|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> 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 - 2 - 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 - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
n := glob_max_terms;
m := n - 3;
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 - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := -att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (2)) * factorial_3(1,3);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := -att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (2)) * factorial_3(2,4);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := -att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (2)) * factorial_3(3,5);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := -att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,7] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (2)) * factorial_3(4,6);
> 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
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h^2*factorial_3(0, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h^2*factorial_3(1, 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
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h^2*factorial_3(2, 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
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h^2*factorial_3(3, 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
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h^2*factorial_3(4, 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
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # Begin Function number 17
> factorial_1 := proc(nnn)
> if (nnn <= glob_max_terms) then # if number 13
> ret := array_fact_1[nnn];
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_1`
factorial_1 := proc(nnn)
local ret;
if nnn <= glob_max_terms then ret := array_fact_1[nnn]
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> ret := array_fact_2[mmm,nnn];
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_3`
factorial_3 := proc(mmm, nnn)
local ret;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
ret := array_fact_2[mmm, nnn]
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - 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
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> glob_max_terms,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_current_iter,
> glob_orig_start_sec,
> glob_smallish_float,
> glob_no_eqs,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_look_poles,
> years_in_century,
> djd_debug,
> glob_html_log,
> glob_normmax,
> glob_iter,
> glob_max_trunc_err,
> glob_hmin,
> glob_h,
> sec_in_min,
> glob_max_minutes,
> glob_unchanged_h_cnt,
> glob_optimal_clock_start_sec,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_iter,
> glob_almost_1,
> hours_in_day,
> glob_dump,
> glob_log10relerr,
> glob_hmax,
> glob_percent_done,
> glob_optimal_start,
> glob_max_rel_trunc_err,
> glob_max_hours,
> glob_log10_abserr,
> glob_large_float,
> glob_clock_start_sec,
> glob_display_flag,
> glob_log10normmin,
> glob_max_sec,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug2,
> glob_max_opt_iter,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_abserr,
> days_in_year,
> glob_warned2,
> glob_warned,
> glob_relerr,
> glob_hmin_init,
> glob_not_yet_start_msg,
> glob_clock_sec,
> glob_subiter_method,
> glob_start,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_initial_pass,
> glob_not_yet_finished,
> min_in_hour,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> #END CONST
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y,
> array_x,
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_type_pole,
> array_fact_1,
> array_m1,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_fact_2,
> array_poles,
> array_y_higher_work2,
> array_y_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_iolevel := 5;
> glob_current_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_no_eqs := 0;
> glob_log10_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_look_poles := false;
> years_in_century := 100.0;
> djd_debug := true;
> glob_html_log := true;
> glob_normmax := 0.0;
> glob_iter := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_h := 0.1;
> sec_in_min := 60.0;
> glob_max_minutes := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_optimal_clock_start_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_optimal_expect_sec := 0.1;
> glob_curr_iter_when_opt := 0;
> glob_small_float := 0.1e-50;
> glob_max_iter := 1000;
> glob_almost_1 := 0.9990;
> hours_in_day := 24.0;
> glob_dump := false;
> glob_log10relerr := 0.0;
> glob_hmax := 1.0;
> glob_percent_done := 0.0;
> glob_optimal_start := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_clock_start_sec := 0.0;
> glob_display_flag := true;
> glob_log10normmin := 0.1;
> glob_max_sec := 10000.0;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> djd_debug2 := true;
> glob_max_opt_iter := 10;
> glob_log10abserr := 0.0;
> MAX_UNCHANGED := 10;
> glob_abserr := 0.1e-10;
> days_in_year := 365.0;
> glob_warned2 := false;
> glob_warned := false;
> glob_relerr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_not_yet_start_msg := true;
> glob_clock_sec := 0.0;
> glob_subiter_method := 3;
> glob_start := 0;
> glob_last_good_h := 0.1;
> glob_reached_optimal_h := false;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> min_in_hour := 60.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/h2sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 2 ) = sin(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 50;");
> 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,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.001 ;");
> 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,"#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 := 50;
> 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_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= 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_pole:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> 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_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_g[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_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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 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 <=3 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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while iiif <= glob_max_terms do # do number 2
> jjjf := 0;
> while jjjf <= glob_max_terms do # do number 3
> temp1 := iiif !;
> temp2 := jjjf !;
> array_fact_1[iiif] := temp1;
> array_fact_2[iiif,jjjf] := temp1/temp2;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> glob_h := 0.00001;
> glob_look_poles := true;
> glob_max_iter := 100;
> #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] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 2;
> #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 := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #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 := 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 := 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 , 2 ) = sin(x);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-16T22:07:56-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"h2sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 2 ) = sin(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 091 | ")
> ;
> logitem_str(html_log_file,"h2sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"h2sin maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly for speeding factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `iiif` is implicitly declared local to procedure `mainprog`
Warning, `jjjf` is implicitly declared local to procedure `mainprog`
Warning, `temp1` is implicitly declared local to procedure `mainprog`
Warning, `temp2` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, iiif,
jjjf, temp1, temp2;
global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel,
glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs,
glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century,
djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err,
glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt,
glob_optimal_clock_start_sec, centuries_in_millinium,
glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float,
glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr,
glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec,
glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr,
glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr,
MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned,
glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec,
glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h,
glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2,
array_const_0D0, array_last_rel_error, array_y_init, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error,
array_pole, array_norms, array_type_pole, array_fact_1, array_m1,
array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole,
array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_iolevel := 5;
glob_current_iter := 0;
glob_orig_start_sec := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_no_eqs := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_look_poles := false;
years_in_century := 100.0;
djd_debug := true;
glob_html_log := true;
glob_normmax := 0.;
glob_iter := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_h := 0.1;
sec_in_min := 60.0;
glob_max_minutes := 0.;
glob_unchanged_h_cnt := 0;
glob_optimal_clock_start_sec := 0.;
centuries_in_millinium := 10.0;
glob_optimal_expect_sec := 0.1;
glob_curr_iter_when_opt := 0;
glob_small_float := 0.1*10^(-50);
glob_max_iter := 1000;
glob_almost_1 := 0.9990;
hours_in_day := 24.0;
glob_dump := false;
glob_log10relerr := 0.;
glob_hmax := 1.0;
glob_percent_done := 0.;
glob_optimal_start := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_clock_start_sec := 0.;
glob_display_flag := true;
glob_log10normmin := 0.1;
glob_max_sec := 10000.0;
glob_disp_incr := 0.1;
glob_optimal_done := false;
djd_debug2 := true;
glob_max_opt_iter := 10;
glob_log10abserr := 0.;
MAX_UNCHANGED := 10;
glob_abserr := 0.1*10^(-10);
days_in_year := 365.0;
glob_warned2 := false;
glob_warned := false;
glob_relerr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_not_yet_start_msg := true;
glob_clock_sec := 0.;
glob_subiter_method := 3;
glob_start := 0;
glob_last_good_h := 0.1;
glob_reached_optimal_h := false;
glob_initial_pass := true;
glob_not_yet_finished := true;
min_in_hour := 60.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/h2sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 2 ) = sin(x);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 50;");
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, "glob_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.001 ;");
