = 1.0496568826884012366278833041831
absolute error = 2.29962663e-23
relative error = 2.1908365180344956112387758724552e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0486
y[1] (analytic) = 1.0497616179493164938436910112751
y[1] (numeric) = 1.0497616179493164938437140537376
absolute error = 2.30424625e-23
relative error = 2.1950185743133649580855832093459e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0487
y[1] (analytic) = 1.0498663627126155636477035950802
y[1] (numeric) = 1.0498663627126155636477266837339
absolute error = 2.30886537e-23
relative error = 2.1991993000274985010304282396666e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0488
y[1] (analytic) = 1.0499711169772509984077802343195
y[1] (numeric) = 1.0499711169772509984078033691592
absolute error = 2.31348397e-23
relative error = 2.2033786764156529317349238744936e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0489
y[1] (analytic) = 1.050075880742175255478439533597
y[1] (numeric) = 1.0500758807421752554784627146176
absolute error = 2.31810206e-23
relative error = 2.2075567132935250663297148961757e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 1.0501806540063406972113119535802
y[1] (numeric) = 1.0501806540063406972113351807767
absolute error = 2.32271965e-23
relative error = 2.2117334204729847061805058707677e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0491
y[1] (analytic) = 1.0502854367686995909656161874748
y[1] (numeric) = 1.0502854367686995909656394608421
absolute error = 2.32733673e-23
relative error = 2.2159087887196331840729284854116e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0492
y[1] (analytic) = 1.0503902290282041091186364874238
y[1] (numeric) = 1.0503902290282041091186598069569
absolute error = 2.33195331e-23
relative error = 2.2200828278433886133103909557936e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0493
y[1] (analytic) = 1.0504950307838063290762009407261
y[1] (numeric) = 1.0504950307838063290762243064197
absolute error = 2.33656936e-23
relative error = 2.2242555095730576222850164131920e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0494
y[1] (analytic) = 1.0505998420344582332831606957689
y[1] (numeric) = 1.050599842034458233283184107618
absolute error = 2.34118491e-23
relative error = 2.2284268627590487942492825663879e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0495
y[1] (analytic) = 1.050704662779111709233870137571
y[1] (numeric) = 1.0507046627791117092338935955706
absolute error = 2.34579996e-23
relative error = 2.2325968876880814894519998147278e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0496
y[1] (analytic) = 1.0508094930167185494826680128308
y[1] (numeric) = 1.0508094930167185494826915169756
absolute error = 2.35041448e-23
relative error = 2.2367655560974309968184286901714e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0497
y[1] (analytic) = 1.050914332746230451654359504373
y[1] (numeric) = 1.0509143327462304516543830546581
absolute error = 2.35502851e-23
relative error = 2.2409329063444037464811157271463e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0498
y[1] (analytic) = 1.0510191819665990184546992548934
y[1] (numeric) = 1.0510191819665990184547228513135
absolute error = 2.35964201e-23
relative error = 2.2450989006544968148337142709178e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0499
y[1] (analytic) = 1.0511240406767757576808753398911
y[1] (numeric) = 1.0511240406767757576808989824412
absolute error = 2.36425501e-23
relative error = 2.2492635678637441729855456147682e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.3MB, time=8.80
NO POLE
x[1] = 0.05
y[1] (analytic) = 1.051228908875712082231994189689
y[1] (numeric) = 1.051228908875712082232017878364
absolute error = 2.36886750e-23
relative error = 2.2534268987460596339893489508424e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0501
y[1] (analytic) = 1.0513337865623593101195664604333
y[1] (numeric) = 1.0513337865623593101195901952281
absolute error = 2.37347948e-23
relative error = 2.2575888935908541868801426534154e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0502
y[1] (analytic) = 1.0514386737356686644779938539701
y[1] (numeric) = 1.0514386737356686644780176348797
absolute error = 2.37809096e-23
relative error = 2.2617495621982906845142229223382e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0503
y[1] (analytic) = 1.0515435703945912735750568864925
y[1] (numeric) = 1.0515435703945912735750807135117
absolute error = 2.38270192e-23
relative error = 2.2659088858352223359924510224894e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0504
y[1] (analytic) = 1.0516484765380781708224036058538
y[1] (numeric) = 1.0516484765380781708224274789775
absolute error = 2.38731237e-23
relative error = 2.2700668743027081309921164188287e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0505
y[1] (analytic) = 1.0517533921650802947860392574427
y[1] (numeric) = 1.0517533921650802947860631766658
absolute error = 2.39192231e-23
relative error = 2.2742235278900536311334889175003e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0506
y[1] (analytic) = 1.0518583172745484891968168985142
y[1] (numeric) = 1.0518583172745484891968408638317
absolute error = 2.39653175e-23
relative error = 2.2783788563935217970607985800360e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0507
y[1] (analytic) = 1.0519632518654335029609289608726
y[1] (numeric) = 1.0519632518654335029609529722793
absolute error = 2.40114067e-23
relative error = 2.2825328410874493634895305843377e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0508
y[1] (analytic) = 1.0520681959366859901703997618004
y[1] (numeric) = 1.0520681959366859901704238192912
absolute error = 2.40574908e-23
relative error = 2.2866854917689948187570403397451e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0509
y[1] (analytic) = 1.0521731494872565101135789631296
y[1] (numeric) = 1.0521731494872565101136030666995
absolute error = 2.41035699e-23
relative error = 2.2908368182314970353884458535517e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 1.0522781125160955272856359783499
y[1] (numeric) = 1.0522781125160955272856601279936
absolute error = 2.41496437e-23
relative error = 2.2949867922517118567028432640799e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0511
y[1] (analytic) = 1.052383085022153411399055327647
y[1] (numeric) = 1.0523830850221534113990795233596
absolute error = 2.41957126e-23
relative error = 2.2991354521334465447691366881778e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0512
y[1] (analytic) = 1.0524880670043804373941329407705
y[1] (numeric) = 1.0524880670043804373941571825468
absolute error = 2.42417763e-23
relative error = 2.3032827696562479069195334477429e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0513
y[1] (analytic) = 1.0525930584617267854494734076211
y[1] (numeric) = 1.052593058461726785449497695456
absolute error = 2.42878349e-23
relative error = 2.3074287546124005868934150720031e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0514
y[1] (analytic) = 1.0526980593931425409924881764565
y[1] (numeric) = 1.0526980593931425409925125103448
absolute error = 2.43338883e-23
relative error = 2.3115733977915714582899045128541e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=125.8MB, alloc=4.3MB, time=9.09
x[1] = 0.0515
y[1] (analytic) = 1.0528030697975776947098946996078
y[1] (numeric) = 1.0528030697975776947099190795445
absolute error = 2.43799367e-23
relative error = 2.3157167184825484186269282510842e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0516
y[1] (analytic) = 1.0529080896739821425582165266044
y[1] (numeric) = 1.0529080896739821425582409525844
absolute error = 2.44259800e-23
relative error = 2.3198587074739974363558530213203e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0517
y[1] (analytic) = 1.0530131190213056857742843445996
y[1] (numeric) = 1.0530131190213056857743088166177
absolute error = 2.44720181e-23
relative error = 2.3239993555583476068647484048100e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0518
y[1] (analytic) = 1.0531181578384980308857379659933
y[1] (numeric) = 1.0531181578384980308857624840445
absolute error = 2.45180512e-23
relative error = 2.3281386820186220561938978721885e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0519
y[1] (analytic) = 1.0532232061245087897215292631474
y[1] (numeric) = 1.0532232061245087897215538272265
absolute error = 2.45640791e-23
relative error = 2.3322766681515855763936570019196e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 1.0533282638782874794224260500869
y[1] (numeric) = 1.053328263878287479422450660189
absolute error = 2.46101021e-23
relative error = 2.3364133427301356047678978520112e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0521
y[1] (analytic) = 1.0534333310987835224515169110843
y[1] (numeric) = 1.0534333310987835224515415672041
absolute error = 2.46561198e-23
relative error = 2.3405486680663917193818083123478e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0522
y[1] (analytic) = 1.053538407784946246604716976019
y[1] (numeric) = 1.0535384077849462466047416781515
absolute error = 2.47021325e-23
relative error = 2.3446826729303568108117402370260e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0523
y[1] (analytic) = 1.0536434939357248850212746424102
y[1] (numeric) = 1.0536434939357248850212993905502
absolute error = 2.47481400e-23
relative error = 2.3488153386262643937077230028520e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0524
y[1] (analytic) = 1.0537485895500685761942792440151
y[1] (numeric) = 1.0537485895500685761943040381576
absolute error = 2.47941425e-23
relative error = 2.3529466844256129935723719195799e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0525
y[1] (analytic) = 1.0538536946269263639811696658896
y[1] (numeric) = 1.0538536946269263639811945060294
absolute error = 2.48401398e-23
relative error = 2.3570766916363690993406969563801e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0526
y[1] (analytic) = 1.053958809165247197614243905805
y[1] (numeric) = 1.053958809165247197614268791937
absolute error = 2.48861320e-23
relative error = 2.3612053700381543370254151970878e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0527
y[1] (analytic) = 1.0540639331639799317111695819162
y[1] (numeric) = 1.0540639331639799317111945140353
absolute error = 2.49321191e-23
relative error = 2.3653327199196871695954088686859e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0528
y[1] (analytic) = 1.0541690666220733262854953865766
y[1] (numeric) = 1.0541690666220733262855203646776
absolute error = 2.49781010e-23
relative error = 2.3694587320835146997536688903949e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0529
y[1] (analytic) = 1.0542742095384760467571634861931
y[1] (numeric) = 1.0542742095384760467571885102711
absolute error = 2.50240780e-23
relative error = 2.3735834352767347030149120082527e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 1.054379361912136663963022867019
y[1] (numeric) = 1.0543793619121366639630479370688
absolute error = 2.50700498e-23
relative error = 2.3777068013295514899149025736244e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.3MB, time=9.37
x[1] = 0.0531
y[1] (analytic) = 1.0544845237420036541673436267759
y[1] (numeric) = 1.0544845237420036541673687427924
absolute error = 2.51160165e-23
relative error = 2.3818288400167199960946496180628e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0532
y[1] (analytic) = 1.0545896950270253990723322120025
y[1] (numeric) = 1.0545896950270253990723573739806
absolute error = 2.51619781e-23
relative error = 2.3859495516268237015162877933947e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0533
y[1] (analytic) = 1.0546948757661501858286476010239
y[1] (numeric) = 1.0546948757661501858286728089583
absolute error = 2.52079344e-23
relative error = 2.3900689174855886682156691358308e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0534
y[1] (analytic) = 1.0548000659583262070459184324358
y[1] (numeric) = 1.0548000659583262070459436863215
absolute error = 2.52538857e-23
relative error = 2.3941869663286263502453552482452e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0535
y[1] (analytic) = 1.0549052656025015608032610790001
y[1] (numeric) = 1.0549052656025015608032863788321
absolute error = 2.52998320e-23
relative error = 2.3983036984416020318267168666990e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0536
y[1] (analytic) = 1.0550104746976242506597986668446
y[1] (numeric) = 1.0550104746976242506598240126177
absolute error = 2.53457731e-23
relative error = 2.4024190951529967265264317245258e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0537
y[1] (analytic) = 1.055115693242642185665181039863
y[1] (numeric) = 1.055115693242642185665206431572
absolute error = 2.53917090e-23
relative error = 2.4065331567540940128633447340347e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0538
y[1] (analytic) = 1.0552209212365031803701056692096
y[1] (numeric) = 1.0552209212365031803701311068495
absolute error = 2.54376399e-23
relative error = 2.4106459024895267190357982859637e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0539
y[1] (analytic) = 1.0553261586781549548368395077837
y[1] (numeric) = 1.0553261586781549548368649913494
absolute error = 2.54835657e-23
relative error = 2.4147573231691091623300076601164e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 1.055431405566545134649741789598
y[1] (numeric) = 1.0554314055665451346497673190845
absolute error = 2.55294865e-23
relative error = 2.4188674285560058988285107545318e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0541
y[1] (analytic) = 1.0555366619006212509257877739268
y[1] (numeric) = 1.0555366619006212509258133493287
absolute error = 2.55754019e-23
relative error = 2.4229761810403060560945230252449e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0542
y[1] (analytic) = 1.0556419276793307403250934341263
y[1] (numeric) = 1.0556419276793307403251190554386
absolute error = 2.56213123e-23
relative error = 2.4270836188104600438085700532699e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0543
y[1] (analytic) = 1.0557472029016209450614410910258
y[1] (numeric) = 1.0557472029016209450614667582434
absolute error = 2.56672176e-23
relative error = 2.4311897326799530704296655861911e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0544
y[1] (analytic) = 1.0558524875664391129128059907807
y[1] (numeric) = 1.0558524875664391129128317038985
absolute error = 2.57131178e-23
relative error = 2.4352945229370416122779157571676e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0545
y[1] (analytic) = 1.0559577816727323972318838270838
y[1] (numeric) = 1.0559577816727323972319095860967
absolute error = 2.57590129e-23
relative error = 2.4393979898699547936492232275290e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0546
y[1] (analytic) = 1.0560630852194478569566192076298
y[1] (numeric) = 1.0560630852194478569566450125327
absolute error = 2.58049029e-23
relative error = 2.4435001337668943632961497431650e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.3MB, time=9.64
NO POLE
x[1] = 0.0547
y[1] (analytic) = 1.0561683982055324566207350647272
y[1] (numeric) = 1.0561683982055324566207609155148
absolute error = 2.58507876e-23
relative error = 2.4476009359796604772119776023168e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0548
y[1] (analytic) = 1.0562737206299330663642630099517
y[1] (numeric) = 1.056273720629933066364288906619
absolute error = 2.58966673e-23
relative error = 2.4517004252037936088619215488518e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0549
y[1] (analytic) = 1.0563790524915964619440746327377
y[1] (numeric) = 1.0563790524915964619441005752797
absolute error = 2.59425420e-23
relative error = 2.4557986017245806727195405249111e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 1.0564843937894693247444137428009
