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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> 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 - 3 - 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 - 3 - 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
array_poles, glob_last;
n := glob_max_terms;
m := n - 4;
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 - 4;
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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> array_poles,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_y_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_m1[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * (glob_h ^ (3)) * factorial_3(0,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,2] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_y_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * (glob_h ^ (3)) * factorial_3(1,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,3] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_y_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * (glob_h ^ (3)) * factorial_3(2,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,4] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_y_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,7] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * (glob_h ^ (3)) * factorial_3(3,6);
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,5] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_y_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,8] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * (glob_h ^ (3)) * factorial_3(4,7);
> array_y[8] := temporary;
> array_y_higher[1,8] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,7] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,6] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[4,5] := 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 diff $eq_no = 1
> array_tmp1[kkk] := array_y_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_m1,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 3;
> 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_tmp3[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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
array_poles, glob_last;
array_tmp1[1] := array_y_higher[2, 1];
array_tmp2[1] := array_m1[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y_set_initial[1, 4] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*glob_h^3*factorial_3(0, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 2] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_y_higher[2, 2];
array_tmp2[2] := ats(2, array_m1, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
if not array_y_set_initial[1, 5] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*glob_h^3*factorial_3(1, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 3] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_y_higher[2, 3];
array_tmp2[3] := ats(3, array_m1, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
if not array_y_set_initial[1, 6] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*glob_h^3*factorial_3(2, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 4] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_y_higher[2, 4];
array_tmp2[4] := ats(4, array_m1, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
if not array_y_set_initial[1, 7] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*glob_h^3*factorial_3(3, 6);
array_y[7] := temporary;
array_y_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_y_higher[2, 5];
array_tmp2[5] := ats(5, array_m1, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
if not array_y_set_initial[1, 8] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*glob_h^3*factorial_3(4, 7);
array_y[8] := temporary;
array_y_higher[1, 8] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 7] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[4, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_y_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_m1, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
order_d := 3;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp3[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)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 13
> if array_fact_1[nnn] = 0 then # if number 14
> ret := nnn!;
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> if array_fact_2[mmm,nnn] = 0 then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y := proc(x) 2.0 - cos(x) end proc
> exact_soln_yp := proc(x)
> sin(x)
> end;
exact_soln_yp := proc(x) sin(x) end proc
> exact_soln_ypp := proc(x)
> cos(x)
> end;
exact_soln_ypp := proc(x) cos(x) end proc
> exact_soln_yppp := proc(x)
> -sin(x)
> end;
exact_soln_yppp := proc(x) -sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> glob_iolevel,
> INFO,
> #Top Generate Globals Decl
> glob_log10relerr,
> glob_start,
> glob_warned2,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> glob_h,
> glob_display_flag,
> glob_normmax,
> MAX_UNCHANGED,
> glob_optimal_start,
> glob_max_iter,
> djd_debug,
> glob_small_float,
> glob_max_hours,
> glob_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_hmin_init,
> glob_max_rel_trunc_err,
> glob_log10_relerr,
> glob_optimal_done,
> glob_html_log,
> glob_smallish_float,
> centuries_in_millinium,
> days_in_year,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> sec_in_min,
> glob_log10normmin,
> glob_max_sec,
> glob_initial_pass,
> glob_max_minutes,
> glob_iter,
> glob_orig_start_sec,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_abserr,
> glob_hmin,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_subiter_method,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_look_poles,
> glob_last_good_h,
> glob_large_float,
> glob_clock_start_sec,
> years_in_century,
> djd_debug2,
> glob_dump,
> glob_optimal_expect_sec,
> hours_in_day,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> array_const_3,
> #END CONST
> array_m1,
> array_y,
> array_x,
> array_1st_rel_error,
> array_norms,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_type_pole,
> array_pole,
> array_last_rel_error,
> array_fact_1,
> array_complex_pole,
> array_real_pole,
> array_y_set_initial,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_higher,
> array_fact_2,
> array_poles,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> DEBUGL := 3;
> glob_max_terms := 30;
> ALWAYS := 1;
> glob_iolevel := 5;
> INFO := 2;
> glob_log10relerr := 0.0;
> glob_start := 0;
> glob_warned2 := false;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_display_flag := true;
> glob_normmax := 0.0;
> MAX_UNCHANGED := 10;
> glob_optimal_start := 0.0;
> glob_max_iter := 1000;
> djd_debug := true;
> glob_small_float := 0.1e-50;
> glob_max_hours := 0.0;
> glob_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_hmin_init := 0.001;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_optimal_done := false;
> glob_html_log := true;
> glob_smallish_float := 0.1e-100;
> centuries_in_millinium := 10.0;
> days_in_year := 365.0;
> glob_percent_done := 0.0;
> glob_log10abserr := 0.0;
> glob_warned := false;
> glob_disp_incr := 0.1;
> glob_not_yet_start_msg := true;
> glob_almost_1 := 0.9990;
> sec_in_min := 60.0;
> glob_log10normmin := 0.1;
> glob_max_sec := 10000.0;
> glob_initial_pass := true;
> glob_max_minutes := 0.0;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_reached_optimal_h := false;
> glob_not_yet_finished := true;
> glob_clock_sec := 0.0;
> min_in_hour := 60.0;
> glob_subiter_method := 3;
> glob_current_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_look_poles := false;
> glob_last_good_h := 0.1;
> glob_large_float := 9.0e100;
> glob_clock_start_sec := 0.0;
> years_in_century := 100.0;
> djd_debug2 := true;
> glob_dump := false;
> glob_optimal_expect_sec := 0.1;
> hours_in_day := 24.0;
> glob_max_opt_iter := 10;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/diff2postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"array_y_init[2 + 1] := exact_soln_ypp(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"sin(x)");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_ypp := proc(x)");
> omniout_str(ALWAYS,"cos(x)");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yppp := proc(x)");
> omniout_str(ALWAYS,"-sin(x)");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(4+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(4+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(4+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[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_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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[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
> ;
> 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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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_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 <=4 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 <=4 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 <=4 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 <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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 := 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_const_3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3[1] := 3;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while iiif <= glob_max_terms do # do number 2
> jjjf := 0;
> while jjjf <= glob_max_terms do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> array_y_init[2 + 1] := exact_soln_ypp(x_start);
> glob_h := 0.001 ;
> glob_look_poles := true;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := true;
> array_y_set_initial[1,3] := true;
> 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 := 3;
> #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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[4,iii] := array_y_higher[4,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 := 4;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[3,iii] := array_y_higher[3,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 := 3;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 3;
> #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 := 3;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #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 := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 4;
> #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 := 4;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #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 := 3;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;");
> 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,"2012-06-17T20:10:25-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"diff2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;")
> ;
> 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," 092 | ")
> ;
> logitem_str(html_log_file,"diff2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"diff2 maple results")
> ;
> logitem_str(html_log_file,"Mostly affecting speed of factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp;
global DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, glob_iolevel, INFO,
glob_log10relerr, glob_start, glob_warned2, glob_unchanged_h_cnt,
glob_no_eqs, glob_hmax, glob_h, glob_display_flag, glob_normmax,
MAX_UNCHANGED, glob_optimal_start, glob_max_iter, djd_debug,
glob_small_float, glob_max_hours, glob_relerr, glob_log10_abserr,
glob_dump_analytic, glob_hmin_init, glob_max_rel_trunc_err,
glob_log10_relerr, glob_optimal_done, glob_html_log, glob_smallish_float,
centuries_in_millinium, days_in_year, glob_percent_done, glob_log10abserr,
glob_warned, glob_disp_incr, glob_not_yet_start_msg, glob_almost_1,
sec_in_min, glob_log10normmin, glob_max_sec, glob_initial_pass,
glob_max_minutes, glob_iter, glob_orig_start_sec,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_abserr, glob_hmin,
glob_reached_optimal_h, glob_not_yet_finished, glob_clock_sec, min_in_hour,
glob_subiter_method, glob_current_iter, glob_curr_iter_when_opt,
glob_look_poles, glob_last_good_h, glob_large_float, glob_clock_start_sec,
years_in_century, djd_debug2, glob_dump, glob_optimal_expect_sec,
hours_in_day, glob_max_opt_iter, array_const_0D0, array_const_1,
array_const_3, array_m1, array_y, array_x, array_1st_rel_error, array_norms,
array_y_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_type_pole, array_pole, array_last_rel_error, array_fact_1,
array_complex_pole, array_real_pole, array_y_set_initial,
array_y_higher_work, array_y_higher_work2, array_y_higher, array_fact_2,
array_poles, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
DEBUGL := 3;
glob_max_terms := 30;
ALWAYS := 1;
glob_iolevel := 5;
INFO := 2;
glob_log10relerr := 0.;
glob_start := 0;
glob_warned2 := false;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_hmax := 1.0;
glob_h := 0.1;
glob_display_flag := true;
glob_normmax := 0.;
MAX_UNCHANGED := 10;
glob_optimal_start := 0.;
glob_max_iter := 1000;
djd_debug := true;
glob_small_float := 0.1*10^(-50);
glob_max_hours := 0.;
glob_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_hmin_init := 0.001;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_optimal_done := false;
glob_html_log := true;
glob_smallish_float := 0.1*10^(-100);
centuries_in_millinium := 10.0;
days_in_year := 365.0;
glob_percent_done := 0.;
glob_log10abserr := 0.;
glob_warned := false;
glob_disp_incr := 0.1;
glob_not_yet_start_msg := true;
glob_almost_1 := 0.9990;
sec_in_min := 60.0;
glob_log10normmin := 0.1;
glob_max_sec := 10000.0;
glob_initial_pass := true;
glob_max_minutes := 0.;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_optimal_clock_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_reached_optimal_h := false;
glob_not_yet_finished := true;
glob_clock_sec := 0.;
min_in_hour := 60.0;
glob_subiter_method := 3;
glob_current_iter := 0;
glob_curr_iter_when_opt := 0;
glob_look_poles := false;
glob_last_good_h := 0.1;
glob_large_float := 0.90*10^101;
glob_clock_start_sec := 0.;
years_in_century := 100.0;
djd_debug2 := true;
glob_dump := false;
glob_optimal_expect_sec := 0.1;
hours_in_day := 24.0;
glob_max_opt_iter := 10;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/diff2postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "array_y_init[2 + 1] := exact_soln_ypp(x_start);");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0 \t\t- cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "sin(x)");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_ypp := proc(x)");
omniout_str(ALWAYS, "cos(x)");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yppp := proc(x)");
omniout_str(ALWAYS, "-sin(x)");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 5, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 5, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 5, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_1st_rel_error[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_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[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;
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_fact_1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 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 <= 4 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 <= 4 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 <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_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 := 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_const_3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3[term] := 0.; term := term + 1
end do;
array_const_3[1] := 3;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
array_y_init[3] := exact_soln_ypp(x_start);
glob_h := 0.001;
glob_look_poles := true;
glob_h := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := true;
array_y_set_initial[1, 3] := true;
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 := 3;
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 := 3;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[4, iii] := array_y_higher[4, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 2;
calc_term := 3;
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 := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 2;
calc_term := 2;
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 := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 4;
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 := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 3;
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 := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;");
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, "2012-06-17T20:10:25-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "diff2");
logitem_str(html_log_file,
"diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;");
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, " 092 | ");
logitem_str(html_log_file,
"diff2 diffeq.mxt");
logitem_str(html_log_file,
"diff2 maple results");
logitem_str(html_log_file, "Mostly affecting speed of factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/diff2postode.ode#################
diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
array_y_init[2 + 1] := exact_soln_ypp(x_start);
glob_h := 0.001 ;
glob_look_poles := true;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 - cos(x);
end;
exact_soln_yp := proc(x)
sin(x)
end;
exact_soln_ypp := proc(x)
cos(x)
end;
exact_soln_yppp := proc(x)
-sin(x)
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y[1] (analytic) = 1.0049958347219742339044380121961
y[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.005096165624023340621597000171
y[1] (numeric) = 1.0050961656240233403435905297027
absolute error = 2.780064704683e-19
relative error = 2.7659688692145898956617454459283e-17 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.0051974914298239146653143235401
y[1] (numeric) = 1.0051974914298239057483765614687
absolute error = 8.9169377620714e-18
relative error = 8.8708316903852124681651244032850e-16 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.0052998120380501586788328071734
y[1] (numeric) = 1.0052998120380500908331114549775
absolute error = 6.78457213521959e-17
relative error = 6.7488047386233838356700314162331e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.0054031273463814729626255055154
y[1] (numeric) = 1.0054031273463811865432049068345
absolute error = 2.864194205986809e-16
relative error = 2.8488017672537404468209086296272e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.0055074372515025577949868753959
y[1] (numeric) = 1.0055074372515016821860594783651
absolute error = 8.756089273970308e-16
relative error = 8.7081297955434128557421058294701e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.0056127416491035167473238881278
y[1] (numeric) = 1.0056127416491013342251758642118
absolute error = 2.1825221480239160e-15
relative error = 2.1703405870184179502424319280656e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.0057190404338799609940437656082
y[1] (numeric) = 1.005719040433875235737419106463
absolute error = 4.7252566246591452e-15
relative error = 4.6983863630747306007592227122386e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.0058263334995331146169340305467
y[1] (numeric) = 1.0058263334995238865333995047332
absolute error = 9.2280835345258135e-15
relative error = 9.1746290857377885505670973492265e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.0059346207387699209039295664461
y[1] (numeric) = 1.0059346207387532639409215305349
absolute error = 1.66569630080359112e-14
relative error = 1.6558693442524969023527007602215e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.16
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.0060439020433031496421603885802
y[1] (numeric) = 1.0060439020432748942514536122334
absolute error = 2.82553907067763468e-14
relative error = 2.8085643826664882426351124058568e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.006154177303851505405172832928
y[1] (numeric) = 1.0061541773038059248295712148574
absolute error = 4.55805756016180706e-14
relative error = 4.5301780412777689461446152819768e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.0062654464101397368342158758533
y[1] (numeric) = 1.0062654464100691968853251970518
absolute error = 7.05399488906788015e-14
relative error = 7.0100736482933653161538526787234e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.0063777092508987469134833032516
y[1] (numeric) = 1.0063777092507933189094869855066
absolute error = 1.054280039963177450e-13
relative error = 1.0475987596624482010785201002507e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.0064909657138657042392014539315
y[1] (numeric) = 1.0064909657137127407716216652717
absolute error = 1.529634675797886598e-13
relative error = 1.5197699014744508779593459300632e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.0066052156857841552824512681535
y[1] (numeric) = 1.0066052156855678284809396424795
absolute error = 2.163268015116256740e-13
relative error = 2.1490729249226635285627090444952e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.006720459052404137645612378511
y[1] (numeric) = 1.0067204590521049396098770941404
absolute error = 2.991980357352843706e-13
relative error = 2.9720071052982327803970987017708e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.006836695698482294312315986721
y[1] (numeric) = 1.0068366956980764993803549778525
absolute error = 4.057949319610088685e-13
relative error = 4.0303947372467680291922549700531e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.00695392550778198889079227638
y[1] (numeric) = 1.0069539255072410774126659324781
absolute error = 5.409114781263439019e-13
relative error = 5.3717599626375715863344649966123e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.0070721483630734218504971183478
y[1] (numeric) = 1.0070721483623634651369379590818
absolute error = 7.099567135591592660e-13
relative error = 7.0497105367589116687232990495734e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.0071913641461337477519018321424
y[1] (numeric) = 1.0071913641452147538671233297042
absolute error = 9.189938847785024382e-13
relative error = 9.1243225219429631012715774838806e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.0073115727377471934693287735644
y[1] (numeric) = 1.0073115727365724135374607298568
absolute error = 1.1747799318680437076e-12
relative error = 1.1662527897650757704936206465019e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.007432774017705177406714525728
y[1] (numeric) = 1.0074327740162203721013581989714
absolute error = 1.4848053053563267566e-12
relative error = 1.4738505075974746597751746919087e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.0075549678648064297061814777427
y[1] (numeric) = 1.0075549678629490955926439914173
absolute error = 1.8573341135374863254e-12
relative error = 1.8434072311444382957812570553716e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.007678154156857113449297582485
y[1] (numeric) = 1.0076781541545556688491320391186
absolute error = 2.3014446001655433664e-12
relative error = 2.2839083993948489305924940466764e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.0078023327706709468509030922118
y[1] (numeric) = 1.0078023327678438768984482552555
absolute error = 2.8270699524548369563e-12
relative error = 2.8051829813517080966346085904856e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=4.3MB, time=0.34
x[1] = 0.126
y[1] (analytic) = 1.0079275035820693264453820781963
y[1] (numeric) = 1.007927503578624287006063477021
absolute error = 3.4450394393186011753e-12
relative error = 3.4179436785634779930102818691278e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.0080536664658814512652555481279
y[1] (numeric) = 1.008053666461714331385478403931
absolute error = 4.1671198797771441969e-12
relative error = 4.1338274125687973864799697877143e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.0081808212959444480119719826911
y[1] (numeric) = 1.0081808212909383905705054467436
absolute error = 5.0060574414665359475e-12
relative error = 4.9654360961078456211761665362760e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.0083089679451034972187701205446
y[1] (numeric) = 1.0083089679391278774495919606439
absolute error = 5.9756197691781599007e-12
relative error = 5.9263776869467428061932010569346e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.0084381062852119604054878288482
y[1] (numeric) = 1.0084381062781213219621288949831
absolute error = 7.0906384433589338651e-12
relative error = 7.0313075231545453541273033916000e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.0085682361871315082251899045384
y[1] (numeric) = 1.0085682361787644564566884505325
absolute error = 8.3670517685014540059e-12
relative error = 8.2959699386656240471632953407346e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.008699357520732249602486659737
y[1] (numeric) = 1.0086993575109103017111338939239
absolute error = 9.8219478913527658131e-12
relative error = 9.7372401579534969810922591693481e-10 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.0088314701548928618634141529829
y[1] (numeric) = 1.0088314701434192536145442376929
absolute error = 1.14736082488699152900e-11
relative error = 1.1373166468635532342408016609529e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.0089645739575007218567459364203
y[1] (numeric) = 1.0089645739441591705108960531288
absolute error = 1.33415513458498832915e-11
relative error = 1.3223012670821336275072239311890e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.0090986687954520380666051976395
y[1] (numeric) = 1.0090986687800054612044442419572
absolute error = 1.54465768621609556823e-11
relative error = 1.5307300802011099336860576193555e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.009233754534651983716245183572
y[1] (numeric) = 1.0092337545168411736267431517448
absolute error = 1.78108100895020318272e-11
relative error = 1.7647854136343691498123340061663e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.0093698310400148308628648026684
y[1] (numeric) = 1.0093698310195570841652489788173
absolute error = 2.04577466976158238511e-11
relative error = 2.0267840456987870527366794156098e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.0095068981754640854833253105562
y[1] (numeric) = 1.0095068981520517876534439614214
absolute error = 2.34122978298813491348e-11
relative error = 2.3191815600463602200929920725072e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.0096449558039326235506329934705
y[1] (numeric) = 1.0096449557772317880224224248443
absolute error = 2.67008355282105686262e-11
relative error = 2.6445767271674183289187542396539e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.0097840037873628281010517729886
y[1] (numeric) = 1.0097840037570115896138782992216
absolute error = 3.03512384871734737670e-11
relative error = 3.0057159128423609965784971991127e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.0099240419867067272917086649643
y[1] (numeric) = 1.009924041952313789154433289829
absolute error = 3.43929381372753751353e-11
relative error = 3.4054975134187445363175970428674e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.0100650702619261334485540350706
memory used=11.4MB, alloc=4.4MB, time=0.53
y[1] (numeric) = 1.0100650702230691683912444387502
absolute error = 3.88569650573095963204e-11
relative error = 3.8469764177899310719263999031000e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.0102070884719927831045376030009
y[1] (numeric) = 1.0102070884282167873888293759589
absolute error = 4.37759957157082270420e-11
relative error = 4.3333684959509055113446283014440e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.0103500964748884780278601571639
y[1] (numeric) = 1.010350096425704078487047117034
absolute error = 4.91843995408130401299e-11
relative error = 4.8680551140062649421907152256850e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.010494094127605227240159951634
y[1] (numeric) = 1.0104940940724869409201718239516
absolute error = 5.51182863199881276824e-11
relative error = 5.4545876755047901036083001657891e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.0106390812861453900244917671803
y[1] (numeric) = 1.0106390812245298360969965046647
absolute error = 6.16155539274952625156e-11
relative error = 6.0966921889744197288632678563500e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.0107850578055218199229556284092
y[1] (numeric) = 1.0107850577368058835419031864883
absolute error = 6.87159363810524419209e-11
relative error = 6.7982738615308657642878052172659e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.0109320235397580097238311794022
y[1] (numeric) = 1.0109320234632969574968356576584
absolute error = 7.64610522269955217438e-11
relative error = 7.5634217184325307706044030694021e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.0110799783418882374380727307282
y[1] (numeric) = 1.0110799782569937841841104308278
absolute error = 8.48944532539622999004e-11
relative error = 8.3964132484538182237888617664603e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.0112289220639577132650190013457
y[1] (numeric) = 1.0112289219698960397300011416944
absolute error = 9.40616735350178596513e-11
relative error = 9.3017190749483619730396663586202e-09 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.0113788545570227275471705896988
y[1] (numeric) = 1.01137885445301244874903115544
absolute error = 1.040102787981394342588e-10
relative error = 1.0284007652473142802314744826891e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.0115297756711507997138872192414
y[1] (numeric) = 1.0115297755563608835889087131778
absolute error = 1.147899161249785060636e-10
relative error = 1.1348149988843907897890866226828e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.0116816852554208282138558147042
y[1] (numeric) = 1.0116816851289684642360385101738
absolute error = 1.264523639778173045304e-10
relative error = 1.2499224392491763065453661028780e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.0118345831579232414361794766499
y[1] (numeric) = 1.0118345830188716588815431572174
absolute error = 1.390515825546363194325e-10
relative error = 1.3742521244990267784448296697062e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.0119884692257601496199364332395
y[1] (numeric) = 1.0119884690731163851477275361713
absolute error = 1.526437644722088970682e-10
relative error = 1.5083547798621829651503344274122e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.0121433433050454977520570596639
y[1] (numeric) = 1.0121433431377581119749186204295
absolute error = 1.672873857771384392344e-10
relative error = 1.6528032998851667466277915112787e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.0122992052409052194533660673757
y[1] (numeric) = 1.0122992050578619621686128907563
absolute error = 1.830432572847531766194e-10
relative error = 1.8081932331577091167883022969575e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.0124560548774773918526359770927
y[1] (numeric) = 1.0124560546775028156068630367694
absolute error = 1.999745762457729403233e-10
relative error = 1.9751432695019332054635090067067e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=4.4MB, time=0.72
x[1] = 0.159
y[1] (analytic) = 1.0126138920579123914484970015328
y[1] (numeric) = 1.0126138918397654131078351941634
absolute error = 2.181469783406618073694e-10
relative error = 2.1542957296124648229740635274161e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.0127727166243730509590474759817
y[1] (numeric) = 1.0127727163867444609574675276523
absolute error = 2.376285900015799483294e-10
relative error = 2.3463170571340928025295783801548e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.0129325284180348171590079870976
y[1] (numeric) = 1.0129325281595447360971605295348
absolute error = 2.584900810618474575628e-10
relative error = 2.5518983131635518282776419105598e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.0130933272790859097042613628125
y[1] (numeric) = 1.0130933269982811919714289637604
absolute error = 2.808047177328323990521e-10
relative error = 2.7717556731619514822829836274194e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.0132551130467274809436196988004
y[1] (numeric) = 1.0132551127420790650354449453934
absolute error = 3.046484159081747534070e-10
relative error = 3.0066309262643269235183084834059e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.0134178855591737767176586097624
y[1] (numeric) = 1.0134178852290739819224012054388
absolute error = 3.300997947952574043236e-10
relative error = 3.2572919769727389275353324685437e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.0135816446536522981444579067051
y[1] (numeric) = 1.0135816442964120672706231511078
absolute error = 3.572402308738347555973e-10