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, "#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 := 50;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := 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_pole := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
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_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_g[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_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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
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 <= 3 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 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;
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_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
temp1 := iiif!;
temp2 := jjjf!;
array_fact_1[iiif] := temp1;
array_fact_2[iiif, jjjf] := temp1/temp2;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
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] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 2;
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 := 2;
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 := 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 := 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 , 2 ) = sin(x);");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-16T22:07:56-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "h2sin");
logitem_str(html_log_file, "diff ( y , x , 2 ) = sin(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 091 | ");
logitem_str(html_log_file,
"h2sin diffeq.mxt");
logitem_str(html_log_file,
"h2sin maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly for speeding factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/h2sinpostode.ode#################
diff ( y , x , 2 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits := 50;
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);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
#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;
#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) = 1.0050957182211592450002505135296
absolute error = 4.4740286409562134648664143211856e-07
relative error = 4.4513438554195169991043675258269e-05 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.0051974914298239146653143235401
y[1] (numeric) = 1.005195702548706583302547040273
absolute error = 1.7888811173313627672832671789245e-06
relative error = 0.00017796314978729235509063066070597 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.0052998120380501586788328071734
y[1] (numeric) = 1.0052957886994694202844078633664
absolute error = 4.0233385807383944249438070110668e-06
relative error = 0.00040021280542984054764995263739006 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.0054031273463814729626255055154
y[1] (numeric) = 1.0053959776681991042118998418611
absolute error = 7.1496781823687507256636542783716e-06
relative error = 0.00071112551651189997611342783179656 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.0055074372515025577949868753959
y[1] (numeric) = 1.0054962704495441653928110527955
absolute error = 1.1166801958392402175822600431405e-05
relative error = 0.0011105638352030712751795164792041 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.0056127416491035167473238881278
y[1] (numeric) = 1.0055966680380493215282033707819
absolute error = 1.6073611054195219120517345855789e-05
relative error = 0.0015983897566608113409636112367587 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.0057190404338799609940437656082
y[1] (numeric) = 1.0056971714281544831677776456682
absolute error = 2.1869005725477826266119939983739e-05
relative error = 0.0021744647208869844587317596349434 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.0058263334995331146169340305467
y[1] (numeric) = 1.005797781614193759270046022827
absolute error = 2.8551885339355346888007719695583e-05
relative error = 0.0028386496145925970756197855112094 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=3.8MB, alloc=3.0MB, time=0.16
x[1] = 0.109
y[1] (analytic) = 1.0059346207387699209039295664461
y[1] (numeric) = 1.0058984995903944628683058458161
absolute error = 3.6121148375458035623720629926680e-05
relative error = 0.003590804773070664377958475585722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.0060439020433031496421603885802
y[1] (numeric) = 1.0059993263508761168434094753551
absolute error = 4.4575692427032798750913225041804e-05
relative error = 0.0044307899820771566224000135581127 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.006154177303851505405172832928
y[1] (numeric) = 1.0061002628896494598043242517632
absolute error = 5.3914414202045600848581164818357e-05
relative error = 0.0053584644797199729619917450140278 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.0062654464101397368342158758533
y[1] (numeric) = 1.0062013102006154520774767202177
absolute error = 6.4136209524284756739155635679122e-05
relative error = 0.0063736869583558903026784493966881 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.0063777092508987469134833032515
y[1] (numeric) = 1.0063024692775642818058751294045
absolute error = 7.5239973334465107608173847021135e-05
relative error = 0.0074763155664954345224412270103994 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.0064909657138657042392014539315
y[1] (numeric) = 1.0064037411141743711590041043565
absolute error = 8.7224599691333080197349574984850e-05
relative error = 0.0086662079107156211844073651526171 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.0066052156857841552824512681535
y[1] (numeric) = 1.0065051267040113826544852835008
absolute error = 0.00010008898177277262796598465268132
relative error = 0.0099432210575805126767984523509175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.006720459052404137645612378511
y[1] (numeric) = 1.0066066270405272255924975981734
absolute error = 0.00011383201187691205311478033762765
relative error = 0.011307211535569538516530725993234 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.006836695698482294312315986721
y[1] (numeric) = 1.0067082431170590626039507600962
absolute error = 0.00012845258142323170836522662481455
relative error = 0.012758035337013525359649167121704 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.00695392550778198889079227638
y[1] (numeric) = 1.0068099759268283163134054085616
absolute error = 0.00014394958095367257738686781832511
relative error = 0.014295547920038383070572035326086 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.0070721483630734218504971183478
y[1] (numeric) = 1.0069118264629396761177332543212
absolute error = 0.00016032190013374573276386402662099
relative error = 0.015919604210516393013352042546884 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.0071913641461337477519018321424
y[1] (numeric) = 1.007013795718380105081510441435
absolute error = 0.00017756842775364267039139070738924
relative error = 0.017630058604025044541830710467689 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.0073115727377471934693287735644
y[1] (numeric) = 1.0071158846860178469501372316063
absolute error = 0.00019568805172934651919154195807825
relative error = 0.019426764967813365481679992354109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.007432774017705177406714525728
y[1] (numeric) = 1.0072180943586014332816769977992
absolute error = 0.00021467965910374412503752792882016
relative error = 0.021309576642775692215896153803612 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.0075549678648064297061814777427
y[1] (numeric) = 1.0073204257287586906984073952165
absolute error = 0.00023454213604773900777408252621605
relative error = 0.023278346445432824806341221629062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.007678154156857113449297582485
y[1] (numeric) = 1.0074228797889957482590764580047
absolute error = 0.00025527436786136519022112448032273
relative error = 0.025332926669920512407422886143564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.0078023327706709468509030922117
y[1] (numeric) = 1.0075254575316960449528562493478
absolute error = 0.00027687523897490189804684286399888
relative error = 0.027473169089985214053970275817319 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.2MB, time=0.37
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.0079275035820693264453820781963
y[1] (numeric) = 1.0076281599491193373159865709119
absolute error = 0.00029934363294998912939550728441699
relative error = 0.029698924960987079733806047087311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.0080536664658814512652555481279
y[1] (numeric) = 1.007730988033400707172101114916
absolute error = 0.00032267843248074409315443321189479
relative error = 0.032010045021910096486440114398572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.0081808212959444480119719826911
y[1] (numeric) = 1.007833942776549569497228318419
absolute error = 0.00034687851939487851474366427211748
relative error = 0.034406379497379344102722290523378 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.0083089679451034972187701205446
y[1] (numeric) = 1.0079370251704486804104590547394
absolute error = 0.00037194277465481680831106580517724
relative error = 0.036887778099685304836195154709988 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.0084381062852119604054878288482
y[1] (numeric) = 1.0080402362068531452912731712587
absolute error = 0.00039787007835881511421465758951754
relative error = 0.039454090030815171375289491708572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.0085682361871315082251899045384
y[1] (numeric) = 1.0081435768773894270245167561967
absolute error = 0.00042465930974208120067314834170255
relative error = 0.042105163984491097166407359161258 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.008699357520732249602486659737
y[1] (numeric) = 1.0082470481735543543740218893022
absolute error = 0.00045230934717789522846477043480233
relative error = 0.044840848148215333021346790606859 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.0088314701548928618634141529829
y[1] (numeric) = 1.008350651086714130485860502753
absolute error = 0.00048081906817873137755365022995618
relative error = 0.047660990205322193788441708191829 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.0089645739575007218567459364203
y[1] (numeric) = 1.0084543866081033415222238489321
absolute error = 0.00051018734939738033452208748821259
relative error = 0.050565437337036798715225020181236 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.0090986687954520380666051976395
y[1] (numeric) = 1.0085582557288239654269189411156
absolute error = 0.00054041306662807263968625652390713
relative error = 0.053554036224540528981376165914977 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.009233754534651983716245183572
y[1] (numeric) = 1.0086622594398443808234732014945
absolute error = 0.0005714950948076028927719820774893
relative error = 0.056626633051043145734190432634776 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.0093698310400148308628648026684