y[1] (numeric) = 1.0564843937894693247444397312123
absolute error = 2.59884114e-23
relative error = 2.4598954374312162792823323969540e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0551
y[1] (analytic) = 1.0565897445224982417874295562864
y[1] (numeric) = 1.0565897445224982417874555905621
absolute error = 2.60342757e-23
relative error = 2.4639909515462503486470986046373e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0552
y[1] (analytic) = 1.0566951046896297057437108255389
y[1] (numeric) = 1.0566951046896297057437369056739
absolute error = 2.60801350e-23
relative error = 2.4680851538211869690084923120493e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0553
y[1] (analytic) = 1.0568004742898101149428209123883
y[1] (numeric) = 1.0568004742898101149428470383773
absolute error = 2.61259890e-23
relative error = 2.4721780161536318585899886498080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0554
y[1] (analytic) = 1.0569058533219857733838338048445
y[1] (numeric) = 1.0569058533219857733838599766825
absolute error = 2.61718380e-23
relative error = 2.4762695672219694182081350858868e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0555
y[1] (analytic) = 1.0570112417851028907458710770986
y[1] (numeric) = 1.0570112417851028907458972947805
absolute error = 2.62176819e-23
relative error = 2.4803597978506856320344300745174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0556
y[1] (analytic) = 1.0571166396781075823986397927226
y[1] (numeric) = 1.0571166396781075823986660562433
absolute error = 2.62635207e-23
relative error = 2.4844487083277065822463849306507e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0557
y[1] (analytic) = 1.0572220469999458694129713509636
y[1] (numeric) = 1.0572220469999458694129976603179
absolute error = 2.63093543e-23
relative error = 2.4885362894821798073325572319301e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0558
y[1] (analytic) = 1.0573274637495636785713612760266
y[1] (numeric) = 1.0573274637495636785713876312094
absolute error = 2.63551828e-23
relative error = 2.4926225510626131077194737627457e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0559
y[1] (analytic) = 1.0574328899259068423785099492409
y[1] (numeric) = 1.057432889925906842378536350247
absolute error = 2.64010061e-23
relative error = 2.4967074838999843679340779488810e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 1.0575383255279210990718642840042
y[1] (numeric) = 1.0575383255279210990718907308285
absolute error = 2.64468243e-23
relative error = 2.5007910977408592876589239316424e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0561
y[1] (analytic) = 1.0576437705545520926321603433994
y[1] (numeric) = 1.0576437705545520926321868360369
absolute error = 2.64926375e-23
relative error = 2.5048734023280042702472174837864e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0562
y[1] (analytic) = 1.0577492250047453727939669003787
y[1] (numeric) = 1.0577492250047453727939934388241
absolute error = 2.65384454e-23
relative error = 2.5089543695842406088203662536016e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.3MB, time=9.92
NO POLE
x[1] = 0.0563
y[1] (analytic) = 1.0578546888774463950562299404085
y[1] (numeric) = 1.0578546888774463950562565246568
absolute error = 2.65842483e-23
relative error = 2.5130340281622378662043686623227e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0564
y[1] (analytic) = 1.0579601621716005206928181064718
y[1] (numeric) = 1.0579601621716005206928447365178
absolute error = 2.66300460e-23
relative error = 2.5171123594425686970974312384331e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0565
y[1] (analytic) = 1.0580656448861530167630690863205
y[1] (numeric) = 1.058065644886153016763095762159
absolute error = 2.66758385e-23
relative error = 2.5211893637157359959722290314701e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0566
y[1] (analytic) = 1.0581711370200490561223369418728
y[1] (numeric) = 1.0581711370200490561223636634988
absolute error = 2.67216260e-23
relative error = 2.5252650601727486156946841656769e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0567
y[1] (analytic) = 1.0582766385722337174325403806516
y[1] (numeric) = 1.05827663857223371743256714806
absolute error = 2.67674084e-23
relative error = 2.5293394396490747155668302259901e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0568
y[1] (analytic) = 1.0583821495416519851727119691563
y[1] (numeric) = 1.0583821495416519851727387823419
absolute error = 2.68131856e-23
relative error = 2.5334124929839232331137028156244e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0569
y[1] (analytic) = 1.0584876699272487496495482880633
y[1] (numeric) = 1.0584876699272487496495751470209
absolute error = 2.68589576e-23
relative error = 2.5374842204676840021986890833034e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 1.0585931997279688070079610291504
y[1] (numeric) = 1.058593199727968807007987933875
absolute error = 2.69047246e-23
relative error = 2.5415546412837170511985748730725e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0571
y[1] (analytic) = 1.0586987389427568592416290338394
y[1] (numeric) = 1.0586987389427568592416559843258
absolute error = 2.69504864e-23
relative error = 2.5456237368255895295677286244518e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0572
y[1] (analytic) = 1.0588042875705575142035512732498
y[1] (numeric) = 1.0588042875705575142035782694929
absolute error = 2.69962431e-23
relative error = 2.5496915168282222361011345256161e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0573
y[1] (analytic) = 1.0589098456103152856166007696603
y[1] (numeric) = 1.0589098456103152856166278116551
absolute error = 2.70419948e-23
relative error = 2.5537579910227413763570013957294e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0574
y[1] (analytic) = 1.0590154130609745930840794592717
y[1] (numeric) = 1.0590154130609745930841065470129
absolute error = 2.70877412e-23
relative error = 2.5578231313655467782922058993426e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0575
y[1] (analytic) = 1.0591209899214797621002739961643
y[1] (numeric) = 1.0591209899214797621003011296467
absolute error = 2.71334824e-23
relative error = 2.5618869475914739189496050087069e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0576
y[1] (analytic) = 1.0592265761907750240610124973466
y[1] (numeric) = 1.0592265761907750240610396765652
absolute error = 2.71792186e-23
relative error = 2.5659494588724149706797698743537e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0577
y[1] (analytic) = 1.0593321718678045162742222287886
y[1] (numeric) = 1.0593321718678045162742494537382
absolute error = 2.72249496e-23
relative error = 2.5700106466130661427786913205766e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0578
y[1] (analytic) = 1.0594377769515122819704882323329
y[1] (numeric) = 1.0594377769515122819705155030085
absolute error = 2.72706756e-23
relative error = 2.5740705299814986737496890526207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.3MB, time=10.20
NO POLE
x[1] = 0.0579
y[1] (analytic) = 1.0595433914408422703136128933811
y[1] (numeric) = 1.0595433914408422703136402097774
absolute error = 2.73163963e-23
relative error = 2.5781290809480890082710130073811e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 1.0596490153347383364111764492458
y[1] (numeric) = 1.0596490153347383364112038113578
absolute error = 2.73621120e-23
relative error = 2.5821863281169975364176901779664e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0581
y[1] (analytic) = 1.059754648632144241325098438067
y[1] (numeric) = 1.0597546486321442413251258458895
absolute error = 2.74078225e-23
relative error = 2.5862422529003353360686596898555e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0582
y[1] (analytic) = 1.0598602913320036520822000881835
y[1] (numeric) = 1.0598602913320036520822275417114
absolute error = 2.74535279e-23
relative error = 2.5902968650233278537229219173042e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0583
y[1] (analytic) = 1.0599659434332601416847676478563
y[1] (numeric) = 1.0599659434332601416847951470844
absolute error = 2.74992281e-23
relative error = 2.5943501553388791135131577325691e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0584
y[1] (analytic) = 1.0600716049348571891211166552364
y[1] (numeric) = 1.0600716049348571891211442001596
absolute error = 2.75449232e-23
relative error = 2.5984021335702763388086934857383e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0585
y[1] (analytic) = 1.0601772758357381793761571484734
y[1] (numeric) = 1.0601772758357381793761847390865
absolute error = 2.75906131e-23
relative error = 2.6024527905722473092009545716139e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0586
y[1] (analytic) = 1.0602829561348464034419598158572
y[1] (numeric) = 1.0602829561348464034419874521552
absolute error = 2.76362980e-23
relative error = 2.6065021454975859860147546089076e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0587
y[1] (analytic) = 1.0603886458311250583283230858888
y[1] (numeric) = 1.0603886458311250583283507678665
absolute error = 2.76819777e-23
relative error = 2.6105501797695186839444555409070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0588
y[1] (analytic) = 1.0604943449235172470733411571733
y[1] (numeric) = 1.0604943449235172470733688848255
absolute error = 2.77276522e-23
relative error = 2.6145968936778928021742312779849e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0589
y[1] (analytic) = 1.0606000534109659787539729680301
y[1] (numeric) = 1.0606000534109659787540007413517
absolute error = 2.77733216e-23
relative error = 2.6186422969411515816990325258327e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 1.0607057712924141684966121057147
y[1] (numeric) = 1.0607057712924141684966399247005
absolute error = 2.78189858e-23
relative error = 2.6226863804185801331352533883960e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0591
y[1] (analytic) = 1.0608114985668046374876576551456
y[1] (numeric) = 1.0608114985668046374876855197907
absolute error = 2.78646451e-23
relative error = 2.6267291726801755720607377680687e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0592
y[1] (analytic) = 1.0609172352330801129840859870323
y[1] (numeric) = 1.0609172352330801129841138973314
absolute error = 2.79102991e-23
relative error = 2.6307706363039899930130272868070e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0593
y[1] (analytic) = 1.0610229812901832283240234852957
y[1] (numeric) = 1.0610229812901832283240514412436
absolute error = 2.79559479e-23
relative error = 2.6348107810074116590169573532592e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0594
y[1] (analytic) = 1.0611287367370565229373202136787
y[1] (numeric) = 1.0611287367370565229373482152703
absolute error = 2.80015916e-23
relative error = 2.6388496165040418593517855893747e-21 %
h = 0.0001
memory used=144.9MB, alloc=4.3MB, time=10.49
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0595
y[1] (analytic) = 1.0612345015726424423561245214385
y[1] (numeric) = 1.0612345015726424423561525686687
absolute error = 2.80472302e-23
relative error = 2.6428871430807079005007424892634e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0596
y[1] (analytic) = 1.0613402757958833382254585880169
y[1] (numeric) = 1.0613402757958833382254866808804
absolute error = 2.80928635e-23
relative error = 2.6469233421801107231126282107429e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0597
y[1] (analytic) = 1.0614460594057214683137949065803
y[1] (numeric) = 1.0614460594057214683138230450722
absolute error = 2.81384919e-23
relative error = 2.6509582517790942456639853367938e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0598
y[1] (analytic) = 1.0615518524010989965236337063273
y[1] (numeric) = 1.0615518524010989965236618904423
absolute error = 2.81841150e-23
relative error = 2.6549918344780820366487381876265e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0599
y[1] (analytic) = 1.0616576547809579929020813134538
y[1] (numeric) = 1.0616576547809579929021095431869
absolute error = 2.82297331e-23
relative error = 2.6590241188271166187839207540134e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 1.0617634665442404336514294506742
y[1] (numeric) = 1.06176346654424043365145772602
absolute error = 2.82753458e-23
relative error = 2.6630550674368915941401485544574e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0601
y[1] (analytic) = 1.0618692876898882011397354751883
y[1] (numeric) = 1.0618692876898882011397637961419
absolute error = 2.83209536e-23
relative error = 2.6670847276892845238937382139791e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0602
y[1] (analytic) = 1.0619751182168430839114035549935
y[1] (numeric) = 1.0619751182168430839114319215496
absolute error = 2.83665561e-23
relative error = 2.6711130621996245359456724234708e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0603
y[1] (analytic) = 1.0620809581240467766977667834305
y[1] (numeric) = 1.0620809581240467766977951955841
absolute error = 2.84121536e-23
relative error = 2.6751400995065740491708037909634e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0604
y[1] (analytic) = 1.0621868074104408804276702318624
y[1] (numeric) = 1.0621868074104408804276986896082
absolute error = 2.84577458e-23
relative error = 2.6791658116502673012907705722961e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0605
y[1] (analytic) = 1.0622926660749669022380549403762
y[1] (numeric) = 1.0622926660749669022380834437092
absolute error = 2.85033330e-23
relative error = 2.6831902271636783949651367491035e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0606
y[1] (analytic) = 1.0623985341165662554845428464056
y[1] (numeric) = 1.0623985341165662554845713953206
absolute error = 2.85489150e-23
relative error = 2.6872133275051767011611511356095e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0607
y[1] (analytic) = 1.0625044115341802597520226511655
y[1] (numeric) = 1.0625044115341802597520512456573
absolute error = 2.85944918e-23
relative error = 2.6912351129640583942037820535055e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0608
y[1] (analytic) = 1.062610298326750140865236623794
y[1] (numeric) = 1.0626102983267501408652652638576
absolute error = 2.86400636e-23
relative error = 2.6952556026511657730668005954027e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0609
y[1] (analytic) = 1.0627161944932170308993683430971
y[1] (numeric) = 1.0627161944932170308993970287271
absolute error = 2.86856300e-23
relative error = 2.6992747592107095694454867921307e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=148.7MB, alloc=4.3MB, time=10.76
x[1] = 0.061
y[1] (analytic) = 1.0628221000325219681906313767867
y[1] (numeric) = 1.0628221000325219681906601079782
absolute error = 2.87311915e-23
relative error = 2.7032926299820859982849005140933e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0611
y[1] (analytic) = 1.0629280149436058973468588981111
y[1] (numeric) = 1.0629280149436058973468876748588
absolute error = 2.87767477e-23
relative error = 2.7073091776141362420259123712113e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0612
y[1] (analytic) = 1.0630339392254096692580942397665
y[1] (numeric) = 1.0630339392254096692581230620653
absolute error = 2.88222988e-23
relative error = 2.7113244212128971913877973093623e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0613
y[1] (analytic) = 1.0631398728768740411071823849887
y[1] (numeric) = 1.0631398728768740411072112528335
absolute error = 2.88678448e-23
relative error = 2.7153383610646768013982108924316e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0614
y[1] (analytic) = 1.0632458158969396763803623957155
y[1] (numeric) = 1.0632458158969396763803913091011