relative error = 3.5245333492193039679485540739029e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.0137463901664039643920869144861
y[1] (numeric) = 1.0137463897802500522103578917631
absolute error = 3.861539121817290227230e-10
relative error = 3.8091766927854886116837921929688e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.0139121219326832764376716571557
y[1] (numeric) = 1.0139121215157553835101679609919
absolute error = 4.169278929275036961638e-10
relative error = 4.1120712920639567302406270164088e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.014078839786758481812880152039
y[1] (numeric) = 1.0140788393371063333828570255139
absolute error = 4.496521484300231265251e-10
relative error = 4.4340945771492129001208361417420e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.0142465435619117403356610670895
y[1] (numeric) = 1.014246543077492109950854431936
absolute error = 4.844196303848066351535e-10
relative error = 4.7761526372432408783994181422416e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.0144152330904392908280700097875
y[1] (numeric) = 1.0144152325691129683709850027214
absolute error = 5.213263224570850070661e-10
relative error = 5.1391807363622921950217950526877e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.0145849082036516188200167297711
y[1] (numeric) = 1.0145849076431803226185500531427
absolute error = 5.604712962014666766284e-10
relative error = 5.5241438313309367030707352958289e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.0147555687318736252387655314679
y[1] (numeric) = 1.0147555681299168579306451614446
absolute error = 6.019567673081203700233e-10
relative error = 5.9320370920494443728186061834537e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.0149272145044447960840202072392
y[1] (numeric) = 1.0149272138585566439086397849407
absolute error = 6.458881521753804222985e-10
relative error = 6.3638864240205257059134305115547e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.0150998453497193730884238159675
y[1] (numeric) = 1.0150998446573452482797433753245
absolute error = 6.923741248086804406430e-10
relative error = 6.8207489931214168834417269770373e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.0152734610950665253633026466005
y[1] (numeric) = 1.0152734603535398513175822070764
absolute error = 7.415266740457204395241e-10
relative error = 7.3037137526072551467318025631689e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=19.0MB, alloc=4.4MB, time=0.91
x[1] = 0.176
y[1] (analytic) = 1.0154480615668705220294827209227
y[1] (numeric) = 1.0154480607734093609217106935008
absolute error = 7.934611611077720274219e-10
relative error = 7.8139019723316499435180397160944e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.0156236465905309058330062047525
y[1] (numeric) = 1.0156236457422345283559805256329
absolute error = 8.482963774770256791196e-10
relative error = 8.3524677701703160551820529179075e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.0158002159904626677455741118622
y[1] (numeric) = 1.0158002150843080646456905300089
absolute error = 9.061546030998835818533e-10
relative error = 8.9205986456335962540539459690025e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.0159777695900964225495407001936
y[1] (numeric) = 1.0159777686229347576334397021
absolute error = 9.671616649161009980936e-10
relative error = 9.5195160156536630238960631840939e-08 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.0161563072118785854072839753885
y[1] (numeric) = 1.0161563061804315896936054330691
absolute error = 1.0314469957136785423194e-09
relative error = 1.0150475752532151512332788634638e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.0163358286772715494147757322793
y[1] (numeric) = 1.016335827578127856105368508418
absolute error = 1.0991436933094072238613e-09
relative error = 1.0814768724033939171850268444504e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.016516333806753864139173580784
y[1] (numeric) = 1.016516332636365284084206018057
absolute error = 1.1703885800549675627270e-09
relative error = 1.1513721335612751486544748026328e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.0166978224198204151402564186277
y[1] (numeric) = 1.0166978211744981524717728783419
absolute error = 1.2453222626684835402858e-09
relative error = 1.2248696074754237775703474094480e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.0168802943349826044755238294719
y[1] (numeric) = 1.0168802930108934120840922276916
absolute error = 1.3240891923914316017803e-09
relative error = 1.3021092057422126313023211207390e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.0170637493697685321887789013652
y[1] (numeric) = 1.0170637479629308067179745185212
absolute error = 1.4068377254708043828440e-09
relative error = 1.3832345576593033902199620420553e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.0172481873407231787820129769491
y[1] (numeric) = 1.0172481858470029948155846893984
absolute error = 1.4937201839664282875507e-09
relative error = 1.4683930652865471606338716811749e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.0174336080634085886704098635492
y[1] (numeric) = 1.0174336064785156717870763625596
absolute error = 1.5848929168833335009896e-09
relative error = 1.5577359587128555540367701126148e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.0176200113524040546202860481617
y[1] (numeric) = 1.0176200096718876929912115732038
absolute error = 1.6805163616290744749579e-09
relative error = 1.6514183515275899502778433919198e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.0178073970213063031697824794125
y[1] (numeric) = 1.0178073952405511973738840983186
absolute error = 1.7807551057958983810939e-09
relative error = 1.7495992964950134745946821787383e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.0179957648827296810321224958101
y[1] (numeric) = 1.0179957629969517317644640141838
absolute error = 1.8857779492676584816263e-09
relative error = 1.8524418414303471363068776319179e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.0181851147483063424812494970519
y[1] (numeric) = 1.0181851127525483758298806731431
absolute error = 1.9957579666513688239088e-09
relative error = 1.9601130852759685604834942318197e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.0183754464286864377196569727608
y[1] (numeric) = 1.0183754443178138676863608517352
absolute error = 2.1108725700332961210256e-09
relative error = 2.0727842343762887930325867388738e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=22.8MB, alloc=4.4MB, time=1.10
x[1] = 0.193
y[1] (analytic) = 1.0185667597335383022282225208382
y[1] (numeric) = 1.0185667575022347301687383838332
absolute error = 2.2313035720594841370050e-09
relative error = 2.1906306589498397744490326308279e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.0187590544715486470978565056148
y[1] (numeric) = 1.0187590521143113977572511540513
absolute error = 2.3572372493406053515635e-09
relative error = 2.3138319497571022579041961991353e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.0189523304504227503427750241667
y[1] (numeric) = 1.0189523279615583441617408883474
absolute error = 2.4888644061810341358193e-09
relative error = 2.4425719749626011934694347826237e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.0191465874768846491952058675394
y[1] (numeric) = 1.0191465848505042105631707404739
absolute error = 2.6263804386320351270655e-09
relative error = 2.5770389371897929120390209768152e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.019341825356677333381335182191
y[1] (numeric) = 1.0193418225866919345123752347101
absolute error = 2.7699853988689599474809e-09
relative error = 2.7174254307672658199541704882997e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.0195380438945629393783015557216
y[1] (numeric) = 1.0195380409746788794859566871486
absolute error = 2.9198840598923448685730e-09
relative error = 2.8639284991647737584137135868444e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.0197352428943229456520432699139
y[1] (numeric) = 1.019735239818036965099241789701
absolute error = 3.0762859805528014802129e-09
relative error = 3.0167496926176186904955621409648e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.0199334221587583688758034832518
y[1] (numeric) = 1.0199334189193527979762116029438
absolute error = 3.2394055708995918803080e-09
relative error = 3.1760951259378969529637688801611e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.020132581489689961129097124429
y[1] (numeric) = 1.0201325780802278032763177659337
absolute error = 3.4094621578527793584953e-09
relative error = 3.3421755365111209500077224323295e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.0203327206879584080769422978976
y[1] (numeric) = 1.0203327171012783568780972931907
absolute error = 3.5866800511988450047069e-09
relative error = 3.5152063424767258716104300161423e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.0205338395534245281291580222406
y[1] (numeric) = 1.0205338357821359182194978911755
absolute error = 3.7712886099096601310651e-09
relative error = 3.6954077010909687903489243947479e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.020735937884969472579529142089
y[1] (numeric) = 1.020735933921447163794825288771
absolute error = 3.9635223087847038533180e-09
relative error = 3.8830045672707253270700935658815e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.0209390154804949267246382744327
y[1] (numeric) = 1.0209390113168741213082236385253
absolute error = 4.1636208054164146359074e-09
relative error = 4.0782267523166869780038075686576e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.0211430721369233119621636705127
y[1] (numeric) = 1.0211430677650943044835996077146
absolute error = 4.3718290074785640627981e-09
relative error = 4.2813089828144601634606027569833e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.0213481076501979888684408950116
y[1] (numeric) = 1.0213481030618008485309003406502
absolute error = 4.5883971403375405543614e-09
relative error = 4.4924909597120660912400973376150e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.0215541218152834612550852449989
y[1] (numeric) = 1.021554117001702646268655036075
absolute error = 4.8135808149864302089239e-09
relative error = 4.7120174175723386262285710357815e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.0217611144261655812044708520248
y[1] (numeric) = 1.0217611093785244849026894459804
absolute error = 5.0476410963017814060444e-09
relative error = 4.9401381839987155213172344636729e-07 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.5MB, time=1.29
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.0219690852758517550838614319006
y[1] (numeric) = 1.0219690799850071834609221647165
absolute error = 5.2908445716229392671841e-09
relative error = 5.1771082392329165936879395855855e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.0221780341563711505379866680538
y[1] (numeric) = 1.0221780286129077308841511398743
absolute error = 5.5434634196538355281795e-09
relative error = 5.4231877759230007246221799982850e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.022387960858774904459857235895
y[1] (numeric) = 1.0223879550529994247727383990834
absolute error = 5.8057754796871188368116e-09
relative error = 5.6786422590602919202270241358349e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.0225988651731363319396104974034
y[1] (numeric) = 1.0225988590950720107891005495965
absolute error = 6.0780643211505099478069e-09
relative error = 5.9437424860836630947881534945196e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.0228107468885511361911779170994
y[1] (numeric) = 1.0228107405279318227159121703186
absolute error = 6.3606193134752657467808e-09
relative error = 6.2187646471496647277603356075377e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.0230236057931376194565642727558
y[1] (numeric) = 1.0230235991394019231699287787919
absolute error = 6.6537356962866354939639e-09
relative error = 6.5039903855669840996356292539379e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.0232374416740368948875277565849
y[1] (numeric) = 1.0232374347163222449713356185573
absolute error = 6.9577146499161921380276e-09
relative error = 6.7997068583937194310020082153687e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.0234522543174130994044490852411
y[1] (numeric) = 1.0234522470445497331685280752899
absolute error = 7.2728633662359210099512e-09
relative error = 7.1062067971959519329411428977615e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.023668043508453607532176759785
y[1] (numeric) = 1.0236680359089584877182290931431
absolute error = 7.5994951198139476666419e-09
relative error = 7.4237885689660975254210917147138e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.0238848090313692462126346397834
y[1] (numeric) = 1.0238848010934399068208485258373
absolute error = 7.9379293393917861139461e-09
relative error = 7.7527562371995187934415866639364e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.0241025506693945105939770189553
y[1] (numeric) = 1.0241025423809028309109889201917
absolute error = 8.2884916796829880987636e-09
relative error = 8.0934196231278766282812449750969e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.0243212682047877807960754132258
y[1] (numeric) = 1.0243212595532736873030017930282
absolute error = 8.6515140934930736201976e-09
relative error = 8.4460943671076999431816747597692e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.0245409614188315396521202957203
y[1] (numeric) = 1.0245409523914966354914980256648
absolute error = 9.0273349041606222700555e-09
relative error = 8.8111019901626508590941691446140e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.024761630091832591426120037115
y[1] (numeric) = 1.0247616206755337131067155635752
absolute error = 9.4162988783194044735398e-09
relative error = 9.1887699556779618265873387641482e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.0249832740031222815060783338625
y[1] (numeric) = 1.0249832641843649825246471722085
absolute error = 9.8187572989814311616540e-09
relative error = 9.5794317312455202845786068464002e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.0252058929310567170726304311345
y[1] (numeric) = 1.0252058826959886781318305634507
absolute error = 1.02350680389407998676838e-08
relative error = 9.9834268506580756550854296052714e-07 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.0254294866530169887429174718627
y[1] (numeric) = 1.0254294759874213542447027707584
absolute error = 1.06655956344982147011043e-08
relative error = 1.0401100976051042735582530632276e-06 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.5MB, time=1.48
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.0256540549454093931894773280223
y[1] (numeric) = 1.0256540438346980336834202146109
absolute error = 1.11107113595060571134114e-08
relative error = 1.0832805960190374876681825502805e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.0258795975836656567339292952864
y[1] (numeric) = 1.02587958601287235700004546361
absolute error = 1.15707932997338838316764e-08
relative error = 1.1278899908904979722595184536842e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.0261061143422431599152290573844
y[1] (numeric) = 1.0261061022960167323610012603008
absolute error = 1.20462264275542277970836e-08
relative error = 1.1739747243662149745076526596708e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.0263336049946251630322693519284
y[1] (numeric) = 1.0263335924572224860836919446038
absolute error = 1.25374026769485774073246e-08
relative error = 1.2215718764284479318131921803439e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.0265620693133210326606007951267
y[1] (numeric) = 1.0265620562686000138271919716265
absolute error = 1.30447210188334088235002e-08
relative error = 1.2707191711806739660610511799784e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.0267915070698664691430463486806
y[1] (numeric) = 1.0267914935012789324369007845699
absolute error = 1.35685875367061455641107e-08
relative error = 1.3214549831471182616697442446286e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.0270219180348237350539819382704
y[1] (numeric) = 1.0270219039254082324430628674608
absolute error = 1.41094155026109190708096e-08
relative error = 1.3738183435859743950193102898636e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.027253301977781884637054759369
y[1] (numeric) = 1.0272532873101564312130513665202
absolute error = 1.46676254534240033928488e-08
relative error = 1.4278489468161616597131184915880e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.0274856586673569942161098326828
y[1] (numeric) = 1.0274856434237117267573132331283
absolute error = 1.52436452674587965995545e-08
relative error = 1.4835871565574664152612766227841e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.0277189878711923935790943983139
y[1] (numeric) = 1.0277189720332821521888734055643
absolute error = 1.58379102413902209927496e-08
relative error = 1.5410740122839144761570877002865e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.0279532893559588983347087647578
y[1] (numeric) = 1.0279532729050957308362951109837
absolute error = 1.64508631674984136537741e-08
relative error = 1.6003512355902215539368975848880e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.0281885628873550432415712561047
y[1] (numeric) = 1.0281885458044006320099929334499
absolute error = 1.70829544112315783226548e-08
relative error = 1.6614612365711687666524305184977e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.0284248082301073165096639283
y[1] (numeric) = 1.0284247904954653274217948582605
absolute error = 1.77346419890878690700395e-08
relative error = 1.7244471202137502382271841238523e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.0286620251479703950738247530366
y[1] (numeric) = 1.0286620067415787482576490673
absolute error = 1.84063916468161756857366e-08
relative error = 1.7893526928019398243979549908787e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.0289002134037273808390509958078
y[1] (numeric) = 1.0289001943050504429033708247125
absolute error = 1.90986769379356801710953e-08
relative error = 1.8562224683339240223429486051083e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.0291393727591900378973775428355
y[1] (numeric) = 1.0291393529472107353233243568191
absolute error = 1.98119793025740531860164e-08
relative error = 1.9251016749516481476512719200457e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.0293795029751990307160929600163
y[1] (numeric) = 1.029379482428410884091934194906
absolute error = 2.05467881466241587651103e-08
relative error = 1.9960362613825228949785515538183e-06 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.5MB, time=1.68
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.0296206038116241632970550956892
y[1] (numeric) = 1.0296205825080232420779200142806
absolute error = 2.13036009212191350814086e-08
relative error = 2.0690729033931384375413430867234e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.0298626750273646193068670679285
y[1] (numeric) = 1.029862652944441416781148567836
absolute error = 2.20829232025257185000925e-08
relative error = 2.1442590102548332655111584847219e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.0301057163803492031776735062069
y[1] (numeric) = 1.0301056934950804313219958772756
absolute error = 2.28852687718556776289313e-08
relative error = 2.2216427312209650143595219952186e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.0303497276275365821783359466519
y[1] (numeric) = 1.0303497039163768860831124101361
absolute error = 2.37111596960952235365158e-08
relative error = 2.3012729620157305912585668131528e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.0305947085249155294557453097401
y[1] (numeric) = 1.0305946839637891210034835358008
absolute error = 2.45611264084522617739393e-08
relative error = 2.3831993513343829707396999174959e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.0308406588275051680460284191387
y[1] (numeric) = 1.0308406333917973785246771188239
absolute error = 2.54357077895213513003148e-08
relative error = 2.4674723073546920999355984159081e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.0310875782893552158554045505058
y[1] (numeric) = 1.031087551953903967189169673086
absolute error = 2.63354512486662348774198e-08
relative error = 2.5541430042594974288584646853292e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.0313354666635462316104470294153
y[1] (numeric) = 1.0313354394026334258906420655719
absolute error = 2.72609128057198049638434e-08
relative error = 2.6432633887701996622813842080543e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.0315843237021898617775039281638
y[1] (numeric) = 1.0315842954895326887761353239079
absolute error = 2.82126571730013686042559e-08
relative error = 2.7348861866910394168677224350286e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.0318341491564290884510309420608
y[1] (numeric) = 1.0318341199651712507999566672121
absolute error = 2.91912578376510742748487e-08
relative error = 2.8290649094640105602170920667757e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.0320849427764384782105885568886
y[1] (numeric) = 1.032084912579141333929225445302
absolute error = 3.01972971442813631115866e-08
relative error = 2.9258538607342561074431205908202e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.0323367043114244319462546505563
y[1] (numeric) = 1.0323366730800580540009482368689
absolute error = 3.12313663779453064136874e-08
relative error = 3.0253081429257946557479911365250e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.0325894335096254356522027035565
y[1] (numeric) = 1.0325894012155595882305119228653
absolute error = 3.22940658474216907806912e-08
relative error = 3.1274836638274254481896496805999e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.032843130118312312188194824666
y[1] (numeric) = 1.0328430967323073433714831170644
absolute error = 3.33860049688167117076016e-08
relative error = 3.2324371431886602744276438275226e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.0330977938837884740087378304194
y[1] (numeric) = 1.0330977593759861245266019015375
absolute error = 3.45078023494821359288819e-08
relative error = 3.3402261193255305386615525628200e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.0333534245513901768596496492213
y[1] (numeric) = 1.033353388891304304609857380655
absolute error = 3.56600858722497922685663e-08
relative error = 3.4509089557361179532190170000585e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.0336100218654867744417823535499
y[1] (numeric) = 1.0336099850219939944595321331542
memory used=38.1MB, alloc=4.5MB, time=1.87
absolute error = 3.68434927799822502203957e-08
relative error = 3.5645448477256574502855139057915e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.0338675855694809740416471565521
y[1] (numeric) = 1.0338675475108112136021022078278
absolute error = 3.80586697604395449487243e-08
relative error = 3.6811938290410610440736719827915e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.0341261154058090931286857424248
y[1] (numeric) = 1.0341260760995360616668788744737
absolute error = 3.93062730314618068679511e-08
relative error = 3.8009167785147115212813760465319e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.0343856111159413169189313333344
y[1] (numeric) = 1.0343855705289728904512779079096
absolute error = 4.05869684264676534254248e-08
relative error = 3.9237754267173749889631109719062e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.0346460724403819569048019292326
y[1] (numeric) = 1.0346460305389504766366017490951
absolute error = 4.19014314802682001801375e-08
relative error = 4.0498323626200814659128393273354e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.0349074991186697103507671907983
y[1] (numeric) = 1.0349074558683221951542194537182
absolute error = 4.32503475151965477370801e-08
relative error = 4.1791510402648228663068911407497e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.0351698908893779207546294698607
y[1] (numeric) = 1.0351698462549661932020289049961
absolute error = 4.46344117275526005648646e-08
relative error = 4.3117957854439178926560294950828e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.0354332474901148392741585260421
y[1] (numeric) = 1.0354332014357855649110853339084
absolute error = 4.60543292743630731921337e-08
relative error = 4.4478318023878935290432457365723e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.0356975686575238871188185030108
y[1] (numeric) = 1.0356975211467085266622797566273
absolute error = 4.75108153604565387463835e-08
relative error = 4.5873251804617330051537938427687e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.0359628541272839189063247726353
y[1] (numeric) = 1.0359628051226885930529505055323
absolute error = 4.90045953258533742671030e-08
relative error = 4.7303429008693402867096794651239e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.0362291036341094869837672905078
y[1] (numeric) = 1.0362290530977047535133105969
absolute error = 5.05364047334704566936078e-08
relative error = 4.8769528433660713385791629411529e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.0364963169117511067130361417346
y[1] (numeric) = 1.0364962648047616495725732451376
absolute error = 5.21069894571404628965970e-08
relative error = 5.0272237929791826030154679003629e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.0367644936929955227202839915894
y[1] (numeric) = 1.036764439975889752774657400288
absolute error = 5.37171057699456265913014e-08
relative error = 5.1812254467360473371628632089607e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.0370336337096659761091591915901
y[1] (numeric) = 1.0370335783421455432433547524705
absolute error = 5.53675204328658044391196e-08
relative error = 5.3390284203999906611266659765443e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.0373037366926224726375423277883
y[1] (numeric) = 1.0373036796336116888968392139375
absolute error = 5.70590107837407031138508e-08
relative error = 5.5007042552135943805095767791800e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.0375748023717620518575180345561
y[1] (numeric) = 1.0375747435793972253113994565219
absolute error = 5.87923648265461185780342e-08
relative error = 5.6663254246493228653439923597123e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.0378468304760190572183129339225
y[1] (numeric) = 1.0378467699076377362342746494257
absolute error = 6.05683813209840382844968e-08
relative error = 5.8359653411673214907718720197340e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=41.9MB, alloc=4.5MB, time=2.06
x[1] = 0.277
y[1] (analytic) = 1.0381198207333654071319295975428
y[1] (numeric) = 1.0381197583454955347454731095539
absolute error = 6.23878698723864564879889e-08
relative error = 6.0096983629802393736127645963174e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.0383937728708108670012054656899
y[1] (numeric) = 1.0383937086191598450684531439328
absolute error = 6.42516510219327523217571e-08
relative error = 6.1875998008249283730901150560385e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.0386686866144033222100246952314
y[1] (numeric) = 1.0386686204538469850295449311674
absolute error = 6.61605563371804797640640e-08
relative error = 6.3697459247408705634280026712124e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.0389445616892290520754099464035
y[1] (numeric) = 1.0389444935738005491659918563875
absolute error = 6.81154285029094180900160e-08
relative error = 6.5562139708551866307575966462447e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.0392213978194130047612201563121
y[1] (numeric) = 1.0392213277022915924824892817104
absolute error = 7.01171214122787308746017e-08
relative error = 6.7470821481740778967564510107995e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.0394991947281190731531793854871
y[1] (numeric) = 1.0394991225616188148560983019048
absolute error = 7.21665002582970810835823e-08
relative error = 6.9424296453805549266569075451444e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.0397779521375503716949608624835
y[1] (numeric) = 1.0397778778731087460894116026812
absolute error = 7.42644416256055492598023e-08
relative error = 7.1423366376383059396729197277169e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.0400576697689495141850493904688
y[1] (numeric) = 1.0400575933571159316118481068564
absolute error = 7.64118335825732012836124e-08
relative error = 7.3468842934015585054797011645612e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.040338347342598892534104318956
y[1] (numeric) = 1.0403382687330231188289526615418
absolute error = 7.86095757737051516574142e-08
relative error = 7.5561547812307882811085830668224e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.0406199845778209564825443233454
y[1] (numeric) = 1.040619903719241444119576587493
absolute error = 8.08585795123629677358524e-08
relative error = 7.7702312766141288184616322430709e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.0409025811929784942780742747098
y[1] (numeric) = 1.0409024980332106204808144798271
absolute error = 8.31597678737972597948827e-08
relative error = 7.9891979687943367535764516150051e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.0411861369054749143128735223236
y[1] (numeric) = 1.0411860513913991258205722174656
absolute error = 8.55140757884923013048580e-08
relative error = 8.2131400676011669747540751781077e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.0414706514317545277201639517677
y[1] (numeric) = 1.0414705635093043918976407068969
absolute error = 8.79224501358225232448708e-08
relative error = 8.4421438102890126576692576994011e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.0417561244873028319298752220681
y[1] (numeric) = 1.0417560341014529939091494541709
absolute error = 9.03858498380207257678972e-08
relative error = 8.6762964683796653515858131745203e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.0420425557866467951831236262249
y[1] (numeric) = 1.0420424628814008407252736274419
absolute error = 9.29052459544578499987830e-08
relative error = 8.9156863545100506017674701234347e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.0423299450433551420052200606774
y[1] (numeric) = 1.0423298495617333657710678408623
absolute error = 9.54816217762341522198151e-08
relative error = 9.1604028292847948990785716130522e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.0426182919700386396369216307212
y[1] (numeric) = 1.0426181938540657185552994592017
absolute error = 9.81159729210816221715195e-08
relative error = 9.4105363081334800585771521270067e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=45.7MB, alloc=4.5MB, time=2.25
x[1] = 0.294
y[1] (analytic) = 1.0429075962783503854236404606493
y[1] (numeric) = 1.0429074954690429568461537912228
absolute error = 1.008093074285774866694265e-07
relative error = 9.6661782681724414445853105697994e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.043197857678986095162322319432
y[1] (numeric) = 1.0431977541163402394936831085861
absolute error = 1.035626458556686392108459e-07
relative error = 9.9274212550709667802476259054502e-06 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.0434890758816843924057067150814
y[1] (numeric) = 1.0434889695046630198988709958825
absolute error = 1.063770213725068357191989e-07
relative error = 1.0194358889921752604926424140435e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.0437812505952270987236791534653
y[1] (numeric) = 1.0437811413417472401291831063054
absolute error = 1.092534798585944960471599e-07
relative error = 1.0467085876115475772901818265782e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.0440743815274395249214253002402
y[1] (numeric) = 1.0440742693343595256804749664729
absolute error = 1.121930799992409503337673e-07
relative error = 1.0745698006219337721712851280845e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.0443684683851907632140958277764
y[1] (numeric) = 1.0443683531882973808851270429938
absolute error = 1.151968933823289687847826e-07
relative error = 1.1030292168859439578063580618048e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.044663510874393980357689772432
y[1] (numeric) = 1.044663392608389384966276852543
absolute error = 1.182660045953914129198890e-07
relative error = 1.1320966355606846513490588258771e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.0449595087000067117358632713184
y[1] (numeric) = 1.04495938729849538873801746647
absolute error = 1.214015113229978458048484e-07
relative error = 1.1617819667867200110916529484504e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.0452564615660311564023695917739
y[1] (numeric) = 1.0452563369615067119514313303082
absolute error = 1.246045244444509382614657e-07
relative error = 1.1920952323773737856764519113000e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.0455543691755144730788354111266
y[1] (numeric) = 1.0455542412993463412863278879854
absolute error = 1.278761681317925075231412e-07