y[1] (numeric) = 1.0087663987319983760468384183427
absolute error = 0.00060343230801645481602638432570626
relative error = 0.059783073503861511814809927591339 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.0095068981754640854833253105561
y[1] (numeric) = 1.0088706745959841583096849805449
absolute error = 0.0006362235794799271736403300112537
relative error = 0.063023202776504860221988703314704 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.0096449558039326235506329934705
y[1] (numeric) = 1.0089750880223633630042772231072
absolute error = 0.00066986778156926054635577036326944
relative error = 0.066346865570766552221230597524698 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.0097840037873628281010517729886
y[1] (numeric) = 1.0090796400015600631409205816934
absolute error = 0.0007043637858027649601311912952295
relative error = 0.069753906098822267870741090893181 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.0099240419867067272917086649643
y[1] (numeric) = 1.0091843315238597789239711176555
absolute error = 0.00073971046284694836773754730876573
relative error = 0.073244168085334571601776970217549 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.3MB, time=0.58
x[1] = 0.142
y[1] (analytic) = 1.0100650702619261334485540350706
y[1] (numeric) = 1.0092891635794084874663978374691
absolute error = 0.00077590668251764598215619760151107
relative error = 0.076817494769563795359662711524955 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.0102070884719927831045376030009
y[1] (numeric) = 1.0093941371582116326438880919257
absolute error = 0.00081295131378115046064951107514749
relative error = 0.080473728907485181682973002815054 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.0103500964748884780278601571639
y[1] (numeric) = 1.0094992532501331350894862008967
absolute error = 0.00085084322475534293837395626723361
relative error = 0.084212712773912228972159280903462 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.010494094127605227240159951634
y[1] (numeric) = 1.009604512844894402329755308946
absolute error = 0.00088958128271082491040464268797492
relative error = 0.088034288164626181075226968326538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.0106390812861453900244917671803
y[1] (numeric) = 1.0097099169320733390634523355486
absolute error = 0.0009291643540720509610394316317186
relative error = 0.091938296398511603196951507662105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.0107850578055218199229556284092
y[1] (numeric) = 1.0098154665011033575837057411557
absolute error = 0.00096959130441846233924988725345647
relative error = 0.095924578319697986019557381182767 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.0109320235397580097238311794022
y[1] (numeric) = 1.0099211625412723883446856868484
absolute error = 0.0010108609984856213791454925538494
relative error = 0.099992974299707319806776989043915 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.0110799783418882374380727307282
y[1] (numeric) = 1.0100270060417218906737560208251
absolute error = 0.0010529723001663467643167099030922
relative error = 0.10414332423960758014975729123105 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.0112289220639577132650190013457
y[1] (numeric) = 1.0101329979914458636300973794905
absolute error = 0.0010959240725118496349216218551644
relative error = 0.10837546757217206690239308591347 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.0113788545570227275471705896988
y[1] (numeric) = 1.0102391393792898570107905444383
absolute error = 0.0011397151777328705363800452605004
relative error = 0.11268924326404453774533812518902 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.0115297756711507997138872192414
y[1] (numeric) = 1.0103454311939499825053490491637
absolute error = 0.0011843444772008172085381700777126
relative error = 0.11708448981791007771218022104408 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.0116816852554208282138558147042
y[1] (numeric) = 1.0104518744239719249996898808896
absolute error = 0.0012298108314489032141659338145418
relative error = 0.12156104527467164590806516958416 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.0118345831579232414361794766499
y[1] (numeric) = 1.0105584700577499540305309734543
absolute error = 0.0012761131001732874056485031955492
relative error = 0.1261187472156322405504176576527 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.0119884692257601496199364332395
y[1] (numeric) = 1.0106652190835259353912040367795
absolute error = 0.0013232501422342142287323964600211
relative error = 0.13075743276468262336333608809746 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.0121433433050454977520570596639
y[1] (numeric) = 1.0107721224893883428898711170249
absolute error = 0.0013712208156571548621859426389912
relative error = 0.1354769385904945442617330814973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.0122992052409052194533660673757
y[1] (numeric) = 1.0108791812632712702611331291296
absolute error = 0.0014200239776339491922329382460149
relative error = 0.14027710090871940716835473482982 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.0124560548774773918526359770927
y[1] (numeric) = 1.0109863963929534432320184500495
absolute error = 0.0014696584845239486206175270432052
relative error = 0.14515775548419231771643983171698 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=15.2MB, alloc=4.3MB, time=0.80
x[1] = 0.159
y[1] (analytic) = 1.0126138920579123914484970015328
y[1] (numeric) = 1.01109376886605723174333950662
absolute error = 0.0015201231918551597051574949128816
relative error = 0.15011873763314145350297523389322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.0127727166243730509590474759817
y[1] (numeric) = 1.0112012996700476623274051366048
absolute error = 0.0015714169543253886316423393768437
relative error = 0.15515988222540269747226560807499 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.0129325284180348171590079870977
y[1] (numeric) = 1.0113089897922314306430763451371
absolute error = 0.0016235386258033865159316419605707
relative error = 0.16028102368663947492686426480785 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.0130933272790859097042613628125
y[1] (numeric) = 1.0114168402197559141691529214131
absolute error = 0.001676487059329995535108441399416
relative error = 0.16548199600056773458280685447175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.0132551130467274809436196988004
y[1] (numeric) = 1.0115248519396081850570782221715
absolute error = 0.0017302611071192958865414766289363
relative error = 0.17076263271118601400855046916745 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.0134178855591737767176586097624
y[1] (numeric) = 1.0116330259386140231439492691698
absolute error = 0.0017848596205597535737093405926905
relative error = 0.17612276692501052971204666717648 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.0135816446536522981444579067051
y[1] (numeric) = 1.0117413632034369291268191475661
absolute error = 0.0018402814502153690176387591390046
relative error = 0.18156223131331523206796723973486 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.0137463901664039643920869144861
y[1] (numeric) = 1.011849864720577137899278530822
absolute error = 0.0018965254458268264928083836641401
relative error = 0.1870808581143767652072551902025 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.0139121219326832764376716571557
y[1] (numeric) = 1.0119585314763706320513029954618
absolute error = 0.0019535904563126443863686616938611
relative error = 0.19267847913572427192388924755133 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.014078839786758481812880152039
y[1] (numeric) = 1.0120673644569881555333526257596
absolute error = 0.0020114753297703262795275262793827
relative error = 0.19835492575639398358902698606227 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.0142465435619117403356610670895
y[1] (numeric) = 1.0121763646484342274857102441716
absolute error = 0.0020701789134775128499508229179364
relative error = 0.2041100289291885350005278107114 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.0144152330904392908280700097875
y[1] (numeric) = 1.012285533036546156234044438094
absolute error = 0.0021297000538931345940255716935162
relative error = 0.20994361918294094403625107576575 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.0145849082036516188200167297711
y[1] (numeric) = 1.0123948706069930534521833873005
absolute error = 0.0021900375966585653678333424706044
relative error = 0.21585552662478319592247465922856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.0147555687318736252387655314679
y[1] (numeric) = 1.0125043783452748484930853292042
absolute error = 0.0022511903865987767456802022636294
relative error = 0.22184558094241937187428348888998 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.0149272145044447960840202072392
y[1] (numeric) = 1.0126140572367213028889913308908
absolute error = 0.0023131572677234931950288763484057
relative error = 0.22791361140640326181283372255566 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.0150998453497193730884238159675
y[1] (numeric) = 1.0127239082664910250217458676878
absolute error = 0.0023759370832283480666779482796583
relative error = 0.23405944687242040081500428654355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.0152734610950665253633026466005
y[1] (numeric) = 1.0128339324195704849642705378687
absolute error = 0.002439528675496040399032108731765
relative error = 0.24028291578357446890410087957772 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.01
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.0154480615668705220294827209227
y[1] (numeric) = 1.0129441306807730294941760719338
absolute error = 0.0025039308860974925353066489888684
relative error = 0.24658384617267799374597580694321 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.0156236465905309058330062047525
y[1] (numeric) = 1.0130545040347378972804976227762
absolute error = 0.0025691425557930085525085819763306
relative error = 0.25296206566454729577316742227489 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.0158002159904626677455741118622
y[1] (numeric) = 1.0131650534659292342445381499133
absolute error = 0.0026351625245334335010359619489468
relative error = 0.25941740147830161522044266917608 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.0159777695900964225495407001936
y[1] (numeric) = 1.0132757799586351090958045368604
absolute error = 0.0027019896314613134537361633332012
relative error = 0.26594968042966636051844222757284 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.0161563072118785854072839753885
y[1] (numeric) = 1.0133866844969665290440209056265
absolute error = 0.0027696227149120563632630697619566
relative error = 0.27255872893328041745797692449857 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.0163358286772715494147757322793
y[1] (numeric) = 1.0134977680648564556882034162382
absolute error = 0.0028380606124150937265723160411266