absolute error = 2.89133856e-23
relative error = 2.7193509880505912970024564957747e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0615
y[1] (analytic) = 1.0633517682845471448778607777152
y[1] (numeric) = 1.0633517682845471448778897366365
absolute error = 2.89589213e-23
relative error = 2.7233623118639278264604804449485e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0616
y[1] (analytic) = 1.0634577300386369227244857825761
y[1] (numeric) = 1.0634577300386369227245147870278
absolute error = 2.90044517e-23
relative error = 2.7273723139843298958988106384977e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0617
y[1] (analytic) = 1.0635637011581493923802226464488
y[1] (numeric) = 1.0635637011581493923802516964259
absolute error = 2.90499771e-23
relative error = 2.7313810229106660258874396999562e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0618
y[1] (analytic) = 1.0636696816420248426508297654386
y[1] (numeric) = 1.0636696816420248426508588609358
absolute error = 2.90954972e-23
relative error = 2.7353884107220432148589905152418e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0619
y[1] (analytic) = 1.0637756714892034686984358075377
y[1] (numeric) = 1.06377567148920346869846494855
absolute error = 2.91410123e-23
relative error = 2.7393945059116497744895156704684e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 1.0638816706986253720521377609965
y[1] (numeric) = 1.0638816706986253720521669475187
absolute error = 2.91865222e-23
relative error = 2.7433992899636964798552662193794e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0621
y[1] (analytic) = 1.0639876792692305606185999190228
y[1] (numeric) = 1.0639876792692305606186291510497
absolute error = 2.92320269e-23
relative error = 2.7474027631670678526977940894389e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0622
y[1] (analytic) = 1.0640936971999589486926538007067
y[1] (numeric) = 1.0640936971999589486926830782332
absolute error = 2.92775265e-23
relative error = 2.7514049352082873598000192016902e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0623
y[1] (analytic) = 1.0641997244897503569678990080635
y[1] (numeric) = 1.0641997244897503569679283310844
absolute error = 2.93230209e-23
relative error = 2.7554057969766387830215908744454e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0624
y[1] (analytic) = 1.0643057611375445125473050190886
y[1] (numeric) = 1.0643057611375445125473343875988
absolute error = 2.93685102e-23
relative error = 2.7594053581567138910675436681305e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0625
y[1] (analytic) = 1.0644118071422810489538139167194
y[1] (numeric) = 1.0644118071422810489538433307137
absolute error = 2.94139943e-23
relative error = 2.7634036096396101285803573843740e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.3MB, time=11.04
NO POLE
x[1] = 0.0626
y[1] (analytic) = 1.0645178625028995061409440535966
y[1] (numeric) = 1.0645178625028995061409735130699
absolute error = 2.94594733e-23
relative error = 2.7674005611079878944526544940377e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0627
y[1] (analytic) = 1.0646239272183393305033946525204
y[1] (numeric) = 1.0646239272183393305034241574675
absolute error = 2.95049471e-23
relative error = 2.7713962034547577929629215156065e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0628
y[1] (analytic) = 1.0647300012875398748876513424946
y[1] (numeric) = 1.0647300012875398748876808929104
absolute error = 2.95504158e-23
relative error = 2.7753905463606491816464638449944e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0629
y[1] (analytic) = 1.0648360847094403986025926302533
y[1] (numeric) = 1.0648360847094403986026222261325
absolute error = 2.95958792e-23
relative error = 2.7793835713292685630727238436021e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 1.0649421774829800674300973071622
y[1] (numeric) = 1.0649421774829800674301269484998
absolute error = 2.96413376e-23
relative error = 2.7833753068225836703127974219703e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0631
y[1] (analytic) = 1.0650482796070979536356527913924
y[1] (numeric) = 1.0650482796070979536356824781832
absolute error = 2.96867908e-23
relative error = 2.7873657343450774841775645496925e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0632
y[1] (analytic) = 1.0651543910807330359789644052557
y[1] (numeric) = 1.0651543910807330359789941374945
absolute error = 2.97322388e-23
relative error = 2.7913548541853079100971387680485e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0633
y[1] (analytic) = 1.0652605119028241997245655875989
y[1] (numeric) = 1.0652605119028241997245953652806
absolute error = 2.97776817e-23
relative error = 2.7953426760191779844987232601138e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0634
y[1] (analytic) = 1.0653666420723102366524290411499
y[1] (numeric) = 1.0653666420723102366524588642692
absolute error = 2.98231193e-23
relative error = 2.7993291813595003140973547375141e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0635
y[1] (analytic) = 1.0654727815881298450685788147086
y[1] (numeric) = 1.0654727815881298450686086832605
absolute error = 2.98685519e-23
relative error = 2.8033143986540629769884940439490e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0636
y[1] (analytic) = 1.0655789304492216298157033200786
y[1] (numeric) = 1.0655789304492216298157332340578
absolute error = 2.99139792e-23
relative error = 2.8072983000319843808105127234100e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0637
y[1] (analytic) = 1.0656850886545241022837692836306
y[1] (numeric) = 1.0656850886545241022837992430321
absolute error = 2.99594015e-23
relative error = 2.8112809139353828356646284351767e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0638
y[1] (analytic) = 1.0657912562029756804206366323946
y[1] (numeric) = 1.0657912562029756804206666372132
absolute error = 3.00048186e-23
relative error = 2.8152622218816272920811647197106e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0639
y[1] (analytic) = 1.0658974330935146887426743145721
y[1] (numeric) = 1.0658974330935146887427043648026
absolute error = 3.00502305e-23
relative error = 2.8192422241590663826259163703394e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 1.0660036193250793583453770543635
y[1] (numeric) = 1.0660036193250793583454071500008
absolute error = 3.00956373e-23
relative error = 2.8232209304368498128582342782102e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0641
y[1] (analytic) = 1.0661098148966078269139830410047
y[1] (numeric) = 1.0661098148966078269140131820435
absolute error = 3.01410388e-23
relative error = 2.8271983222406691549703104600554e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.3MB, time=11.31
NO POLE
x[1] = 0.0642
y[1] (analytic) = 1.0662160198070381387340925519051
y[1] (numeric) = 1.0662160198070381387341227383404
absolute error = 3.01864353e-23
relative error = 2.8311744279984732242111933994043e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0643
y[1] (analytic) = 1.0663222340553082447022875097838
y[1] (numeric) = 1.0663222340553082447023177416104
absolute error = 3.02318266e-23
relative error = 2.8351492292368283044371629170080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0644
y[1] (analytic) = 1.0664284576403560023367519736941
y[1] (numeric) = 1.0664284576403560023367822509068
absolute error = 3.02772127e-23
relative error = 2.8391227262439328556655484092799e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0645
y[1] (analytic) = 1.0665346905611191757878935638331
y[1] (numeric) = 1.0665346905611191757879238864267
absolute error = 3.03225936e-23
relative error = 2.8430949193079551141380806536433e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0646
y[1] (analytic) = 1.0666409328165354358489658200287
y[1] (numeric) = 1.0666409328165354358489961879981
absolute error = 3.03679694e-23
relative error = 2.8470658180922592527448071475236e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0647
y[1] (analytic) = 1.0667471844055423599666914937985
y[1] (numeric) = 1.0667471844055423599667219071385
absolute error = 3.04133400e-23
relative error = 2.8510354135078592061766442213837e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0648
y[1] (analytic) = 1.0668534453270774322518867738733
y[1] (numeric) = 1.0668534453270774322519172325787
absolute error = 3.04587054e-23
relative error = 2.8550037058428327227488169235622e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0649
y[1] (analytic) = 1.0669597155800780434900864450803
y[1] (numeric) = 1.0669597155800780434901169491459
absolute error = 3.05040656e-23
relative error = 2.8589706953852272413353914360729e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 1.0670659951634814911521699804788
y[1] (numeric) = 1.0670659951634814911522005298995
absolute error = 3.05494207e-23
relative error = 2.8629363917945514603298867065271e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0651
y[1] (analytic) = 1.0671722840762249794049885666427
y[1] (numeric) = 1.0671722840762249794050191614134
absolute error = 3.05947707e-23
relative error = 2.8669007953559919720683489664045e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0652
y[1] (analytic) = 1.0672785823172456191219930619832
y[1] (numeric) = 1.0672785823172456191220237020987
absolute error = 3.06401155e-23
relative error = 2.8708638969850807008755192671482e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0653
y[1] (analytic) = 1.0673848898854804278938628880051
y[1] (numeric) = 1.0673848898854804278938935734601
absolute error = 3.06854550e-23
relative error = 2.8748256876010525196996220709816e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0654
y[1] (analytic) = 1.0674912067798663300391358533912
y[1] (numeric) = 1.0674912067798663300391665841807
absolute error = 3.07307895e-23
relative error = 2.8787861955978788406728629465115e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0655
y[1] (analytic) = 1.0675975329993401566148389108086
y[1] (numeric) = 1.0675975329993401566148696869273
absolute error = 3.07761187e-23
relative error = 2.8827453931573502057528438302618e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0656
y[1] (analytic) = 1.0677038685428386454271198463287
y[1] (numeric) = 1.0677038685428386454271506677715
absolute error = 3.08214428e-23
relative error = 2.8867032993018864770629136928939e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0657
y[1] (analytic) = 1.0678102134092984410418799013575
y[1] (numeric) = 1.0678102134092984410419107681194
absolute error = 3.08667619e-23
relative error = 2.8906599236814542432691091381753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.3MB, time=11.59
NO POLE
x[1] = 0.0658
y[1] (analytic) = 1.0679165675976560947954073269679
y[1] (numeric) = 1.0679165675976560947954382390435
absolute error = 3.09120756e-23
relative error = 2.8946152291221225770416941285446e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0659
y[1] (analytic) = 1.0680229311068480648050118705272
y[1] (numeric) = 1.0680229311068480648050428279113
absolute error = 3.09573841e-23
relative error = 2.8985692346434212343470798281396e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 1.0681293039358107159796601945154
y[1] (numeric) = 1.068129303935810715979691197203
absolute error = 3.10026876e-23
relative error = 2.9025219592573885665232583824523e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0661
y[1] (analytic) = 1.0682356860834803200306122274274
y[1] (numeric) = 1.0682356860834803200306432754133
absolute error = 3.10479859e-23
relative error = 2.9064733845236533988057657366446e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0662
y[1] (analytic) = 1.0683420775487930554820584466505
y[1] (numeric) = 1.0683420775487930554820895399295
absolute error = 3.10932790e-23
relative error = 2.9104235107298687710488218472645e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0663
y[1] (analytic) = 1.0684484783306850076817580932143
y[1] (numeric) = 1.0684484783306850076817892317812
absolute error = 3.11385669e-23
relative error = 2.9143723381636571164331311360844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0664
y[1] (analytic) = 1.0685548884280921688116783183038
y[1] (numeric) = 1.0685548884280921688117095021535
absolute error = 3.11838497e-23
relative error = 2.9183198764710438672339699896129e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0665
y[1] (analytic) = 1.0686613078399504378986342614313
y[1] (numeric) = 1.0686613078399504378986654905586
absolute error = 3.12291273e-23
relative error = 2.9222661165792926904603290798466e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0666
y[1] (analytic) = 1.0687677365651956208249300601592
y[1] (numeric) = 1.0687677365651956208249613345588
absolute error = 3.12743996e-23
relative error = 2.9262110494193645168744616508924e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0667
y[1] (analytic) = 1.0688741746027634303390007912677
y[1] (numeric) = 1.0688741746027634303390321109346
absolute error = 3.13196669e-23
relative error = 2.9301547033484690589836625071140e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0668
y[1] (analytic) = 1.0689806219515894860660553432624
y[1] (numeric) = 1.0689806219515894860660867081914
absolute error = 3.13649290e-23
relative error = 2.9340970599390726341938558793119e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0669
y[1] (analytic) = 1.0690870786106093145187202201126
y[1] (numeric) = 1.0690870786106093145187516302985
absolute error = 3.14101859e-23
relative error = 2.9380381194786142180228405628781e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 1.0691935445787583491076842761166
y[1] (numeric) = 1.0691935445787583491077157315542
absolute error = 3.14554376e-23
relative error = 2.9419778822545020321924645360836e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0671
y[1] (analytic) = 1.0693000198549719301523443817856
y[1] (numeric) = 1.0693000198549719301523758824698
absolute error = 3.15006842e-23
relative error = 2.9459163579060258161406808532069e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0672
y[1] (analytic) = 1.0694065044381853048914520206413
y[1] (numeric) = 1.0694065044381853048914835665668
absolute error = 3.15459255e-23
relative error = 2.9498535280157764333564232732665e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0673
y[1] (analytic) = 1.069512998327333627493760816819
y[1] (numeric) = 1.0695129983273336274937924079806
absolute error = 3.15911616e-23
relative error = 2.9537894022239133180851899468960e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.3MB, time=11.86
NO POLE
x[1] = 0.0674
y[1] (analytic) = 1.0696195015213519590686749933714
y[1] (numeric) = 1.0696195015213519590687066297641
absolute error = 3.16363927e-23
relative error = 2.9577239995159594593703259417589e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0675
y[1] (analytic) = 1.0697260140191752676768987611662
y[1] (numeric) = 1.0697260140191752676769304427847
absolute error = 3.16816185e-23
relative error = 2.9616572921290193365870477033494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0676
y[1] (analytic) = 1.0698325358197384283410866382691
y[1] (numeric) = 1.0698325358197384283411183651083
absolute error = 3.17268392e-23
relative error = 2.9655892990476238310452542547742e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0677
y[1] (analytic) = 1.0699390669219762230564946997096
y[1] (numeric) = 1.0699390669219762230565264717641
absolute error = 3.17720545e-23
relative error = 2.9695199925171936595202771921004e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0678
y[1] (analytic) = 1.0700456073248233408016327575183
y[1] (numeric) = 1.0700456073248233408016645747831
absolute error = 3.18172648e-23
relative error = 2.9734494102120585864619829906187e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0679