relative error = 1.2230465665083579231448065711504e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.0458532312305490771075773489994
y[1] (numeric) = 1.0458531000129691289885530700563
absolute error = 1.312175799481190242789431e-07
relative error = 1.2546462164077138233750112193778e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.0461530474322729383591617993617
y[1] (numeric) = 1.0461529128023619921527382748839
absolute error = 1.346299109462064235244778e-07
relative error = 1.2869045430460522541827539804467e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.0464538174808698800944101547946
y[1] (numeric) = 1.0464536793665441126503560413949
absolute error = 1.381143257674440541133997e-07
relative error = 1.3198320218270779885293753784661e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.0467555410755698787805505609892
y[1] (numeric) = 1.0467553994035671377029491818165
absolute error = 1.416720027410776013791727e-07
relative error = 1.3534392432783852579007645734714e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.0470582179146493648612163853508
y[1] (numeric) = 1.0470580726105153811003997126773
absolute error = 1.453041339837608166726735e-07
relative error = 1.3877369137425101549799340892932e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.0473618476954315244799906297348
y[1] (numeric) = 1.0473616986835060250641034923155
absolute error = 1.490119254994158871374193e-07
relative error = 1.4227358560682261572359165341988e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.0476664301142866021571945637978
y[1] (numeric) = 1.0476662773176893227549160431907
absolute error = 1.527965972794022785206071e-07
relative error = 1.4584470103020689819872615378851e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=49.5MB, alloc=4.6MB, time=2.44
x[1] = 0.311
y[1] (analytic) = 1.0479719648666322044196179021966
y[1] (numeric) = 1.047971808207248801425734607436
absolute error = 1.566593834029938832947606e-07
relative error = 1.4948814343800770228666532003294e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.0482784516469336043828868959338
y[1] (numeric) = 1.0482782910454014662185810543194
absolute error = 1.606015321381643058416144e-07
relative error = 1.5320503048197336574108525188640e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.0485858901487040472861657555049
y[1] (numeric) = 1.0485857255243980046060498286033
absolute error = 1.646243060426801159269016e-07
relative error = 1.5699649174120977557237071922233e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.0488942800645050569788858711721
y[1] (numeric) = 1.0488941113355229914769846992052
absolute error = 1.687289820655019011719669e-07
relative error = 1.6086366879141087608061349762970e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.0492036210859467433591963436608
y[1] (numeric) = 1.0492034481690950948662476380634
absolute error = 1.729168516484929487055974e-07
relative error = 1.6480771527410527522123217169307e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.0495139129036881107638283868539
y[1] (numeric) = 1.0495137357144672823284427297064
absolute error = 1.771892208284353856571475e-07
relative error = 1.6882979696591759461724667736967e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.0498251552074373673090652126448
y[1] (numeric) = 1.0498249736600270279554575827099
absolute error = 1.815474103393536076299349e-07
relative error = 1.7293109184784321272158520020352e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.0501373476859522351825080570062
y[1] (numeric) = 1.0501371616931965200376842850021
absolute error = 1.859927557151448237720041e-07
relative error = 1.7711279017453505486303900381628e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.0504504900270402618853280555329
y[1] (numeric) = 1.0504502995004328693687815158464
absolute error = 1.905266073925165465396865e-07
relative error = 1.8137609454360108818026207555321e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.0507645819175591324246927262339
y[1] (numeric) = 1.0507643867672283181938389982923
absolute error = 1.951503308142308537279416e-07
relative error = 1.8572221996491118375919995713455e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.0510796230434169824560548671731
y[1] (numeric) = 1.0510794231781104498008050469385
absolute error = 1.998653065326552498202346e-07
relative error = 1.9015239392991201264017157730520e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.0513956130895727123749907266948
y[1] (numeric) = 1.0513954084166423987550375369984
absolute error = 2.046729303136199531896964e-07
relative error = 1.9466785648094864675117529942733e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.051712551740036302358273354424
y[1] (numeric) = 1.0517123421654230617768381918983
absolute error = 2.095746132405814351625257e-07
relative error = 1.9926986028059154025349933558032e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.0520304386778691283538660919921
y[1] (numeric) = 1.05203022410608730926182965797
absolute error = 2.145717818190920364340221e-07
relative error = 2.0395967068096757125402966210554e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.0523492735851842790195202135225
y[1] (numeric) = 1.0523490539193061974440344062279
absolute error = 2.196658780815754858072946e-07
relative error = 2.0873856579309382834542453616127e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.0526690561431468736096597773046
y[1] (numeric) = 1.0526688312847871812015140727393
absolute error = 2.248583596924081457045653e-07
relative error = 2.1360783655621283098020527209012e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.0529897860319743808102358017967
y[1] (numeric) = 1.0529895558812743275044274207121
absolute error = 2.301507000533058083810846e-07
relative error = 2.1856878680712787726744602090305e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.6MB, time=2.64
x[1] = 0.328
y[1] (analytic) = 1.0533114629309369385212309311322
y[1] (numeric) = 1.0533112273865485295053646791331
absolute error = 2.355443884090158662519991e-07
relative error = 2.2362273334953721740078373284593e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.0536340865183576745864948076487
y[1] (numeric) = 1.0536338454774277212718155845941
absolute error = 2.410409299533146792230546e-07
relative error = 2.2877100602336575558354680081144e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.0539576564716130284705894216338
y[1] (numeric) = 1.0539574098297670931606280248414
absolute error = 2.466418459353099613967924e-07
relative error = 2.3401494777409298801057865938031e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.0542821724671330738823227614669
y[1] (numeric) = 1.0542819201184593078343137545793
absolute error = 2.523486737660480090068876e-07
relative error = 2.3935591472207588919643533276919e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.0546076341804018423446481406519
y[1] (numeric) = 1.0546073760174347169190572261484
absolute error = 2.581629671254255909145035e-07
relative error = 2.4479527623186546370572537924339e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.0549340412859576477106056318672
y[1] (numeric) = 1.0549337771996615783042831498841
absolute error = 2.640862960694063224819831e-07
relative error = 2.5033441498151568514306600240503e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.0552613934573934116249810921192
y[1] (numeric) = 1.0552611233371462740836379712445
absolute error = 2.701202471375413431208747e-07
relative error = 2.5597472703188354909709864963134e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.0555896903673569899313573173679
y[1] (numeric) = 1.055589414100933529137240024175
absolute error = 2.762664234607941172931929e-07
relative error = 2.6171762189591897160488088223594e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.0559189316875515000242309195995
y[1] (numeric) = 1.0559186491611066303550526926512
absolute error = 2.825264448696691782269483e-07
relative error = 2.6756452260794326960938789971384e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.056249117088735649145867574257
y[1] (numeric) = 1.0562488281867876465012344849162
absolute error = 2.889019480026446330893408e-07
relative error = 2.7351686579291496482345778781180e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.0565802462407240636275673412012
y[1] (numeric) = 1.0565799508461376487193194975972
absolute error = 2.953945864149082478436040e-07
relative error = 2.7957610173568165738793921056266e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.0569123188123876190750108179637
y[1] (numeric) = 1.0569120168063569316780813196532
absolute error = 3.020060306873969294983105e-07
relative error = 2.8574369445021672071968561915452e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.0572453344716537714973559399734
y[1] (numeric) = 1.057245025733685235357932998973
absolute error = 3.087379685361394229410004e-07
relative error = 2.9202112174883957398602400505461e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.0575792928855068893797542986879
y[1] (numeric) = 1.0575789772934019674777152674041
absolute error = 3.155921049219020390312838e-07
relative error = 2.9840987531141829371605117210765e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.0579141937199885866989549051396
y[1] (numeric) = 1.0579138711498264265617247930575
absolute error = 3.225701621601372301120821e-07
relative error = 3.0491146075455333116520291632490e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.0582500366401980568816623833228
y[1] (numeric) = 1.058249706966318025646833801892
absolute error = 3.296738800312348285814308e-07
relative error = 3.1152739770074110718765473823427e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.0585868213102924077053156350886
y[1] (numeric) = 1.0585864844052765166295519838443
absolute error = 3.369050158910757636512443e-07
relative error = 3.1825921984751626154085957817275e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.6MB, time=2.83
x[1] = 0.345
y[1] (analytic) = 1.0589245473934869971409520758003
y[1] (numeric) = 1.0589242031281422152528811721283
absolute error = 3.442653447818880709036720e-07
relative error = 3.2510847503657133874757307361133e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.0592632145520557701378215979091
y[1] (numeric) = 1.0592628627953962267328128577871
absolute error = 3.517566595434050087401220e-07
relative error = 3.3207672532285269787266369694484e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.0596028224473315963494134778678
y[1] (numeric) = 1.0596024630665606720243181751405
absolute error = 3.593807709243250953027273e-07
relative error = 3.3916554704363143883451978336174e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.0599433707397066088005585003816
y[1] (numeric) = 1.0599430036001989147266795674288
absolute error = 3.671395076940738789329528e-07
relative error = 3.4637653088754814316355661288685e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.0602848590886325434952676329222
y[1] (numeric) = 1.0602844840539157886280129157146
absolute error = 3.750347167548672547172076e-07
relative error = 3.5371128196363023244284512567099e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.0606272871526210799649676426963
y[1] (numeric) = 1.0606269040843578258888284879639
absolute error = 3.830682632540761391547324e-07
relative error = 3.6117141987028075301785949412405e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.0609706545892441827567931078597
y[1] (numeric) = 1.0609702633472134858644786391897
absolute error = 3.912420306968923144686700e-07
relative error = 3.6875857876423740094340103298878e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.0613149610551344438615933347137
y[1] (numeric) = 1.0613145614972133845663397676039
absolute error = 3.995579210592952535671098e-07
relative error = 3.7647440742950060654554494889326e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.0616602062059854260813117529063
y[1] (numeric) = 1.0616597981881305247615756058879
absolute error = 4.080178549013197361470184e-07
relative error = 3.8432056934622950341460099435420e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.0620063896965520073353944212866
y[1] (numeric) = 1.0620059730727805267113285009587
absolute error = 4.166237714806240659203279e-07
relative error = 3.9229874275960461211121186494873e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.062353511180650725905883338033
y[1] (numeric) = 1.0623530858030218595471849099759
absolute error = 4.253776288663586984280571e-07
relative error = 4.0041062074865607436147215564979e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.0627015703111601266208493099901
y[1] (numeric) = 1.0627011360297560732857609148059
absolute error = 4.342814040533350883951842e-07
relative error = 4.0865791129505627903796423561125e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.0630505667400211079758181978111
y[1] (numeric) = 1.0630501234029280314812531317331
absolute error = 4.433370930764945650660780e-07
relative error = 4.1704233735187572677151274298130e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.0634005001182372701928434155077
y[1] (numeric) = 1.0634000475715261445157999678862
absolute error = 4.525467111256770434476215e-07
relative error = 4.2556563691230098561288270138856e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.0637513700958752642168766253644
y[1] (numeric) = 1.0637509081835826035274977506255
absolute error = 4.619122926606893788747389e-07
relative error = 4.3422956307831359576423077984608e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.0641031763220651416490876318753
y[1] (numeric) = 1.0641027048861736149759158310233
absolute error = 4.714358915266731718008520e-07
relative error = 4.4303588412932878702648562445947e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.064455918445000705616783541413
y[1] (numeric) = 1.0644554373254196358449543375559
absolute error = 4.811195810697718292038571e-07
relative error = 4.5198638359079287826062523269607e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.6MB, time=3.01
x[1] = 0.362
y[1] (analytic) = 1.0648095961119398625795763177395
y[1] (numeric) = 1.0648091051464856094828878312174
absolute error = 4.909654542530966884865221e-07
relative error = 4.6108286030273823383766312107412e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.0651642089692049750714469272204
y[1] (numeric) = 1.0651637079935812020794376884629
absolute error = 5.009756237729920092387575e-07
relative error = 4.7032712848829465775368473545285e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.0655197566621832153783533317088
y[1] (numeric) = 1.0655192455099610397797156136886
absolute error = 5.111522221755986377180202e-07
relative error = 4.7972101782215611181212910543593e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.0658762388353269201510286515192
y[1] (numeric) = 1.0658757173379249464348802583637
absolute error = 5.214974019737161483931555e-07
relative error = 4.8926637349900165002531146396210e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.0662336551321539459526148857234
y[1] (numeric) = 1.0662331231188181819893484994388
absolute error = 5.320133357639632663862846e-07
relative error = 4.9896505630186946716057644883729e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.0665920051952480257407766421643
y[1] (numeric) = 1.0665914624930316815044025052746
absolute error = 5.427022163442363741368897e-07
relative error = 5.0881894267048296515307977340097e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.0669512886662591262839383951033
y[1] (numeric) = 1.0669507351000022948180332930556
absolute error = 5.535662568314659051020477e-07
relative error = 5.1882992476952774692666255605970e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.0673115051859038065112878542941
y[1] (numeric) = 1.0673109405782130268408610574838
absolute error = 5.646076907796704267968103e-07
relative error = 5.2899991055687845300623437664185e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.0676726543939655767961870955091
y[1] (numeric) = 1.0676720785651932784879721264826
absolute error = 5.758287722983082149690265e-07
relative error = 5.3933082385177436216915548407866e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.0680347359292952591726321691378
y[1] (numeric) = 1.0680341486975190882465119756831
absolute error = 5.872317761709261201934547e-07
relative error = 5.4982460440294268326894080339627e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.0683977494298113484844009704265
y[1] (numeric) = 1.0683971506108133743788733096151
absolute error = 5.988189979741055276608114e-07
relative error = 5.6048320795666847127182854906182e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.0687616945325003744665282222431
y[1] (numeric) = 1.0687610839397461777613177937802
absolute error = 6.105927541967052104284629e-07
relative error = 5.7130860632481010647500916547836e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.0691265708734172647587454889206
y[1] (numeric) = 1.0691259483180349053578695981501
absolute error = 6.225553823594008758907705e-07
relative error = 5.8230278745275928182421688916853e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.0694923780876857088505232077704
y[1] (numeric) = 1.0694917433784445743293184891039
absolute error = 6.347092411345212047186665e-07
relative error = 5.9346775548734444921759855480250e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.0698591158094985229573507932542
y[1] (numeric) = 1.0698584687527880567771697833991
absolute error = 6.470567104661801810098551e-07
relative error = 6.0480553084467668167191608205351e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.070226783672118015827889937563
y[1] (numeric) = 1.0702261240719263251223780544596
absolute error = 6.596001916907055118831034e-07
relative error = 6.1631815027793691423585046642963e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.0705953813078763554816353004824
y[1] (numeric) = 1.0705947089657686981187010580604
absolute error = 6.723421076573629342424220e-07
relative error = 6.2800766694510353256310086576256e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.6MB, time=3.21
x[1] = 0.379
y[1] (analytic) = 1.070964908348175936876715850913
y[1] (numeric) = 1.0709642230632730875005099213957
absolute error = 6.852849028493762059295173e-07
relative error = 6.3987615047661928410473555021201e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.0713353644234897505074691922754
y[1] (numeric) = 1.0713346659924462452648912165329
absolute error = 6.984310435052425779757425e-07
relative error = 6.5192568704299649294550261305883e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.0717067491633617519314202742562
y[1] (numeric) = 1.0717060373803440115878761163788
absolute error = 7.117830177403435441578774e-07
relative error = 6.6415837942235956539218154437022e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.0720790621964072322252949639468
y[1] (numeric) = 1.0720783368530715633746314085205
absolute error = 7.253433356688506635554263e-07
relative error = 6.7657634706792377952318858994463e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.072452303150313189369698020393
y[1] (numeric) = 1.0724515640357836634434467196475
absolute error = 7.391145295259262513007455e-07
relative error = 6.8918172617540935802718475411434e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.0728264716518387005620840879077
y[1] (numeric) = 1.0728257185526849103433518807182
absolute error = 7.530991537902187322071895e-07
relative error = 7.0197666975038982979400790037434e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.0732015673268152954576493952072
y[1] (numeric) = 1.0732008000270299888051979405977
absolute error = 7.672997853066524514546095e-07
relative error = 7.1496334767557369187351063189146e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.0735775898001473303377709195101
y[1] (numeric) = 1.0735768080811239208260349135745
absolute error = 7.817190234095117360059356e-07
relative error = 7.2814394677801838958646167533083e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.0739545386958123632056188471909
y[1] (numeric) = 1.0739537423363223173866189239475
absolute error = 7.963594900458189999232434e-07
relative error = 7.4152067089627563875621883575465e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.0743324136368615298085672354074
y[1] (numeric) = 1.074331602413031630801880988779
absolute error = 8.112238298990066862466284e-07
relative error = 7.5509574094746712023003154555971e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.0747112142454199205870268523226
y[1] (numeric) = 1.0747103879307094077041892579171
absolute error = 8.263147105128828375944055e-07
relative error = 7.6887139499428958307424006763988e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.0750909401426869585493232471189
y[1] (numeric) = 1.0750900985078645426592361085177
absolute error = 8.416348224158900871386012e-07
relative error = 7.8284988831194839905793633162909e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.0754715909489367780722421749589
y[1] (numeric) = 1.0754707337620575324143810695302
absolute error = 8.571868792456578611054287e-07
relative error = 7.9703349345501861728449731740636e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.0758531662835186046268635763786
y[1] (numeric) = 1.0758522933099007307792801299606
absolute error = 8.729736178738475834464180e-07
relative error = 8.1142450032423257408942882544659e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.0762356657648571354293043853106
y[1] (numeric) = 1.0762347767670586041386315631875
absolute error = 8.889977985312906728221231e-07
relative error = 8.2602521623319311959581944437623e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.0766190890104529210159895150267
y[1] (numeric) = 1.076618183748247987596867978181
absolute error = 9.052622049334191215368457e-07
relative error = 8.4083796597501152860504744888972e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 1.0770034356368827477430694467592
y[1] (numeric) = 1.0770025138672383417546238871628
absolute error = 9.217696444059884455595964e-07
relative error = 8.5586509188886916979985192348424e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.6MB, time=3.40
x[1] = 0.396
y[1] (analytic) = 1.0773887052598000212096019216175
y[1] (numeric) = 1.0773877667368520101168076580482
absolute error = 9.385229480110927942635693e-07
relative error = 8.7110895392650201354913028695821e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.0777748974939351506041143126486
y[1] (numeric) = 1.0777739419689644771321062989265
absolute error = 9.555249706734720080137221e-07
relative error = 8.8657192971860706492849561113686e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.0781620119530959339741623305114
y[1] (numeric) = 1.0781610391745046268637511008672
absolute error = 9.727785913071104112296442e-07
relative error = 9.0225641464116981490738072707304e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.0785500482501679444184997932385
y[1] (numeric) = 1.0785490579634550022913717444838
absolute error = 9.902867129421271280487547e-07
relative error = 9.1816482188171180900195820808595e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.0789390059971149172014732679482
y[1] (numeric) = 1.0789379979448520652437660549484
absolute error = 1.0080522628519577072129998e-06
relative error = 9.3429958250545743905300704508464e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.0793288848049791377892544701431
y[1] (numeric) = 1.0793278587267864569624121695238
absolute error = 1.0260781926808268423006193e-06
relative error = 9.5066314552141907015875508125953e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.0797196842838818308075223843972
y[1] (numeric) = 1.0797186399164032592955494611712
absolute error = 1.0443674785715119729232260e-06
relative error = 9.6725797794839962117431601931379e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.0801114040430235499202061487794
y[1] (numeric) = 1.0801103411199022565226541413985
absolute error = 1.0629231212933975520073809e-06
relative error = 9.8408656488091172358126755539859e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.0805040436906845686288988243055
y[1] (numeric) = 1.0805029619425381978091350452355
absolute error = 1.0817481463708197637790700e-06
relative error = 0.00010011514095550125899328560982226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.0808976028342252719925512500355
y[1] (numeric) = 1.080896501988621060291074681062
absolute error = 1.1008456042117014765689735e-06
relative error = 0.0001018455033414053729491900247352 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.0812920810800865492670542641556
y[1] (numeric) = 1.0812909608615163127898402079692
absolute error = 1.1202185702364772140561864e-06
relative error = 0.00010359999761743446550993770784252 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.0816874780337901874643166514964
y[1] (numeric) = 1.0816863381636451801563885834077
absolute error = 1.1398701450073079280680887e-06
relative error = 0.00010537887958907297317415598534881 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.0820837932999392658304452584406
y[1] (numeric) = 1.0820826334964849082450897040636
absolute error = 1.1598034543575853555543770e-06
relative error = 0.00010718240690220773237220961156635 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.0824810264822185512426327970737
y[1] (numeric) = 1.0824798464605690295168909432125
absolute error = 1.1800216495217257418538612e-06
relative error = 0.00010901083904966804037922358534472 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.082879177183394894524357941723
y[1] (numeric) = 1.0828779766554876292716460682235
absolute error = 1.2005279072652527118734995e-06
relative error = 0.00011086443737775677940472019925969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.0832782450053176276785014027179
y[1] (numeric) = 1.0832770236798876125094311024297
absolute error = 1.2213254300151690703002882e-06
relative error = 0.00011274346509277252148590996223889 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.0836782295489189620379807442877
y[1] (numeric) = 1.0836769871314729714206692762406
absolute error = 1.2424174459906173114680471e-06
relative error = 0.00011464818726752253245864571270955 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.6MB, time=3.58
x[1] = 0.413
y[1] (analytic) = 1.084079130414214387333505795996
y[1] (numeric) = 1.0840778666070050535048867931522
absolute error = 1.2638072093338286190028438e-06
relative error = 0.00011657887084782659392771447227797 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.0844809472003030716780555899898
y[1] (numeric) = 1.0844796617023028303179207172073
absolute error = 1.2854980002413601348727825e-06
relative error = 0.00011853578465901156280646919907896 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.0848836795053682624676768396186
y[1] (numeric) = 1.0848823720122431668473998694772
absolute error = 1.3074931250956202769701414e-06
relative error = 0.00012051919941239658864475904466742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.0852873269266776881982030586595
y[1] (numeric) = 1.0852859971307610915163192022704
absolute error = 1.3297959165966818838563891e-06
relative error = 0.00012252938771176890961366998127902 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.0856918890605839611974925044623
y[1] (numeric) = 1.0856905366508500668145277010317
absolute error = 1.3524097338943829648034306e-06
relative error = 0.00012456662405985014866570349994518 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.0860973655025249812727822128099
y[1] (numeric) = 1.0860959901645622605579494452704
absolute error = 1.3753379627207148327675395e-06
relative error = 0.00012663118486475303203966774211484 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.0865037558470243402727544771743
y[1] (numeric) = 1.0865023572630088177753570413522
absolute error = 1.3985840155224973974358221e-06
relative error = 0.00012872334844642845293069995390262 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.0869110596876917275639112103343
y[1] (numeric) = 1.0869096375363601332225162216062
absolute error = 1.4221513315943413949887281e-06
relative error = 0.00013084339504310280379744866148702 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.087319276617223336420850712016
y[1] (numeric) = 1.0873178305738461245235199859369
absolute error = 1.4460433772118973307260791e-06
relative error = 0.00013299160681770550143048670105628 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.0877284062274022713300404523114
y[1] (numeric) = 1.0877269359637565059391302439881
absolute error = 1.4702636457653909102083233e-06
relative error = 0.00013516826786428662955846924381911 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.0881384481090989562066785671374
y[1] (numeric) = 1.0881369532934410627619444978863
absolute error = 1.4948156578934447340692511e-06
relative error = 0.00013737366421442462442136281471849 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.088549401852271543524235848908
y[1] (numeric) = 1.0885478821493099263382046876923
absolute error = 1.5197029616171860311612157e-06
relative error = 0.00013960808384362392939321939936113 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.0889612670459663243562691029099
y[1] (numeric) = 1.0889597221168338497160649039138
absolute error = 1.5449291324746402041989961e-06
relative error = 0.00014187181667770254539042221633673 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.0893740432783181393300958276049
y[1] (numeric) = 1.089372472780544483920134253776
absolute error = 1.5704977736554099615738289e-06
relative error = 0.00014416515459916940445505589707458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.089787730136550790491919265217
y[1] (numeric) = 1.0897861337240346548521107504163
absolute error = 1.5964125161356398085148007e-06
relative error = 0.00014648839145359149455702023842229 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.0902023272069774540829919575135
y[1] (numeric) = 1.0902007045299586408173216767589
absolute error = 1.6226770188132656702807546e-06
relative error = 0.00014884182305595066431268369297441 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.0906178340750010942264050306518
y[1] (numeric) = 1.0906161847800324506769854585397
absolute error = 1.6492949686435494195721121e-06
relative error = 0.00015122574719699003697222803142838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=76.2MB, alloc=4.6MB, time=3.77
x[1] = 0.43
y[1] (analytic) = 1.0910342503251148775240895223366
y[1] (numeric) = 1.0910325740550341026260096637883
absolute error = 1.6762700807748980798585483e-06
relative error = 0.00015364046364954996368233817155272 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.09145157554090258856361515432
y[1] (numeric) = 1.0914498719348039035961393290338
absolute error = 1.7036060986849674758252862e-06
relative error = 0.00015608627417489344668551016618145 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.0918698093050390463343710434825
y[1] (numeric) = 1.0918680779982447292842693955872
absolute error = 1.7313067943170501016478953e-06
relative error = 0.00015856348252902096377195485838876 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.0922889511992905215527119353457
y[1] (numeric) = 1.0922871918233223048057346224591
absolute error = 1.7593759682167469773128866e-06
relative error = 0.00016107239446897462595483358833314 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.0927090008045151548956526349088
y[1] (numeric) = 1.0927072129870654859723899258066
absolute error = 1.7878174496689232627091022e-06
relative error = 0.00016361331775913160099434600242391 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.0931299577006633761426924011461
y[1] (numeric) = 1.0931281410655665411952936782593
absolute error = 1.8166350968349473987228868e-06
relative error = 0.00016618656217748673605096649339012 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.0935518214667783242253501633781
y[1] (numeric) = 1.0935499756339814340118060850573
absolute error = 1.8458327968902135440783208e-06
relative error = 0.00016879243952192431340286660627462 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.0939745916809962681839905100158
y[1] (numeric) = 1.0939727162665301062369143376411
absolute error = 1.8754144661619470761723747e-06
relative error = 0.0001714312636164788738172342505569 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.0943982679205470290315194928856
y[1] (numeric) = 1.0943963625364967617385958291677
absolute error = 1.9053840502672929236637179e-06
relative error = 0.0001741033503175850428197772567066 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.0948228497617544025235283834771
y[1] (numeric) = 1.0948209140162301508370303003848
absolute error = 1.9357455242516864980830923e-06
relative error = 0.00017680901752031629576114978227407 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.0952483367800365828344626110016
y[1] (numeric) = 1.0952463702771438553274713683807