relative error = 0.2792443730050074585059030592748 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.016516333806753864139173580784
y[1] (numeric) = 1.0136090316460588210837806621341
absolute error = 0.002907302160695043055392918649895
relative error = 0.28600643826425119162440966203284 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.0166978224198204151402564186277
y[1] (numeric) = 1.013720476224147543988743594228
absolute error = 0.0029773461956728711515128243997231
relative error = 0.29284474993627448791897884587015 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.0168802943349826044755238294719
y[1] (numeric) = 1.0138321027825155462898087274084
absolute error = 0.0030481915524670581857151020635368
relative error = 0.29975913285452232741622757138952 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.0170637493697685321887789013652
y[1] (numeric) = 1.0139439123043737696095782032293
absolute error = 0.0031198370653947625792006981359076
relative error = 0.30674941146294850225130141437309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.0172481873407231787820129769491
y[1] (numeric) = 1.0140559057727501920956801015506
absolute error = 0.0031922815679729866863328753985459
relative error = 0.31381540981834601652546426170808 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.0174336080634085886704098635492
y[1] (numeric) = 1.0141680841704888453928722119054
absolute error = 0.0032655238929197432775376516438083
relative error = 0.32095695159268112207800805924744 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.0176200113524040546202860481617
y[1] (numeric) = 1.0142804484802488317990922924087
absolute error = 0.0033395628721552228211937557529859
relative error = 0.32817386007543092940258945360299 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.0178073970213063031697824794125
y[1] (numeric) = 1.0143929996845033416064376600758
absolute error = 0.003414397336802961563344819336693
relative error = 0.33546595817592453292658091787088 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.0179957648827296810321224958101
y[1] (numeric) = 1.0145057387655386706280567714876
absolute error = 0.0034900261171910104040657243225026
relative error = 0.34283306842568758986299809400855 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.0181851147483063424812494970519
y[1] (numeric) = 1.014618666705453237911935266831
absolute error = 0.0035664480428531045693142302208885
relative error = 0.35027501298079029183802784285018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.0183754464286864377196569727608
y[1] (numeric) = 1.0147317844861566036425587634455
absolute error = 0.0036436619425298340770982093153195
relative error = 0.35779161362419866849312794391107 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=1.22
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.0185667597335383022282225208382
y[1] (numeric) = 1.0148450930893684872314344971314
absolute error = 0.0037216666441698149967880237068086
relative error = 0.3653826917681291622590944657901 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.0187590544715486470978565056148
y[1] (numeric) = 1.0149585934966177855974537206167
absolute error = 0.0038004609749308615004027849981455
relative error = 0.37304806845640641350039132672171 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.0189523304504227503427750241667
y[1] (numeric) = 1.0150722866892415916380765787374
absolute error = 0.0038800437611811587046984454292246
relative error = 0.38078756436682419523140313498434 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.0191465874768846491952058675394
y[1] (numeric) = 1.0151861736483842128923209890663
absolute error = 0.0039604138285004363028848784731118
relative error = 0.38860099981350943661210155127464 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.019341825356677333381335182191
y[1] (numeric) = 1.0153002553549961903965368649174
absolute error = 0.0040415700016811429847983172735747
relative error = 0.39648819474928927443890152091406 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.0195380438945629393783015557216
y[1] (numeric) = 1.0154145327898333177339468248721
absolute error = 0.004123511104729621644354730849505
relative error = 0.40444896876806107185722101503127 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.0197352428943229456520432699139
y[1] (numeric) = 1.0155290069334556602789343392032
absolute error = 0.0042062359608672853731089307107901
relative error = 0.41248314110716534353544049067451 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.0199334221587583688758034832518
y[1] (numeric) = 1.0156436787662265746370600688273
absolute error = 0.0042897433925317942387434144245287
relative error = 0.4205905306497615265555800868166 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.020132581489689961129097124429
y[1] (numeric) = 1.0157585492683117282817869566882
absolute error = 0.0043740322213782328473101677408091
relative error = 0.42877095592720653629406743654944 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.0203327206879584080769422978976
y[1] (numeric) = 1.0158736194196781193888944347632
absolute error = 0.0044591012682802886880478631343812
relative error = 0.43702423512143604658645057983392 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.0205338395534245281291580222406
y[1] (numeric) = 1.0159888902000930968695619121974
absolute error = 0.0045449493533314312595961100432164
relative error = 0.44535018606734843349281235550229 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.020735937884969472579529142089
y[1] (numeric) = 1.0161043625891233806031015114011
absolute error = 0.0046315752958460919764276306879673
relative error = 0.4537486262551913220059582512812 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.0209390154804949267246382744327
y[1] (numeric) = 1.0162200375661340818703198192942
absolute error = 0.0047189779143608448543184551384765
relative error = 0.46221937283295067507217227870183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.0211430721369233119621636705127
y[1] (numeric) = 1.0163359161102877239884882202572
absolute error = 0.0048071560266355879736754502555295
relative error = 0.47076224260874236432445816583521 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.0213481076501979888684408950116
y[1] (numeric) = 1.0164519992005432631489011757328
absolute error = 0.0048961084496547257195397192787785
relative error = 0.47937705205320616196069904331715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.0215541218152834612550852449989
y[1] (numeric) = 1.016568287815655109458001612843
absolute error = 0.0049858339996283517970836321559579
relative error = 0.48806361730190209323407072599558 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=4.3MB, time=1.44
x[1] = 0.209
y[1] (analytic) = 1.0217611144261655812044708520247
y[1] (numeric) = 1.0166847829341721481830523808098
absolute error = 0.005076331491993433021418471214944
relative error = 0.49682175415770908906032442192644 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.0219690852758517550838614319007
y[1] (numeric) = 1.016801485534436761203332529431
absolute error = 0.0051675997414149938805289024696649
relative error = 0.50565127809322587828620686173352 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.0221780341563711505379866680538
y[1] (numeric) = 1.0169183965945838486678369583297
absolute error = 0.0052596375617873018701497097241011
relative error = 0.51455200425317405920530193599665 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.0223879608587749044598572358949
y[1] (numeric) = 1.0170355170925398508604577791985
absolute error = 0.0053524437662350535993994566964208
relative error = 0.52352374745680328995195033080775 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.0225988651731363319396104974034
y[1] (numeric) = 1.0171528480060217702736255257749
absolute error = 0.0054460171671145616659849716284305
relative error = 0.53256632220029853745062461032682 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.0228107468885511361911779170994
y[1] (numeric) = 1.0172703903125361938913881378247
absolute error = 0.0055403565760149422997897792747625
relative error = 0.54167954265918932464719883332253 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.0230236057931376194565642727558
y[1] (numeric) = 1.0173881449893783156829054359735
absolute error = 0.0056354608037593037736588367823371
relative error = 0.5508632226907609157999461073258 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.0232374416740368948875277565849
y[1] (numeric) = 1.0175061130136309593073365938105
absolute error = 0.0057313286604059355801911627743976
relative error = 0.56011717583646737966181635492496 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.0234522543174130994044490852411
y[1] (numeric) = 1.0176242953621636010310979022955
absolute error = 0.0058279589552494983733511829455889
relative error = 0.5694412153243464704415817453364 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.023668043508453607532176759785
y[1] (numeric) = 1.0177426930116313928584679091291
absolute error = 0.0059253504968222146737088506558933
relative error = 0.57883515407143626648978036279151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.0238848090313692462126346397834
y[1] (numeric) = 1.0178613069384741858765168024009
absolute error = 0.0060235020928950603361178373825302
relative error = 0.58829880468619350671603125319715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.0241025506693945105939770189553
y[1] (numeric) = 1.0179801381189155538153366935044
absolute error = 0.0061224125504789567786403254509177
relative error = 0.59783197947091356480722740425068 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.0243212682047877807960754132258
y[1] (numeric) = 1.0180991875289618168245492390066
absolute error = 0.0062220806758259639715261742192559
relative error = 0.60743449042415200138132874559052 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.0245409614188315396521202957203
y[1] (numeric) = 1.0182184561444010654670668248834
absolute error = 0.0063225052744304741850534708369803
relative error = 0.61710614924314763427896606106847 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.024761630091832591426120037115
y[1] (numeric) = 1.018337944940802184931083319279
absolute error = 0.006423685151030406495036717836016
relative error = 0.62684676732624706726481982483092 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.0249832740031222815060783338625
y[1] (numeric) = 1.0184576548935138794612701817163
absolute error = 0.0065256191096084020448081521461848
relative error = 0.63665615577533061748274633114132 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.0252058929310567170726304311345
y[1] (numeric) = 1.0185775869776636970101534974815
absolute error = 0.006628305953393020062476933653052
relative error = 0.64653412539823958208287789489296 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.4MB, time=1.66
x[1] = 0.226
y[1] (analytic) = 1.0254294866530169887429174718627
y[1] (numeric) = 1.018697742168157054110647285724
absolute error = 0.006731744484859934632270186138694