y[1] (analytic) = 1.0701521570272143775489174709341
y[1] (numeric) = 1.070152157027214377548949333404
absolute error = 3.18624699e-23
relative error = 2.9773775337248350971567004724310e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 1.0702587160280838362753263866704
y[1] (numeric) = 1.0702587160280838362753582943403
absolute error = 3.19076699e-23
relative error = 2.9813043726861585644031954633584e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0681
y[1] (analytic) = 1.0703652843263661269730529091368
y[1] (numeric) = 1.0703652843263661269730848620014
absolute error = 3.19528646e-23
relative error = 2.9852299086950974734481959107526e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0682
y[1] (analytic) = 1.070471861920995566660162200508
y[1] (numeric) = 1.0704718619209955666601941985622
absolute error = 3.19980542e-23
relative error = 2.9891541607248303651660894047341e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0683
y[1] (analytic) = 1.0705784488109063793912480105347
y[1] (numeric) = 1.0705784488109063793912800537732
absolute error = 3.20432385e-23
relative error = 2.9930771103780847615050144370929e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0684
y[1] (analytic) = 1.0706850449950326962680904359881
y[1] (numeric) = 1.0706850449950326962681225244058
absolute error = 3.20884177e-23
relative error = 2.9969987766242564854426019063862e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0685
y[1] (analytic) = 1.0707916504723085554503146096339
y[1] (numeric) = 1.0707916504723085554503467432257
absolute error = 3.21335918e-23
relative error = 3.0009191597475010256537636296920e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0686
y[1] (analytic) = 1.070898265241667902166050318627
y[1] (numeric) = 1.0708982652416679021660824973876
absolute error = 3.21787606e-23
relative error = 3.0048382413560330549822708968158e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0687
y[1] (analytic) = 1.071004889302044588722592552221
y[1] (numeric) = 1.0710048893020445887226247761452
absolute error = 3.22239242e-23
relative error = 3.0087560310765505030545788734843e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0688
y[1] (analytic) = 1.0711115226523723745170629786866
y[1] (numeric) = 1.0711115226523723745170952477693
absolute error = 3.22690827e-23
relative error = 3.0126725385320013973255815064183e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=167.8MB, alloc=4.3MB, time=12.14
x[1] = 0.0689
y[1] (analytic) = 1.0712181652915849260470723513317
y[1] (numeric) = 1.0712181652915849260471046655676
absolute error = 3.23142359e-23
relative error = 3.0165877453360851898564218957346e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 1.0713248172186158169213838435158
y[1] (numeric) = 1.0713248172186158169214162028998
absolute error = 3.23593840e-23
relative error = 3.0205016704468543640605838874220e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0691
y[1] (analytic) = 1.0714314784323985278705773125542
y[1] (numeric) = 1.0714314784323985278706097170811
absolute error = 3.24045269e-23
relative error = 3.0244143048149717577434202720604e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0692
y[1] (analytic) = 1.0715381489318664467577144924028
y[1] (numeric) = 1.0715381489318664467577469420675
absolute error = 3.24496647e-23
relative error = 3.0283256580595438860650207515380e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0693
y[1] (analytic) = 1.0716448287159528685890051150189
y[1] (numeric) = 1.0716448287159528685890376098162
absolute error = 3.24947973e-23
relative error = 3.0322357211330302218532766095178e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0694
y[1] (analytic) = 1.0717515177835909955244739602901
y[1] (numeric) = 1.0717515177835909955245065002147
absolute error = 3.25399246e-23
relative error = 3.0361444849915752631020630978141e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0695
y[1] (analytic) = 1.0718582161337139368886288344249
y[1] (numeric) = 1.0718582161337139368886614194716
absolute error = 3.25850467e-23
relative error = 3.0400519592541917728623657482032e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0696
y[1] (analytic) = 1.0719649237652547091811294766991
y[1] (numeric) = 1.0719649237652547091811621068628
absolute error = 3.26301637e-23
relative error = 3.0439581535361457797030630011835e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0697
y[1] (analytic) = 1.0720716406771462360874573944504
y[1] (numeric) = 1.0720716406771462360874900697259
absolute error = 3.26752755e-23
relative error = 3.0478630587934879068603892933818e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0698
y[1] (analytic) = 1.0721783668683213484895866262142
y[1] (numeric) = 1.0721783668683213484896193465964
absolute error = 3.27203822e-23
relative error = 3.0517666846395647542082359861447e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0699
y[1] (analytic) = 1.0722851023377127844766554328955
y[1] (numeric) = 1.0722851023377127844766881983791
absolute error = 3.27654836e-23
relative error = 3.0556690127063441279443495560689e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 1.0723918470842531893556389168682
y[1] (numeric) = 1.072391847084253189355671727448
absolute error = 3.28105798e-23
relative error = 3.0595700526080383983101773976057e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0701
y[1] (analytic) = 1.0724986011068751156620225688965
y[1] (numeric) = 1.0724986011068751156620554245674
absolute error = 3.28556709e-23
relative error = 3.0634698139551151818299036682214e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0702
y[1] (analytic) = 1.0726053644045110231704767427717
y[1] (numeric) = 1.0726053644045110231705096435284
absolute error = 3.29007567e-23
relative error = 3.0673682783850181447254188535116e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0703
y[1] (analytic) = 1.0727121369760932789055320575559
y[1] (numeric) = 1.0727121369760932789055650033932
absolute error = 3.29458373e-23
relative error = 3.0712654555090802395311479751950e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0704
y[1] (analytic) = 1.0728189188205541571522557273279
y[1] (numeric) = 1.0728189188205541571522887182407
absolute error = 3.29909128e-23
relative error = 3.0751613549348908538674855067866e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.3MB, time=12.42
NO POLE
x[1] = 0.0705
y[1] (analytic) = 1.0729257099368258394669288183241
y[1] (numeric) = 1.0729257099368258394669618543072
absolute error = 3.30359831e-23
relative error = 3.0790559676256772484174094007947e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0706
y[1] (analytic) = 1.0730325103238404146877244333665
y[1] (numeric) = 1.0730325103238404146877575144147
absolute error = 3.30810482e-23
relative error = 3.0829492938677285949263993449337e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0707
y[1] (analytic) = 1.0731393199805298789453868234719
y[1] (numeric) = 1.07313931998052987894541994958
absolute error = 3.31261081e-23
relative error = 3.0868413339473025500997741830568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0708
y[1] (analytic) = 1.0732461389058261356739114265358
y[1] (numeric) = 1.0732461389058261356739445976986
absolute error = 3.31711628e-23
relative error = 3.0907320881506252354081708091934e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0709
y[1] (analytic) = 1.0733529670986609956212258329835
y[1] (numeric) = 1.0733529670986609956212590491958
absolute error = 3.32162123e-23
relative error = 3.0946215567638912169129604298176e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 1.0734598045579661768598716782817
y[1] (numeric) = 1.0734598045579661768599049395384
absolute error = 3.32612567e-23
relative error = 3.0985097493889360026473951357333e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0711
y[1] (analytic) = 1.0735666512826733047976874622046
y[1] (numeric) = 1.0735666512826733047977207685005
absolute error = 3.33062959e-23
relative error = 3.1023966569943641851949678812460e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0712
y[1] (analytic) = 1.0736735072717139121884922947465
y[1] (numeric) = 1.0736735072717139121885256460762
absolute error = 3.33513297e-23
relative error = 3.1062822612386391819921594756768e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0713
y[1] (analytic) = 1.0737803725240194391427705685741
y[1] (numeric) = 1.0737803725240194391428039649326
absolute error = 3.33963585e-23
relative error = 3.1101665996649566647163406771620e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0714
y[1] (analytic) = 1.0738872470385212331383575579137
y[1] (numeric) = 1.0738872470385212331383909992957
absolute error = 3.34413820e-23
relative error = 3.1140496446178981094048269733349e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0715
y[1] (analytic) = 1.0739941308141505490311259437632
y[1] (numeric) = 1.0739941308141505490311594301636
absolute error = 3.34864004e-23
relative error = 3.1179314150083245116335758756915e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0716
y[1] (analytic) = 1.074101023849838549065673265325
y[1] (numeric) = 1.0741010238498385490657067967385
absolute error = 3.35314135e-23
relative error = 3.1218118924992066698948769545065e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0717
y[1] (analytic) = 1.0742079261445163028860102975506
y[1] (numeric) = 1.0742079261445163028860438739721
absolute error = 3.35764215e-23
relative error = 3.1256910959976352649279374733935e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0718
y[1] (analytic) = 1.074314837697114787546250354692
y[1] (numeric) = 1.0743148376971147875462839761163
absolute error = 3.36214243e-23
relative error = 3.1295690164784824245765071279786e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0719
y[1] (analytic) = 1.0744217585065648875212995197517
y[1] (numeric) = 1.0744217585065648875213331861735
absolute error = 3.36664218e-23
relative error = 3.1334456449202943815726833435245e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 1.0745286885717973947175477997241
y[1] (numeric) = 1.0745286885717973947175815111383
absolute error = 3.37114142e-23
relative error = 3.1373210002245077570967330644410e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.3MB, time=12.71
NO POLE
x[1] = 0.0721
y[1] (analytic) = 1.0746356278917430084835612065234
y[1] (numeric) = 1.0746356278917430084835949629248
absolute error = 3.37564014e-23
relative error = 3.1411950733686789029566330416177e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0722
y[1] (analytic) = 1.0747425764653323356207747634888
y[1] (numeric) = 1.0747425764653323356208085648721
absolute error = 3.38013833e-23
relative error = 3.1450678553340369658823227076085e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0723
y[1] (analytic) = 1.0748495342914958903941864373609
y[1] (numeric) = 1.0748495342914958903942202837211
absolute error = 3.38463602e-23
relative error = 3.1489393743199939958156794548756e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0724
y[1] (analytic) = 1.0749565013691640945430519956235
y[1] (numeric) = 1.0749565013691640945430858869553
absolute error = 3.38913318e-23
relative error = 3.1528096026986080786101770336029e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0725
y[1] (analytic) = 1.0750634776972672772915807891016
y[1] (numeric) = 1.0750634776972672772916147253997
absolute error = 3.39362981e-23
relative error = 3.1566785407583438429846959201628e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0726
y[1] (analytic) = 1.0751704632747356753596324597104
y[1] (numeric) = 1.0751704632747356753596664409696
absolute error = 3.39812592e-23
relative error = 3.1605461980884841381313519187857e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0727
y[1] (analytic) = 1.0752774581004994329734145732479
y[1] (numeric) = 1.0752774581004994329734485994631
absolute error = 3.40262152e-23
relative error = 3.1644125842745773710681355294121e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0728
y[1] (analytic) = 1.0753844621734886018761811771242
y[1] (numeric) = 1.0753844621734886018762152482901
absolute error = 3.40711659e-23
relative error = 3.1682776810014388461264105818950e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0729
y[1] (analytic) = 1.0754914754926331413389322829193
y[1] (numeric) = 1.0754914754926331413389663990309
absolute error = 3.41161116e-23
relative error = 3.1721415164516278104192227569969e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 1.0755984980568629181711142736652
y[1] (numeric) = 1.0755984980568629181711484347172
absolute error = 3.41610520e-23
relative error = 3.1760040630136721712433323777730e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0731
y[1] (analytic) = 1.0757055298651077067313212357416
y[1] (numeric) = 1.0757055298651077067313554417287
absolute error = 3.42059871e-23
relative error = 3.1798653209758430129405161155688e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0732
y[1] (analytic) = 1.0758125709162971889379972152815
y[1] (numeric) = 1.0758125709162971889380314661985
absolute error = 3.42509170e-23
relative error = 3.1837252999216782318605778610279e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0733
y[1] (analytic) = 1.0759196212093609542801393989777
y[1] (numeric) = 1.0759196212093609542801736948195
absolute error = 3.42958418e-23
relative error = 3.1875840094309836644734043699111e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0734
y[1] (analytic) = 1.0760266807432284998280022191841
y[1] (numeric) = 1.0760266807432284998280365599455
absolute error = 3.43407614e-23
relative error = 3.1914414404929344000034626935605e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0735
y[1] (analytic) = 1.076133749516829230243802383204
y[1] (numeric) = 1.0761337495168292302438367688797
absolute error = 3.43856757e-23
relative error = 3.1952975841003726472753927132397e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0736
y[1] (analytic) = 1.0762408275290924577924248266591
y[1] (numeric) = 1.0762408275290924577924592572439
absolute error = 3.44305848e-23
relative error = 3.1991524498330080238307078453322e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.3MB, time=12.99
NO POLE
x[1] = 0.0737
y[1] (analytic) = 1.0763479147789474023521295908318
y[1] (numeric) = 1.0763479147789474023521640663204
absolute error = 3.44754886e-23
relative error = 3.2030060286854671920117129091342e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0738
y[1] (analytic) = 1.0764550112653231914252596238732
y[1] (numeric) = 1.0764550112653231914252941442607
absolute error = 3.45203875e-23
relative error = 3.2068583581048015633036669078409e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0739
y[1] (analytic) = 1.076562116987148860148949505772
y[1] (numeric) = 1.076562116987148860148984071053
absolute error = 3.45652810e-23
relative error = 3.2107093919237929820418285774017e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 1.0766692319433533513058350969725
y[1] (numeric) = 1.0766692319433533513058697071419
absolute error = 3.46101694e-23
relative error = 3.2145591582969039495563992711140e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0741
y[1] (analytic) = 1.0767763561328655153347641105409
y[1] (numeric) = 1.0767763561328655153347987655933
absolute error = 3.46550524e-23
relative error = 3.2184076296455980240058326313780e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0742
y[1] (analytic) = 1.0768834895546141103415076077666
y[1] (numeric) = 1.0768834895546141103415423076969
absolute error = 3.46999303e-23
relative error = 3.2222548341187279563551925905140e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0743
y[1] (analytic) = 1.0769906322075278021094724170966
y[1] (numeric) = 1.0769906322075278021095071618996
absolute error = 3.47448030e-23
relative error = 3.2261007627134999994413830157601e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0744