absolute error = 1.9665028927275069912426209e-06
relative error = 0.00017954858516461259823333362301664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.0956747285499065871393922061318
y[1] (numeric) = 1.0956727308897165741265874749382
absolute error = 1.9976601900130128047311936e-06
relative error = 0.00018232237524149685904311576250965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.0961020246449726811009591686834
y[1] (numeric) = 1.0960999954234924095420818755597
absolute error = 2.0292214802715588772931237e-06
relative error = 0.00018513071179928013360369607856738 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.0965302246379388052610762723304
y[1] (numeric) = 1.0965281634470811541654008746944
absolute error = 2.0611908576510956753976360e-06
relative error = 0.00018797392094975551625910912450929 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.0969593281006050023369509146883
y[1] (numeric) = 1.0969572345281585783873390972912
absolute error = 2.0935724464239496118173971e-06
relative error = 0.0001908523308743806607095191358107 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.0973893346038678454210067167782
y[1] (numeric) = 1.0973872082334667185363501715194
absolute error = 2.1263704011268846565452588e-06
relative error = 0.00019376627183044886835852152956679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.0978202437177208670842746719854
y[1] (numeric) = 1.0978180841288141656393707823481
absolute error = 2.1595889067014449038896373e-06
relative error = 0.00019671607615724868505632665095096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=80.1MB, alloc=4.6MB, time=3.96
x[1] = 0.447
y[1] (analytic) = 1.0982520550112549893828247411573
y[1] (numeric) = 1.098249861779076354804965640648
absolute error = 2.1932321786345778591005093e-06
relative error = 0.00019970207828221194736508514815369 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.0986847680526589547668078874449
y[1] (numeric) = 1.098682540748195855228600497585
absolute error = 2.2273044630995382073898599e-06
relative error = 0.00020272461472705022012460966087667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.0991183824092197578916776418816
y[1] (numeric) = 1.0991161205991826608198499193042
absolute error = 2.2618100370970718277225774e-06
relative error = 0.00020578402411387956774832721303718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.0995528976473230783311593885136
y[1] (numeric) = 1.0995506008941144814513461222673
absolute error = 2.2967532085968798132662463e-06
relative error = 0.00020888064717133360233043174982882 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.0999883133324537141915346561489
y[1] (numeric) = 1.0999859811941370348292747550921
absolute error = 2.3321383166793622599010568e-06
relative error = 0.00021201482674066475229587005742315 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.1004246290291960166268068024775
y[1] (numeric) = 1.1004222610594643389852230983652
absolute error = 2.3679697316776415837041123e-06
relative error = 0.00021518690778183369597495774633487 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.100861844301234325254313575431
y[1] (numeric) = 1.1008594400493790053891857396464
absolute error = 2.4042518553198651278357846e-06
relative error = 0.00021839723737958690513405826385499 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.101299958711353404470351136208
y[1] (numeric) = 1.1012975177222325326835323667625
absolute error = 2.4409891208717868187694455e-06
relative error = 0.00022164616474952224414284011879458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.1017389718214388806653732283767
y[1] (numeric) = 1.1017364936354456010377419084965
absolute error = 2.4781859932796276313198802e-06
relative error = 0.00022493404124414257110712719867564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.1021788831924776803383282778904
y[1] (numeric) = 1.1021763673455083671237068379187
absolute error = 2.5158469693132146214399717e-06
relative error = 0.00022826122035889728794424800013612 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.1026196923845584691096963097179
y[1] (numeric) = 1.102617138407980759711411039876
absolute error = 2.5539765777093982852698419e-06
relative error = 0.00023162805773821178702504536734039 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.1030613989568720916327866680871
y[1] (numeric) = 1.1030588063774927758847842305565
absolute error = 2.5925793793157480024375306e-06
relative error = 0.00023503491118150474265330095255516 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.1035040024677120124028566290802
y[1] (numeric) = 1.1035013708077447778775355035798
absolute error = 2.6316599672345253211255004e-06
relative error = 0.00023848214064919319629923262634838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.1039475024744747574636100964996
y[1] (numeric) = 1.1039448312515077905287681637268
absolute error = 2.6712229669669348419327728e-06
relative error = 0.00024197010826868538514891200499094 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.104391898533660357010634674543
y[1] (numeric) = 1.1043891872606237993581775962195
absolute error = 2.7112730365576524570783235e-06
relative error = 0.00024549917834036126417589645011023 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.1048371902008727888913345138855
y[1] (numeric) = 1.1048344383860060492606335063889
absolute error = 2.7518148667396307010074966e-06
relative error = 0.00024906971734354067258504961792103 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.1052833770308204230009154312754
y[1] (numeric) = 1.1052805841776393438199474516303
absolute error = 2.7928531810791809679796451e-06
relative error = 0.00025268209394243909612141166429057 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=83.9MB, alloc=4.6MB, time=4.15
x[1] = 0.464
y[1] (analytic) = 1.1057304585773164665739779066934
y[1] (numeric) = 1.1057276241845803452416261747372
absolute error = 2.8343927361213323517319562e-06
relative error = 0.0002563366789921109773790477228973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.1061784343932794103712726665209
y[1] (numeric) = 1.1061755579549578749044108350328
absolute error = 2.8764383215354668618314881e-06
relative error = 0.0002600338455443805268860270045274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.1066273040307334757611726659979
y[1] (numeric) = 1.1066243850359732145304018211767
absolute error = 2.9189947602612307708448212e-06
relative error = 0.00026377396885375998838203866841135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.1070770670408090626954143895363
y[1] (numeric) = 1.1070741049739004079735684171171
absolute error = 2.9620669086547218459724192e-06
relative error = 0.00026755742638335531234461010920409 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.107527722973743198578660493185
y[1] (numeric) = 1.107524717314086563626442180386
absolute error = 3.0056596566349522183127990e-06
relative error = 0.00027138459781075919245843301781988 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.1079792713788799880314349197206
y[1] (numeric) = 1.1079762216009521574447924797957
absolute error = 3.0497779278305866424399249e-06
relative error = 0.00027525586503393142035989794960817 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.1084317118046710635459807234666
y[1] (numeric) = 1.1084286173779913365900822275892
absolute error = 3.0944266797269558984958774e-06
relative error = 0.00027917161217706651462556502469711 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.1088850437986760370345899490213
y[1] (numeric) = 1.1088819041877722236895014292283
absolute error = 3.1396109038133450885197930e-06
relative error = 0.0002831322255964485806089317566125 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.109339266907562952269954015601
y[1] (numeric) = 1.109336081571937221713375762266
absolute error = 3.1853356257305565782533350e-06
relative error = 0.00028713809388629335836447518830377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.1097943806771087382170821666872
y[1] (numeric) = 1.1097911490712033194697469841512
absolute error = 3.2316059054187473351825360e-06
relative error = 0.00029118960788457741653152042888581 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.1102503846521996632563346530956
y[1] (numeric) = 1.1102471062253623977159215573478
absolute error = 3.2784268372655404130957478e-06
relative error = 0.00029528716067885445068299721852859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.1107072783768317902971164264731
y[1] (numeric) = 1.1107039525732815358867834688219
absolute error = 3.3258035502544103329576512e-06
relative error = 0.00029943114761205864527556730618866 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.1111650613941114327817762295659
y[1] (numeric) = 1.1111616876529033194396668097567
absolute error = 3.3737412081133421094198092e-06
relative error = 0.00030362196628829505896791403293897 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.1116237332462556115792550793985
y[1] (numeric) = 1.1116203110012461478155832702991
absolute error = 3.4222450094637636718090994e-06
relative error = 0.00030786001657861699370315891261542 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.1120832934745925127680272497516
y[1] (numeric) = 1.1120798221544045430165992932211
absolute error = 3.4713201879697514279565305e-06
relative error = 0.00031214570062679030857938467292474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.1125437416195619463078759700387
y[1] (numeric) = 1.112540220647549458799157219595
absolute error = 3.5209720124875087187504437e-06
relative error = 0.00031647942285504464015907813867912 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.1130050772207158056000451688413
y[1] (numeric) = 1.1130015060149285904831343489355
absolute error = 3.5712057872151169108199058e-06
relative error = 0.00032086158996981149149393526443774 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.6MB, time=4.34
x[1] = 0.481
y[1] (analytic) = 1.1134672998167185279353077019906
y[1] (numeric) = 1.1134636777898666853764334257533
absolute error = 3.6220268518425588742762373e-06
relative error = 0.00032529261096744915276587384410215 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.1139304089453475558294896171662
y[1] (numeric) = 1.1139267355047658538148976540923
absolute error = 3.6734405817020145919630739e-06
relative error = 0.0003297728971399544170682535087171 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.1143944041434937992459891195241
y[1] (numeric) = 1.1143906786911058808173429313887
absolute error = 3.7254523879184286461881354e-06
relative error = 0.00033430286208066105547318557247636 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.1148592849471620987048280158762
y[1] (numeric) = 1.1148555068794445383554995828963
absolute error = 3.7780677175603493284329799e-06
relative error = 0.00033888292168992501615140582076393 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.1153250508914716892777725284065
y[1] (numeric) = 1.1153212195994178982386554679643
absolute error = 3.8312920537910391170604422e-06
relative error = 0.000343513494180796312930458656628 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.115791701510656665469059482842
y[1] (numeric) = 1.1157878163797406456127919196358
absolute error = 3.8851309160198562675632062e-06
relative error = 0.00034819500008467756929488068328596 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.1162592363380664469812629903921
y[1] (numeric) = 1.1162552967482063930740035693556
absolute error = 3.9395898600539072594210365e-06
relative error = 0.00035292786225696918444865390531108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.1167276549061662453658358576272
y[1] (numeric) = 1.1167236602316879953959926990371
absolute error = 3.9946744782499698431585901e-06
relative error = 0.00035771250588270108867540168629515 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.117196956746537531557859073795
y[1] (numeric) = 1.117192906356137864871428353336
absolute error = 4.0503903996666864307204590e-06
relative error = 0.00036254935848215105584560462575424 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.1176671413898785042945318408633
y[1] (numeric) = 1.1176630346465882872669600357198
absolute error = 4.1067432902170275718051435e-06
relative error = 0.00036743884991644954153249642407197 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.1181382083660045594169337278386
y[1] (numeric) = 1.118134044627151738391675402799
absolute error = 4.1637388528210252583250396e-06
relative error = 0.00037238141239317101580924233768807 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.1186101572038487600545896476376
y[1] (numeric) = 1.1186059358210212012787909624085
absolute error = 4.2213828275587757986852291e-06
relative error = 0.00037737748047191176040948337207507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.1190829874314623076923674719854
y[1] (numeric) = 1.1190787077504704839803643720862
absolute error = 4.2796809918237120030998992e-06
relative error = 0.00038242749106985410054132868022707 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.1195566985760150141192372174827
y[1] (numeric) = 1.1195523599368545379748165258973
absolute error = 4.3386391604761444206915854e-06
relative error = 0.00038753188346731704225137628705845 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.1200312901637957742584198541208
y[1] (numeric) = 1.1200268919006097771870512089965
absolute error = 4.3982631859970713686451243e-06
relative error = 0.00039269109931329328684031810485751 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.1205067617202130398784529061372
y[1] (numeric) = 1.120502303161254397620959690903
absolute error = 4.4585589586422574932152342e-06
relative error = 0.00039790558263097259443512069696987 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.1209831127697952941846991341835
y[1] (numeric) = 1.1209785932373886976040972201893
absolute error = 4.5195324065965806019139942e-06
relative error = 0.00040317577982325146942464738005902 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.6MB, time=4.54
x[1] = 0.498
y[1] (analytic) = 1.1214603428361915272908237073372
y[1] (numeric) = 1.1214557616466953986443179751524
absolute error = 4.5811894961286465057321848e-06
relative error = 0.00040850213967822914106588234500389 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.1219384514421717125697643935207
y[1] (numeric) = 1.1219338079059399668981546170466
absolute error = 4.6435362317456716097764741e-06
relative error = 0.0004138851133746898131666134662444 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.1224174381096272838837184173962
y[1] (numeric) = 1.1224127315309709352507281846077
absolute error = 4.7065786563486329902327885e-06
relative error = 0.0004193251544875711573475088907632 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.1228973023595716136926687557886
y[1] (numeric) = 1.1228925320367202260069736608964
absolute error = 4.7703228513876856950948922e-06
relative error = 0.0004248227189934190249819643618722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.1233780437121404920409717621522
y[1] (numeric) = 1.1233732089372034741939661359244
absolute error = 4.8347749370178470056262278e-06
relative error = 0.00043037826527582835350588608994774 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.1238596616865926064215271335312
y[1] (numeric) = 1.1238547617455203514741320811101
absolute error = 4.8999410722549473950524211e-06
relative error = 0.0004359922541308702433816877420811 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.1243421558013100225170503558855
y[1] (numeric) = 1.1243371899738548906691298443352
absolute error = 4.9658274551318479205115503e-06
relative error = 0.00044166514877250518259120374863796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.1248255255737986658179668865485
y[1] (numeric) = 1.1248204931334758108941830672436
absolute error = 5.0324403228549237838193049e-06
relative error = 0.00044739741483798239612093504843556 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.1253097705206888041164464559634
y[1] (numeric) = 1.1253046707347368433026503194357
absolute error = 5.0997859519608137961365277e-06
relative error = 0.00045318952039322529849003120811538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.1257948901577355308760949947039
y[1] (numeric) = 1.1257897222870770574406138373719
absolute error = 5.1678706584734354811573320e-06
relative error = 0.00045904193593820302795665590177177 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 1.1262808839998192494768208161278
y[1] (numeric) = 1.1262756472990211882112698490979
absolute error = 5.2367007980612655509670299e-06
relative error = 0.00046495513441228804162186495817551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.126767751560946158334390809836
y[1] (numeric) = 1.1267624452781799634489025593552
absolute error = 5.3062827661948854882504808e-06
relative error = 0.00047092959119959975123182901693801 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.1272554923542487368941915264245
y[1] (numeric) = 1.1272501157312504321022234632311
absolute error = 5.3766229983047919680631934e-06
relative error = 0.00047696578413433418005914123321487 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.1277441058919862324987091598053
y[1] (numeric) = 1.127738658164016293026857250241
absolute error = 5.4477279699394718519095643e-06
relative error = 0.00048306419350607962182204540183655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.1282335916855451481282415596589
y[1] (numeric) = 1.1282280720813482243867551546207
absolute error = 5.5196041969237414864050382e-06
relative error = 0.00048922530206511828317668710961178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.1287239492454397310143545333464
y[1] (numeric) = 1.1287183569872042136643162016352
absolute error = 5.5922582355173500383317112e-06
relative error = 0.00049544959502771389189191212695337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.1292151780813124621255938238659
y[1] (numeric) = 1.1292095123846298882789963938884
absolute error = 5.6656966825738465974299775e-06
relative error = 0.00050173756008138525338869670766036 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.6MB, time=4.73
x[1] = 0.515
y[1] (analytic) = 1.1297072777019345465249632781811
y[1] (numeric) = 1.1297015377757588468141854759397
absolute error = 5.7399261756997107778022414e-06
relative error = 0.00050808968739016573889697782242421 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.1302002476152064045986788484863
y[1] (numeric) = 1.1301944326618129908521305100046
absolute error = 5.8149533934137465483384817e-06
relative error = 0.00051450646959984868905144187099595 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.1306940873281581641557071976931
y[1] (numeric) = 1.130688196543102857416685090133
absolute error = 5.8907850553067390221075601e-06
relative error = 0.00052098840184321871731471210549804 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.1311887963469501533975968096429
y[1] (numeric) = 1.1311828289190279520236626170233
absolute error = 5.9674279222013739341926196e-06
relative error = 0.00052753598174526889818133337084086 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.1316843741768733947581086342535
y[1] (numeric) = 1.1316783292880770823385716505423
absolute error = 6.0448887963124195369837112e-06
relative error = 0.00053414970942840382567897153685353 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.1321808203223500996121524280115
y[1] (numeric) = 1.1321746971478286924415109520822
absolute error = 6.1231745214071706414759293e-06
relative error = 0.00054083008751762852824431017870417 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.1326781342869341638535340809147
y[1] (numeric) = 1.1326719319949511976990014240931
absolute error = 6.2022919829661545326568216e-06
relative error = 0.00054757762114572322661022323871299 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.1331763155733116643410183521593
y[1] (numeric) = 1.1331700333252033202425317494865
absolute error = 6.2822481083440984866026728e-06
relative error = 0.00055439281795840392189791534737774 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.133675363683301356212210568549
y[1] (numeric) = 1.1336690006334344250535941291113
absolute error = 6.3630498669311586164394377e-06
relative error = 0.0005612761881194688016628362672024 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.134175278117855171064759971788
y[1] (numeric) = 1.1341688334135848566549861111585
absolute error = 6.4447042703144097738606295e-06
relative error = 0.00056822824431593045219627926280832 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.1346760583770587160043865334936
y[1] (numeric) = 1.1346695311586862764081541021542
absolute error = 6.5272183724395962324313394e-06
relative error = 0.0005752495017631338659356498003834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.135177703960131773559232189945
y[1] (numeric) = 1.1351710933608620004163537451544
absolute error = 6.6105992697731428784447906e-06
relative error = 0.00058234047820986023338542841967231 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.1356802143654288024600365822581
y[1] (numeric) = 1.1356735195113273380334019468583
absolute error = 6.6948541014644266346353998e-06
relative error = 0.00058950169394341650949783499937782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.1361835890904394392856365218521
y[1] (numeric) = 1.1361768091003899309777949316104
absolute error = 6.7799900495083078415902417e-06
relative error = 0.00059673367179471074500711827881437 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.1366878276317890009732875357502
y[1] (numeric) = 1.1366809616174500930519662966659
absolute error = 6.8660143389079213212390843e-06
relative error = 0.00060403693714331317375423087135134 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.1371929294852389881933049814358
y[1] (numeric) = 1.1371859765510011504664586396473
absolute error = 6.9529342378377268463417885e-06
relative error = 0.00061141201792250304757939329395138 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.1376988941456875895875213566629
y[1] (numeric) = 1.137691853388629782768781925827
absolute error = 7.0407570578068187394308359e-06
relative error = 0.00061885944462430121089868704336199 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=99.1MB, alloc=4.6MB, time=4.93
x[1] = 0.532
y[1] (analytic) = 1.138205721107170186871055565808
y[1] (numeric) = 1.1381985916170163643767313597259
absolute error = 7.1294901538224943242060821e-06
relative error = 0.00062637975030448840761733534012755 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.1387134098628598607968890410339
y[1] (numeric) = 1.1387061907219353067159371225272
absolute error = 7.2191409245540809519185067e-06
relative error = 0.0006339734705876093135667163017869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.1392219599050678979827427537335
y[1] (numeric) = 1.1392146501882554009614179339637
absolute error = 7.3097168124970213248197698e-06
relative error = 0.00064164114367196228818439675944549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.1397313707252442985997482894172
y[1] (numeric) = 1.1397239694999401613829099946493
absolute error = 7.4012253041372168382947679e-06
relative error = 0.00064938331033457483968656174280244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.1402416418139782849224052974161
y[1] (numeric) = 1.1402341481400481692937424622882
absolute error = 7.4936739301156286628351279e-06
relative error = 0.00065720051393616479851013443758998 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.1407527726609988107393167654858
y[1] (numeric) = 1.1407451855907334176030302128141
absolute error = 7.5870702653931362865526717e-06
relative error = 0.0006650933004260871943276210719354 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.1412647627551750716241927086173
y[1] (numeric) = 1.1412570813332456559709542352784
absolute error = 7.6814219294156532384733389e-06
relative error = 0.00067306221834726683246126425832989 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.1417776115845170160666120010952
y[1] (numeric) = 1.1417698348479307365668996072308
absolute error = 7.7767365862794997123938644e-06
relative error = 0.00068110781884111656604443477034771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.1422913186361758574620312210822
y[1] (numeric) = 1.1422834456142309604302205954113
absolute error = 7.8730219448970318106256709e-06
relative error = 0.00068923065565244126079732429108046 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.1428058833964445869605285177651
y[1] (numeric) = 1.1427979131106854244334020248008
absolute error = 7.9702857591625271264929643e-06
relative error = 0.00069743128513432744980091023142043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.1433213053507584871737696523608
y[1] (numeric) = 1.1433132368149303688473856574618
absolute error = 8.0685358281183263839948990e-06
relative error = 0.00070571026625301867616783619923044 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.1438375839836956467396825060591
y[1] (numeric) = 1.1438294162036995255088299211381
absolute error = 8.1677799961212308525849210e-06
relative error = 0.00071406816059277652202127837384791 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.1443547187789774757443254902696
y[1] (numeric) = 1.1443464507528244665890709262735
absolute error = 8.2680261530091552545639961e-06
relative error = 0.0007225055323607273227030381032609 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.1448727092194692220004344373497
y[1] (numeric) = 1.1448643399372349539645523089567
absolute error = 8.3692822342680358821283930e-06
relative error = 0.00073102294839169456564000457691501 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.1453915547871804881821316933069
y[1] (numeric) = 1.1453830832309592891884910363008
absolute error = 8.4715562211989936406570061e-06
relative error = 0.00073962097815301697380375737320354 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.1459112549632657498152802778119
y[1] (numeric) = 1.1459026801071246640635459099219
absolute error = 8.5748561410857517343678900e-06
relative error = 0.00074830019374935227420141880680041 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.1464318092280248741229651212096
y[1] (numeric) = 1.1464231300379575118152551024945
absolute error = 8.6791900673623077100187151e-06
relative error = 0.00075706116992746665233690861323481 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=102.9MB, alloc=4.6MB, time=5.12
x[1] = 0.549
y[1] (analytic) = 1.1469532170609036397255825330915
y[1] (numeric) = 1.146944432494783858866008661828
absolute error = 8.7845661197808595738712635e-06
relative error = 0.00076590448408100989408049095780151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.1474754779404942571950182023822
y[1] (numeric) = 1.1474665869480296772093215165335
absolute error = 8.8909924645799856966858487e-06
relative error = 0.00077483071625527621688092507151696 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.1479985913445358904623931748063
y[1] (numeric) = 1.1479895928672212373841721171298
absolute error = 8.9984773146530782210576765e-06
relative error = 0.00078384044915195079274862809004892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.1485225567499151790788564000321
y[1] (numeric) = 1.1485134497209854620491714463738
absolute error = 9.1070289297170296849536583e-06
relative error = 0.00079293426813384196593002200847917 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.1490473736326667613289015877443
y[1] (numeric) = 1.1490381569770502801563267326949
absolute error = 9.2166556164811725748550494e-06
relative error = 0.00080211276122959916868265786975771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.1495730414679737981956852593716
y[1] (numeric) = 1.1495637141022449817241638008626
absolute error = 9.3273657288164715214585090e-06
relative error = 0.00081137651913841653904778026185477 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.150099559730168498177822030195
y[1] (numeric) = 1.1500901205625005732099715944253
absolute error = 9.4391676679249678504357697e-06
relative error = 0.00082072613523472224500170577260293 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.1506269278927326429571323050854
y[1] (numeric) = 1.1506173758228501334809320050229
absolute error = 9.5520698825094762003000625e-06
relative error = 0.00083016220557285351984973191778157 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.1511551454282981139168167201663
y[1] (numeric) = 1.1511454793474291703838977444003
absolute error = 9.6660808689435329189757660e-06
relative error = 0.00083968532889171741420625983560188 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 1.1516842118086474195095308122717
y[1] (numeric) = 1.1516744305994759779135805958289
absolute error = 9.7812091714415959502164428e-06
relative error = 0.00084929610661943727038239736796033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.1522141265047142234748325481675
y[1] (numeric) = 1.1522042290413319939789119826855
absolute error = 9.8974633822294959205654820e-06
relative error = 0.00085899514287798492547750035306862 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.1527448889865838739054744961337
y[1] (numeric) = 1.1527348741344421587673373931337
absolute error = 1.00148521417151381371030000e-05
relative error = 0.00086878304448779864994390278071403 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.153276498723493933162011573659
y[1] (numeric) = 1.1532663653393552737068058012128
absolute error = 1.01333841386594552057724462e-05
relative error = 0.00087866042097238682886447204031537 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.1538089551838347086351944566842
y[1] (numeric) = 1.1537987021157243610252148261552
absolute error = 1.02530681103476099796305290e-05
relative error = 0.00088862788456291739365059769966922 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.1543422578351497843556178880455
y[1] (numeric) = 1.1543318839223070239070719734294
absolute error = 1.03739128427604485459146161e-05
relative error = 0.00089868605020279301233377358233856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.1548764061441365534500922755128
y[1] (numeric) = 1.154865910216965807247131902841
absolute error = 1.04959271707462029603726718e-05
relative error = 0.0009088355355522120470870564566233 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.1554113995766467514442061230971
y[1] (numeric) = 1.1554007804566685590007692710227
absolute error = 1.06191199781924434368520744e-05
relative error = 0.00091907696099271528807337378605352 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.6MB, time=5.31
x[1] = 0.566
y[1] (analytic) = 1.1559472375976869904105459931083
y[1] (numeric) = 1.1559364940974887921308462977964
absolute error = 1.07435001981982796996953119e-05
relative error = 0.0009294109496317184731759013892758 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.1564839196714192939620398507875
y[1] (numeric) = 1.1564730505946060471508338082117
absolute error = 1.08690768132468112060425758e-05
relative error = 0.00093983812730703060362153238589754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.157021445261161633089888798216
y[1] (numeric) = 1.1570104494023062552639441045392
absolute error = 1.09958588553778259446936768e-05
relative error = 0.00095035912259135806596180659071738 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.1575598138293884628455513596132
y[1] (numeric) = 1.1575486899739821020980336251379
absolute error = 1.11238554063607475177344753e-05
relative error = 0.00096097456679679457132655698237235 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.158099024837731259866243636084
y[1] (numeric) = 1.1580877717621333920360329499144
absolute error = 1.12530755978678302106861696e-05
relative error = 0.00097168509397929692331395246867951 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.158639077746979060743417804361
y[1] (numeric) = 1.1586276942183674131416613150549
absolute error = 1.13835286116476017564893061e-05
relative error = 0.00098249134094314662632656733200857 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.1591799720170790012336805911064
y[1] (numeric) = 1.1591684567933993026801824028322
absolute error = 1.15152236796985534981882742e-05
relative error = 0.000993393947245397346606582370005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.1597217071071368563116125119018
y[1] (numeric) = 1.159710058937052413233957775578
absolute error = 1.16481700844430776547363238e-05
relative error = 0.001004393555200308238664215419747 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.1602642824754175810639478221502
y[1] (numeric) = 1.1602525000982586794125539263563
absolute error = 1.17823771589016513938957939e-05
relative error = 0.0010154908098837631502319842991031 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.1608076975793458524245742857562