relative error = 0.65648048671120478451541505226355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.0256540549454093931894773280223
y[1] (numeric) = 1.0188181214396762609707182086582
absolute error = 0.0068359335057331322187591193640741
relative error = 0.66649504994127634106454717328435 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.0258795975836656567339292952864
y[1] (numeric) = 1.0189387257666795467911565871197
absolute error = 0.0069408718169861099427727081667
relative error = 0.67657762502875458827687418321514 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.0261061143422431599152290573844
y[1] (numeric) = 1.0190595561234000853074284046246
absolute error = 0.0070465582188430746078006527597401
relative error = 0.68672802162962211202184654019507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.0263336049946251630322693519284
y[1] (numeric) = 1.0191806134838450205565827579988
absolute error = 0.0071529915107801424756865939295559
relative error = 0.69694604911797681900708348606926 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.0265620693133210326606007951267
y[1] (numeric) = 1.0193018988217944928701889875883
absolute error = 0.0072601704915265397904118075384178
relative error = 0.70723151658846599165896102074005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.0267915070698664691430463486806
y[1] (numeric) = 1.0194234131108006650942774940319
absolute error = 0.0073680939590658040487688546487534
relative error = 0.71758423285872126736857108586102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.0270219180348237350539819382704
y[1] (numeric) = 1.0195451573241867490372580215751
absolute error = 0.0074767607106369860167239166953832
relative error = 0.7280040064717944831950320130783 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.027253301977781884637054759369
y[1] (numeric) = 1.0196671324350460321467889599254
absolute error = 0.0075861695427358524902657994435774
relative error = 0.73849064569859432721216722218421 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.0274856586673569942161098326828
y[1] (numeric) = 1.0197893394162409044165709876986
absolute error = 0.0076963192511160897995388449841596
relative error = 0.74904395854032373778075416837745 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.0277189878711923935790943983139
y[1] (numeric) = 1.0199117792404018855240381505809
absolute error = 0.0078072086307905080550562477330372
relative error = 0.75966375273091799212686825532722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.0279532893559588983347087647578
y[1] (numeric) = 1.0200344528799266521999192364356
absolute error = 0.0079188364760322461347895283221969
relative error = 0.77034983573948342570729637012124 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.0281885628873550432415712561047
y[1] (numeric) = 1.0201573613069790658306420777116
absolute error = 0.0080312015803759774109291783931062
relative error = 0.78110201477273672394556127492851 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.0284248082301073165096639283
y[1] (numeric) = 1.0202805054934882002945531786676
absolute error = 0.0081443027366191162151107496323543
relative error = 0.79192009677744472802677062619783 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.0286620251479703950738247530366
y[1] (numeric) = 1.0204038864111473700329248311126
absolute error = 0.0082581387368230250408999219239815
relative error = 0.80280388844286469654627210479313 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.0289002134037273808390509958078
y[1] (numeric) = 1.0205275050314131583567216475738
absolute error = 0.0083727083723142224823293482340289
relative error = 0.8137531962031849649159481515686 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.0291393727591900378973775428355
y[1] (numeric) = 1.0206513623255044459900982050444
absolute error = 0.0084880104336855919072793377911256
relative error = 0.82476782623996594454290913813691 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=1.87
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.0293795029751990307160929600163
y[1] (numeric) = 1.0207754592644014398515992557331
absolute error = 0.0086040437107975908644937042831533
relative error = 0.83584758448458140390833139241183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.0296206038116241632970550956892
y[1] (numeric) = 1.0208997968188447020740337235342
absolute error = 0.008720806992779461223021372154923
relative error = 0.84699227662065997378922517926585 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.0298626750273646193068670679285
y[1] (numeric) = 1.0210243759593341792639934662624
absolute error = 0.0088382990680304400428736016661032
relative error = 0.85820170808652681898299625173214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.0301057163803492031776735062069
y[1] (numeric) = 1.0211491976561282320019875440539
absolute error = 0.0089565187242209711756859621530799
relative error = 0.86947568407764541901377158916547 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.0303497276275365821783359466519
y[1] (numeric) = 1.0212742628792426645841624937181
absolute error = 0.0090754647482939175941734529337431
relative error = 0.88081400954905940042058398653047 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.0305947085249155294557453097401
y[1] (numeric) = 1.021399572598449755006578867239
absolute error = 0.0091951359264657744491664425011041
relative error = 0.89221648921783436335063972481027 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.0308406588275051680460284191387
y[1] (numeric) = 1.0215251277832772851930140500678
absolute error = 0.0093155310442278828530143690708952
relative error = 0.90368292756549964530601701930365 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.0310875782893552158554045505058
y[1] (numeric) = 1.0216509294030075714672611313252
absolute error = 0.0094366488863476443881434191805973
relative error = 0.91521312884048996501924860589624 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.0313354666635462316104470294153
y[1] (numeric) = 1.0217769784266764952708933535319
absolute error = 0.0095584882368697363395536758834278
relative error = 0.92680689706058688956231789470279 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.0315843237021898617775039281638
y[1] (numeric) = 1.0219032758230725341274634240224
absolute error = 0.0096810478791173276500405041414088
relative error = 0.93846403601536006792463272024492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.0318341491564290884510309420608
y[1] (numeric) = 1.0220298225607357928541067237634
absolute error = 0.0098043265956932955969242182974607
relative error = 0.95018434926860817442852188817101 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.0320849427764384782105885568886
y[1] (numeric) = 1.0221566196079570350215172018903
absolute error = 0.0099283231684814431890713549982422
relative error = 0.96196764016079950548571541837957 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.0323367043114244319462546505563
y[1] (numeric) = 1.0222836679327767146632644959084
absolute error = 0.010053036378647717282990154647915
relative error = 0.97381371181151217333510748968185 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.0325894335096254356522027035565
y[1] (numeric) = 1.0224109685029840082354205681577
absolute error = 0.01017846500664142741678213539886
relative error = 0.98572236712187384054084939787698 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.032843130118312312188194824666
y[1] (numeric) = 1.0225385222861158468274638988366
absolute error = 0.010304607832196465360730925829342
relative error = 0.99769340877700093917046606415399 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.0330977938837884740087378304194
y[1] (numeric) = 1.0226663302494559486254290245985
absolute error = 0.010431463634332525383308805820919
relative error = 1.0097266392484373187152214128834 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.0333534245513901768596496492213
y[1] (numeric) = 1.0227943933600338516282689594906
absolute error = 0.010559031191356325231380689730741
relative error = 1.0218218607965922669593628390539 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=2.09
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.0336100218654867744417823535499
y[1] (numeric) = 1.0229227125846239466183977817934
absolute error = 0.010687309280862827823384571756511
relative error = 1.0339788754731778481511404920861 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.0338675855694809740416471565521
y[1] (numeric) = 1.0230512888897445103873804161366
absolute error = 0.010816296679736463654266740415459
relative error = 1.0461974851236455029766106262367 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.0341261154058090931286857424248
y[1] (numeric) = 1.0231801232416567392177363851208
absolute error = 0.010945992164152353910949357303996
relative error = 1.0584774913896218549871811466581 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.0343856111159413169189313333345
y[1] (numeric) = 1.0233092166063637826218240485621
absolute error = 0.011076394509577534297107284772382
relative error = 1.0708186957113436682836289806043 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.0346460724403819569048019292326
y[1] (numeric) = 1.023438569949609777338771591393
absolute error = 0.011207502490772179566030337839576
relative error = 1.0832208993300919014129002204868 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.0349074991186697103507671907983
y[1] (numeric) = 1.0235681842368788815904207632103
absolute error = 0.01133931488179082876034642758805
relative error = 1.0956839032906248025893822448789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.0351698908893779207546294698607
y[1] (numeric) = 1.0236980604333943095972491134431
absolute error = 0.01147183045598361115738035641754
relative error = 1.1082075084436099915094992819214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.0354332474901148392741585260421
y[1] (numeric) = 1.0238281995041173663552362061411
absolute error = 0.011605047985997472918922319901091
relative error = 1.1207915154480554731874161262363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.0356975686575238871188185030108
y[1] (numeric) = 1.0239586024137464826746390374337
absolute error = 0.011738966243777404444179465577116
relative error = 1.1334357247737395294003258784693 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.0359628541272839189063247726353
y[1] (numeric) = 1.0240892701267162504816416168071
absolute error = 0.011873584000567668424683155828193
relative error = 1.1461399367036394334942335039782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.0362291036341094869837672905078
y[1] (numeric) = 1.0242202036071964583838434104661
absolute error = 0.012008900026913028599923880041673
relative error = 1.1589039513363589344653144980787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.0364963169117511067130361417346
y[1] (numeric) = 1.024351403819091127500551081215
absolute error = 0.012144913092659979212485060519587