y[1] (analytic) = 1.0770977840905351641104144762918
y[1] (numeric) = 1.0770977840905351641104492659623
absolute error = 3.47896705e-23
relative error = 3.2299454157149917242059448109152e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0745
y[1] (analytic) = 1.077204945202564677515153097701
y[1] (numeric) = 1.0772049452025646775151879322337
absolute error = 3.48345327e-23
relative error = 3.2337887841249639062802553781769e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0746
y[1] (analytic) = 1.0773121155425447312042861565433
y[1] (numeric) = 1.0773121155425447312043210359331
absolute error = 3.48793898e-23
relative error = 3.2376308867959221091508952512099e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0747
y[1] (analytic) = 1.0774192951094036217789062020936
y[1] (numeric) = 1.0774192951094036217789411263353
absolute error = 3.49242417e-23
relative error = 3.2414717147286389135204836367315e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0748
y[1] (analytic) = 1.0775264839020695535713174916627
y[1] (numeric) = 1.077526483902069553571352460751
absolute error = 3.49690883e-23
relative error = 3.2453112589275483463539671680658e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0749
y[1] (analytic) = 1.0776336819194706386557539472649
y[1] (numeric) = 1.0776336819194706386557889611947
absolute error = 3.50139298e-23
relative error = 3.2491495382395183312638704062421e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 1.0777408891605348968590980348673
y[1] (numeric) = 1.0777408891605348968591330936333
absolute error = 3.50587660e-23
relative error = 3.2529865343893268043370809315300e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0751
y[1] (analytic) = 1.0778481056241902557716005661117
y[1] (numeric) = 1.0778481056241902557716356697087
absolute error = 3.51035970e-23
relative error = 3.2568222569423390900116857800917e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0752
y[1] (analytic) = 1.0779553313093645507576014224032
y[1] (numeric) = 1.077955331309364550757636570826
absolute error = 3.51484228e-23
relative error = 3.2606567061833737551383009971744e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.3MB, time=13.27
NO POLE
x[1] = 0.0753
y[1] (analytic) = 1.078062566214985524966251201258
y[1] (numeric) = 1.0780625662149855249662863945013
absolute error = 3.51932433e-23
relative error = 3.2644898731213174606046035261033e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0754
y[1] (analytic) = 1.0781698103399808293422337848026
y[1] (numeric) = 1.0781698103399808293422690228614
absolute error = 3.52380588e-23
relative error = 3.2683217858686223542867474207714e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0755
y[1] (analytic) = 1.0782770636832780226364898303188
y[1] (numeric) = 1.0782770636832780226365251131878
absolute error = 3.52828690e-23
relative error = 3.2721524168823112273022942353192e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0756
y[1] (analytic) = 1.0783843262438045714169411827244
y[1] (numeric) = 1.0783843262438045714169765103984
absolute error = 3.53276740e-23
relative error = 3.2759817757229723192398762690374e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0757
y[1] (analytic) = 1.0784915980204878500792162088857
y[1] (numeric) = 1.0784915980204878500792515813594
absolute error = 3.53724737e-23
relative error = 3.2798098534030524245541152281940e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0758
y[1] (analytic) = 1.078598879012255140857376053652
y[1] (numeric) = 1.0785988790122551408574114709202
absolute error = 3.54172682e-23
relative error = 3.2836366594812292311066028538563e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0759
y[1] (analytic) = 1.0787061692180336338346418175061
y[1] (numeric) = 1.0787061692180336338346772795636
absolute error = 3.54620575e-23
relative error = 3.2874621942420936240102203632119e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 1.0788134686367504269541226557232
y[1] (numeric) = 1.0788134686367504269541581625648
absolute error = 3.55068416e-23
relative error = 3.2912864579702039302489970176037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0761
y[1] (analytic) = 1.0789207772673325260295447989308
y[1] (numeric) = 1.0789207772673325260295803505513
absolute error = 3.55516205e-23
relative error = 3.2951094509500858995263255463096e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0762
y[1] (analytic) = 1.0790280951087068447559814949627
y[1] (numeric) = 1.0790280951087068447560170913568
absolute error = 3.55963941e-23
relative error = 3.2989311641986334026574070440624e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0763
y[1] (analytic) = 1.0791354221598002047205838718988
y[1] (numeric) = 1.0791354221598002047206195130614
absolute error = 3.56411626e-23
relative error = 3.3027516165364272655079610590123e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0764
y[1] (analytic) = 1.0792427584195393354133127221855
y[1] (numeric) = 1.0792427584195393354133484081113
absolute error = 3.56859258e-23
relative error = 3.3065707897136183408946033869256e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0765
y[1] (analytic) = 1.0793501038868508742376712077262
y[1] (numeric) = 1.07935010388685087423770693841
absolute error = 3.57306838e-23
relative error = 3.3103886932822008479450510327888e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0766
y[1] (analytic) = 1.0794574585606613665214384858379
y[1] (numeric) = 1.0794574585606613665214742612745
absolute error = 3.57754366e-23
relative error = 3.3142053275265370505563176425283e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0767
y[1] (analytic) = 1.0795648224398972655274042559645
y[1] (numeric) = 1.0795648224398972655274400761487
absolute error = 3.58201842e-23
relative error = 3.3180206927309565208343817365758e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=186.9MB, alloc=4.3MB, time=13.56
x[1] = 0.0768
y[1] (analytic) = 1.0796721955234849324641042270395
y[1] (numeric) = 1.0796721955234849324641400919662
absolute error = 3.58649267e-23
relative error = 3.3218347984418266276467081847809e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0769
y[1] (analytic) = 1.0797795778103506364965565053925
y[1] (numeric) = 1.0797795778103506364965924150563
absolute error = 3.59096638e-23
relative error = 3.3256476171571999797819907511198e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 1.079886969299420554756998903089
y[1] (numeric) = 1.0798869692994205547570348574847
absolute error = 3.59543957e-23
relative error = 3.3294591676872910658951524698614e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0771
y[1] (analytic) = 1.0799943699896207723556271665998
y[1] (numeric) = 1.0799943699896207723556631657222
absolute error = 3.59991224e-23
relative error = 3.3332694503162981881330236572261e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0772
y[1] (analytic) = 1.08010177987987728239133412569
y[1] (numeric) = 1.080101779879877282391370169534
absolute error = 3.60438440e-23
relative error = 3.3370784745867736050215049965703e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0773
y[1] (analytic) = 1.0802091989691159859624497624212
y[1] (numeric) = 1.0802091989691159859624858509815
absolute error = 3.60885603e-23
relative error = 3.3408862222651558598570083614496e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0774
y[1] (analytic) = 1.0803166272562626921774822001589
y[1] (numeric) = 1.0803166272562626921775183334302
absolute error = 3.61332713e-23
relative error = 3.3446926936383068792866897036748e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0775
y[1] (analytic) = 1.0804240647402431181658596124787
y[1] (numeric) = 1.0804240647402431181658957904557
absolute error = 3.61779770e-23
relative error = 3.3484978889930551208825930359117e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0776
y[1] (analytic) = 1.0805315114199828890886730518627
y[1] (numeric) = 1.0805315114199828890887092745405
absolute error = 3.62226778e-23
relative error = 3.3523018456350141423806342705629e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0777
y[1] (analytic) = 1.0806389672944075381494201980808
y[1] (numeric) = 1.0806389672944075381494564654539
absolute error = 3.62673731e-23
relative error = 3.3561045083171959446231629536151e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0778
y[1] (analytic) = 1.0807464323624425066047500261452
y[1] (numeric) = 1.0807464323624425066047863382084
absolute error = 3.63120632e-23
relative error = 3.3599059050904433444411485909406e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0779
y[1] (analytic) = 1.0808539066230131437752083937359
y[1] (numeric) = 1.080853906623013143775244750484
absolute error = 3.63567481e-23
relative error = 3.3637060362386911960951806435550e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 1.080961390075044707055984547986
y[1] (numeric) = 1.0809613900750447070560209494139
absolute error = 3.64014279e-23
relative error = 3.3675049112968656358967062533438e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0781
y[1] (analytic) = 1.0810688827174623619276585515214
y[1] (numeric) = 1.0810688827174623619276949976237
absolute error = 3.64461023e-23
relative error = 3.3713025027957629656123292293704e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0782
y[1] (analytic) = 1.0811763845491911819669496276449
y[1] (numeric) = 1.0811763845491911819669861184164
absolute error = 3.64907715e-23
relative error = 3.3750988295231071977973730276927e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0783
y[1] (analytic) = 1.0812838955691561488574654245611
y[1] (numeric) = 1.0812838955691561488575019599966
absolute error = 3.65354355e-23
relative error = 3.3788938917627010112513767505187e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=190.7MB, alloc=4.3MB, time=13.84
x[1] = 0.0784
y[1] (analytic) = 1.081391415776282152400452198531
y[1] (numeric) = 1.0813914157762821524004887786252
absolute error = 3.65800942e-23
relative error = 3.3826876805509686115303595432523e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0785
y[1] (analytic) = 1.0814989451694939905255459158503
y[1] (numeric) = 1.0814989451694939905255825405981
absolute error = 3.66247478e-23
relative error = 3.3864802146672569843147089204483e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0786
y[1] (analytic) = 1.0816064837477163693015242735447
y[1] (numeric) = 1.0816064837477163693015609429409
absolute error = 3.66693962e-23
relative error = 3.3902714851470047209206632059075e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0787
y[1] (analytic) = 1.0817140315098739029470596386726
y[1] (numeric) = 1.0817140315098739029470963527119
absolute error = 3.67140393e-23
relative error = 3.3940614830292948514093629354551e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0788
y[1] (analytic) = 1.0818215884548911138414729061297
y[1] (numeric) = 1.0818215884548911138415096648068
absolute error = 3.67586771e-23
relative error = 3.3978502086005221536984409073361e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0789
y[1] (analytic) = 1.0819291545816924325354882748466
y[1] (numeric) = 1.0819291545816924325355250781564
absolute error = 3.68033098e-23
relative error = 3.4016376806325463921720679481103e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 1.0820367298892021977619889422729
y[1] (numeric) = 1.0820367298892021977620257902101
absolute error = 3.68479372e-23
relative error = 3.4054238809225205152648131873478e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0791
y[1] (analytic) = 1.0821443143763446564467737170393
y[1] (numeric) = 1.0821443143763446564468106095986
absolute error = 3.68925593e-23
relative error = 3.4092088097567386762952448938244e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0792
y[1] (analytic) = 1.0822519080420439637193145496904
y[1] (numeric) = 1.0822519080420439637193514868666
absolute error = 3.69371762e-23
relative error = 3.4129924766614541908822879248053e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0793
y[1] (analytic) = 1.0823595108852241829235149813813
y[1] (numeric) = 1.0823595108852241829235519631693
absolute error = 3.69817880e-23
relative error = 3.4167748911592121907258010387947e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0794
y[1] (analytic) = 1.0824671229048092856284695104297
y[1] (numeric) = 1.0824671229048092856285065368241
absolute error = 3.70263944e-23
relative error = 3.4205560258162271886804362128889e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0795
y[1] (analytic) = 1.0825747440997231516392238766154
y[1] (numeric) = 1.0825747440997231516392609476111
absolute error = 3.70709957e-23
relative error = 3.4243359086331266110894410788235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0796
y[1] (analytic) = 1.0826823744688895690075362631217
y[1] (numeric) = 1.0826823744688895690075733787134
absolute error = 3.71155917e-23
relative error = 3.4281145214178880310689255195884e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0797
y[1] (analytic) = 1.0827900140112322340426394160082
y[1] (numeric) = 1.0827900140112322340426765761906
absolute error = 3.71601824e-23
relative error = 3.4318918644566038520645179110274e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0798
y[1] (analytic) = 1.0828976627256747513220036811095
y[1] (numeric) = 1.0828976627256747513220408858776
absolute error = 3.72047681e-23
relative error = 3.4356679657387814208223265416594e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0799
y[1] (analytic) = 1.0830053206111406337021009582524
y[1] (numeric) = 1.0830053206111406337021382076008
absolute error = 3.72493484e-23
relative error = 3.4394427886079236938448577955204e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.3MB, time=14.12
NO POLE
x[1] = 0.08
y[1] (analytic) = 1.083112987666553302329169572681
y[1] (numeric) = 1.0831129876665533023292068666045
absolute error = 3.72939235e-23
relative error = 3.4432163518180700847434946568235e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0801
y[1] (analytic) = 1.083220663890836086649980063586
y[1] (numeric) = 1.0832206638908360866500174020794
absolute error = 3.73384934e-23
relative error = 3.4469886556524246392368886637376e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0802
y[1] (analytic) = 1.0833283492829122244226018896282
y[1] (numeric) = 1.0833283492829122244226392726862
absolute error = 3.73830580e-23
relative error = 3.4507596911633463584595319847090e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0803
y[1] (analytic) = 1.0834360438417048617271710513483
y[1] (numeric) = 1.0834360438417048617272084789657
absolute error = 3.74276174e-23
relative error = 3.4545294678666193791347675738006e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0804
y[1] (analytic) = 1.0835437475661370529766586303569
y[1] (numeric) = 1.0835437475661370529766961025284
absolute error = 3.74721715e-23
relative error = 3.4582979768163706408155193891455e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0805
y[1] (analytic) = 1.0836514604551317609276402451957
y[1] (numeric) = 1.0836514604551317609276777619162
absolute error = 3.75167205e-23
relative error = 3.4620652367545411255659065548828e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0806
y[1] (analytic) = 1.083759182507611856691066423763
y[1] (numeric) = 1.0837591825076118566911039850272
absolute error = 3.75612642e-23
relative error = 3.4658312295071313865112918402158e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0807
y[1] (analytic) = 1.0838669137225001197430338921948
y[1] (numeric) = 1.0838669137225001197430714979975
absolute error = 3.76058027e-23
relative error = 3.4695959645861211930237972476812e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0808
y[1] (analytic) = 1.0839746540987192379355577800952
y[1] (numeric) = 1.0839746540987192379355954304312