y[1] (numeric) = 1.1607957797250589851571585224864
absolute error = 1.19178542868672674157632698e-05
relative error = 0.0010266863591376757193134183942856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.1613519518755066117498110266296
y[1] (numeric) = 1.161339897264603531639061021836
absolute error = 1.20546109030801107500047936e-05
relative error = 0.0010379808535743803773283512312108 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.1618970448196456082334218877795
y[1] (numeric) = 1.1618848521631522057519524457419
absolute error = 1.21926564934024814694420376e-05
relative error = 0.0010493749465810092727879405916904 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.162442975866669943160820883031
y[1] (numeric) = 1.1624306438660749491977986965174
absolute error = 1.23320005949939630221865136e-05
relative error = 0.0010608692943238551303610705496638 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.1629897444706486150019254872046
y[1] (numeric) = 1.1629772718178521281660414117664
absolute error = 1.24726527964868358840754382e-05
relative error = 0.0010724645557527200606197872233404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.16353735008481306534211267195
y[1] (numeric) = 1.1635247354620749036058799521555
absolute error = 1.26146227381617362327197945e-05
relative error = 0.0010841613926052503361749018912436 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.1640857921615577256507317563242
y[1] (numeric) = 1.164073034241445602091387723884
absolute error = 1.27579201121235593440324402e-05
relative error = 0.001095960469411257150333858678588 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.1646350701524405648866273036464
y[1] (numeric) = 1.1646221675977780872792156418517
absolute error = 1.29025546624776074116617947e-05
relative error = 0.0011078624534970233748314039302151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.6MB, time=5.51
x[1] = 0.583
y[1] (analytic) = 1.165185183508183637940124459152
y[1] (numeric) = 1.1651721349719981319586351444426
absolute error = 1.30485361855059814893147094e-05
relative error = 0.0011198680149895963335995082303718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.1657361316786736349109282865074
y[1] (numeric) = 1.165722935804143790693672775931
absolute error = 1.31958745298442172555105764e-05
relative error = 0.0011319778268210666099563753453863 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.1662879141129624312213878253303
y[1] (numeric) = 1.1662745695333657730570879577671
absolute error = 1.33445795966581642998675632e-05
relative error = 0.0011441925647328329050052218459914 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.1668405302592676385645747564984
y[1] (numeric) = 1.1668270355979278174559451754172
absolute error = 1.34946613398211086295810812e-05
relative error = 0.0011565129072798529654418240371268 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.1673939795649731566866257272142
y[1] (numeric) = 1.1673803334352070655485314130158
absolute error = 1.36461297660911380943141984e-05
relative error = 0.0011689395358348805993756014515349 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.1679482614766297260027965535271
y[1] (numeric) = 1.1679344624816944372523692738361
absolute error = 1.37989949352887504272796910e-05
relative error = 0.0011814731345926887991722354755795 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 1.1685033754399554810466756843086
y[1] (numeric) = 1.1684894221729950063430758305019
absolute error = 1.39532669604747035998538067e-05
relative error = 0.0011941143905742789907265058469206 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.1690593208998365047520034775093
y[1] (numeric) = 1.1690452119438283766438168549441
absolute error = 1.41089560081281081866225652e-05
relative error = 0.0012068639936310764289721624393752 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.1696160973003273835665430069271
y[1] (numeric) = 1.1696018312280290588051056843551
absolute error = 1.42660722983247614373225720e-05
relative error = 0.0012197226364491117598312343699083 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.1701737040846517633974472856612
y[1] (numeric) = 1.1701592794585468476746955858108
absolute error = 1.44246261049157227516998504e-05
relative error = 0.0012326910145531887691982089315711 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.1707321406952029063875669609314
y[1] (numeric) = 1.1707175560674472002573140888123
absolute error = 1.45846277557061302528721191e-05
relative error = 0.0012457698263110383399449882452099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.1712914065735442485221417040005
y[1] (numeric) = 1.1712766604859116142639873617504
absolute error = 1.47460876326342581543422501e-05
relative error = 0.0012589597729374586383204489619074 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.1718515011604099580653176885558
y[1] (numeric) = 1.1718365921442380072507023152161
absolute error = 1.49090161719508146153733397e-05
relative error = 0.0012722615584984415515037883912036 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.172412423895705494825932721079
y[1] (numeric) = 1.1723973504718410963461537221668
absolute error = 1.50734238643984797789989122e-05
relative error = 0.0012856758899152853984536370848773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.1729741742185081702520097574644
y[1] (numeric) = 1.1729589348972527785683232522132
absolute error = 1.52393212553916836865052512e-05
relative error = 0.0012992034769686939365751514896534 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.1735367515670677083533987114403
y[1] (numeric) = 1.1735213448481225117296369247168
absolute error = 1.54067189451966237617867235e-05
relative error = 0.0013128450323028616871049698114787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.1741001553788068074520056321979
y[1] (numeric) = 1.1740845797512176959304470929808
absolute error = 1.55756275891115215585392171e-05
relative error = 0.001326601271429545602489017615787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=114.4MB, alloc=4.6MB, time=5.70
x[1] = 0.6
y[1] (analytic) = 1.1746643850903217027590475010446
y[1] (numeric) = 1.1746486390324240556405846795798
absolute error = 1.57460578976471184628214648e-05
relative error = 0.0013404729127321230994006862964193 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.1752294401373827297787700698751
y[1] (numeric) = 1.1752135221167460223687269908057
absolute error = 1.59180206367074100430790694e-05
relative error = 0.0013544606774696364814168763753135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.1757953199549348885380653377883
y[1] (numeric) = 1.1757792284283071179193260463092
absolute error = 1.60915266277706187392914791e-05
relative error = 0.0013685652897808237757367971527345 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.1763620239770984086414244362806
y[1] (numeric) = 1.1763457573903503382368419682873
absolute error = 1.62665867480704045824679933e-05
relative error = 0.0013827874766881360086932446353615 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.1769295516371693151506608681084
y[1] (numeric) = 1.17691310842523853783702558301
absolute error = 1.64432119307773136352850984e-05
relative error = 0.0013971279681017409451683393062555 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.177497902367619995288838220145
y[1] (numeric) = 1.1774812809544548148249939960918
absolute error = 1.66214131651804638442240532e-05
relative error = 0.0014115874968235133173853947284731 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.1780670756000997659678356463513
y[1] (numeric) = 1.1780502743986028964998425116964
absolute error = 1.68012014968694679931346549e-05
relative error = 0.0014261667985510115689057060199285 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.1786370707654354421389835933405
y[1] (numeric) = 1.1786200881774075255455358748177
absolute error = 1.69825880279165934477185228e-05
relative error = 0.0014408666118814411400135939302784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.1792078872936319059662014179512
y[1] (numeric) = 1.1791907217097148468078214249067
absolute error = 1.71655839170591583799930445e-05
relative error = 0.001455687678315604321025016060725 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.1797795246138726768210677237362
y[1] (numeric) = 1.1797621744134927946569063584098
absolute error = 1.73502003798821641613653264e-05
relative error = 0.0014706307422618367004044606694177 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.1803519821545204820992534213452
y[1] (numeric) = 1.1803344457058314809356409072539
absolute error = 1.75364486890011636125140913e-05
relative error = 0.0014856965510399302349216719009856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.1809252593431178288577466964165
y[1] (numeric) = 1.180907535002943583492948849955
absolute error = 1.77243401742453647978464615e-05
relative error = 0.0015008858548850429694240176574279 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.1814993556063875762722982477992
y[1] (numeric) = 1.1814814417201647353022463818404
absolute error = 1.79138862228409700518659588e-05
relative error = 0.0015161994069515954341420033475438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 1.1820742703702335089145143387088
y[1] (numeric) = 1.1820561652719539141645899808604
absolute error = 1.81050982795947499243578484e-05
relative error = 0.0015316379633171537477845574053635 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.1826500030597409108480243837716
y[1] (numeric) = 1.1826317050718938329962935156252
absolute error = 1.82979878470778517308681464e-05
relative error = 0.0015472022829862994550172679705521 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.1832265530991771405431489758368
y[1] (numeric) = 1.1832080605326913307007544526345
absolute error = 1.84925664858098423945232023e-05
relative error = 0.0015628931278944861272507354492841 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.1838039199119922066094934379379
y[1] (numeric) = 1.1837852310661777636242286301727
absolute error = 1.86888458144429852648077652e-05
relative error = 0.0015787112629118827559976243216009 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=118.2MB, alloc=4.6MB, time=5.89
x[1] = 0.617
y[1] (analytic) = 1.1843821029208193443458911678558
y[1] (numeric) = 1.1843632160833093975952926770224
absolute error = 1.88868375099467505984908334e-05
relative error = 0.0015946574558472039683858495928739 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.1849611015474755931071202253905
y[1] (numeric) = 1.1849420149941678005477327650016
absolute error = 1.90865533077925593874603889e-05
relative error = 0.0016107324774515270947416213446 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.1855409152129623744868157956707
y[1] (numeric) = 1.1855216272079602357265979953574
absolute error = 1.92880050021387602178003133e-05
relative error = 0.001626937101422096118479794756824 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.1861215433374660713160003456393
y[1] (numeric) = 1.1861020521330200554771563302511
absolute error = 1.94912044460158388440153882e-05
relative error = 0.0016432721044061125388601357526775 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.1867029853403586074766524752305
y[1] (numeric) = 1.1866832891768070956164905919456
absolute error = 1.96961635515118601618832849e-05
relative error = 0.0016597382660045131774867142315915 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.1872852406401980285297346497202
y[1] (numeric) = 1.187265337745908070387471663858
absolute error = 1.99028942899581422629858622e-05
relative error = 0.0016763363687757349597436808575122 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.1878683086547290831570991852689
y[1] (numeric) = 1.1878481972460369679948456393664
absolute error = 2.01114086921151622535459025e-05
relative error = 0.0016930671982394667026741701100255 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 1.1884521888008838054166910457999
y[1] (numeric) = 1.1884318670820354467231712761623
absolute error = 2.03217188483586935197696376e-05
relative error = 0.0017099315428803879411200047729565 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 1.1890368804947820978104651960589
y[1] (numeric) = 1.1890163466578732316363437260176
absolute error = 2.05338369088661741214700413e-05
relative error = 0.0017269301941518948242482568361981 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.189622383151732315164435442986
y[1] (numeric) = 1.1896016353766485118584401220893
absolute error = 2.07477750838033059953208967e-05
relative error = 0.0017440639464798131148965491494742 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.1902086961862318493202708853993
y[1] (numeric) = 1.1901877326405883384356222183152
absolute error = 2.09635456435108846486670841e-05
relative error = 0.001761333597266098324472263562875 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.1907958190119677146378552804441
y[1] (numeric) = 1.1907746378510490227788308880599
absolute error = 2.11811609186918590243923842e-05
relative error = 0.0017787399468925230164415574322222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.1913837510418171343082238242947
y[1] (numeric) = 1.1913623504085165356870069019538
absolute error = 2.14006333005986212169223409e-05
relative error = 0.0017962837987243513117422829448782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.1919724916878481274762910342229
y[1] (numeric) = 1.1919508697126069069505720178293
absolute error = 2.16219752412205257190163936e-05
relative error = 0.0018139659591140006297505566549503 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.1925620403613200971727826093538
y[1] (numeric) = 1.1925401951620666255349040287944
absolute error = 2.18451992534716378785805594e-05
relative error = 0.0018317872374046906987238417297119 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 1.1931523964726844190547833382246
y[1] (numeric) = 1.1931303261547730403435390287999
absolute error = 2.20703179113787112443094247e-05
relative error = 0.0018497484459340798699339858842614 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.1937435594315850309543123126502
y[1] (numeric) = 1.1937212620877347615608337685498
absolute error = 2.22973438502693934785441004e-05
relative error = 0.0018678504000378887699917073890756 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=122.0MB, alloc=4.6MB, time=6.09
x[1] = 0.634
y[1] (analytic) = 1.1943355286468590232343358993664
y[1] (numeric) = 1.1943130023570920625738205882745
absolute error = 2.25262897669606605153110919e-05
relative error = 0.0018860939180535113261495418540969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.1949283035265372299516281134903
y[1] (numeric) = 1.1949055463581172824729870277365
absolute error = 2.27571684199474786410857538e-05
relative error = 0.0019044798213236131996532585554133 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.1955218834778448208258872309833
y[1] (numeric) = 1.1954988934852152291317118278659
absolute error = 2.29899926295916941754031174e-05
relative error = 0.0019230089341997176624922283297873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 1.1961162679072018940145166710524
y[1] (numeric) = 1.1960930431319235828640886526299
absolute error = 2.32247752783111504280184225e-05
relative error = 0.0019416820840457789531771810949461 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.1967114562202240696924773737563
y[1] (numeric) = 1.1966879946909133006608684741259
absolute error = 2.34615293107690316088996304e-05
relative error = 0.0019605001012417431474492314461967 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 1.1973074478217230844366180930148
y[1] (numeric) = 1.1972837475539890210032511784537
absolute error = 2.37002677340634333669145611e-05
relative error = 0.0019794638191870965800969807358691 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.1979042421157073864138892207397
y[1] (numeric) = 1.1978803011120894692542565646661
absolute error = 2.39410036179171596326560736e-05
relative error = 0.0019985740743044018543289263908773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.198501838505382731372844953923
y[1] (numeric) = 1.1984776547552878636274045240224
absolute error = 2.41837500948677454404299006e-05
relative error = 0.0020178317060428214754163283730773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.1991002363931527794378378132311
y[1] (numeric) = 1.1990758078727923217324338018744
absolute error = 2.44285203604577054040113567e-05
relative error = 0.0020372375568816291455871024950976 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.1996994351806196927053087189588
y[1] (numeric) = 1.1996747598529462676977883597981
absolute error = 2.46753276734250075203591607e-05
relative error = 0.0020567924723337087574142346821997 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.2002994342685847336415750281037
y[1] (numeric) = 1.2002745100832288398695999710516
absolute error = 2.49241853558937719750570521e-05
relative error = 0.0020764973009490411232026437322347 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.2009002330570488642815181348221
y[1] (numeric) = 1.2008750579502552990868952980859
absolute error = 2.51751067935651946228367362e-05
relative error = 0.0020963528943181784781363666589743 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.2015018309452133462275714356296
y[1] (numeric) = 1.2014764028397774375327553166617
absolute error = 2.54281054359086948161189679e-05
relative error = 0.0021163601070757067952034052140515 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.2021042273314803414484086604078
y[1] (numeric) = 1.2020785441366839881611545671362
absolute error = 2.56831947963532872540932716e-05
relative error = 0.0021365197969036959501685583060623 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.2027074216134535138767317705792
y[1] (numeric) = 1.202681481225001034699207329674
absolute error = 2.59403884524791775244409052e-05
relative error = 0.0021568328245351377751150782986801 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 1.203311413187938631805556826712
y[1] (numeric) = 1.2032852134878924222245474365082
absolute error = 2.61997000462095810093902038e-05
relative error = 0.0021773000537573720393240336952302 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.2039162014509441710823954293201
y[1] (numeric) = 1.2038897403076601683175680509333
absolute error = 2.64611432840027648273783868e-05
relative error = 0.002197922351415500396505841540204 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=125.8MB, alloc=4.6MB, time=6.28
x[1] = 0.651
y[1] (analytic) = 1.2045217857976819191007285387257
y[1] (numeric) = 1.2044950610657448747882473594489
absolute error = 2.67247319370443124811792768e-05
relative error = 0.0022187005874157883376415545028038 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.2051281656225675795881686825627
y[1] (numeric) = 1.205101175142726139977285740392
absolute error = 2.69904798414396108829421707e-05
relative error = 0.0022396356347290551889321558751969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.2057353403192213781907057628076
y[1] (numeric) = 1.2057080819183229716312795895006
absolute error = 2.72584008984065594261733070e-05
relative error = 0.0022607283693940521945923343386885 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.2063433092804686688524308781435
y[1] (numeric) = 1.2063157807713942003516566001342
absolute error = 2.75285090744685007742780093e-05
relative error = 0.002281979670520828724460986169358 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.2069520718983405409901317819836
y[1] (numeric) = 1.20692427107993889361709691335
absolute error = 2.78008184016473730348686336e-05
relative error = 0.0023033904202940866466340290505258 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.207561627564074427462152801609
y[1] (numeric) = 1.2075335522210967703791641706827
absolute error = 2.80753429776570829886309263e-05
relative error = 0.0023249615039765229055560157990183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.2081719756681147133309112496125
y[1] (numeric) = 1.2081436235711486162308701203169
absolute error = 2.83520969660971000411292956e-05
relative error = 0.0023466938099121603462355122199958 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.2087831156001133454184615651814
y[1] (numeric) = 1.208754484505516699147896045359
absolute error = 2.86310945966462705655198224e-05
relative error = 0.0023685882295296668254752573763651 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.2093950467489304426544976297072
y[1] (numeric) = 1.2093661343987651858021939011232
absolute error = 2.89123501652568523037285840e-05
relative error = 0.002390645657345662651231762038843 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.2100077685026349072161829087698
y[1] (numeric) = 1.2099785726246005584476896667361
absolute error = 2.91958780343487684932420337e-05
relative error = 0.0024128669909680163914402275197062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 1.2106212802485050364591972807178
y[1] (numeric) = 1.2105917985558720323778110349399
absolute error = 2.94816926330040813862457779e-05
relative error = 0.0024352531310991290938594887240885 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.2112355813730291356393886208484
y[1] (numeric) = 1.2112058115645719739545611827341
absolute error = 2.97698084571616848274381143e-05
relative error = 0.002457804981539206958708107462826 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.2118506712619061314244164195866
y[1] (numeric) = 1.2118206110218363192088599844434
absolute error = 3.00602400698122155564351432e-05
relative error = 0.0024805234491895225060767709998573 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.2124665493000461861947739230711
y[1] (numeric) = 1.212436196297944993011873647929
absolute error = 3.03530021011931829002751421e-05
relative error = 0.002503409444055664280313792716869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.2130832148715713131335744951767
y[1] (numeric) = 1.2130525667623223288170533739807
absolute error = 3.06481092489843165211211960e-05
relative error = 0.0025264638792507751337897722514541 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.666
y[1] (analytic) = 1.213700667359815992104487111237
y[1] (numeric) = 1.2136697217835374889726032584295
absolute error = 3.09455762785031318838528075e-05
relative error = 0.002549687670998779132654358099892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.2143189061473277863172051055833
y[1] (numeric) = 1.2142876607293048856040972762113
absolute error = 3.12454180229007131078293720e-05
relative error = 0.0025730817386375971274025726931084 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.6MB, time=6.47
x[1] = 0.668
y[1] (analytic) = 1.2149379306158679597798315074841
y[1] (numeric) = 1.2149063829664846020669648064909
absolute error = 3.15476493833577128667009932e-05
relative error = 0.0025966470046223510312703145884755 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.2155577401464120955375635131482
y[1] (numeric) = 1.2155258878610828149685637780172
absolute error = 3.18522853292805689997351310e-05
relative error = 0.0026203843945285568496784509087906 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.2161783341191507146970578551619
y[1] (numeric) = 1.2161461747782522167595601341347
absolute error = 3.21593408984979374977210272e-05
relative error = 0.0026442948370553065041423627309982 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.2167997119134898962358580450436
y[1] (numeric) = 1.2167672430822924388943319373138
absolute error = 3.24688311974573415261077298e-05
relative error = 0.0026683792640284384942589121326545 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.2174218729080518975962636795423
y[1] (numeric) = 1.2173890921366504755601160536892
absolute error = 3.27807714014220361476258531e-05
relative error = 0.0026926386104036974415755702036921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.2180448164806757760630212168607
y[1] (numeric) = 1.218011721303921107974614978912
absolute error = 3.30951767546680884062379487e-05
relative error = 0.002717073814269882559336885597226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.2186685420084180109242148451658
y[1] (numeric) = 1.2186351299458473292517809876216
absolute error = 3.34120625706816724338575442e-05
relative error = 0.0027416858168519850922915917101421 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.219293048867553126414735282546
y[1] (numeric) = 1.2192593174233207698354944100375
absolute error = 3.37314442323565792408725085e-05
relative error = 0.0027664755625143147709294522498222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.2199183364335743154417035649992
y[1] (numeric) = 1.2198842830963821235008524605502
absolute error = 3.40533371921919408511044490e-05
relative error = 0.0027914439987636153247004386143762 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.2205444040811940640912260970796
y[1] (numeric) = 1.22051002632422157392278466476
absolute error = 3.43777569724901684414323196e-05
relative error = 0.002816592076252169098950023746829 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.2211712511843447769158564585004
y[1] (numeric) = 1.2211365464651792218117105531705
absolute error = 3.47047191655551041459053299e-05
relative error = 0.0028419207487808908204832738289712 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.221798877116179403002138679282
y[1] (numeric) = 1.2217638428767455126159549116934
absolute error = 3.50342394338903861837675886e-05
relative error = 0.0028674309733024105568470278990357 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.2224272812490720628176059159557
y[1] (numeric) = 1.2223919149155616647906355012567
absolute error = 3.53663335103980269704146990e-05
relative error = 0.0028931237099241459145937842928733 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.2230564629546186758366076818755
y[1] (numeric) = 1.223020761937420098632737781139
absolute error = 3.57010171985772038699007365e-05
relative error = 0.0029189999219113635219629677073366 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.223686421603637588944338005864
y[1] (numeric) = 1.2236503832972648656820907931687
absolute error = 3.60383063727232622472126953e-05
relative error = 0.0029450605756902298415850404554452 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 1.2243171565661702056184361152149
y[1] (numeric) = 1.2242807783491920786879579866361
absolute error = 3.63782169781269304781285788e-05
relative error = 0.0029713066408508513589814522337551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.2249486672114816158875304615069
y[1] (numeric) = 1.2249119464464503421409563866676
absolute error = 3.67207650312737465740748393e-05
relative error = 0.0029977390901503041927987030075337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.6MB, time=6.66
x[1] = 0.685
y[1] (analytic) = 1.2255809529080612270660961307334
y[1] (numeric) = 1.2255438869414411833700171318986
absolute error = 3.70659666200436960789988348e-05
relative error = 0.0030243588995156531728778298872607 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.2262140130236233952649949029474
y[1] (numeric) = 1.2261765991857194842041000305674
absolute error = 3.74138379039110608948723800e-05
relative error = 0.0030511670480469604324214299770704 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.2268478469251080576770664509304
y[1] (numeric) = 1.2268100825299939131983744076216
absolute error = 3.77643951141444786920433088e-05
relative error = 0.0030781645180202835606789034073875 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.2274824539786813656371383923497
y[1] (numeric) = 1.227444336324127358424578139098
absolute error = 3.81176545540072125602532517e-05
relative error = 0.0031053522948906633627269530145901 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.2281178335497363184558221354451
y[1] (numeric) = 1.2280793599171373608252663938899
absolute error = 3.84736325989576305557415552e-05
relative error = 0.0031327313672951012730765164494485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.2287539850028933980264606845022
y[1] (numeric) = 1.2287151526571965481316612270696
absolute error = 3.88323456968498947994574326e-05
relative error = 0.0031603027270555264699892407514192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.2293909077020012042045937982186
y[1] (numeric) = 1.2293517138916330693448127931713
absolute error = 3.91938103681348597810050473e-05
relative error = 0.003188067369181752737536347339668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.2300286010101370909593051215486
y[1] (numeric) = 1.2299890429669310297797825722789
absolute error = 3.95580432060611795225492697e-05
relative error = 0.0032160262918744251225802831238426 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.2306670642896078032958151397345
y[1] (numeric) = 1.2306271392287309266725586263877
absolute error = 3.99250608768766232565133468e-05
relative error = 0.003244180496527956434004921401036 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.2313062969019501149486830319832
y[1] (numeric) = 1.2312660020218300853494125283315
absolute error = 4.02948801200295992705036517e-05
relative error = 0.0032725309877334536316632701158588 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.2319462982079314668449797316401
y[1] (numeric) = 1.2319056306901830959584072305822
absolute error = 4.06675177483708865725010579e-05
relative error = 0.0033010787732816341526526745679566 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.2325870675675506063367937297397
y[1] (numeric) = 1.2325460245769022507627647664352
absolute error = 4.10429906483555740289633045e-05
relative error = 0.0033298248641657322226663743724074 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.2332286043400382272024303894814
y[1] (numeric) = 1.2331871830242579819958023014987
absolute error = 4.14213157802452066280879827e-05
relative error = 0.0033587702745843952003069985468466 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.2338709078838576104156647704838
y[1] (numeric) = 1.2338291053736793002771446790001
absolute error = 4.18025101783101385200914837e-05
relative error = 0.0033879160219445700023821664185951 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.234513977556705265682407193618
y[1] (numeric) = 1.2344717909657542335899212282161
absolute error = 4.21865909510320924859654019e-05
relative error = 0.0034172631268643796583348137766676 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 1.2351578127155115737441400098081
y[1] (numeric) = 1.235115239140230266818654231316
absolute error = 4.25735752813069254857784921e-05
relative error = 0.0034468126131759900420911922122673 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.2358024127164414294474832694162
y[1] (numeric) = 1.2357594492360147818475460700929
absolute error = 4.29634804266475999371993233e-05
relative error = 0.0034765655079284668297377022961307 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=137.3MB, alloc=4.6MB, time=6.85
x[1] = 0.702
y[1] (analytic) = 1.2364477769148948855792462226979
y[1] (numeric) = 1.2364044205911754982188717004304
absolute error = 4.33563237193873603745222675e-05
relative error = 0.0035065228413906227315638275815445 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.2370939046655077974663208163335
y[1] (numeric) = 1.2370501525429409143511827289267
absolute error = 4.37521225668831151380874068e-05
relative error = 0.0035366856470538550471324446274019 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.2377407953221524683397725861917
y[1] (numeric) = 1.2376966444277007493170289928652
absolute error = 4.41508944517190227435933265e-05
relative error = 0.003567054961634973592160702033553 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.2383884482379382954624835822915
y[1] (numeric) = 1.2383438955810063851799031716833
absolute error = 4.45526569319102825804106082e-05
relative error = 0.0035976318250790190461144992315582 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.2390368627652124170197011983717
y[1] (numeric) = 1.2389919053375713098901135852537
absolute error = 4.49574276411071295876131180e-05
relative error = 0.0036284172805620717695373598772602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.2396860382555603597718460155734
y[1] (numeric) = 1.2396406730312715607392899616467
absolute error = 4.53652242887990325560539267e-05
relative error = 0.0036594123744940511402501958779341 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.2403359740598066874689310074817
y[1] (numeric) = 1.2402901979951461683732265845971
absolute error = 4.57760646605190957044228846e-05
relative error = 0.0036906181565215054576721036746745 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.709
y[1] (analytic) = 1.2409866695280156500259436921618
y[1] (numeric) = 1.2409404795613976013627668586483