relative error = 1.1717275685885544563978137310874 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.0367644936929955227202839915894
y[1] (numeric) = 1.0244828717260375475588376944829
absolute error = 0.012281621966957975161446297106491
relative error = 1.1846105881973599595070402970897 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.0370336337096659761091591915901
y[1] (numeric) = 1.0246146082914053132563332943556
absolute error = 0.012419025418260662852825897234528
relative error = 1.1975528097228104092052965155329 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.0373037366926224726375423277883
y[1] (numeric) = 1.0247466144782953608917104867426
absolute error = 0.012557122214327111745831841045744
relative error = 1.2105540325502637997795396848868 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.0375748023717620518575180345561
y[1] (numeric) = 1.0248788912495390052638283991128
absolute error = 0.012695911122223046593689635443315
relative error = 1.223614055892821679442200255303 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.0378468304760190572183129339225
y[1] (numeric) = 1.025011439567696976840498117576
absolute error = 0.01283539090832208037781481634653
relative error = 1.2367326787937481236908562082642 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=2.31
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.0381198207333654071319295975428
y[1] (numeric) = 1.025144260395058459197832432463
absolute error = 0.012975560338306947934097165079764
relative error = 1.2499097001288871040883769859309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.0383937728708108670012054656899
y[1] (numeric) = 1.0252773546936401267311424529759
absolute error = 0.013116418177170740270063012714029
relative error = 1.2631449186090781997526876271988 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.0386686866144033222100246952314
y[1] (numeric) = 1.0254107234251851826383433799298
absolute error = 0.013257963189218139571681315301653
relative error = 1.2764381327825705990244511141503 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.0389445616892290520754099464035
y[1] (numeric) = 1.0255443675511623971768314531026
absolute error = 0.013400194138066654898578493300946
relative error = 1.2897891410374353389617105324191 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.0392213978194130047612201563121
y[1] (numeric) = 1.0256782880327651461947938162331
absolute error = 0.013543109786647858566426340078961
relative error = 1.3031977416039757304928586720203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.0394991947281190731531793854871
y[1] (numeric) = 1.0258124858309104499379127682796
absolute error = 0.013686708897208623215266617207502
relative error = 1.3166637325571359172431972618787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.0397779521375503716949608624835
y[1] (numeric) = 1.0259469619062380121324255941527
absolute error = 0.013830990231312359562535268330853
relative error = 1.3301869118189075162357972136636 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.0400576697689495141850493904688
y[1] (numeric) = 1.0260817172191092593455008917846
absolute error = 0.013975952549840254839548498684165
relative error = 1.3437670771607342888543610734706 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.040338347342598892534104318956
y[1] (numeric) = 1.0262167527296063806238920350764
absolute error = 0.014121594612992511910212283879632
relative error = 1.3574040262059147906443053222156 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.0406199845778209564825443233454
y[1] (numeric) = 1.0263520693975313674118281339912
absolute error = 0.014267915180289589070716189354195
relative error = 1.3710975564320029487183091613463 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.0409025811929784942780742747098
y[1] (numeric) = 1.0264876681824050537491025738215
absolute error = 0.014414913010573440528971700888284
relative error = 1.3848474651732065157241038600242 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.0411861369054749143128735223236
y[1] (numeric) = 1.0266235500434661567503189354629
absolute error = 0.014562586862008757562554586860626
relative error = 1.398653549622783349525288471215 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.0414706514317545277201639517677
y[1] (numeric) = 1.0267597159396703173662538173675
absolute error = 0.014710935492084210353910134400204
relative error = 1.4125156068354354679404395538445 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.0417561244873028319298752220681
y[1] (numeric) = 1.0268961668296891414282957977345
absolute error = 0.014859957657613690501579424333599
relative error = 1.4264334337297008280817202329187 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.0420425557866467951831236262249
y[1] (numeric) = 1.0270329036719092409769194924199
absolute error = 0.015009652114737554206204133804998
relative error = 1.4404068270903427800315732170081 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.0423299450433551420052200606774
y[1] (numeric) = 1.0271699274244312758751533800097
absolute error = 0.015160017618923866130066680667656
relative error = 1.454435583570737144794888962737 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.0426182919700386396369216307212
y[1] (numeric) = 1.0273072390450689957079997805109
absolute error = 0.015311052924969643928921850210321
relative error = 1.4685194996952568666642596824018 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=2.52
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.0429075962783503854236404606493
y[1] (numeric) = 1.0274448394913482819687650881586
absolute error = 0.015462756787002103454875372490715
relative error = 1.4826583718616541903375479516722 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.0431978576789860951623223194319
y[1] (numeric) = 1.0275827297205061905332580719307
absolute error = 0.015615127958479904629064247501251
relative error = 1.4968519963434403133300008734765 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.0434890758816843924057067150814
y[1] (numeric) = 1.0277209106894899944228137694909
absolute error = 0.015768165192194397982892945590489
relative error = 1.5111001692922624644275126425767 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.0437812505952270987236791534653
y[1] (numeric) = 1.0278593833549562268571002114573
absolute error = 0.015921867240270871866578942008008
relative error = 1.525402686740278359133365452146 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.0440743815274395249214253002402
y[1] (numeric) = 1.0279981486732697245976649231092
absolute error = 0.016076232854169800323760377131093
relative error = 1.5397593446025279832678464773284 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.0443684683851907632140958277764
y[1] (numeric) = 1.0281372076005026715831778599069
absolute error = 0.016231260784688091630917967869567
relative error = 1.5541699386793026560885326202928 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.044663510874393980357689772432
y[1] (numeric) = 1.0282765610924336428573271415011
absolute error = 0.0163869497819603375003626309309
relative error = 1.568634264658511324508740237345 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.0449595087000067117358632713184
y[1] (numeric) = 1.0284162101045466487903236562564
absolute error = 0.016543298595460062945539615062072
relative error = 1.5831521181180440402026395947571 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.0452564615660311564023695917739
y[1] (numeric) = 1.0285561555920301795949703147057
absolute error = 0.016700305974000976807399277068218
relative error = 1.5977232945281325715978186936192 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.0455543691755144730788354111266
y[1] (numeric) = 1.0286963985097762501382514357851
absolute error = 0.016857970665738222940583975341482
relative error = 1.6123475892537081029696337179017 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.0458532312305490771075773489994
y[1] (numeric) = 1.028836939812379445049397454182
absolute error = 0.01701629141816963205817989481746
relative error = 1.6270247975567559730664890230318 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.0461530474322729383591617993617
y[1] (numeric) = 1.02897778045413596412537984065
absolute error = 0.017175266978136974233781958711715
relative error = 1.6417547145986674059112336011077 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.0464538174808698800944101547946
y[1] (numeric) = 1.0291189213890426680347908297187
absolute error = 0.017334896091827212059619325075844
relative error = 1.6565371354425881866411286184881 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.0467555410755698787805505609893
y[1] (numeric) = 1.0292603635707961243210622508372
absolute error = 0.017495177504773754459488310152022
relative error = 1.6713718550557642354673171867602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.0470582179146493648612163853508
y[1] (numeric) = 1.0294021079527916537059774596532
absolute error = 0.017656109961857711155238925697574
relative error = 1.686258668311884033054398244785 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.0473618476954315244799906297348
y[1] (numeric) = 1.0295441554881223766944300658372
absolute error = 0.017817692207309147785560563897599
relative error = 1.7011973699934178508415565254536 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.0476664301142866021571945637978
y[1] (numeric) = 1.0296865071295782604813828526133
absolute error = 0.017979922984708341675811711184532
relative error = 1.7161877547939537400487152669842 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=2.74
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.0479719648666322044196179021966
y[1] (numeric) = 1.029829163829645166161979980957
absolute error = 0.018142801036987038257637921239593
relative error = 1.7312296173205302333343428003723 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.0482784516469336043828868959338
y[1] (numeric) = 1.0299721265405038962457652682709
absolute error = 0.018306325106429708137121627662845
relative error = 1.7463227520959657132958435827592 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.0485858901487040472861657555049
y[1] (numeric) = 1.0301153962140292424759590272381
absolute error = 0.018470493934674804810206728266806
relative error = 1.761466953561184402228883818371 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.0488942800645050569788858711721
y[1] (numeric) = 1.0302589738017890339547456454983
absolute error = 0.018635306262716023024140225673831
relative error = 1.7766620160775389277885266693584 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.0492036210859467433591963436608
y[1] (numeric) = 1.0304028602550431855755237807803
absolute error = 0.018800760830903557783672562880512
relative error = 1.791907733929129419422667352214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.0495139129036881107638283868539
y[1] (numeric) = 1.0305470565247427467630707391603
absolute error = 0.018966856378945364000757647693644