absolute error = 3.76503360e-23
relative error = 3.4733594422744801584469421781328e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0809
y[1] (analytic) = 1.0840824036351918075073447420074
y[1] (numeric) = 1.0840824036351918075073824368713
absolute error = 3.76948639e-23
relative error = 3.4771216444063623618901337940493e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 1.0841901623308403330945669950168
y[1] (numeric) = 1.0841901623308403330946047344035
absolute error = 3.77393867e-23
relative error = 3.4808825989405940039358259968531e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0811
y[1] (analytic) = 1.0842979301845872277416372723815
y[1] (numeric) = 1.0842979301845872277416750562857
absolute error = 3.77839042e-23
relative error = 3.4846422877121784604347000850358e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0812
y[1] (analytic) = 1.0844057071953548129119846930783
y[1] (numeric) = 1.0844057071953548129120225214948
absolute error = 3.78284165e-23
relative error = 3.4884007202283417436291301641315e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0813
y[1] (analytic) = 1.0845134933620653184988315471598
y[1] (numeric) = 1.0845134933620653184988694200834
absolute error = 3.78729236e-23
relative error = 3.4921578967718852888970719821583e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0814
y[1] (analytic) = 1.0846212886836408828359709968133
y[1] (numeric) = 1.0846212886836408828360089142387
absolute error = 3.79174254e-23
relative error = 3.4959138084057689984257606760542e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0815
y[1] (analytic) = 1.0847290931590035527085456930135
y[1] (numeric) = 1.0847290931590035527085836549354
absolute error = 3.79619219e-23
relative error = 3.4996684554154760577504955515993e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.3MB, time=14.41
NO POLE
x[1] = 0.0816
y[1] (analytic) = 1.0848369067870752833638273076623
y[1] (numeric) = 1.0848369067870752833638653140755
absolute error = 3.80064132e-23
relative error = 3.5034218473044308992100622031569e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0817
y[1] (analytic) = 1.0849447295667779385219969811074
y[1] (numeric) = 1.0849447295667779385220350320065
absolute error = 3.80508991e-23
relative error = 3.5071739659211811973853798297887e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0818
y[1] (analytic) = 1.0850525614970332903869266849307
y[1] (numeric) = 1.0850525614970332903869647803106
absolute error = 3.80953799e-23
relative error = 3.5109248392022858649979227798221e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0819
y[1] (analytic) = 1.0851604025767630196569614999015
y[1] (numeric) = 1.085160402576763019656999639757
absolute error = 3.81398555e-23
relative error = 3.5146744582123682636645262820568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 1.0852682528048887155357028089837
y[1] (numeric) = 1.0852682528048887155357409933095
absolute error = 3.81843258e-23
relative error = 3.5184228140196818182719541416379e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0821
y[1] (analytic) = 1.0853761121803318757427924052904
y[1] (numeric) = 1.0853761121803318757428306340814
absolute error = 3.82287910e-23
relative error = 3.5221699253362971477294264046883e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0822
y[1] (analytic) = 1.0854839807020139065246975148793
y[1] (numeric) = 1.0854839807020139065247357881302
absolute error = 3.82732509e-23
relative error = 3.5259157740170040035093566878604e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0823
y[1] (analytic) = 1.0855918583688561226654967342783
y[1] (numeric) = 1.0855918583688561226655350519838
absolute error = 3.83177055e-23
relative error = 3.5296603603470128136833362620319e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0824
y[1] (analytic) = 1.0856997451797797474976668826363
y[1] (numeric) = 1.0856997451797797474977052447911
absolute error = 3.83621548e-23
relative error = 3.5334036846114996349872208964323e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0825
y[1] (analytic) = 1.0858076411337059129128707683887
y[1] (numeric) = 1.0858076411337059129129091749877
absolute error = 3.84065990e-23
relative error = 3.5371457655150749637392833371637e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0826
y[1] (analytic) = 1.0859155462295556593727458703327
y[1] (numeric) = 1.0859155462295556593727843213706
absolute error = 3.84510379e-23
relative error = 3.5408865849197166252140975760195e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0827
y[1] (analytic) = 1.0860234604662499359196939330013
y[1] (numeric) = 1.0860234604662499359197324284729
absolute error = 3.84954716e-23
relative error = 3.5446261523184022964128911754343e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0828
y[1] (analytic) = 1.0861313838427096001876714762307
y[1] (numeric) = 1.0861313838427096001877100161306
absolute error = 3.85398999e-23
relative error = 3.5483644495794476213700904840875e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0829
y[1] (analytic) = 1.086239316357855418412981218811
y[1] (numeric) = 1.0862393163578554184130198031341
absolute error = 3.85843231e-23
relative error = 3.5521015046088252893092931382089e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 1.0863472580106080654450644161152
y[1] (numeric) = 1.0863472580106080654451030448562
absolute error = 3.86287410e-23
relative error = 3.5558372992756975736917470047272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0831
y[1] (analytic) = 1.0864552087998881247572941115952
y[1] (numeric) = 1.0864552087998881247573327847488
absolute error = 3.86731536e-23
relative error = 3.5595718338650006829097386451136e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.3MB, time=14.68
NO POLE
x[1] = 0.0832
y[1] (analytic) = 1.0865631687246160884577693020388
y[1] (numeric) = 1.0865631687246160884578080195999
absolute error = 3.87175611e-23
relative error = 3.5633051270682974014100353963041e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0833
y[1] (analytic) = 1.0866711377837123573001100164806
y[1] (numeric) = 1.0866711377837123573001487784438
absolute error = 3.87619632e-23
relative error = 3.5670371515577199924981806752380e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0834
y[1] (analytic) = 1.0867791159760972406942533086559
y[1] (numeric) = 1.086779115976097240694292115016
absolute error = 3.88063601e-23
relative error = 3.5707679260238482594032735830898e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0835
y[1] (analytic) = 1.0868871033006909567172501628929
y[1] (numeric) = 1.0868871033006909567172890136446
absolute error = 3.88507517e-23
relative error = 3.5744974415481503275483467446822e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0836
y[1] (analytic) = 1.0869950997564136321240633133328
y[1] (numeric) = 1.086995099756413632124102208471
absolute error = 3.88951382e-23
relative error = 3.5782257168147372566805239866752e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0837
y[1] (analytic) = 1.0871031053421853023583659763717
y[1] (numeric) = 1.0871031053421853023584049158911
absolute error = 3.89395194e-23
relative error = 3.5819527337053355401681648130741e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0838
y[1] (analytic) = 1.0872111200569259115633414962144
y[1] (numeric) = 1.0872111200569259115633804801096
absolute error = 3.89838952e-23
relative error = 3.5856784833067950811289539751825e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0839
y[1] (analytic) = 1.0873191438995553125924839034335
y[1] (numeric) = 1.0873191438995553125925229316994
absolute error = 3.90282659e-23
relative error = 3.5894029934973134821044226780992e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 1.0874271768689932670203993864259
y[1] (numeric) = 1.0874271768689932670204384590573
absolute error = 3.90726314e-23
relative error = 3.5931262553600163810306737569657e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0841
y[1] (analytic) = 1.0875352189641594451536086756576
y[1] (numeric) = 1.0875352189641594451536477926491
absolute error = 3.91169915e-23
relative error = 3.5968482507865458258841563940082e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0842
y[1] (analytic) = 1.0876432701839734260413503405892
y[1] (numeric) = 1.0876432701839734260413895019355
absolute error = 3.91613463e-23
relative error = 3.6005689892583907473154243862962e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0843
y[1] (analytic) = 1.0877513305273546974863849991746
y[1] (numeric) = 1.0877513305273546974864242048706
absolute error = 3.92056960e-23
relative error = 3.6042884894466288852933082348520e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0844
y[1] (analytic) = 1.0878593999932226560558004398248
y[1] (numeric) = 1.0878593999932226560558396898653
absolute error = 3.92500405e-23
relative error = 3.6080067424379039264141052698808e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0845
y[1] (analytic) = 1.0879674785804966070918176557277
y[1] (numeric) = 1.0879674785804966070918569501073
absolute error = 3.92943796e-23
relative error = 3.6117237301310275277419044769328e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0846
y[1] (analytic) = 1.0880755662880957647225977914166
y[1] (numeric) = 1.0880755662880957647226371301301
absolute error = 3.93387135e-23
relative error = 3.6154394711942343173047895600623e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0847
y[1] (analytic) = 1.08818366311493925187305000148
y[1] (numeric) = 1.0881836631149392518730893845222
absolute error = 3.93830422e-23
relative error = 3.6191539659091694622739600462839e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.3MB, time=14.97
NO POLE
x[1] = 0.0848
y[1] (analytic) = 1.0882917690599461002756402213037
y[1] (numeric) = 1.0882917690599461002756796486692
absolute error = 3.94273655e-23
relative error = 3.6228671961800192938631561309724e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0849
y[1] (analytic) = 1.0883998841220352504812008497363
y[1] (numeric) = 1.08839988412203525048124032142
absolute error = 3.94716837e-23
relative error = 3.6265791898572358724873419484826e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 1.0885080083001255518697413435729
y[1] (numeric) = 1.0885080083001255518697808595694
absolute error = 3.95159965e-23
relative error = 3.6302899196589624303574208856140e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0851
y[1] (analytic) = 1.0886161415931357626612597237449
y[1] (numeric) = 1.0886161415931357626612992840491
absolute error = 3.95603042e-23
relative error = 3.6339994134301054667207657286080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0852
y[1] (analytic) = 1.0887242839999845499265549931121
y[1] (numeric) = 1.0887242839999845499265945977187
absolute error = 3.96046066e-23
relative error = 3.6377076530792769593907685248854e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0853
y[1] (analytic) = 1.088832435519590489598040465745
y[1] (numeric) = 1.0888324355195904895980801146486
absolute error = 3.96489036e-23
relative error = 3.6414146297065035445250403435122e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0854
y[1] (analytic) = 1.0889405961508720664805580075917
y[1] (numeric) = 1.0889405961508720664805977007872
absolute error = 3.96931955e-23
relative error = 3.6451203711483754408899510085840e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0855
y[1] (analytic) = 1.0890487658927476742621931884208
y[1] (numeric) = 1.0890487658927476742622329259029
absolute error = 3.97374821e-23
relative error = 3.6488248593188754895222709871761e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0856
y[1] (analytic) = 1.0891569447441356155250913449314
y[1] (numeric) = 1.0891569447441356155251311266947
absolute error = 3.97817633e-23
relative error = 3.6525280853206622580255299126993e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0857
y[1] (analytic) = 1.0892651327039541017562745549221
y[1] (numeric) = 1.0892651327039541017563143809616
absolute error = 3.98260395e-23
relative error = 3.6562300861625136770477303440099e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0858
y[1] (analytic) = 1.089373329771121253358459522413
y[1] (numeric) = 1.0893733297711212533584993927233
absolute error = 3.98703103e-23
relative error = 3.6599308254018669431834888244220e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0859
y[1] (analytic) = 1.0894815359445550996608763736082
y[1] (numeric) = 1.089481535944555099660916288184
absolute error = 3.99145758e-23
relative error = 3.6636303125041025179486679350505e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 1.0895897512231735789300883635951
y[1] (numeric) = 1.0895897512231735789301283224312
absolute error = 3.99588361e-23
relative error = 3.6673285569309188195890166113753e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0861
y[1] (analytic) = 1.0896979756058945383808124936697
y[1] (numeric) = 1.0896979756058945383808524967609
absolute error = 4.00030912e-23
relative error = 3.6710255589634785396087929904951e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0862
y[1] (analytic) = 1.0898062090916357341867410391808
y[1] (numeric) = 1.0898062090916357341867810865216
absolute error = 4.00473408e-23
relative error = 3.6747212913550800081145694006412e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=209.8MB, alloc=4.3MB, time=15.25
x[1] = 0.0863
y[1] (analytic) = 1.089914451679314831491363987783
y[1] (numeric) = 1.0899144516793148314914040793683
absolute error = 4.00915853e-23
relative error = 3.6784157910951467847975418807697e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0864
y[1] (analytic) = 1.0900227033678494044187923879938
y[1] (numeric) = 1.0900227033678494044188325238184
absolute error = 4.01358246e-23
relative error = 3.6821090492878829324845781650283e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0865
y[1] (analytic) = 1.0901309641561569360845826079432
y[1] (numeric) = 1.0901309641561569360846227880018
absolute error = 4.01800586e-23
relative error = 3.6858010570411029989926471475335e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0866
y[1] (analytic) = 1.0902392340431548186065615042088
y[1] (numeric) = 1.0902392340431548186066017284961
absolute error = 4.02242873e-23
relative error = 3.6894918146385297394176155730373e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0867
y[1] (analytic) = 1.0903475130277603531156525006289
y[1] (numeric) = 1.0903475130277603531156927691396
absolute error = 4.02685107e-23
relative error = 3.6931813223638507830219144569339e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0868
y[1] (analytic) = 1.0904558011088907497667025769839
y[1] (numeric) = 1.0904558011088907497667428897128
absolute error = 4.03127289e-23
relative error = 3.6968695896711957595344860647354e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0869
y[1] (analytic) = 1.0905640982854631277493101674392
y[1] (numeric) = 1.090564098285463127749350524381
absolute error = 4.03569418e-23
relative error = 3.7005566076718835249614161126290e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 1.0906724045563945152986539686397
y[1] (numeric) = 1.0906724045563945152986943697892
absolute error = 4.04011495e-23
relative error = 3.7042423858181524625738852865137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0871
y[1] (analytic) = 1.0907807199206018497063226573496
y[1] (numeric) = 1.0907807199206018497063631027015
absolute error = 4.04453519e-23
relative error = 3.7079269152230730100297821156171e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0872
y[1] (analytic) = 1.0908890443770019773311455175269
y[1] (numeric) = 1.0908890443770019773311860070759
absolute error = 4.04895490e-23
relative error = 3.7116101961701575370862462350004e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0873