absolute error = 4.61899666180486631768335135e-05
relative error = 0.0037220356795303924646239339498912 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.2416381240094918334585420558604
y[1] (numeric) = 1.2415915170613922113324329578959
absolute error = 4.66069480996221261090979645e-05
relative error = 0.0037536659996488505360859375300377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.2422903368527808105784143127322
y[1] (numeric) = 1.2422433098256606786465038523961
absolute error = 4.70270271201319319104603361e-05
relative error = 0.0037855101762499605844883238255792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.2429433074056697924476518052839
y[1] (numeric) = 1.2428958571838984586522446346492
absolute error = 4.74502217713337954071706347e-05
relative error = 0.0038175692719544987312190810645359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.2435970350151882805914835912195
y[1] (numeric) = 1.2435491584649662284799896971081
absolute error = 4.78765502220521114938941114e-05
relative error = 0.0038498443526336797941369105230493 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.2442515190276087199687205040045
y[1] (numeric) = 1.2442032129968903343997819404018
absolute error = 4.83060307183855689385636027e-05
relative error = 0.0038823364874118916409786270533177 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.2449067587884471526992557167609
y[1] (numeric) = 1.2448580201068632397342698209019
absolute error = 4.87386815839129649858958590e-05
relative error = 0.0039150467486694204586498860740329 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.2455627536424638725479680820458
y[1] (numeric) = 1.2455135791212439733275636753958
absolute error = 4.91745212198992204044066500e-05
relative error = 0.0039479762120451669884856207038604 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 1.2462195029336640801643737636656
y[1] (numeric) = 1.2461698893655585785697523899667
absolute error = 4.96135681055015946213736989e-05
relative error = 0.0039811259564393537776621216061645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.2468770060052985390773709209283
y[1] (numeric) = 1.2468269501645005629767811097153
absolute error = 5.00558407979761005898112130e-05
relative error = 0.0040144970640162234970362750504209 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=141.1MB, alloc=4.6MB, time=7.04
x[1] = 0.719
y[1] (analytic) = 1.2475352621998642324444214506442
y[1] (numeric) = 1.2474847608419313483253903156921
absolute error = 5.05013579328841190311349521e-05
relative error = 0.0040480906202067283757791011891821 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.248194270859105020554513037748
y[1] (numeric) = 1.2481433207208807213428162253436
absolute error = 5.09501382242992116968124044e-05
relative error = 0.0040819077137112108032604134310789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.2488540313240122990842440116342
y[1] (numeric) = 1.2488026291235472849509521029096
absolute error = 5.14022004650141332919087246e-05
relative error = 0.0041159494365020751487291603902226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.249514542934825658106372752177
y[1] (numeric) = 1.2494626853712989100646696965439
absolute error = 5.18575635267480417030556331e-05
relative error = 0.0041502168838264508494198235948361 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.2501758050310335418501726369398
y[1] (numeric) = 1.2501234887846731879439996494641
absolute error = 5.23162463603539061729874757e-05
relative error = 0.0041847111542088468177991359246566 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.2508378169513739092129327692739
y[1] (numeric) = 1.2507850386833778830998693631731
absolute error = 5.27782679960261130634061008e-05
relative error = 0.0042194333494537972187493669261109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.2515005780338348950219439758613
y[1] (numeric) = 1.2514473343862913867530964217316
absolute error = 5.32436475435082688475541297e-05
relative error = 0.0042543845746484986675645013112128 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.2521640876156554720463088117698
y[1] (numeric) = 1.2521103752114631708463353171973
absolute error = 5.37124041923011999734945725e-05
relative error = 0.0042895659381654388997138251645967 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.2528283450333261137579135612673
y[1] (numeric) = 1.2527741604761142426086748476869
absolute error = 5.41845572118711492387135804e-05
relative error = 0.0043249785516650169634037402386786 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.2534933496225894578408994734763
y[1] (numeric) = 1.2534386894966375996725831910583
absolute error = 5.46601259518581683162824180e-05
relative error = 0.0043606235300981549860430590127126 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.2541591007184409704489697234547
y[1] (numeric) = 1.2541039615885986857428972889522
absolute error = 5.51391298422847060724345025e-05
relative error = 0.0043965019917089015657896025855524 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.2548255976551296112098678414497
y[1] (numeric) = 1.2547699760667358468175528078784
absolute error = 5.56215883937643923150335713e-05
relative error = 0.0044326150580370268394266378349008 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.2554928397661584989763626059028
y[1] (numeric) = 1.2554367322449607879597505761792
absolute error = 5.61075211977110166120297236e-05
relative error = 0.0044689638539206092778865604906172 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.2561608263842855783230736492765
y[1] (numeric) = 1.2561042294363590306212550280538
absolute error = 5.65969479265477018186212227e-05
relative error = 0.0045055495074986142608062652904315 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 1.2568295568415242867884712799312
y[1] (numeric) = 1.2567724669531903705165198183789
absolute error = 5.70898883339162719514615523e-05
relative error = 0.0045423731502134644815638533669968 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 1.2574990304691442228613832781104
y[1] (numeric) = 1.2574414441068893360473354048188
absolute error = 5.75863622548868140478732916e-05
relative error = 0.0045794359168136022343097199039954 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.2581692465976718147113406795812
y[1] (numeric) = 1.2581111602080656472776930266781
absolute error = 5.80863896061674336476529031e-05
relative error = 0.004616738945356043634566650833736 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.6MB, time=7.24
x[1] = 0.736
y[1] (analytic) = 1.2588402045568909896620938166407
y[1] (numeric) = 1.2587816145665046754585591431128
absolute error = 5.85899903863142035346735279e-05
relative error = 0.0046542833772089248250333465991025 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.2595119036758438444076291430284
y[1] (numeric) = 1.259452806491167903102254026684
absolute error = 5.90971846759413053751163444e-05
relative error = 0.0046920703570540402182837924037226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.2601843432828313159700166267826
y[1] (numeric) = 1.2601247352901933846061278418099
absolute error = 5.96079926379313638887849727e-05
relative error = 0.0047301010328893728281111179106562 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.2608575227054138533984167532507
y[1] (numeric) = 1.2607974002708962074252271714475
absolute error = 6.01224345176459731895818032e-05
relative error = 0.0047683765560316167413190449752942 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.2615314412704120902085754393012
y[1] (numeric) = 1.2614708007397689537936445893168
absolute error = 6.06405306431364149308499844e-05
relative error = 0.0048068980811186917818167185721911 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.2622060983039075175621344192991
y[1] (numeric) = 1.2621449360024821629942435091659
absolute error = 6.11623014253545678909101332e-05
relative error = 0.0048456667661122504189236641433317 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.2628814931312431581850839235906
y[1] (numeric) = 1.2628198053638847941764501769654
absolute error = 6.16877673583640086337466252e-05
relative error = 0.0048846837723001769718408233354165 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.2635576250770242410246837310994
y[1] (numeric) = 1.2634954081280046897218043065186
absolute error = 6.22169490195513028794245808e-05
relative error = 0.004923950264299079162291099027838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 1.2642344934651188766441779391716
y[1] (numeric) = 1.2641717435980490391569594937732
absolute error = 6.27498670698374872184453984e-05
relative error = 0.0049634674100567720673786003974161 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.2649120976186587333546280560096
y[1] (numeric) = 1.2648488110764048436138241801307
absolute error = 6.32865422538897408038758789e-05
relative error = 0.005003236380854754524759827644519 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.2655904368600397140831882839174
y[1] (numeric) = 1.2655266098646393808365335702617
absolute error = 6.38269954003332466547136557e-05
relative error = 0.005043258351310678042262385185873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.266269510510922633977146125141
y[1] (numeric) = 1.2662051392635006707349425453563
absolute error = 6.43712474219632422035797847e-05
relative error = 0.0050835344993808082641274707814242 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.2669493178922338987430507063167
y[1] (numeric) = 1.2668843985729179414843292483652
absolute error = 6.49193193159572587214579515e-05
relative error = 0.0051240660063624790460913653142776 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.2676298583241661837202504824584
y[1] (numeric) = 1.2675643870920020961709986536219
absolute error = 6.54712321640875492518288365e-05
relative error = 0.005164854056896539191558454982413 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.2683111311261791136881612469999
y[1] (numeric) = 1.2682451041190461799834750692753
absolute error = 6.60270071329337046861777246e-05
relative error = 0.0052058998389697919011539627961964 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 1.2689931356169999434065846406836
y[1] (numeric) = 1.2689265489515258479489721572123
absolute error = 6.65866654740954576124834713e-05
relative error = 0.0052472045439174269879785605834885 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.2696758711146242388883966190315
y[1] (numeric) = 1.2696087208860998332148286916036
absolute error = 6.71502285244056735679274279e-05
relative error = 0.0052887693664254459109193849086551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=148.7MB, alloc=4.6MB, time=7.43
x[1] = 0.753
y[1] (analytic) = 1.270359336936316559403924605769
y[1] (numeric) = 1.2702916192186104158745979138717
absolute error = 6.77177177061435293266918973e-05
relative error = 0.0053305955045330796784027011520799 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.2710435323986111402163313278786
y[1] (numeric) = 1.2709752432440838923384779787492
absolute error = 6.82891545272478778533491294e-05
relative error = 0.005372684159635199675002558539351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.2717284568173125760473225969591
y[1] (numeric) = 1.2716595922567310452477706231775
absolute error = 6.88645605815307995519737816e-05
relative error = 0.0054150365364847214633472657661553 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.2724141095074965052724955712377
y[1] (numeric) = 1.2723446655499476139330548270835
absolute error = 6.94439575488913394407441542e-05
relative error = 0.0054576538431950016137914009612043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 1.2731004897835102948456433029448
y[1] (numeric) = 1.2730304624163147654157618725692
absolute error = 7.00273671955294298814303756e-05
relative error = 0.0055005372912422276143453619031107 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.2737875969589737259513306468032
y[1] (numeric) = 1.2737169821475995659528378457553
absolute error = 7.06148113741599984928010479e-05
relative error = 0.0055436880954678009133771716748635 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.274475430346779680385055877114
y[1] (numeric) = 1.274404224034755453124179263436
absolute error = 7.12063120242272608766136780e-05
relative error = 0.0055871074740807131476223917722238 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.275163989259094827660311633333
y[1] (numeric) = 1.2750921873679227084625271448263
absolute error = 7.18018911721191977844885067e-05
relative error = 0.0056307966486599156080575684463225 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.2758532730073603128418580871366
y[1] (numeric) = 1.2757808714364289306255044870193
absolute error = 7.24015709313822163536001173e-05
relative error = 0.0056747568441566819962106592736985 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.2765432809022924451045204977583
y[1] (numeric) = 1.2764702755287895091094817413144
absolute error = 7.30053735029359950387564439e-05
relative error = 0.0057189892888969645234983645128464 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.2772340122538833870168225968583
y[1] (numeric) = 1.2771603989327080985049545263331
absolute error = 7.36133211752885118680705252e-05
relative error = 0.0057634952145837434061952329158664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.277925466371401844548766519348
y[1] (numeric) = 1.2778512409350770932931174528044
absolute error = 7.42254363247512556490665436e-05
relative error = 0.0058082758562993698086528327090666 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.2786176425633937578030692724491
y[1] (numeric) = 1.2785428008219781031833175740788
absolute error = 7.48417414156546197516983703e-05
relative error = 0.0058533324525079022873991867336326 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.2793105401376829924691650118068
y[1] (numeric) = 1.2792350778786824289910706158157
absolute error = 7.54622590005634780943959911e-05
relative error = 0.0058986662450574367887590750112682 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.2800041584013720319992816707128
y[1] (numeric) = 1.2799280713896515390563227778886
absolute error = 7.60870117204929429588928242e-05
relative error = 0.0059442784791824302526447188620153 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 1.2806984966608426705058997664195
y[1] (numeric) = 1.280621780638537546201640541362
absolute error = 7.67160223051243042592250575e-05
relative error = 0.0059901704035060178751737877642949 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.2813935542217567063799004861449
y[1] (numeric) = 1.2813162049081836852300105534152
absolute error = 7.73493135730211498899327297e-05
relative error = 0.0060363432700423240827776233358453 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=152.5MB, alloc=4.6MB, time=7.62
x[1] = 0.77
y[1] (analytic) = 1.2820893303890566366287094346757
y[1] (numeric) = 1.2820113434806247909619313033221
absolute error = 7.79869084318456667781313536e-05
relative error = 0.0060827983341987672704670637173658 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.2827858244669663519337417054856
y[1] (numeric) = 1.2827071956370877768114779430416
absolute error = 7.86288298785751222637624440e-05
relative error = 0.0061295368547783583569262870866261 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.2834830357589918324264532179796
y[1] (numeric) = 1.2834037606579921139010212466304
absolute error = 7.92751009997185254319713492e-05
relative error = 0.0061765600939819932091066835106905 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.2841809635679218441823025448716
y[1] (numeric) = 1.2841010378229503107142813435625
absolute error = 7.99257449715334680212013091e-05
relative error = 0.0062238693174107389889929208539873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.2848796071958286364319267357915
y[1] (numeric) = 1.2847990264107683932873965021211
absolute error = 8.05807850602431445302336704e-05
relative error = 0.0062714657940681144752121025313833 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.2855789659440686394888339260045
y[1] (numeric) = 1.2854977256994463859376868803271
absolute error = 8.12402446222535511470456774e-05
relative error = 0.0063193507963623644121542321276313 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 1.2862790391132831633929148026071
y[1] (numeric) = 1.2861971349661787925297928033773
absolute error = 8.19041471043708631219992298e-05
relative error = 0.006367525600108727939268112469701 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.2869798260033990972690742847478
y[1] (numeric) = 1.2868972534873550782788667682888
absolute error = 8.25725160440189902075164590e-05
relative error = 0.006415991484531701153191324638959 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.2876813259136296094002840592981
y[1] (numeric) = 1.2875980805385601520904980183853
absolute error = 8.32453750694573097860409128e-05
relative error = 0.0064647497322672938553660647724743 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.28838353814247484801435589898
y[1] (numeric) = 1.2882996153945748494370481724106
absolute error = 8.39227478999985773077265694e-05
relative error = 0.0065138016293652805377843742526419 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.2890864619877226427837349762354
y[1] (numeric) = 1.2890018573293764157700760354206
absolute error = 8.46046583462270136589408148e-05
relative error = 0.0065631484652914456594966910188718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 1.289790096746449207037611673102
y[1] (numeric) = 1.2897048056161389904685293611875
absolute error = 8.52911303102165690823119145e-05
relative error = 0.0066127915329298232665066861644111 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.2904944417150198406856496750424
y[1] (numeric) = 1.2904084595272340913223809786428
absolute error = 8.59821877857493632686963996e-05
relative error = 0.0066627321285849310076630411813071 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.2911994961890896338526274250576
y[1] (numeric) = 1.2911128183342310995513863378964
absolute error = 8.66778548585343012410871612e-05
relative error = 0.0067129715519839985991451763656529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.2919052594636041712232893035015
y[1] (numeric) = 1.291817881307897745358639174596
absolute error = 8.73781557064258646501289055e-05
relative error = 0.0067635111062791907901249697792642 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 1.2926117308328002370967021888034
y[1] (numeric) = 1.2925236477182005940186016348302
absolute error = 8.80831145996430781005539732e-05
relative error = 0.0068143520980498248821702191710435 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 1.293318909590206521149412344802
y[1] (numeric) = 1.2932301168343055324992848464366
absolute error = 8.87927559009886501274983654e-05
relative error = 0.0068654958373045828549380057386532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=156.4MB, alloc=4.6MB, time=7.81
x[1] = 0.787
y[1] (analytic) = 1.2940267950286443249066968715924
y[1] (numeric) = 1.293937287924578256618255566448
absolute error = 8.95071040660682884413051444e-05
relative error = 0.0069169436374837181506872283239541 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 1.2947353864402282689212032486917
y[1] (numeric) = 1.2946451602565847587321441784999
absolute error = 9.02261836435101890590701918e-05
relative error = 0.0069686968154612571701193993390595 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 1.2954446831163670006582697919461
y[1] (numeric) = 1.2953537330970918159593289583267
absolute error = 9.09500192751846989408336194e-05
relative error = 0.0070207566915471955320353400152669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 1.296154684347763903087219138915
y[1] (numeric) = 1.2960630057120674789354711699969
absolute error = 9.16786356964241517479689181e-05
relative error = 0.007073124589489689149272690432262 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 1.2968653894244178039779161714986
y[1] (numeric) = 1.2967729773666815611015752002757
absolute error = 9.24120577362428763409712229e-05
relative error = 0.0071258018364772401733651709825464 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 1.2975767976356236859018810793109
y[1] (numeric) = 1.2974836473253061285242475834612
absolute error = 9.31503103175573776334958497e-05
relative error = 0.0071787897631408778603393047190475 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 1.2982889082699733969372475627432
y[1] (numeric) = 1.2981950148515159902478284142119
absolute error = 9.38934184574066894191485313e-05
relative error = 0.0072320897035563344100378448306146 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 1.2990017206153563620768554708199
y[1] (numeric) = 1.2989070792080891891780682912758
absolute error = 9.46414072671728987871795441e-05
relative error = 0.0072857029952462158313314578273318 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 1.2997152339589602953387664658126
y[1] (numeric) = 1.2996198396570074934970235806406
absolute error = 9.53943019528018417428851720e-05
relative error = 0.0073396309791821678855513004351669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 1.3004294475872719125784906041565
y[1] (numeric) = 1.3003332954594568886088424324501
absolute error = 9.61521278150239696481717064e-05
relative error = 0.0073938749997870371604450068395644 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 1.3011443607860776450022110215024
y[1] (numeric) = 1.3010474458758280696161136320799
absolute error = 9.69149102495753860973894225e-05
relative error = 0.007448436404937027326927281752578 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 1.3018599728404643533802932087375
y[1] (numeric) = 1.3017622901657169343264500120271
absolute error = 9.76826747474190538431967104e-05
relative error = 0.0075033165459638506308637840450514 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 1.3025762830348200429603646655274
y[1] (numeric) = 1.3024778275879250767889777977534
absolute error = 9.84554468949661713868677740e-05
relative error = 0.0075585167776568746720932949193512 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 1.3032932906528345790792500183577
y[1] (numeric) = 1.3031940574004602813604029073225
absolute error = 9.92332523742977188471110352e-05
relative error = 0.0076140384582652645228583029053287 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 1.3040109949775004034730459911998
y[1] (numeric) = 1.3039109788605370173003248715936
absolute error = 0.0001000161169633861727211196062
relative error = 0.0076698829495001202377781157394066 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 1.3047293952911132512846199187868
y[1] (numeric) = 1.3046285912245769338954686888744
absolute error = 0.0001008040665363173891512299124
relative error = 0.0077260516165366098074614354916026 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 1.3054484908752728687678147950589
y[1] (numeric) = 1.3053468937482093561125045752961
absolute error = 0.0001015971270635126553102197628
relative error = 0.0077825458280160976078170176953235 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=160.2MB, alloc=4.6MB, time=8.00
x[1] = 0.804
y[1] (analytic) = 1.3061682810108837316876431526351
y[1] (numeric) = 1.3060658856862717807791252197559
absolute error = 0.0001023953246119509085179328792
relative error = 0.0078393669560482683970815876330639 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 1.3068887649781557644157513731752
y[1] (numeric) = 1.3067855662928103732930498000709
absolute error = 0.0001031986853453911227015731043
relative error = 0.0078965163762132469125436164073021 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 1.3076099420566050597204353332294
y[1] (numeric) = 1.3075059348210804648586236650097
absolute error = 0.0001040072355245948618116682197
relative error = 0.0079539954675637131188998760514672 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 1.3083318115250545992504875956188
y[1] (numeric) = 1.3082269905235470502506822351103
absolute error = 0.0001048210015075489998053605085
relative error = 0.0080118056126270131601389054616233 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 1.3090543726616349747121556625597
y[1] (numeric) = 1.3089487326518852861053473236546
absolute error = 0.0001056400097496886068083389051
relative error = 0.0080699481974072660668016376734072 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 1.3097776247437851097384901136346
y[1] (numeric) = 1.3096711604569809897374237278554
absolute error = 0.0001064642868041200010663857792
relative error = 0.00812842461138746627042447280645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 1.3105015670482529824503607593199
y[1] (numeric) = 1.310394273188931138484063589216
absolute error = 0.0001072938593218439662971701039
relative error = 0.008187236247531581976924039410375 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 1.311226198851096348708418249117
y[1] (numeric) = 1.3111180700970443695743656711504
absolute error = 0.0001081287540519791340525779666
relative error = 0.0082463845022866494506357799241838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 1.3119515194276834660552778823829
y[1] (numeric) = 1.3118425504298414805245763513007
absolute error = 0.0001089689978419855307015310822
relative error = 0.0083058707755848632606703318095096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 1.3126775280526938183472016797382
y[1] (numeric) = 1.3125677134350559300585587755594
absolute error = 0.0001098146176378882886429041788
relative error = 0.0083656964708456625412024653514956 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 1.3134042240001188410745540834314
y[1] (numeric) = 1.313293558359634339553196270598
absolute error = 0.0001106656404845015213578128334
relative error = 0.008425862994977813317257090448476 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 1.3141316065432626473703059662622
y[1] (numeric) = 1.3140200844497369950083957617193
absolute error = 0.0001115220935256523619102045429
relative error = 0.0084863717583814869475055675367833 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 1.314859674954742754705860940622
y[1] (numeric) = 1.3147472909507383495413565930895
absolute error = 0.0001123840040044051645043475325
relative error = 0.0085472241749503347355332620502418 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 1.315588428506490812273477271886
y[1] (numeric) = 1.3154751771072275264047697978675
absolute error = 0.0001132513992632858687074740185
relative error = 0.0086084216620735587609859759256185 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 1.316317866469753329054558013794
y[1] (numeric) = 1.3162037421630088225286125164352
absolute error = 0.0001141243067445065259454973588
relative error = 0.0086699656406379789819485831277034 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 1.3170479881150924025730812975917
y[1] (numeric) = 1.31693298536110221258520191184
absolute error = 0.0001150027539901899878793857517
relative error = 0.0087318575350300966598538989276102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 1.3177787927123864483334420215631
y[1] (numeric) = 1.3176629059437438535771725826938
absolute error = 0.0001158867686425947562694388693
relative error = 0.0087940987731381541581635329605826 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=164.0MB, alloc=4.6MB, time=8.19
x[1] = 0.821
y[1] (analytic) = 1.3185102795308309299419755031717
y[1] (numeric) = 1.3183935031523865899480411251291
absolute error = 0.0001167763784443399939343780426
relative error = 0.0088566907863541911660052235970424 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 1.3192424478389390899114329723498
y[1] (numeric) = 1.3191247762277004592150211469927
absolute error = 0.0001176716112386306964118253571
relative error = 0.0089196350095760973978929354702481 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 1.3199752969045426811476781015192
y[1] (numeric) = 1.3198567244095731981237516892634
absolute error = 0.0001185724949694830239264122558
relative error = 0.008982932881209661820596831139272 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 1.3207088259947926991178730857087
y[1] (numeric) = 1.320589346937110749324601661709
absolute error = 0.0001194790576819497932714239997
relative error = 0.0090465858431706184581701123470834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 1.3214430343761601146994221046441
y[1] (numeric) = 1.3213226430486377685702125520531
absolute error = 0.000120391327522346129209552591
relative error = 0.0091105953408866888260786742338043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 1.3221779213144366077089393179268
y[1] (numeric) = 1.3220566119816981324339413204011
absolute error = 0.0001213093327384752749979975257
relative error = 0.0091749628232996210453175365784759 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 1.3229134860747353011105078643946
y[1] (numeric) = 1.3227912529730554465488650433805
absolute error = 0.0001222331016798545616428210141
relative error = 0.0092396897428672256873351189905922 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 1.3236497279214914959024956574681
y[1] (numeric) = 1.3235265652586935543670085253813
absolute error = 0.0001231626627979415354871320868
relative error = 0.0093047775555654084005226207288844 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 1.3243866461184634066821930897261
y[1] (numeric) = 1.324262548073817046438455747438
absolute error = 0.0001240980446463602437373422881
relative error = 0.0093702277208901993689610593071342 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 1.3251242399287328978875370821356
y[1] (numeric) = 1.324999200652851770210005677678
absolute error = 0.0001250392758811276775314044576
relative error = 0.0094360417018597796540529249160699 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 1.3258625086147062207151852362717
y[1] (numeric) = 1.3257365222294453403430326208695
absolute error = 0.0001259863852608803721526154022
relative error = 0.0095022209650165044695989279560415 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 1.3266014514381147507142031715169
y[1] (numeric) = 1.3264745120364676495502109384379
absolute error = 0.000126939401647101163992233079
relative error = 0.0095687669804289234408129646234124 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 1.3273410676600157260546274536119
y[1] (numeric) = 1.3272131693060113799507636243811
absolute error = 0.0001278983540043461038638292308
relative error = 0.0096356812216937978977002083383102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 1.3280813565407929864701658460576
y[1] (numeric) = 1.3279524932693925149438938768037
absolute error = 0.0001288632714004715262719692539
relative error = 0.0097029651659381152531541627367924 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 1.3288223173401577128742959417292
y[1] (numeric) = 1.3286924831571508516000584593061
absolute error = 0.0001298341830068612742374824231
relative error = 0.0097706202938211005160585930692724 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 1.3295639493171491676490225586661
y[1] (numeric) = 1.3294331381990505135697413012082
absolute error = 0.0001308111180986540792812574579
relative error = 0.0098386480895362249896094964450143 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 1.3303062517301354356055536113409
y[1] (numeric) = 1.3301744576240804645093854405589
absolute error = 0.000131794106054971096168170782
relative error = 0.0099070500408132122050006858330586 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=167.8MB, alloc=4.6MB, time=8.38
x[1] = 0.838
y[1] (analytic) = 1.3310492238368141656161534967937
y[1] (numeric) = 1.3309164406604550220241410690821
absolute error = 0.0001327831763591435920124277116
relative error = 0.0099758276389200411405441572825125 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 1.3317928648942133129164323638407
y[1] (numeric) = 1.3316590865356143721270870936365
absolute error = 0.0001337783585989407893452702042
relative error = 0.010044982378664946776223192977637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 1.3325371741586918820773289631291
y[1] (numeric) = 1.3324023944762250842145832844239
absolute error = 0.0001347796824667978627456787052
relative error = 0.010114515758398418033602132919014 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 1.3332821508859406706460441061175
y[1] (numeric) = 1.3331463637081806265574097360625
absolute error = 0.000135787177760044088634370055
relative error = 0.01018442928001519315094193465288 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 1.3340277943309830134551810921098
y[1] (numeric) = 1.3338909934566018823073500237582
absolute error = 0.0001368008743811311478310683516
relative error = 0.010254724448956252543295041208167 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 1.334774103748175527599348794266