relative error = 1.807203901325119090676949275276 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.0498251552074373673090652126448
y[1] (numeric) = 1.0306915635615289505225722962021
absolute error = 0.019133591645908416786492916442731
relative error = 1.8225503124020462627000939239906 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.0501373476859522351825080570062
y[1] (numeric) = 1.0308363823157322627984689118722
absolute error = 0.019300965370219972384039145133974
relative error = 1.837946761226132784509374560111 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.0504504900270402618853280555329
y[1] (numeric) = 1.0309815137373714321440689803018
absolute error = 0.019468976289668829741259075231026
relative error = 1.8533930417955888058077920791049 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.0507645819175591324246927262339
y[1] (numeric) = 1.0311269587761525397028794447049
absolute error = 0.019637623141406592721813281528996
relative error = 1.8688889480429138583773556713398 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.0510796230434169824560548671731
y[1] (numeric) = 1.031272718381468049502603796042
absolute error = 0.019806904661948932953451071131042
relative error = 1.8844342738371942023067163571498 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.0513956130895727123749907266948
y[1] (numeric) = 1.031418793502395859062757161353
absolute error = 0.019976819587176853312233565341873
relative error = 1.9000288129863963935462331102455 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.051712551740036302358273354424
y[1] (numeric) = 1.0315651850876983503168478740637
absolute error = 0.02014736665233795204142548036038
relative error = 1.9156723592396570295193542423 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.0520304386778691283538660919921
y[1] (numeric) = 1.0317118940858214408500746040071
absolute error = 0.020318544592047687503791487984954
relative error = 1.9313647062895686297559560868147 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.0523492735851842790195202135225
y[1] (numeric) = 1.031858921444893635453487809382
absolute error = 0.020490352140290643566032404140525
relative error = 1.9471056477744616087509818852005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.0526690561431468736096597773046
y[1] (numeric) = 1.032006268112725077995563956408
absolute error = 0.020662788030421795614095820896585
relative error = 1.9628949772806822984903512358987 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.0529897860319743808102358017967
y[1] (numeric) = 1.0321539350368066036121406350257
memory used=53.4MB, alloc=4.4MB, time=2.95
absolute error = 0.020835850995167777198095166771062
relative error = 1.9787324883448669783256496137147 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.0533114629309369385212309311322
y[1] (numeric) = 1.0323019231643087912156603806256
absolute error = 0.021009539766628147305570550506544
relative error = 1.994617974456211870119543399716 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.0536340865183576745864948076487
y[1] (numeric) = 1.0324502334420810163246706924851
absolute error = 0.021183853076276658261824115163607
relative error = 2.0105512290587390568251836844401 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.0539576564716130284705894216338
y[1] (numeric) = 1.0325988668166505042145274193322
absolute error = 0.021358789654962524256062002301553
relative error = 2.0265320455535582829050469262311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.0542821724671330738823227614669
y[1] (numeric) = 1.0327478242342213833902483612566
absolute error = 0.021534348232911690492074400210313
relative error = 2.0425602173011245952376974758427 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.0546076341804018423446481406519
y[1] (numeric) = 1.0328971066406737393824636150327
absolute error = 0.021710527539728102962184525619218
relative error = 2.0586355376234917834048311387453 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.0549340412859576477106056318672
y[1] (numeric) = 1.0330467149815626688674088668277
absolute error = 0.021887326304394978843196765039478
relative error = 2.0747577998065615784956554667646 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.0552613934573934116249810921192
y[1] (numeric) = 1.0331966502021173341119075122211
absolute error = 0.02206474325527607751307357989809
relative error = 2.0909267971023285698111664888948 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.0555896903673569899313573173679
y[1] (numeric) = 1.0333469132472400177442871584757
absolute error = 0.022242777120116972187070158892191
relative error = 2.1071423227311207990971782557447 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.0559189316875515000242309195995
y[1] (numeric) = 1.0334975050615051778521757380643
absolute error = 0.02242142662604632217205518153517
relative error = 2.1234041698838359921820360427088 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.056249117088735649145867574257
y[1] (numeric) = 1.0336484265891585034081221355772
absolute error = 0.022600690499577145737745438679803
relative error = 2.1397121317241733881427815055224 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.0565802462407240636275673412012
y[1] (numeric) = 1.0337996787741159700239859023114
absolute error = 0.02278056746660809360358143888985
relative error = 2.1560660013908611263721236935077 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.0569123188123876190750108179637
y[1] (numeric) = 1.033951262559962896035040304073
absolute error = 0.022961056252424723039970513890653
relative error = 2.1724655719998791521678888000189 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.0572453344716537714973559399734
y[1] (numeric) = 1.0341031788899529989147326180116
absolute error = 0.023142155581700772582623321961776
relative error = 2.1889106366466776017166590810411 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.0575792928855068893797542986879
y[1] (numeric) = 1.0342554287070074520210452636465
absolute error = 0.02332386417849943735870903504144
relative error = 2.2054009884083906275940527325754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.0579141937199885866989549051397
y[1] (numeric) = 1.0344080129537139416754010216458
absolute error = 0.023506180766274645023553883493821
relative error = 2.2219364203460456261555269335588 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.0582500366401980568816623833228
y[1] (numeric) = 1.0345609325723257245750552613758
absolute error = 0.023689104067872332306607121947004
relative error = 2.2385167255067678284436910000438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=57.2MB, alloc=4.4MB, time=3.17
x[1] = 0.344
y[1] (analytic) = 1.0585868213102924077053156350886
y[1] (numeric) = 1.0347141885047606855399177647466
absolute error = 0.023872632805531722165397870342
relative error = 2.2551416969259802164908809438205 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.0589245473934869971409520758003
y[1] (numeric) = 1.0348677816926003955947463994579
absolute error = 0.024056765700886601546205676342427
relative error = 2.2718111276295987271491559903523 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.0592632145520557701378215979091
y[1] (numeric) = 1.0350217130770891703876545593683
absolute error = 0.024241501474966599750167038540755
relative error = 2.2885248106362227058339171136914 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.0596028224473315963494134778678
y[1] (numeric) = 1.0351759835991331289458739534067
absolute error = 0.024426838848198467403539524461137
relative error = 2.3052825389593205728220027388639 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.0599433707397066088005585003815
y[1] (numeric) = 1.0353305941992992527697139871803
absolute error = 0.024612776540407356030844513201282
relative error = 2.3220841056094106650003728169886 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.0602848590886325434952676329222
y[1] (numeric) = 1.0354855458178144452656586432449
absolute error = 0.024799313270818098229608989677257
relative error = 2.3389293035962372162173348909972 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.0606272871526210799649676426963
y[1] (numeric) = 1.0356408393945645915195414268602
absolute error = 0.02498644775805648844542621583611
relative error = 2.3558179259309414396446799609817 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.0609706545892441827567931078597
y[1] (numeric) = 1.0357964758690936184107386039774
absolute error = 0.025174178720150564346054503882374
relative error = 2.3727497656282276758160673744593 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.0613149610551344438615933347137
y[1] (numeric) = 1.0359524561806025550683206171873
absolute error = 0.02536250487453188879327271752645
relative error = 2.3897246157085245702645120814573 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.0616602062059854260813117529063
y[1] (numeric) = 1.0361087812679485936701012234001
absolute error = 0.025551424938036832411210529506215
relative error = 2.4067422692001412449398699081692 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.0620063896965520073353944212866
y[1] (numeric) = 1.0362654520696441505855235541282
absolute error = 0.025740937626907856749870867158465
relative error = 2.423802519141418427845772545426 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.062353511180650725905883338033
y[1] (numeric) = 1.0364224695238559278633219554084
absolute error = 0.025931041656794798042561382624681
relative error = 2.4409051585828745055945192782154 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.0627015703111601266208493099901
y[1] (numeric) = 1.0365798345684039750648981196235
absolute error = 0.026121735742756151555951190366632
relative error = 2.4580499805893464638379726891225 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.0630505667400211079758181978111
y[1] (numeric) = 1.036737548140760751444349675769
absolute error = 0.026313018599260356531468522042103
relative error = 2.4752367782421256807925162722477 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.0634005001182372701928434155077
y[1] (numeric) = 1.0368956111780501884760890580575
absolute error = 0.026504888940187081716754357450167
relative error = 2.4924653446410885393365987473226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.0637513700958752642168766253643
y[1] (numeric) = 1.0370540246170467527309901251648
absolute error = 0.026697345478828511485886500199514
relative error = 2.5097354729068218234202985518212 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.0641031763220651416490876318753
y[1] (numeric) = 1.0372127893941745091019996538923
absolute error = 0.026890386927890632547087977982911
relative error = 2.5270469561827428647876782310724 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=61.0MB, alloc=4.4MB, time=3.38
x[1] = 0.361
y[1] (analytic) = 1.064455918445000705616783541413
y[1] (numeric) = 1.0373719064455061843801504815564
absolute error = 0.027084011999494521236633059856648
relative error = 2.5443995876372144062744479966373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.0648095961119398625795763177395