y[1] (analytic) = 1.0909973779245116536100239767264
y[1] (numeric) = 1.0909973779245116536100645104673
absolute error = 4.05337409e-23
relative error = 3.7152922381088080556416763271715e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0874
y[1] (analytic) = 1.0911057205620475430687640517216
y[1] (numeric) = 1.0911057205620475430688046296491
absolute error = 4.05779275e-23
relative error = 3.7189730321547213083425566120779e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0875
y[1] (analytic) = 1.0912140722885262193329097032376
y[1] (numeric) = 1.0912140722885262193329503253464
absolute error = 4.06221088e-23
relative error = 3.7226525785913042419133534374056e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0876
y[1] (analytic) = 1.0913224331028641651385770996866
y[1] (numeric) = 1.0913224331028641651386177659715
absolute error = 4.06662849e-23
relative error = 3.7263308868651232832235984093207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0877
y[1] (analytic) = 1.0914308030039777723432897897978
y[1] (numeric) = 1.0914308030039777723433305002535
absolute error = 4.07104557e-23
relative error = 3.7300079480945003872534268199137e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0878
y[1] (analytic) = 1.0915391819907833419368147840331
y[1] (numeric) = 1.0915391819907833419368555386543
absolute error = 4.07546212e-23
relative error = 3.7336837625627369247800465715845e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.3MB, time=15.53
NO POLE
x[1] = 0.0879
y[1] (analytic) = 1.0916475700621970840519995446803
y[1] (numeric) = 1.0916475700621970840520403434617
absolute error = 4.07987814e-23
relative error = 3.7373583305530989363006123006372e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 1.0917559672171351179756098845156
y[1] (numeric) = 1.091755967217135117975650727452
absolute error = 4.08429364e-23
relative error = 3.7410316615083731883353081998935e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0881
y[1] (analytic) = 1.0918643734545134721591687739272
y[1] (numeric) = 1.0918643734545134721592096610133
absolute error = 4.08870861e-23
relative error = 3.7447037465503801157068606053247e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0882
y[1] (analytic) = 1.0919727887732480842297960563906
y[1] (numeric) = 1.0919727887732480842298369876212
absolute error = 4.09312306e-23
relative error = 3.7483745951200173363182830017664e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0883
y[1] (analytic) = 1.0920812131722548010010490721888
y[1] (numeric) = 1.0920812131722548010010900475586
absolute error = 4.09753698e-23
relative error = 3.7520441983408539537504666393405e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0884
y[1] (analytic) = 1.0921896466504493784837641902673
y[1] (numeric) = 1.092189646650449378483805209771
absolute error = 4.10195037e-23
relative error = 3.7557125564959797301205333723448e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0885
y[1] (analytic) = 1.0922980892067474818968992481169
y[1] (numeric) = 1.0922980892067474818969403117493
absolute error = 4.10636324e-23
relative error = 3.7593796790234590604209383468483e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0886
y[1] (analytic) = 1.0924065408400646856783768995751
y[1] (numeric) = 1.0924065408400646856784180073309
absolute error = 4.11077558e-23
relative error = 3.7630455570494829854495500992372e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0887
y[1] (analytic) = 1.0925150015493164734959288704379
y[1] (numeric) = 1.0925150015493164734959700223118
absolute error = 4.11518739e-23
relative error = 3.7667101908570352355987798715136e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0888
y[1] (analytic) = 1.0926234713334182382579411217732
y[1] (numeric) = 1.0926234713334182382579823177599
absolute error = 4.11959867e-23
relative error = 3.7703735807290640593780822369097e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0889
y[1] (analytic) = 1.092731950191285282124299920828
y[1] (numeric) = 1.0927319501912852821243411609223
absolute error = 4.12400943e-23
relative error = 3.7740357360998573433063331448546e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 1.0928404381218328165172388194208
y[1] (numeric) = 1.0928404381218328165172801036173
absolute error = 4.12841965e-23
relative error = 3.7776966389486335776762145602630e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0891
y[1] (analytic) = 1.0929489351239759621321865397095
y[1] (numeric) = 1.0929489351239759621322278680031
absolute error = 4.13282936e-23
relative error = 3.7813563170096347753283726457960e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0892
y[1] (analytic) = 1.0930574411966297489486157672292
y[1] (numeric) = 1.0930574411966297489486571396145
absolute error = 4.13723853e-23
relative error = 3.7850147431142674059108593546073e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0893
y[1] (analytic) = 1.0931659563387091162408928510873
y[1] (numeric) = 1.093165956338709116240934267559
absolute error = 4.14164717e-23
relative error = 3.7886719266957690365379392462876e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0894
y[1] (analytic) = 1.0932744805491289125891284112113
y[1] (numeric) = 1.0932744805491289125891698717642
absolute error = 4.14605529e-23
relative error = 3.7923278771837088126493835825268e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.3MB, time=15.80
NO POLE
x[1] = 0.0895
y[1] (analytic) = 1.0933830138268038958900288525388
y[1] (numeric) = 1.0933830138268038958900703571676
absolute error = 4.15046288e-23
relative error = 3.7959825857121367308113647977207e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0896
y[1] (analytic) = 1.0934915561706487333677487860411
y[1] (numeric) = 1.0934915561706487333677903347405
absolute error = 4.15486994e-23
relative error = 3.7996360525637172093275576338604e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0897
y[1] (analytic) = 1.0936001075795780015847443564727
y[1] (numeric) = 1.0936001075795780015847859492375
absolute error = 4.15927648e-23
relative error = 3.8032882871651893273581530939853e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0898
y[1] (analytic) = 1.0937086680525061864526274767378
y[1] (numeric) = 1.0937086680525061864526691135627
absolute error = 4.16368249e-23
relative error = 3.8069392806532206584982377353800e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0899
y[1] (analytic) = 1.093817237588347683243020968765
y[1] (numeric) = 1.0938172375883476832430626496447
absolute error = 4.16808797e-23
relative error = 3.8105890333103689885082525420979e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 1.093925816186016796598414610782
y[1] (numeric) = 1.0939258161860167965984563357113
absolute error = 4.17249293e-23
relative error = 3.8142375545605441206949968470341e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0901
y[1] (analytic) = 1.0940344038444277405430220908818
y[1] (numeric) = 1.0940344038444277405430638598554
absolute error = 4.17689736e-23
relative error = 3.8178848355430301168225069057149e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0902
y[1] (analytic) = 1.0941430005624946384936388667717
y[1] (numeric) = 1.0941430005624946384936806797842
absolute error = 4.18130125e-23
relative error = 3.8215308674007048221751255305650e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0903
y[1] (analytic) = 1.0942516063391315232705009315955
y[1] (numeric) = 1.0942516063391315232705427886417
absolute error = 4.18570462e-23
relative error = 3.8251756686960369411583536539785e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0904
y[1] (analytic) = 1.0943602211732523371081444857231
y[1] (numeric) = 1.0943602211732523371081863867976
absolute error = 4.19010745e-23
relative error = 3.8288192214331665857599896388030e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0905
y[1] (analytic) = 1.0944688450637709316662665143953
y[1] (numeric) = 1.0944688450637709316663084594929
absolute error = 4.19450976e-23
relative error = 3.8324615441708624942659612033807e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0906
y[1] (analytic) = 1.0945774780096010680405862711183
y[1] (numeric) = 1.0945774780096010680406282602337
absolute error = 4.19891154e-23
relative error = 3.8361026280527666015592854898578e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0907
y[1] (analytic) = 1.0946861200096564167737076666972
y[1] (numeric) = 1.0946861200096564167737496998251
absolute error = 4.20331279e-23
relative error = 3.8397424733611510908474089513856e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0908
y[1] (analytic) = 1.0947947710628505578659825638008
y[1] (numeric) = 1.0947947710628505578660246409361
absolute error = 4.20771353e-23
relative error = 3.8433810986465164198875165064439e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0909
y[1] (analytic) = 1.0949034311680969807863749769496
y[1] (numeric) = 1.0949034311680969807864170980868
absolute error = 4.21211372e-23
relative error = 3.8470184676527219783259138292340e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 1.0950121003243090844833261778163
y[1] (numeric) = 1.0950121003243090844833683429501
absolute error = 4.21651338e-23
relative error = 3.8506545989320097306311504471844e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.3MB, time=16.09
NO POLE
x[1] = 0.0911
y[1] (analytic) = 1.0951207785304001773956207057327
y[1] (numeric) = 1.095120778530400177395662914858
absolute error = 4.22091253e-23
relative error = 3.8542895110293343001624254622170e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0912
y[1] (analytic) = 1.0952294657852834774632532832932
y[1] (numeric) = 1.0952294657852834774632955364046
absolute error = 4.22531114e-23
relative error = 3.8579231768298314288987728793720e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0913
y[1] (analytic) = 1.095338162087872112138296636945
y[1] (numeric) = 1.0953381620878721121383389340374
absolute error = 4.22970924e-23
relative error = 3.8615556240070789674348805460541e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0914
y[1] (analytic) = 1.0954468674370791183957702224592
y[1] (numeric) = 1.0954468674370791183958125635271
absolute error = 4.23410679e-23
relative error = 3.8651868163228838317419187848782e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0915
y[1] (analytic) = 1.0955555818318174427445098551706
y[1] (numeric) = 1.0955555818318174427445522402088
absolute error = 4.23850382e-23
relative error = 3.8688167814480338249573950426135e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0916
y[1] (analytic) = 1.0956643052709999412380382448811
y[1] (numeric) = 1.0956643052709999412380806738843
absolute error = 4.24290032e-23
relative error = 3.8724455105348781935517585364615e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0917
y[1] (analytic) = 1.0957730377535393794854364353149
y[1] (numeric) = 1.0957730377535393794854789082778
absolute error = 4.24729629e-23
relative error = 3.8760730038653308767507727145206e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0918
y[1] (analytic) = 1.0958817792783484326622161480189
y[1] (numeric) = 1.0958817792783484326622586649362
absolute error = 4.25169173e-23
relative error = 3.8796992617212698371720326040802e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0919
y[1] (analytic) = 1.0959905298443396855211930305984
y[1] (numeric) = 1.0959905298443396855212355914649
absolute error = 4.25608665e-23
relative error = 3.8833242935087034746100914583351e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 1.09609928945042563240336080918
y[1] (numeric) = 1.0960992894504256324034034139903
absolute error = 4.26048103e-23
relative error = 3.8869480812601995514836473334115e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0921
y[1] (analytic) = 1.0962080580955186772487663449923
y[1] (numeric) = 1.0962080580955186772488089937412
absolute error = 4.26487489e-23
relative error = 3.8905706435049557338589869647165e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0922
y[1] (analytic) = 1.0963168357785311336073855949569
y[1] (numeric) = 1.096316835778531133607428287639
absolute error = 4.26926821e-23
relative error = 3.8941919622790890711097138459757e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0923
y[1] (analytic) = 1.0964256224983752246500004761788
y[1] (numeric) = 1.096425622498375224650043212789
absolute error = 4.27366102e-23
relative error = 3.8978120652286498977385164550112e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0924
y[1] (analytic) = 1.0965344182539630831790766342305
y[1] (numeric) = 1.0965344182539630831791194147634
absolute error = 4.27805329e-23
relative error = 3.9014309252709481057146281841191e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0925
y[1] (analytic) = 1.0966432230442067516396421151175
y[1] (numeric) = 1.0966432230442067516396849395678
absolute error = 4.28244503e-23
relative error = 3.9050485518090604099136741317366e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0926
y[1] (analytic) = 1.0967520368680181821301669408191
y[1] (numeric) = 1.0967520368680181821302098091815
absolute error = 4.28683624e-23
relative error = 3.9086649451245766912595512321799e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.3MB, time=16.37
NO POLE
x[1] = 0.0927
y[1] (analytic) = 1.0968608597243092364134435882948
y[1] (numeric) = 1.0968608597243092364134865005641
absolute error = 4.29122693e-23
relative error = 3.9122801146159773557449932481052e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0928
y[1] (analytic) = 1.0969696916119916859274683718474
y[1] (numeric) = 1.0969696916119916859275113280182
absolute error = 4.29561708e-23
relative error = 3.9158940423300222276798716939464e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0929
y[1] (analytic) = 1.0970785325299772117963237287336
y[1] (numeric) = 1.0970785325299772117963667288007
absolute error = 4.30000671e-23
relative error = 3.9195067467811417740184629078284e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 1.0971873824771774048410614079145
y[1] (numeric) = 1.0971873824771774048411044518726
absolute error = 4.30439581e-23
relative error = 3.9231182191338549583402159738535e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0931
y[1] (analytic) = 1.0972962414525037655905865618359
y[1] (numeric) = 1.0972962414525037655906296496796
absolute error = 4.30878437e-23
relative error = 3.9267284505562619435525816873176e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0932
y[1] (analytic) = 1.0974051094548677042925427411296
y[1] (numeric) = 1.0974051094548677042925858728538
absolute error = 4.31317242e-23
relative error = 3.9303374686696637372145370837272e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0933
y[1] (analytic) = 1.097513986483180540924197792129
y[1] (numeric) = 1.0975139864831805409242409677284
absolute error = 4.31755994e-23
relative error = 3.9339452555269707546745529734669e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0934
y[1] (analytic) = 1.0976228725363535052033306570867
y[1] (numeric) = 1.0976228725363535052033738765558
absolute error = 4.32194691e-23
relative error = 3.9375517931882894417344109785910e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0935
y[1] (analytic) = 1.0977317676132977365991190769872
y[1] (numeric) = 1.0977317676132977365991623403208
absolute error = 4.32633336e-23
relative error = 3.9411571092693879062202245381884e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0936
y[1] (analytic) = 1.0978406717129242843430281968468
y[1] (numeric) = 1.0978406717129242843430715040398
absolute error = 4.33071930e-23
relative error = 3.9447612131575729673486487067253e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0937
y[1] (analytic) = 1.09794958483414410743970007339
y[1] (numeric) = 1.0979495848341441074397434244369
absolute error = 4.33510469e-23