y[1] (numeric) = 1.3346362829458376660188740931457
absolute error = 0.0001378208023378615804747011203
relative error = 0.010325402774210809197276702143731 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 1.3355210783912088580784824280462
y[1] (numeric) = 1.3353822313994652406855765789456
absolute error = 0.0001388469917436173929058491006
relative error = 0.010396465768318296650132748238362 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 1.3362687175131084241071363588314
y[1] (numeric) = 1.336128838040290835291025904383
absolute error = 0.0001398794728175888161104544484
relative error = 0.010467914947370354602645917477912 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 1.3370170203662351660890026394896
y[1] (numeric) = 1.3368761020903501628736791703444
absolute error = 0.0001409182758850032153234691452
relative error = 0.010539751831012812215344175317724 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 1.3377659862022862932559083034306
y[1] (numeric) = 1.3376240227709089391055175005108
absolute error = 0.0001419634313773541503908029198
relative error = 0.010611977942447669137395075294141 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 1.3385156142722960319705437742155
y[1] (numeric) = 1.3383725993024634013840561661946
absolute error = 0.0001430149698326305864876080209
relative error = 0.01068459480843507431749007528635 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 1.3392659038266363746921740890535
y[1] (numeric) = 1.3391218309047408284373834723312
absolute error = 0.0001440729218955462547906167223
relative error = 0.010757603959295302645941867852214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 1.3400168541150178296045839705385
y[1] (numeric) = 1.3398717167967000604418820440262
absolute error = 0.0001451373183177691627019265123
relative error = 0.010831006928910729477136209673914 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 1.3407684643864901709055071187424
y[1] (numeric) = 1.3406222561965320196522858112436
absolute error = 0.0001462081899581512532213074988
relative error = 0.010904805254727803081397452361833 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 1.3415207338894431897567894342973
y[1] (numeric) = 1.341373448321660231543725647633
absolute error = 0.0001472855677829582130637866643
relative error = 0.010979000477759015075243993957164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 1.3422736618716074458945352223685
y[1] (numeric) = 1.3421252923887413464654162781399
absolute error = 0.0001483694828660994291189442286
relative error = 0.011053594142584868878926195592294 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 1.3430272475800550198984847674316
y[1] (numeric) = 1.3428777876136656618056367289208
absolute error = 0.0001494599663893580928480385108
relative error = 0.011128587797355846250054948374933 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=171.6MB, alloc=4.6MB, time=8.57
x[1] = 0.855
y[1] (analytic) = 1.3437814902612002661198710095412
y[1] (numeric) = 1.3436309332115576446676562521913
absolute error = 0.0001505570496426214522147573499
relative error = 0.011203982993794371942044041652253 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 1.3445363891608005662670023942965
y[1] (numeric) = 1.3443847283967764550562573179787
absolute error = 0.0001516607640241112107450763178
relative error = 0.01127978128719677653600378155984 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 1.3452919435239570836478183109831
y[1] (numeric) = 1.3451391723829164695745069243209
absolute error = 0.0001527711410406140733113866622
relative error = 0.011355984236435257494636948001968 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 1.3460481525951155180686628763995
y[1] (numeric) = 1.3458942643828078056304271372615
absolute error = 0.000153888212307712438235739138
relative error = 0.011432593403959838486601166196637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 1.3468050156180668613885221656564
y[1] (numeric) = 1.3466500036085168461532154320272
absolute error = 0.0001550120095500152353067336292
relative error = 0.011509610355800327029714114116715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 1.3475625318359481537279693357761
y[1] (numeric) = 1.3474063892713467648186650670445
absolute error = 0.0001561425646013889093042687316
relative error = 0.01158703666156827050128969782769 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 1.3483207004912432403320614332074
y[1] (numeric) = 1.3481634205818380517834353829586
absolute error = 0.0001572799094051885486260502488
relative error = 0.01166487389445891056380441008151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 1.3490795208257835290864310224247
y[1] (numeric) = 1.3489210967497690399278215795535
absolute error = 0.0001584240760144891586094428712
relative error = 0.011743123631253136054003553144961 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 1.3498389920807487486858151195816
y[1] (numeric) = 1.3496794169841564316066731844434
absolute error = 0.0001595750965923170791419351382
relative error = 0.011821787452319434383466861077448 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 1.3505991134966677074542632627533
y[1] (numeric) = 1.3504383804932558259081100886116
absolute error = 0.0001607330034118815461531741417
relative error = 0.011900866941615841498562308512002 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 1.3513598843134190528162658986232
y[1] (numeric) = 1.3511979864845622464196846853113
absolute error = 0.0001618978288568063965812133119
relative error = 0.011980363686691890447625550159714 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 1.3521213037702320314180436145485
y[1] (numeric) = 1.3519582341648106695016383105155
absolute error = 0.000163069605421361916405304033
relative error = 0.012060279278690558603110505525756 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 1.3528833711056872498982370947791
y[1] (numeric) = 1.352719122739976553066899845013
absolute error = 0.0001642483657106968313372497661
relative error = 0.012140615312350213586364094488156 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 1.3536460855577174363072370302028
y[1] (numeric) = 1.3534806514152763658674740003872
absolute error = 0.0001654341424410704397630298156
relative error = 0.012221373386006557942585049711099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 1.3544094463636082021743925623504
y[1] (numeric) = 1.354242819395168117286866473495
absolute error = 0.0001666269684400848875260888554
relative error = 0.012302555101594572613433088498592 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 1.3551734527599988052223361945172
y[1] (numeric) = 1.355005625883351887638192816673
absolute error = 0.0001678268766469175841433778442
relative error = 0.012384162064650459254660528265734 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 1.3559381039828829127276624557362
y[1] (numeric) = 1.3557690700827703589676175337487
absolute error = 0.0001690339001125537600449219875
relative error = 0.012466195884313581446043682708056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
memory used=175.4MB, alloc=4.6MB, time=8.76
y[1] (analytic) = 1.3567033992676093655271969569926
y[1] (numeric) = 1.3565331511956093463627695750157
absolute error = 0.0001702480720000191644273819769
relative error = 0.012548658173328404840796089824474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 1.3574693378488829426690918334692
y[1] (numeric) = 1.357297868423298329765780067654
absolute error = 0.0001714694255846129033117658152
relative error = 0.012631550548046436301549802891771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 1.3582359189607651267079829217956
y[1] (numeric) = 1.3580632209665109862905877816306
absolute error = 0.000172697994254140417395140165
relative error = 0.012714874628428162069894632323565 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 1.359003141836674869643443377204
y[1] (numeric) = 1.3588292080251657230441574949074
absolute error = 0.0001739338115091465992858822966
relative error = 0.012798632038044985016368364510772 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 1.3597710057093893595009677922045
y[1] (numeric) = 1.3595958287984262104512560858129
absolute error = 0.0001751769109631490497117063916
relative error = 0.012882824404081161017693613243806 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 1.3605395098110447875547202358586
y[1] (numeric) = 1.3603630824847019160824308446994
absolute error = 0.0001764273263428714722893911592
relative error = 0.012967453357335734507959085996405 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 1.3613086533731371161912789909656
y[1] (numeric) = 1.3611309682816486389848341615083
absolute error = 0.0001776850914884772064448294573
relative error = 0.01305252053222447325034467973795 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 1.3620784356265228474136101254846
y[1] (numeric) = 1.3618994853861690445155384106074
absolute error = 0.0001789502403538028980717148772
relative error = 0.013138027566781802375890966247585 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 1.3628488558014197919845013942779
y[1] (numeric) = 1.3626686329944131996769845192391
absolute error = 0.0001802228070065923075168750388
relative error = 0.013223976102662737735714291772573 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 1.3636199131274078392086873278103
y[1] (numeric) = 1.3634384103017791089542073711352
absolute error = 0.0001815028256287302544799566751
relative error = 0.01331036778514481861296890930869 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 1.3643916068334297273528957257406
y[1] (numeric) = 1.3642088165029132506534808623034
absolute error = 0.0001827903305164766994148634372
relative error = 0.013397204263130039840757289391215 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 1.3651639361477918147030451354242
y[1] (numeric) = 1.3649798507917111137420250916838
absolute error = 0.0001840853560807009610200437404
relative error = 0.013484487189146783372089025571178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 1.3659369002981648512578222581931
y[1] (numeric) = 1.3657515123613177351884178353013
absolute error = 0.0001853879368471160694044228918
relative error = 0.01357221821935174934788757047935 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 1.3667104985115847510578675899006
y[1] (numeric) = 1.3665238004041282378033521187071
absolute error = 0.0001866981074565132545154711935
relative error = 0.013660399013531886708942415023033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 1.3674847300144533651497969666091
y[1] (numeric) = 1.367296714111788368580381368908
absolute error = 0.0001880159026649965694155977011
relative error = 0.013749031235106323397602263852185 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 1.3682595940325392551842860514642
y[1] (numeric) = 1.3680702526751950375362932936295
absolute error = 0.0001893413573442176479927578347
relative error = 0.013838116551128296194902271917481 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 1.3690350897909784676474441647341
y[1] (numeric) = 1.3688444152844968570507533026404
absolute error = 0.0001906745064816105966908620937
relative error = 0.013927656632287080238715497177356 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 1.369811216514275308724703225707
y[1] (numeric) = 1.3696192011290946817048579529913
absolute error = 0.0001920153851806270198452727157
memory used=179.2MB, alloc=4.6MB, time=8.96
relative error = 0.014017653152909918268415400242642 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 1.3705879734263031197964469426198
y[1] (numeric) = 1.3703946093976421486182385673837
absolute error = 0.0001933640286609711782083752361
relative error = 0.014108107790963949641432489459788 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 1.3713653597503050535646047550548
y[1] (numeric) = 1.3711706392780462182843548424882
absolute error = 0.0001947204722588352802499125666
relative error = 0.014199022228058139166984077944865 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 1.3721433747088948508094344022757
y[1] (numeric) = 1.3719472899574677159036179318744
absolute error = 0.0001960847514271349058164704013
relative error = 0.014290398149445205802151593157995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 1.3729220175240576177757163607833
y[1] (numeric) = 1.3727245606223218732139821562982
absolute error = 0.0001974569017357445617342044851
relative error = 0.014382237244023551255374967165651 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 1.373701287417150604187582764963
y[1] (numeric) = 1.373502450458278870818644162418
absolute error = 0.000198836958871733368938602545
relative error = 0.014474541204339188542328343991729 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 1.3744811836089039818912027960585
y[1] (numeric) = 1.3742809586502643810104880195734
absolute error = 0.0002002249586396008807147764851
relative error = 0.014567311726587670539035675857247 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 1.3752617053194216241245458968532
y[1] (numeric) = 1.3750600843824601110929144130686
absolute error = 0.0002016209369615130316314837846
relative error = 0.0146605505106160185769787497675 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 1.3760428517681818854134435423582
y[1] (numeric) = 1.3758398268383043471966917614486
absolute error = 0.0002030249298775382167517809096
relative error = 0.014754259259924651124843796225395 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 1.3768246221740383820931696705131
y[1] (numeric) = 1.3766201852004924985924667545447
absolute error = 0.0002044369735458835007029159684
relative error = 0.01484843968166931260144609062854 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 1.3776070157552207734547592513822
y[1] (numeric) = 1.3774011586509776424985714785967
absolute error = 0.0002058571042431309561877727855
relative error = 0.014943093486663002364264870345938 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 1.3783900317293355435152838485929
y[1] (numeric) = 1.3781827463709710693837639645303
absolute error = 0.0002072853583644741315198840626
relative error = 0.015038222389377903917913464773914 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 1.3791736693133667834113024028072
y[1] (numeric) = 1.3789649475409428287645386654838
absolute error = 0.0002087217724239546467637373234
relative error = 0.015133828107947314386761777593552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 1.3799579277236769744147048438388
y[1] (numeric) = 1.3797477613406222754966430399327
absolute error = 0.0002101663830546989180618039061
relative error = 0.015229912364167574295820176832116 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 1.380742806176007771570165515639
y[1] (numeric) = 1.380531186948998616560436087261
absolute error = 0.000211619227009155009729428378
relative error = 0.015326476883499997703885446085333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 1.3815283038854807879534227767624
y[1] (numeric) = 1.3813152235443214583397243533703
absolute error = 0.0002130803411593296136984233921
relative error = 0.015423523395072802732840735309234 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 1.3823144200665983795496005180982
y[1] (numeric) = 1.3820998703041013543937105949004
absolute error = 0.0002145497624970251558899231978
relative error = 0.015521053631683042536892429283818 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 1.3831011539332444307507867196122
y[1] (numeric) = 1.382885126405110353721689961865
absolute error = 0.0002160275281340770290967577472
relative error = 0.015619069329798536755417531956422 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.6MB, time=9.15
NO POLE
x[1] = 0.907
y[1] (analytic) = 1.3838885046986851404720835485838
y[1] (numeric) = 1.3836709910233825495201282299759
absolute error = 0.0002175136753025909519553186079
relative error = 0.015717572229559803492985552017331 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 1.3846764715755698088853428833566
y[1] (numeric) = 1.3844574633342146284317562856449
absolute error = 0.0002190082413551804535865977117
relative error = 0.015816564074781991870008976287978 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 1.3854650537759316247698005289301
y[1] (numeric) = 1.3852445425121664202863147386111
absolute error = 0.000220511263765204483485790319
relative error = 0.015916046612956815187366237918863 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 1.3862542505111884534788217738253
y[1] (numeric) = 1.3860322277310614483325822093431
absolute error = 0.0002220227801270051462395644822
relative error = 0.01601602159525448474823063384684 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 1.3870440609921436255219703215436
y[1] (numeric) = 1.3868205181639874799613205108142
absolute error = 0.0002235428281561455606498107294
relative error = 0.016116490776525644380227925381377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 1.387834484428986725761612014616
y[1] (numeric) = 1.3876094129832970779187696169389
absolute error = 0.0002250714456896478428423976771
relative error = 0.016217455915303305700934374494244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 1.3886255200312943832232641547054
y[1] (numeric) = 1.3883989113606081520103249828961
absolute error = 0.0002266086706862312129391718093
relative error = 0.01631891877380478416961573199463 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 1.3894171670080310615189006084766
y[1] (numeric) = 1.3891890124668045112940294557447
absolute error = 0.0002281545412265502248711527319
relative error = 0.016420881117933635967996208558269 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 1.390209424567549849882422275997
y[1] (numeric) = 1.3899797154720364167635116871646
absolute error = 0.0002297090955134331189105888324
relative error = 0.016523344717281595752734732164749 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 1.3910022919175932548165018862618
y[1] (numeric) = 1.3907710195457211345200026338267
absolute error = 0.0002312723718721202964992524351
relative error = 0.016626311345130515322173831219056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 1.3917957682652939923500114730661
y[1] (numeric) = 1.391562923856543489433061404814
absolute error = 0.0002328444087505029169500682521
relative error = 0.016729782778454303239814288327085 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 1.3925898528171757809052402738607
y[1] (numeric) = 1.3923554275724564192896413896773
absolute error = 0.0002344252447193616155988841834
relative error = 0.016833760797920865456856290876664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 1.3933845447791541347741101844421
y[1] (numeric) = 1.3931485298606815294311272751202
absolute error = 0.0002360149184726053429829093219
relative error = 0.016938247187894046976035167704491 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 1.3941798433565371582025952933256
y[1] (numeric) = 1.3939422298877096478779732329609
absolute error = 0.0002376134688275103246220603647
relative error = 0.017043243736435574598866951692415 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 1.3949757477540263400825514114488
y[1] (numeric) = 1.3947365268193013809415722369223
absolute error = 0.0002392209347249591409791745265
relative error = 0.017148752235307000798305952454717 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 1.3957722571757173492501609054418
y[1] (numeric) = 1.3955314198204876693229861409492
absolute error = 0.0002408373552296799271747644926
relative error = 0.017254774479971648758703267117493 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 1.3965693708251008303901975360864
y[1] (numeric) = 1.3963269080555703446981658271466
absolute error = 0.0002424627695304856920317089398
relative error = 0.017361312269596558624841706518793 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.6MB, time=9.34
NO POLE
x[1] = 0.924
y[1] (analytic) = 1.3973670879050632005453153977649
y[1] (numeric) = 1.3971229906881226867892904070758
absolute error = 0.0002440972169405137560249906891
relative error = 0.017468367407054435001708974466693 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 1.3981654076178874462295654496762
y[1] (numeric) = 1.3979196668809899809218541360352
absolute error = 0.000245740736897465307711313641
relative error = 0.017575941698925595746557115213003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 1.3989643291652539211453425253694
y[1] (numeric) = 1.398716935796290076067129376089
absolute error = 0.0002473933689638450782131492804
relative error = 0.01768403695549992209468224461699 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 1.3997638517482411445029651037137
y[1] (numeric) = 1.3995147965954139433696336199923
absolute error = 0.0002490551528272011333314837214
relative error = 0.017792654990778810160244409120664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 1.4005639745673265999420895217925
y[1] (numeric) = 1.4003132484390262351592282647949
absolute error = 0.0002507261283003647828612569976
relative error = 0.01790179762247712385333307964096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 1.4013646968223875350541597083728
y[1] (numeric) = 1.4011122904870658444474765007858
absolute error = 0.000252406335321690606683207587
relative error = 0.018011466672025149254369290151126 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 1.402166017712701761505092915567
y[1] (numeric) = 1.4019119218987464649078873585715
absolute error = 0.0002540958139552965972055569955
relative error = 0.018121663964570550486820778885353 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 1.4029679364369484557574013260696
y[1] (numeric) = 1.402712141832557151339672634458
absolute error = 0.0002557946043913044177286916116
relative error = 0.018232391328980327129091689466493 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 1.4037704521932089603909488139114
y[1] (numeric) = 1.4035129494462628806146430919341
absolute error = 0.0002575027469460797763057219773
relative error = 0.018343650597842773206333444630203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 1.4045735641789675860215415380431
y[1] (numeric) = 1.4043143438969051131068700149297
absolute error = 0.0002592202820624729146715231134
relative error = 0.018455443607469437802808323286285 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 1.4053772715911124138165504502244
y[1] (numeric) = 1.4051163243408023546047378666474
absolute error = 0.000260947250310059211812583577
relative error = 0.018567772197897087335322056828461 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 1.4061815736259360986067632016613
y[1] (numeric) = 1.4059188899335507187050134861419
absolute error = 0.0002626836923853799017497155194
relative error = 0.018680638212889669528126418592975 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 1.4069864694791366725936623366093
y[1] (numeric) = 1.4067220398300244896885569334438
absolute error = 0.0002644296491121829051054031655
relative error = 0.018794043499940279129577317371196 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 1.4077919583458183496513260657285
y[1] (numeric) = 1.407525773184376685877298772901
absolute error = 0.0002661851614416637740272928275
relative error = 0.018907989910273125410718325542745 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 1.4085980394204923302221473173594
y[1] (numeric) = 1.4083300891500396234721082635343
absolute error = 0.0002679502704527067500390538251
relative error = 0.019022479298845501485843882063246 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 1.409404711897077606805566171065
y[1] (numeric) = 1.4091349868797254808711766045787
absolute error = 0.0002697250173521259343895664863
relative error = 0.019137513524349755494980613677232 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 1.410211974968901770039010184776
y[1] (numeric) = 1.4099404655254268634685390640071
absolute error = 0.0002715094434749065704711207689
relative error = 0.019253094449215263688109321088207 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.6MB, time=9.53
NO POLE
x[1] = 0.941
y[1] (analytic) = 1.4110198278287018153702365346646
y[1] (numeric) = 1.410746524238417368932359497709
absolute error = 0.0002733035902844464378770369556
relative error = 0.019369223939610405450834184358675 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 1.4118282696686249503202692954725
y[1] (numeric) = 1.4115531621692521529626004471252
absolute error = 0.0002751074993727973576688483473
relative error = 0.019485903865444540311089659541372 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 1.4126372996802294023361245984231
y[1] (numeric) = 1.4123603784677684955277016835153
absolute error = 0.0002769212124609068084229149078
relative error = 0.019603136100369986966359371428119 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 1.41344691705448522723251581406
y[1] (numeric) = 1.4131681722830863675798897476669
absolute error = 0.0002787447713988596526260663931
relative error = 0.019720922521784004370765060031415 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 1.4142571209817751182217303183736
y[1] (numeric) = 1.4139765427636089982487407147348
absolute error = 0.0002805782181661199729896036388
relative error = 0.019839265010830774921267316657732 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 1.4150679106518952155308688124071
y[1] (numeric) = 1.4147854890570234425126180950326
absolute error = 0.0002824215948717730182507173745
relative error = 0.019958165452403389782103453826273 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 1.4158792852540559166056375781701
y[1] (numeric) = 1.4155950103103011493476074629837
absolute error = 0.0002842749437547672580301151864
relative error = 0.020077625735145836386471396929583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 1.4166912439768826868998834671338
y[1] (numeric) = 1.4164051056696985303535690880762
absolute error = 0.0002861383071841565463143790576
relative error = 0.020197647751454988154351969292967 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 1.4175037860084168712500608318425
y[1] (numeric) = 1.4172157742807575288569295235557
absolute error = 0.0002880117276593423931313082868
relative error = 0.020318233397482596465245371553359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 1.4183169105361165058338190262395
y[1] (numeric) = 1.4180270152883061894898327907332
absolute error = 0.0002898952478103163439862355063
relative error = 0.020439384573137284924481034925678 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 1.4191306167468571307118985161905
y[1] (numeric) = 1.4188388278364592282452714791793
absolute error = 0.0002917889103979024666270370112
relative error = 0.020561103182086545961643362322406 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 1.419944903826932602952523058373
y[1] (numeric) = 1.4196512110686186030078177657262
absolute error = 0.0002936927583139999447052926468
relative error = 0.020683391131758739799539164346702 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 1.4207597709620559103374748232099
y[1] (numeric) = 1.4204641641274740845595740380983
absolute error = 0.0002956068345818257779007851116
relative error = 0.020806250333345095832015855849006 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 1.4215752173373599856490387558386
y[1] (numeric) = 1.4212776861550038280609624921504
absolute error = 0.0002975311823561575880762636882
relative error = 0.020929682701801716448822705569843 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 1.4223912421373985215370018882395
y[1] (numeric) = 1.4220917762924749450059727550981
absolute error = 0.0002994658449235765310291331414
relative error = 0.021053690155851583345590633019875 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 1.4232078445461467859648927355918
y[1] (numeric) = 1.4229064336804440756514862707914
absolute error = 0.0003014108657027103134064648004
relative error = 0.021178274617986566356889226307365 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 1.4240250237470024382346453306867
y[1] (numeric) = 1.4237216574587579619202958669967
absolute error = 0.00030336628824447631434946369
relative error = 0.021303438014469434850202818123335 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.6MB, time=9.73
NO POLE
x[1] = 0.958
y[1] (analytic) = 1.4248427789227863455888718718004
y[1] (numeric) = 1.4245374467665540207774386088253
absolute error = 0.0003053321562323248114332629751
relative error = 0.021429182275335871718550607779282 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 1.4256611092557434003899273818234
y[1] (numeric) = 1.4253538007422609180794597268723
absolute error = 0.0003073085134824823104676549511
relative error = 0.021555509334396490009358960838644 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 1.4264800139275433378749491996481
y[1] (numeric) = 1.4261707185235991428962250933102
absolute error = 0.0003092954039441949787241063379
relative error = 0.021682421129238852227077158151382 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 1.4272994921192815544860535488458
y[1] (numeric) = 1.4269881992475815823048994041178
absolute error = 0.000311292871699972181154144728
relative error = 0.021809919601229492346911008232889 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 1.4281195430114799267748708535018
y[1] (numeric) = 1.4278062420505140966557069108155
absolute error = 0.0003133009609658301191639426863
relative error = 0.02193800669551594057693188442564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 1.4289401657840876308806008967442
y[1] (numeric) = 1.4286248460679960953090912305243
absolute error = 0.0003153197160915355715096662199
relative error = 0.022066684361028750905701906905244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 1.4297613596164819625807683439772
y[1] (numeric) = 1.4294440104349211128438904488689
absolute error = 0.0003173491815608497368778951083
relative error = 0.022195954550483531472439162158043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 1.4305831236874691579138585801337
y[1] (numeric) = 1.4302637342854773857361434162018
absolute error = 0.0003193894019917721777151639319
relative error = 0.022325819220382977796630045085426 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 1.4314054571752852143730132383785
y[1] (numeric) = 1.4310840167531484295081428238399
absolute error = 0.0003214404221367848648704145386
relative error = 0.022456280331018908903879024213143 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 1.4322283592575967126699642266353
y[1] (numeric) = 1.4319048569707136163473503334749
absolute error = 0.0003235022868830963226138931604
relative error = 0.022587339846474306384669373978537 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 1.4330518291115016390683844880724
y[1] (numeric) = 1.4327262540702487531947887196462
absolute error = 0.0003255750412528858735957684262
relative error = 0.022718999734625356422591693410101 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 1.4338758659135302082858331622636
y[1] (numeric) = 1.4335482071831266603025256721467
absolute error = 0.0003276587304035479833074901169
relative error = 0.022851261967143494828480342141549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 1.4347004688396456869634722451501
y[1] (numeric) = 1.4343707154400177502598635924733
absolute error = 0.0003297533996279367036086526768
relative error = 0.022984128519497455116781276951335 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 1.4355256370652452177027312781524
y[1] (numeric) = 1.4351937779708906074878494059312
absolute error = 0.0003318590943546102148818722212
relative error = 0.023117601370955319660358168324532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 1.4363513697651606436680960298383
y[1] (numeric) = 1.4360173939050125682017180987541
absolute error = 0.0003339758601480754663779310842
relative error = 0.023251682504586573959827122406117 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 1.4371776661136593337551965674268
y[1] (numeric) = 1.4368415623709503008408833776163
absolute error = 0.0003361037427090329143131898105
relative error = 0.023386373907264164063393831649222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 1.4380045252844450083233695501071
y[1] (numeric) = 1.4376662824965703869660885371813
absolute error = 0.0003382427878746213572810129258
relative error = 0.023521677569666557173050532559424 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.6MB, time=9.93
NO POLE
x[1] = 0.975
y[1] (analytic) = 1.4388319464506585654918690116816
y[1] (numeric) = 1.438491553409039902623330309859
absolute error = 0.0003403930416186628685387018226
relative error = 0.02365759548627980547287376522186 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 1.4396599287848789079988993363884
y[1] (numeric) = 1.4393173742348270001741681607303
absolute error = 0.0003425545500519078247311756581
relative error = 0.023794129655399613215047609784435 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 1.4404884714591237706226435689417
y[1] (numeric) = 1.4401437440997014905920311796405
absolute error = 0.0003447273594222800306123893012
relative error = 0.02393128207913340709912082526942 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 1.4413175736448505481634596378282
y[1] (numeric) = 1.4409706621287354262241344117678
absolute error = 0.0003469115161151219393252260604
relative error = 0.024069054763402409979890138094815 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 1.4421472345129571239864165097351
y[1] (numeric) = 1.4417981274463036840186161575315
absolute error = 0.0003491070666534399678003522036
relative error = 0.024207449717943717939185827450424 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 1.4429774532337826991233417326401
y[1] (numeric) = 1.4426261391760845492165074625281
absolute error = 0.000351314057698149906834270112
relative error = 0.024346468956312380756719733773164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 1.4438082289771086219335512655861
y[1] (numeric) = 1.44345469644106029950814470826
absolute error = 0.0003535325360483224254065573261
relative error = 0.024486114495883485815039881066307 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 1.4446395609121592183224319344801
y[1] (numeric) = 1.4442837983635177896536359047628
absolute error = 0.0003557625486414286687960297173
relative error = 0.02462638835785424547352005574554 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 1.4454714482076026225170462954026
y[1] (numeric) = 1.445113444065049036566990976834
absolute error = 0.0003580041425535859500553185686
relative error = 0.024767292567246087946196928833478 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 1.4463038900315516083979291298914
y[1] (numeric) = 1.4459436326665518048635260264247
absolute error = 0.0003602573649998035344031034667
relative error = 0.024908829152906751718151647969229 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 1.4471368855515644213862442404742
y[1] (numeric) = 1.4467743632882301928701512448745
absolute error = 0.0003625222633342285160929955997
relative error = 0.025051000147512383535017264818099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 1.4479704339346456108854696593607
y[1] (numeric) = 1.4476056350495952190981518400466
absolute error = 0.0003647988850503917873178193141
relative error = 0.025193807587569640000077905314578 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 1.4488045343472468632767788286789
y[1] (numeric) = 1.4484374470694654091780710350618
absolute error = 0.0003670872777814540987077936171
relative error = 0.025337253513417792813310238714238 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 1.4496391859552678354672847569453
y[1] (numeric) = 1.4492697984659673832563038872259
absolute error = 0.0003693874893004522109808697194
relative error = 0.02548133996923083768660256052179 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 1.4504743879240569889903136035916
y[1] (numeric) = 1.450102688356536443853010367908
absolute error = 0.0003716995675205451373032356836
relative error = 0.025626069003019606969271676424827 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 1.4513101394184124246568735913464
y[1] (numeric) = 1.4509361158579171641809558365472
absolute error = 0.0003740235604952604759177547992
relative error = 0.025771442666633886017882764651525 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 1.4521464396025827177574845950707
y[1] (numeric) = 1.4517700800861639769248867346477
absolute error = 0.000376359516418740832597860423
relative error = 0.025917463015764533344262504497607 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.6MB, time=10.12
NO POLE
x[1] = 0.992
y[1] (analytic) = 1.4529832876402677538135332052885
y[1] (numeric) = 1.452604580156641763481049018566
absolute error = 0.0003787074836259903324841867225
relative error = 0.0260641321099456045754809938965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 1.4538206826946195648773175151265
y[1] (numeric) = 1.4534396151840264436564565431006
absolute error = 0.0003810675105931212208609720259
relative error = 0.026211452012556480259463341297605 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 1.4546586239282431663799453306873
y[1] (numeric) = 1.4542751842823055658275163013596
absolute error = 0.0003834396459376005524290293277
relative error = 0.026359424790823997549777310993702 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 1.4554971105031973945262489570286
y[1] (numeric) = 1.4551112865647788975576171201132
absolute error = 0.0003858239384184969686318369154
relative error = 0.026508052515824585803029029177168 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 1.4563361415809957442358791649033
y[1] (numeric) = 1.4559479211440590166732881038284
absolute error = 0.0003882204369367275625910610749
relative error = 0.026657337262486406122184524035055 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 1.4571757163226072076297403972349
y[1] (numeric) = 1.456785087132071902798532814838
absolute error = 0.0003906291905353048312075823969
relative error = 0.026807281109591494879020780196273 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 1.4580158338884571130609287289657
y[1] (numeric) = 1.4576227836400575293469448716116
absolute error = 0.0003930502483995837139838573541
relative error = 0.026957886139777911248796039777042 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 1.4588564934384279646893335494061
y[1] (numeric) = 1.4584610097785704559712103418772
absolute error = 0.0003954836598575087181232075289
relative error = 0.027109154439541888790115280957815 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 1.459697694131860282599063392557
y[1] (numeric) = 1.4592997646574804214696020023833
absolute error = 0.0003979294743798611294613901737
relative error = 0.027261088099239991102853155727445 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.001
y[1] (analytic) = 1.4605394351275534434578557980464
y[1] (numeric) = 1.4601390473859729371490702323988
absolute error = 0.0004003877415805063087855656476
relative error = 0.027413689213091271596883172033293 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.002
y[1] (analytic) = 1.4613817155837665217176305433427
y[1] (numeric) = 1.460978857072549880644535003615
absolute error = 0.0004028585112166410730955397277
relative error = 0.027566959879179437404248567504064 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.003
y[1] (analytic) = 1.4622245346582191313553450467597
y[1] (numeric) = 1.4618191928250300901939831249496
absolute error = 0.0004053418331890411613619218101
relative error = 0.027720902199455017467297143197024 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.004
y[1] (analytic) = 1.4630678915080922681533102004696
y[1] (numeric) = 1.4626600537505499593689745968478
absolute error = 0.0004078377575423087843356036218
relative error = 0.027875518279737534835189311365455 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.005
y[1] (analytic) = 1.4639117852900291525181243532775
y[1] (numeric) = 1.4635014389555640322601616260365
absolute error = 0.000410346334465120257962727241
relative error = 0.028030810229717683201075762785577 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.006
y[1] (analytic) = 1.4647562151601360728373826242936
y[1] (numeric) = 1.464343347545845599117423548314
absolute error = 0.0004128676142904737199590759796
relative error = 0.02818678016295950771212848040838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.007
y[1] (analytic) = 1.4656011802739832293733181908644
y[1] (numeric) = 1.4651857786264872924442206038458
absolute error = 0.0004154016474959369290975870186
relative error = 0.028343430196902590084496320033112 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=205.9MB, alloc=4.6MB, time=10.31
x[1] = 1.008
y[1] (analytic) = 1.4664466797866055786925316571923
y[1] (numeric) = 1.4660287313019016835457692065927
absolute error = 0.0004179484847038951467624505996
relative error = 0.028500762452864238055144047945556 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.009
y[1] (analytic) = 1.467292712852503678630964073983
y[1] (numeric) = 1.4668722046758218795306410469159
absolute error = 0.0004205081766817991003230270671
relative error = 0.028658779056041679202421573181003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.01
y[1] (analytic) = 1.4681392786256445337932686442208
y[1] (numeric) = 1.4677161978513021207653880640881
absolute error = 0.0004230807743424130278805801327
relative error = 0.028817482135514259167098141553204 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.011
y[1] (analytic) = 1.4689863762594624415857356157674
y[1] (numeric) = 1.4685607099307183787817950233893
absolute error = 0.0004256663287440628039405923781
relative error = 0.028976873824245644305484471642522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.012
y[1] (analytic) = 1.4698340049068598387819243279326
y[1] (numeric) = 1.4694057400157689546363611306823
absolute error = 0.0004282648910908841455631972503
relative error = 0.02913695625908602880615421384543 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.013
y[1] (analytic) = 1.4706821637202081486201558464534
y[1] (numeric) = 1.4702512872074750777216118158407
absolute error = 0.0004308765127330708985440306127
relative error = 0.029297731580774346301664704004796 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.014
y[1] (analytic) = 1.4715308518513486284320190894609
y[1] (numeric) = 1.4710973506061815050288415151524
absolute error = 0.0004335012451671234031775743085
relative error = 0.029459201933940486006565766427762 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.015
y[1] (analytic) = 1.472380068451593217801042815998
y[1] (numeric) = 1.4719439293115571208618879818315
absolute error = 0.0004361391400360969391548341665
relative error = 0.029621369467107513412874299906212 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.016
y[1] (analytic) = 1.4732298126717253872506853184886
y[1] (numeric) = 1.4727910224225955370015383530525
absolute error = 0.0004387902491298502491469654361
relative error = 0.029784236332693895574081557536362 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.017
y[1] (analytic) = 1.4740800836620009874607931312371
y[1] (numeric) = 1.4736386290376156933201669014649
absolute error = 0.0004414546243852941406262297722
relative error = 0.029947804687015731008649408983528 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.018
y[1] (analytic) = 1.4749308805721490990116795385718
y[1] (numeric) = 1.4744867482542624588462040989589
absolute error = 0.0004441323178866401654754396129
relative error = 0.030112076690288984253841455769343 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.019
y[1] (analytic) = 1.4757822025513728826549731386242
y[1] (numeric) = 1.4753353791695072332780363205328
absolute error = 0.0004468233818656493769368180914
relative error = 0.030277054506631725100624657987393 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.02
y[1] (analytic) = 1.4766340487483504301103861919662
y[1] (numeric) = 1.4761845208796485489469352164575
absolute error = 0.0004495278687018811634509755087
relative error = 0.030442740304066372540267127888798 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.021
y[1] (analytic) = 1.4774864183112356153875519584076
y[1] (numeric) = 1.477034172480312673228615481548
absolute error = 0.0004522458309229421589364768596
relative error = 0.03060913625452194345314795418834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.022
y[1] (analytic) = 1.4783393103876589466320797001881
y[1] (numeric) = 1.4778843330664542114030194512326
absolute error = 0.0004549773212047352290602489555
relative error = 0.030776244533836306070185343569357 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.023
y[1] (analytic) = 1.4791927241247284184949755055798
y[1] (numeric) = 1.4787350017323567099619266552586
absolute error = 0.0004577223923717085330488503212
relative error = 0.030944067321758438237180005066901 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.024
y[1] (analytic) = 1.4800466586690303650245765635492
y[1] (numeric) = 1.4795861775716332603639861612908
absolute error = 0.0004604810973971046605904022584
relative error = 0.031112606801950690512261561213789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=209.8MB, alloc=4.6MB, time=10.51
x[1] = 1.025
y[1] (analytic) = 1.4809011131666303130801459976169
y[1] (numeric) = 1.4804378596772271032367692423428
absolute error = 0.0004632534894032098433767552741
relative error = 0.031281865161991054126516850059909 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.026
y[1] (analytic) = 1.4817560867630738362662748453913
y[1] (numeric) = 1.4812900471414122330254396039343
absolute error = 0.000466039621661603240835241457
relative error = 0.031451844593375433837770286139305 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.027
y[1] (analytic) = 1.4826115786033874093872372494439
y[1] (numeric) = 1.4821427390557940030876381090898
absolute error = 0.0004688395475934062995991403541
relative error = 0.031622547291519925707377978895006 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.028
y[1] (analytic) = 1.4834675878320792634204444052437
y[1] (numeric) = 1.4829959345113097312341786417827
absolute error = 0.000471653320769532186265763461
relative error = 0.03179397545576309982978906689803 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.029
y[1] (analytic) = 1.4843241135931402410081422927682
y[1] (numeric) = 1.4838496325982293057151514521894
absolute error = 0.0004744809949109352929908405788
relative error = 0.031966131289368288044519716814633 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.03
y[1] (analytic) = 1.4851811550300446524664977001626
y[1] (numeric) = 1.4847038324061557916510300301441
absolute error = 0.0004773226238888608154676700185
relative error = 0.032139016999525876660077460520288 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.031
y[1] (analytic) = 1.4860387112857511323112165304354
y[1] (numeric) = 1.4855585330240260379083772564848
absolute error = 0.0004801782617250944028392739506
relative error = 0.032312634797355604219266004340947 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.032
y[1] (analytic) = 1.4868967815027034962988378656402
y[1] (numeric) = 1.4864137335401112844197462855454
absolute error = 0.0004830479625922118790915800948
relative error = 0.03248698689790886433519334282805 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.033
y[1] (analytic) = 1.4877553648228315989828467473245
y[1] (numeric) = 1.487269433042017769947371315887
absolute error = 0.0004859317808138290354754314375
relative error = 0.032662075520171013627198949012147 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.034
y[1] (analytic) = 1.4886144603875521917837481172009
y[1] (numeric) = 1.4881256306166873402902431104663
absolute error = 0.0004888297708648514935050067346
relative error = 0.032837902887063684785808994697099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.035
y[1] (analytic) = 1.489474067337769781572243848041
y[1] (numeric) = 1.4889823253503980569341638318178
absolute error = 0.0004917419873717246380800162232
relative error = 0.033014471225447104795721981543554 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.036
y[1] (analytic) = 1.4903341848138774897646542816844
y[1] (numeric) = 1.4898395163287648061443754624698
absolute error = 0.0004946684851126836202788192146
relative error = 0.033191782766122418345720837697247 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.037
y[1] (analytic) = 1.4911948119557579119297251788145
y[1] (numeric) = 1.490697202636739908500355785735
absolute error = 0.0004976093190180034293693930795
relative error = 0.033369839743834016454301458154719 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.038
y[1] (analytic) = 1.4920559479027839779059604737648
y[1] (numeric) = 1.4915553833586137288723756072007
absolute error = 0.0005005645441702490335848665641
relative error = 0.033548644397271870339701842012883 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.039
y[1] (analytic) = 1.4929175917938198124286207170946
y[1] (numeric) = 1.4924140575780152868394106027061
absolute error = 0.0005035342158045255892101143885
relative error = 0.033728198969073870562910408011399 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.04
y[1] (analytic) = 1.4937797427672215962655265790078
y[1] (numeric) = 1.4932732243779128675480008843197
absolute error = 0.0005065183893087287175256946881
relative error = 0.033908505705828171472126754194567 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.041
y[1] (analytic) = 1.4946423999608384278608062778836
y[1] (numeric) = 1.4941328828406146330116510818346
absolute error = 0.000509517120223794849155196049
relative error = 0.034089566858075540977043069081757 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=213.6MB, alloc=4.6MB, time=10.70
x[1] = 1.042
y[1] (analytic) = 1.4955055625120131854857252902416
y[1] (numeric) = 1.4949930320477692338503634435697
absolute error = 0.0005125304642439516353618466719
relative error = 0.034271384680311715681209603271555 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.043
y[1] (analytic) = 1.4963692295575833898957361913855
y[1] (numeric) = 1.4958536710803664214698961668087
absolute error = 0.0005155584772169684258400245768
relative error = 0.034453961430989761400643073971946 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.044
y[1] (analytic) = 1.4972334002338820674928859697464
y[1] (numeric) = 1.4967147990187376606803388750262
absolute error = 0.0005186012151444068125470947202
relative error = 0.034637299372522439096732601656864 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.045
y[1] (analytic) = 1.4980980736767386139927176525903
y[1] (numeric) = 1.4975764149425567427535968661368
absolute error = 0.0005216587341818712391207864535
relative error = 0.034821400771284576251393770904185 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.046
y[1] (analytic) = 1.4989632490214796585948025762604
y[1] (numeric) = 1.4984385179308403989193754633638
absolute error = 0.0005247310906392596754271128966
relative error = 0.035006267897615443712317667758096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.047
y[1] (analytic) = 1.499828925402929928656039130494
y[1] (numeric) = 1.4993011070619489142992555079564
absolute error = 0.0005278183409810143567836225376
relative error = 0.035191903025821138036058275785529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.048
y[1] (analytic) = 1.5006951019554131148658533035871
y[1] (numeric) = 1.5001641814135867422784507408895
absolute error = 0.0005309205418263725874025626976
relative error = 0.035378308434176969356598414195046 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.049
y[1] (analytic) = 1.5015617778127527369224358532785
y[1] (numeric) = 1.5010277400628031193148375288584
absolute error = 0.0005340377499496176075983244201
relative error = 0.035565486404929854806931475872529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.05
y[1] (analytic) = 1.5024289521082730097091504271879
y[1] (numeric) = 1.5018917820859926801848470983314
absolute error = 0.0005371700222803295243033288565
relative error = 0.035753439224300717521093572712104 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.051
y[1] (analytic) = 1.5032966239747997099702464564727
y[1] (numeric) = 1.5027563065588960736658101501479
absolute error = 0.0005403174159036363044363063248
relative error = 0.035942169182486891243978322109093 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.052
y[1] (analytic) = 1.5041647925446610434850101470624
y[1] (numeric) = 1.5036213125566005786543434361462
absolute error = 0.0005434799880604648306667109162
relative error = 0.036131678573664530576164413590168 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.053
y[1] (analytic) = 1.5050334569496885127394863943916
y[1] (numeric) = 1.5044867991535407207203675885781
absolute error = 0.0005466577961477920191188058135
relative error = 0.036321969695991026880884279996 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.054
y[1] (analytic) = 1.5059026163212177850949039499833
y[1] (numeric) = 1.5053527654234988890963452026102
absolute error = 0.0005498508977188959985587473731
relative error = 0.036513044851607429880160665589824 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.055
y[1] (analytic) = 1.5067722697900895614519356715277
y[1] (numeric) = 1.5062192104396059541013278820324
absolute error = 0.0005530593504836073506077894953
relative error = 0.036704906346640874967036634720882 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.056
y[1] (analytic) = 1.5076424164866504454099251922705
y[1] (numeric) = 1.5070861332743418849994006683868
absolute error = 0.0005562832123085604105245238837
relative error = 0.036897556491207016260723602101566 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.057
y[1] (analytic) = 1.508513055540753812920210850555
y[1] (numeric) = 1.5079535329995363682921119840969
absolute error = 0.0005595225412174446280988664581
relative error = 0.037090997599412465431391289960542 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.058
y[1] (analytic) = 1.5093841860817606824326772262677
y[1] (numeric) = 1.50882140868636942644447693082
absolute error = 0.0005627773953912559882002954477
relative error = 0.037285231989357236321223130682011 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.6MB, time=10.89
NO POLE
x[1] = 1.059
y[1] (analytic) = 1.5102558072385405855346641377078
y[1] (numeric) = 1.5096897594053720370441414951617
absolute error = 0.0005660478331685484905226425461
relative error = 0.037480261983137195388260537198218 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.06
y[1] (analytic) = 1.5111279181394724380813624600436
y[1] (numeric) = 1.5105585842264267523932949250837
absolute error = 0.0005693339130456856880675349599
relative error = 0.037676089906846517999459659161138 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.061
y[1] (analytic) = 1.5120005179124454118168256350344
y[1] (numeric) = 1.5114278822187683195329172518028
absolute error = 0.0005726356936770922839083832316
relative error = 0.037872718090580150599284732528419 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.062
y[1] (analytic) = 1.5128736056848598064847252510766
y[1] (numeric) = 1.5122976524509843006989486437204
absolute error = 0.0005759532338755057857766073562
relative error = 0.038070148868436278780062914603198 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.063
y[1] (analytic) = 1.513747180583627922427978582893
y[1] (numeric) = 1.5131678939910156942099669909405
absolute error = 0.0005792865926122282180115919525
relative error = 0.038268384578518801280226578139271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.064
y[1] (analytic) = 1.5146212417351749336763754913097
y[1] (numeric) = 1.5140386059061575557859598312275
absolute error = 0.0005826358290173778904156600822
relative error = 0.038467427562939809936470417523756 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.065
y[1] (analytic) = 1.5154957882654397615213315955666
y[1] (numeric) = 1.5149097872630596202977764408233
absolute error = 0.0005860010023801412235551547433
relative error = 0.038667280167822075615752399453003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.066
y[1] (analytic) = 1.5163708192998759485768941434805
y[1] (numeric) = 1.51578143712772692394684562639
absolute error = 0.0005893821721490246300485170905
relative error = 0.038867944743301540152969570799446 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.067
y[1] (analytic) = 1.5172463339634525333261265185295
y[1] (numeric) = 1.5166535545655204268747444674653
absolute error = 0.0005927793979321064513820510642
relative error = 0.039069423643529814320042019596377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.068
y[1] (analytic) = 1.5181223313806549251519968375448
y[1] (numeric) = 1.5175261386411576362022029722156
absolute error = 0.0005961927394972889497938653292
relative error = 0.039271719226676681852040871838648 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.069
y[1] (analytic) = 1.5189988106754857798518956081959
y[1] (numeric) = 1.5183991884187132294971293229484
absolute error = 0.0005996222567725503547662852475
relative error = 0.039474833854932609555899099352389 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.07
y[1] (analytic) = 1.5198757709714658756349069318241
y[1] (numeric) = 1.519272702961619678671240101794
absolute error = 0.0006030680098461969636668300301
relative error = 0.039678769894511263527147113239371 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.071
y[1] (analytic) = 1.5207532113916349896009572544251
y[1] (numeric) = 1.5201466813326678743048796011991
absolute error = 0.000606530058967115296077653226
relative error = 0.039883529715652031500018624390044 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.072
y[1] (analytic) = 1.521631131058552774700965186707
y[1] (numeric) = 1.5210211225940077503996120383775
absolute error = 0.0006100084645450243013531483295
relative error = 0.040089115692622551356176069696054 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.073
y[1] (analytic) = 1.5225095290942996371771154331449
y[1] (numeric) = 1.5218960258071489095581702076488
absolute error = 0.0006135032871507276189452254961
relative error = 0.040295530203721245817209029628618 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.074
y[1] (analytic) = 1.5233884046204776144823793898327
y[1] (numeric) = 1.5227713900329612485913438196554
absolute error = 0.0006170145875163658910355701773
relative error = 0.040502775631279863345963502659892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.075
y[1] (analytic) = 1.5242677567582112536784044916836
y[1] (numeric) = 1.5236472143316755845513904917884
absolute error = 0.0006205424265356691270139998952
relative error = 0.04071085436166602528166465450341 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.6MB, time=11.09
NO POLE
x[1] = 1.076
y[1] (analytic) = 1.5251475846281484903108939111643
y[1] (numeric) = 1.5245234977628842811915520697684
absolute error = 0.0006240868652642091193418413959
relative error = 0.040919768785285779233700727669566 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.077
y[1] (analytic) = 1.5260278873504615277615977332555
y[1] (numeric) = 1.5254002393855418758512586762235
absolute error = 0.000627647964919651910339057032
relative error = 0.041129521296586158758841179633664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.078
y[1] (analytic) = 1.5269086640448477170760362547213
y[1] (numeric) = 1.5262774382579657067666025982786
absolute error = 0.0006312257868820103094336564427
relative error = 0.041340114294057749346567818076758 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.079
y[1] (analytic) = 1.527789913830530437266075580037
y[1] (numeric) = 1.5271550934378365408056638426245
absolute error = 0.0006348203926938964604117374125
relative error = 0.041551550180237260737103719515582 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.08
y[1] (analytic) = 1.528671635826259976086475211474
y[1] (numeric) = 1.5280332039821992016282689032627
absolute error = 0.0006384318440607744582063082113
relative error = 0.041763831361710105596631055309535 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.081
y[1] (analytic) = 1.5295538291503144112845268568664
y[1] (numeric) = 1.528911768947463198269764004135
absolute error = 0.0006420602028512130147628527314
relative error = 0.041976960249112984574095606432434 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.082
y[1] (analytic) = 1.5304364929205004923219032054952
y[1] (numeric) = 1.529790787389403354148383796133
absolute error = 0.0006457055310971381735194093622
relative error = 0.04219093925713647776390272804437 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.083
y[1] (analytic) = 1.5313196262541545225678349503138
y[1] (numeric) = 1.5306702583631604364957962055522
absolute error = 0.0006493678909940860720387447616
relative error = 0.042405770804527642598716826582179 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.084
y[1] (analytic) = 1.5322032282681432419627338634115
y[1] (numeric) = 1.5315501809232417862104038489027
absolute error = 0.0006530473449014557523300145088
relative error = 0.042621457314092618196484037820076 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.085
y[1] (analytic) = 1.533087298078864710151379261166
y[1] (numeric) = 1.5324305541235219481329821471154
absolute error = 0.0006567439553427620183971140506
relative error = 0.042838001212699236185705744792875 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.086
y[1] (analytic) = 1.5339718348022491900847847259714
y[1] (numeric) = 1.5333113770172433017442339905908
absolute error = 0.0006604577850058883405507353806
relative error = 0.04305540493127963803289885052474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.087
y[1] (analytic) = 1.5348568375537600320898614827493
y[1] (numeric) = 1.5341926486570166922838405252234
absolute error = 0.0006641888967433398060209575259
relative error = 0.043273670904832898896087323687725 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.088
y[1] (analytic) = 1.5357423054483945584059943606521
y[1] (numeric) = 1.535074368094822062290587348504
absolute error = 0.0006679373535724961154070121481
relative error = 0.043492801572427658028078465894809 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.089
y[1] (analytic) = 1.5366282376006849481876458034578
y[1] (numeric) = 1.5359565343820090835631451240481
absolute error = 0.0006717032186758646245006794097
relative error = 0.043712799377204755753186609256953 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.09
y[1] (analytic) = 1.5375146331246991229721029261249
y[1] (numeric) = 1.5368391465692977895410833424295
absolute error = 0.0006754865554013334310195836954
relative error = 0.043933666766379877040976541870433 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.091
y[1] (analytic) = 1.5384014911340416326114821498343
y[1] (numeric) = 1.5377222037067792081056956760058
absolute error = 0.0006792874272624245057864738285
relative error = 0.044155406191246201700508879158147 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=225.0MB, alloc=4.6MB, time=11.28
x[1] = 1.092
y[1] (analytic) = 1.5392888107418545416681054835882
y[1] (numeric) = 1.5386057048439159948002150955141
absolute error = 0.0006831058979385468678903880741
relative error = 0.044378020107177061218479850619874 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.093
y[1] (analytic) = 1.5401765910608183162723620570624
y[1] (numeric) = 1.5394896490295430664689966365864
absolute error = 0.000686942031275249803365420476
relative error = 0.04460151097362860226455855562602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.094
y[1] (analytic) = 1.5410648312031527114421680469252
y[1] (numeric) = 1.5403740353118682353152454249874
absolute error = 0.0006907958912844761269226219378
relative error = 0.04482588125414245688713565958818 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.095
y[1] (analytic) = 1.5419535302806176588631376772364
y[1] (numeric) = 1.5412588627384728433768672903122
absolute error = 0.0006946675421448154862703869242
relative error = 0.045051133416348419422608753582718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.096
y[1] (analytic) = 1.5428426874045141551285775138303
y[1] (numeric) = 1.5421441303563123974200190190971
absolute error = 0.0006985570482017577085584947332
relative error = 0.045277269931967130141241187593784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.097
y[1] (analytic) = 1.5437323016856851504384158127608
y[1] (numeric) = 1.5430298372117172042499350197962
absolute error = 0.0007024644739679461884807929646
relative error = 0.045504293276812765652543110193405 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.098
y[1] (analytic) = 1.5446223722345164377561782239551
y[1] (numeric) = 1.5439159823503930064386068938562
absolute error = 0.0007063898841234313175713300989
relative error = 0.045732205930795736093035707389308 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.099
y[1] (analytic) = 1.5455128981609375424231206931733
y[1] (numeric) = 1.544802564817421618468892129184
absolute error = 0.0007103333435159239542285639893
relative error = 0.045961010377925389119172230405879 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.1
y[1] (analytic) = 1.5464038785744226122286299482153
y[1] (numeric) = 1.5456895836572615632946278546485
absolute error = 0.0007142949171610489340020935668
relative error = 0.046190709106312720728102337647871 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;
Iterations = 1000
Total Elapsed Time = 11 Seconds
Elapsed Time(since restart) = 11 Seconds
Expected Time Remaining = 44 Seconds
Optimized Time Remaining = 44 Seconds
Time to Timeout = 14 Minutes 48 Seconds
Percent Done = 20.43 %
> quit
memory used=227.0MB, alloc=4.6MB, time=11.38