relative error = 3.9483640686970699540514603072017e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0938
y[1] (analytic) = 1.0980585069758680746778440849931
y[1] (numeric) = 1.0980585069758680746778874798886
absolute error = 4.33948955e-23
relative error = 3.9519656943884216371839496492043e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0939
y[1] (analytic) = 1.0981674381370069646411282437887
y[1] (numeric) = 1.0981674381370069646411716825275
absolute error = 4.34387388e-23
relative error = 3.9555660905127473798776704735835e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 1.0982763783164714657190714098198
y[1] (numeric) = 1.0982763783164714657191148923966
absolute error = 4.34825768e-23
relative error = 3.9591652573511302161340515126523e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0941
y[1] (analytic) = 1.0983853275131721761179364071355
y[1] (numeric) = 1.0983853275131721761179799335451
absolute error = 4.35264096e-23
relative error = 3.9627632042888899434606010177039e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0942
memory used=228.8MB, alloc=4.3MB, time=16.64
y[1] (analytic) = 1.0984942857260196038716240417195
y[1] (numeric) = 1.0984942857260196038716676119565
absolute error = 4.35702370e-23
relative error = 3.9663599133975876322950504812263e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0943
y[1] (analytic) = 1.0986032529539241668525680211417
y[1] (numeric) = 1.0986032529539241668526116352008
absolute error = 4.36140591e-23
relative error = 3.9699553940633734882447244746934e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0944
y[1] (analytic) = 1.0987122291957961927826307758246
y[1] (numeric) = 1.0987122291957961927826744337007
absolute error = 4.36578761e-23
relative error = 3.9735496647703136685532183806566e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0945
y[1] (analytic) = 1.0988212144505459192440001818166
y[1] (numeric) = 1.0988212144505459192440438835042
absolute error = 4.37016876e-23
relative error = 3.9771426893912466737684094962234e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0946
y[1] (analytic) = 1.0989302087170834936900871849596
y[1] (numeric) = 1.0989302087170834936901309304535
absolute error = 4.37454939e-23
relative error = 3.9807344955117304414893303674323e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0947
y[1] (analytic) = 1.0990392119943189734564243263472
y[1] (numeric) = 1.099039211994318973456468115642
absolute error = 4.37892948e-23
relative error = 3.9843250652121728450701577250219e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0948
y[1] (analytic) = 1.0991482242811623257715651689591
y[1] (numeric) = 1.0991482242811623257716090020496
absolute error = 4.38330905e-23
relative error = 3.9879144169719813035390961209568e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0949
y[1] (analytic) = 1.0992572455765234277679846253674
y[1] (numeric) = 1.0992572455765234277680285022483
absolute error = 4.38768809e-23
relative error = 3.9915025419721525442914780991494e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 1.0993662758793120664929801864023
y[1] (numeric) = 1.0993662758793120664930241070683
absolute error = 4.39206660e-23
relative error = 3.9950894404934057561984602338948e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0951
y[1] (analytic) = 1.0994753151884379389195740506702
y[1] (numeric) = 1.0994753151884379389196180151159
absolute error = 4.39644457e-23
relative error = 3.9986751037211762276316022268199e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0952
y[1] (analytic) = 1.099584363502810651957416154814
y[1] (numeric) = 1.0995843635028106519574601630342
absolute error = 4.40082202e-23
relative error = 4.0022595501275069208105801001551e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0953
y[1] (analytic) = 1.0996934208213397224636881044083
y[1] (numeric) = 1.0996934208213397224637321563976
absolute error = 4.40519893e-23
relative error = 4.0058427618034144623573447498288e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0954
y[1] (analytic) = 1.0998024871429345772540080053777
y[1] (numeric) = 1.0998024871429345772540521011309
absolute error = 4.40957532e-23
relative error = 4.0094247572172607455609410282610e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0955
y[1] (analytic) = 1.099911562466504553113336195832
y[1] (numeric) = 1.0999115624665045531133803353438
absolute error = 4.41395118e-23
relative error = 4.0130055275552368906969415520613e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0956
y[1] (analytic) = 1.1000206467909588968068818782074
y[1] (numeric) = 1.1000206467909588968069260614725
absolute error = 4.41832651e-23
relative error = 4.0165850730978428396257039159492e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0957
y[1] (analytic) = 1.1001297401152067650910106516052
y[1] (numeric) = 1.1001297401152067650910548786183
absolute error = 4.42270131e-23
relative error = 4.0201633941255419385585363952874e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=232.7MB, alloc=4.3MB, time=16.92
x[1] = 0.0958
y[1] (analytic) = 1.1002388424381572247241529442193
y[1] (numeric) = 1.1002388424381572247241972149751
absolute error = 4.42707558e-23
relative error = 4.0237404909187609225387036293957e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0959
y[1] (analytic) = 1.1003479537587192524777133457425
y[1] (numeric) = 1.1003479537587192524777576602357
absolute error = 4.43144932e-23
relative error = 4.0273163637578898999399975177896e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 1.1004570740758017351469808396437
y[1] (numeric) = 1.1004570740758017351470251978689
absolute error = 4.43582252e-23
relative error = 4.0308910038361491488043853444717e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0961
y[1] (analytic) = 1.1005662033883134695620399352054
y[1] (numeric) = 1.1005662033883134695620843371574
absolute error = 4.44019520e-23
relative error = 4.0344644296090229108315475622402e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0962
y[1] (analytic) = 1.1006753416951631625986826992144
y[1] (numeric) = 1.1006753416951631625987271448879
absolute error = 4.44456735e-23
relative error = 4.0380366322687569722003220556046e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0963
y[1] (analytic) = 1.1007844889952594311893216871945
y[1] (numeric) = 1.1007844889952594311893661765841
absolute error = 4.44893896e-23
relative error = 4.0416076030111644486914959268282e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0964
y[1] (analytic) = 1.1008936452875108023339037740729
y[1] (numeric) = 1.1008936452875108023339483071734
absolute error = 4.45331005e-23
relative error = 4.0451773602862134893704176326080e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0965
y[1] (analytic) = 1.1010028105708257131108248841725
y[1] (numeric) = 1.1010028105708257131108694609784
absolute error = 4.45768059e-23
relative error = 4.0487458771234850413201710805511e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0966
y[1] (analytic) = 1.1011119848441125106878456204178
y[1] (numeric) = 1.101111984844112510687890240924
absolute error = 4.46205062e-23
relative error = 4.0523131901354292580120621852174e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0967
y[1] (analytic) = 1.1012211681062794523330077926492
y[1] (numeric) = 1.1012211681062794523330524568503
absolute error = 4.46642011e-23
relative error = 4.0558792723542555188199865495625e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0968
y[1] (analytic) = 1.1013303603562347054255518449328
y[1] (numeric) = 1.1013303603562347054255965528235
absolute error = 4.47078907e-23
relative error = 4.0594441331426522329216844786037e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0969
y[1] (analytic) = 1.1014395615928863474668351817592
y[1] (numeric) = 1.1014395615928863474668799333342
absolute error = 4.47515750e-23
relative error = 4.0630077727806420799758472746500e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 1.1015487718151423660912513930206
y[1] (numeric) = 1.1015487718151423660912961882746
absolute error = 4.47952540e-23
relative error = 4.0665701915482109436126255126671e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0971
y[1] (analytic) = 1.1016579910219106590771503776581
y[1] (numeric) = 1.1016579910219106590771952165857
absolute error = 4.48389276e-23
relative error = 4.0701313806480805883061111786462e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0972
y[1] (analytic) = 1.1017672192120990343577593658687
y[1] (numeric) = 1.1017672192120990343578042484646
absolute error = 4.48825959e-23
relative error = 4.0736913494391903835653963525516e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0973
y[1] (analytic) = 1.1018764563846152100321048397643
y[1] (numeric) = 1.1018764563846152100321497660232
absolute error = 4.49262589e-23
relative error = 4.0772500982014154199577910982009e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.3MB, time=17.21
NO POLE
x[1] = 0.0974
y[1] (analytic) = 1.101985702538366814375935352372
y[1] (numeric) = 1.1019857025383668143759803222887
absolute error = 4.49699167e-23
relative error = 4.0808076362891218281614645139962e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0975
y[1] (analytic) = 1.102094957672261385852645244868
y[1] (numeric) = 1.1020949576722613858526902584371
absolute error = 4.50135691e-23
relative error = 4.0843639458321555802639396483076e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0976
y[1] (analytic) = 1.1022042217852063731241992619339
y[1] (numeric) = 1.1022042217852063731242443191501
absolute error = 4.50572162e-23
relative error = 4.0879190361857087462299306090197e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0977
y[1] (analytic) = 1.1023134948761091350620580651283
y[1] (numeric) = 1.1023134948761091350621031659864
absolute error = 4.51008581e-23
relative error = 4.0914729167013383234687631750502e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0978
y[1] (analytic) = 1.1024227769438769407581046441634
y[1] (numeric) = 1.1024227769438769407581497886579
absolute error = 4.51444945e-23
relative error = 4.0950255604432466856822136077795e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0979
y[1] (analytic) = 1.1025320679874169695355716259763
y[1] (numeric) = 1.102532067987416969535616814102
absolute error = 4.51881257e-23
relative error = 4.0985769949065758323028793212848e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 1.1026413680056363109599694814882
y[1] (numeric) = 1.1026413680056363109600147132398
absolute error = 4.52317516e-23
relative error = 4.1021272112991131087689844081421e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0981
y[1] (analytic) = 1.1027506769974419648500156299402
y[1] (numeric) = 1.1027506769974419648500609053123
absolute error = 4.52753721e-23
relative error = 4.1056762008322053961760415851297e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0982
y[1] (analytic) = 1.1028599949617408412885644406962
y[1] (numeric) = 1.1028599949617408412886097596837
absolute error = 4.53189875e-23
relative error = 4.1092239909900943073487117128357e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0983
y[1] (analytic) = 1.1029693218974397606335381324066
y[1] (numeric) = 1.102969321897439760633583495004
absolute error = 4.53625974e-23
relative error = 4.1127705457811515918433213903521e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0984
y[1] (analytic) = 1.1030786578034454535288585694187
y[1] (numeric) = 1.1030786578034454535289039756207
absolute error = 4.54062020e-23
relative error = 4.1163158836213116196806544465524e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0985
y[1] (analytic) = 1.103188002678664560915379955329
y[1] (numeric) = 1.1031880026786645609154254051303
absolute error = 4.54498013e-23
relative error = 4.1198600047900058822579140942956e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0986
y[1] (analytic) = 1.1032973565220036340418224235656
y[1] (numeric) = 1.1032973565220036340418679169608
absolute error = 4.54933952e-23
relative error = 4.1234029005028891787889870720731e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0987
y[1] (analytic) = 1.1034067193323691344757065248914
y[1] (numeric) = 1.1034067193323691344757520618753
absolute error = 4.55369839e-23
relative error = 4.1269445891676965571107170733170e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0988
y[1] (analytic) = 1.1035160911086674341142886117205
y[1] (numeric) = 1.1035160911086674341143341922877
absolute error = 4.55805672e-23
relative error = 4.1304850529371671732604545026252e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0989
y[1] (analytic) = 1.1036254718498048151954971191357
y[1] (numeric) = 1.103625471849804815195542743281
absolute error = 4.56241453e-23
relative error = 4.1340243102153685568967230462421e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.3MB, time=17.50
NO POLE
x[1] = 0.099
y[1] (analytic) = 1.103734861554687470308869742501
y[1] (numeric) = 1.103734861554687470308915410219
absolute error = 4.56677180e-23
relative error = 4.1375623431585586301673763016828e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0991
y[1] (analytic) = 1.1038442602222215024064915115563
y[1] (numeric) = 1.1038442602222215024065372228417
absolute error = 4.57112854e-23
relative error = 4.1410991611078891897343772233815e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0992
y[1] (analytic) = 1.1039536678513129248139337608879
y[1] (numeric) = 1.1039536678513129248139795157353
absolute error = 4.57548474e-23
relative error = 4.1446347552841806577318444284373e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0993
y[1] (analytic) = 1.1040630844408676612411939966634
y[1] (numeric) = 1.1040630844408676612412397950676
absolute error = 4.57984042e-23
relative error = 4.1481691440841675411137354668763e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0994
y[1] (analytic) = 1.1041725099897915457936366595229
y[1] (numeric) = 1.1041725099897915457936825014785
absolute error = 4.58419556e-23
relative error = 4.1517023096711422954251331329925e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0995
y[1] (analytic) = 1.104281944496990322982934783516
y[1] (numeric) = 1.1042819444969903229829806690178
absolute error = 4.58855018e-23
relative error = 4.1552342704381742366559716265367e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0996
y[1] (analytic) = 1.1043913879613696477380125509762
y[1] (numeric) = 1.1043913879613696477380584800188
absolute error = 4.59290426e-23
relative error = 4.1587650085520719012118861103914e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0997
y[1] (analytic) = 1.104500840381835085415988743222
y[1] (numeric) = 1.1045008403818350854160347158002
absolute error = 4.59725782e-23
relative error = 4.1622945424022401901254659409760e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0998
y[1] (analytic) = 1.1046103017572921118131210869776
y[1] (numeric) = 1.1046103017572921118131671030858
absolute error = 4.60161082e-23
relative error = 4.1658228360530699297236097133603e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0999
y[1] (analytic) = 1.1047197720866461131757514963997
y[1] (numeric) = 1.1047197720866461131757975560329
absolute error = 4.60596332e-23
relative error = 4.1693499441039623511634359547636e-21 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 1.1048292513688023862112522106067
y[1] (numeric) = 1.1048292513688023862112983137594
absolute error = 4.61031527e-23
relative error = 4.1728758215698558108159626101366e-21 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = cos ( x ) + sin ( x ) ;
Iterations = 1000
Total Elapsed Time = 17 Seconds
Elapsed Time(since restart) = 17 Seconds
Expected Time Remaining = 29 Minutes 4 Seconds
Optimized Time Remaining = 29 Minutes 3 Seconds
Time to Timeout = 14 Minutes 42 Seconds
Percent Done = 1.001 %
> quit
memory used=242.9MB, alloc=4.3MB, time=17.68