y[1] (numeric) = 1.0375313767067622311819127210133
absolute error = 0.027278219405177631397663596726207
relative error = 2.5617931604656541482056063709421 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.0651642089692049750714469272204
y[1] (numeric) = 1.0376912011133098922288191208913
absolute error = 0.027473007855895082842627806329142
relative error = 2.5792274678926389446802594071654 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.0655197566621832153783533317088
y[1] (numeric) = 1.0378513806001622649803002913251
absolute error = 0.027668376062020950398053040383762
relative error = 2.5967023031740036167937243306488 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.0658762388353269201510286515192
y[1] (numeric) = 1.038011916101977366620665162281
absolute error = 0.027864322733349553530363489238259
relative error = 2.6142174595989343501102844926775 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.0662336551321539459526148857234
y[1] (numeric) = 1.0381728085530571994011616874133
absolute error = 0.028060846579096746551453198310065
relative error = 2.6317727304920566439635661992263 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.0665920051952480257407766421643
y[1] (numeric) = 1.0383340588873468163380524513144
absolute error = 0.02825794630790120940272419084991
relative error = 2.6493679092155177804254402557274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.0669512886662591262839383951033
y[1] (numeric) = 1.0384956680384333872676394820033
absolute error = 0.028455620627825739016298913100054
relative error = 2.6670027891710637810485979741002 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.0673115051859038065112878542941
y[1] (numeric) = 1.0386576369395452652591722135523
absolute error = 0.028653868246358541252115640741836
relative error = 2.6846771638021108197524989814525 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.0676726543939655767961870955091
y[1] (numeric) = 1.0388199665235510533865721858643
absolute error = 0.028852687870414523409614909644812
relative error = 2.7023908265958110604872225543499 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.0680347359292952591726321691378
y[1] (numeric) = 1.038982657722958671859907709799
absolute error = 0.029052078206336587312724459338754
relative error = 2.7201435710851128885748615245181 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.0683977494298113484844009704265
y[1] (numeric) = 1.0391457114699144255175513660952
absolute error = 0.02925203795989692296684960433132
relative error = 2.7379351908508155048934642510759 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.0687616945325003744665282222431
y[1] (numeric) = 1.0393091286962020716799528458543
absolute error = 0.029452565836298302786575376388837
relative error = 2.7557654795236178523341419650484 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.0691265708734172647587454889206
y[1] (numeric) = 1.0394729103332418883659592787347
absolute error = 0.029653660540175376392786210185899
relative error = 2.7736342307861618442278022433009 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.0694923780876857088505232077704
y[1] (numeric) = 1.0396370573120897428726148324584
absolute error = 0.029855320775595965977908375312001
relative error = 2.7915412383750698647040307863492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.0698591158094985229573507932542
y[1] (numeric) = 1.0398015705634361607193710037535
absolute error = 0.030057545246062362237979789500716
relative error = 2.8094862960829765112109094295969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.070226783672118015827889937563
y[1] (numeric) = 1.0399664510176053949576386564434
absolute error = 0.030260332654512620870251281119606
relative error = 2.827469197760554549691014829637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.4MB, time=3.60
x[1] = 0.378
y[1] (analytic) = 1.0705953813078763554816353004824
y[1] (numeric) = 1.0401316996045544958466124970547
absolute error = 0.030463681703321859635022803427634
relative error = 2.8454897373185350531754760036641 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.070964908348175936876715850913
y[1] (numeric) = 1.040297317253872380896298312041
absolute error = 0.030667591094303555980417538871969
relative error = 2.8635477087297216948247663769324 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.0713353644234897505074691922754
y[1] (numeric) = 1.0404633048947789052786729235173
absolute error = 0.030872059528710845228796268758189
relative error = 2.8816429060309991667118537762635 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.0717067491633617519314202742562
y[1] (numeric) = 1.0406296634561239326079064522685
absolute error = 0.031077085707237819323513821987722
relative error = 2.8997751233253356959104165128071 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.0720790621964072322252949639468
y[1] (numeric) = 1.0407963938663864060905761077325
absolute error = 0.031282668330020826134718856214287
relative error = 2.9179441547837796297180419914842 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.072452303150313189369698020393
y[1] (numeric) = 1.0409634970536734200468003546651
absolute error = 0.031488806096639769322897665727839
relative error = 2.9361497946474500621116428863422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.0728264716518387005620840879077
y[1] (numeric) = 1.0411309739457192918032219352772
absolute error = 0.031695497706119408758862152630519
relative error = 2.9543918372295214737997416012651 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.0732015673268152954576493952072
y[1] (numeric) = 1.0412988254698846339587678537822
absolute error = 0.031902741856930661498881541425028
relative error = 2.9726700769172023585037733179921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.0735775898001473303377709195101
y[1] (numeric) = 1.041467052553155427024114057518
absolute error = 0.032110537246991903313656861992103
relative error = 2.9909843081737078083681282956925 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.0739545386958123632056188471909
y[1] (numeric) = 1.0416356561221420924357821750998
absolute error = 0.032318882573670270769836672091087
relative error = 3.0093343255402260316662821602895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.0743324136368615298085672354074
y[1] (numeric) = 1.041804637103078565945795297431
absolute error = 0.032527776533782963862771937976364
relative error = 3.0277199236378787762380356941172 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.0747112142454199205870268523226
y[1] (numeric) = 1.0419739964218213713878194118393
absolute error = 0.032737217823598549199207440483356
relative error = 3.046140897169675632360590149773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.0750909401426869585493232471189
y[1] (numeric) = 1.0421437350038486948207167231177
absolute error = 0.032947205138838263728606524001238
relative error = 3.0645970409224621890239074648619 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.0754715909489367780722421749589
y[1] (numeric) = 1.0423138537742594590504367178426
absolute error = 0.033157737174677319021805457116299
relative error = 3.083088149768862017848534102288 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.0758531662835186046268635763786
y[1] (numeric) = 1.0424843536577723985311704499983
absolute error = 0.033368812625746206095693126380265
relative error = 3.1016140186692124591517897968798 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.0762356657648571354293043853106
y[1] (numeric) = 1.042655235578725134646693146678
absolute error = 0.033580430186132000782611238632621
relative error = 3.1201744426734941849359255246005 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.0766190890104529210159895150267
y[1] (numeric) = 1.0428265004610732513728198524412
absolute error = 0.033792588549379669643169662585515
relative error = 3.1387692169232545138395258552731 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.4MB, time=3.81
x[1] = 0.395
y[1] (analytic) = 1.0770034356368827477430694467591
y[1] (numeric) = 1.0429981492283893713218984497944
absolute error = 0.034005286408493376421170996964735
relative error = 3.1573981366535244533610568928072 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.0773887052598000212096019216175
y[1] (numeric) = 1.0431701828038622321702640112264
absolute error = 0.034218522455937789039337910391055
relative error = 3.1760609971947294449310296974357 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.0777748974939351506041143126486
y[1] (numeric) = 1.0433426021102957634695780552651
absolute error = 0.034432295383639387134536257383519
relative error = 3.1947575939745937876767479319792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.0781620119530959339741623305114
y[1] (numeric) = 1.0435154080701081638429758951409
absolute error = 0.034646603882987770131186435370527
relative error = 3.2134877225200387169910250492457 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.0785500482501679444184997932385
y[1] (numeric) = 1.0436886016053309785669448838322
absolute error = 0.03486144664483696585155490940636
relative error = 3.2322511784590741142835782725234 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.0789390059971149172014732679482
y[1] (numeric) = 1.0438621836376081775398559735375
absolute error = 0.035076822359506739661617294410664
relative error = 3.2510477575226838245610216100754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.0793288848049791377892544701431
y[1] (numeric) = 1.0440361550881952336380706209662
absolute error = 0.035292729716783904151183849176926
relative error = 3.269877255546704558748475944648 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.0797196842838818308075223843971
y[1] (numeric) = 1.0442105168779582014605446822636
absolute error = 0.035509167405923629346977702133568
relative error = 3.2887394684736983579327786705387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.0801114040430235499202061487794
y[1] (numeric) = 1.0443852699273727964628505528907
absolute error = 0.035726134115650753457355595888627
relative error = 3.3076341923548185969740962978037 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.0805040436906845686288988243055
y[1] (numeric) = 1.044560415156523474481538418359
absolute error = 0.035943628534161094147360405946509
relative error = 3.3265612233516695051994088540651 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.0808976028342252719925512500355
y[1] (numeric) = 1.0447359534851025116497570913819
absolute error = 0.036161649349122760342794158653561
relative error = 3.3455203577381591821578328022669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.0812920810800865492670542641556
y[1] (numeric) = 1.0449118858324090847050545197468
absolute error = 0.036380195247677464561999744408765
relative error = 3.3645113919023460866840676360995 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.0816874780337901874643166514964
y[1] (numeric) = 1.0450882131173483516902776570292
absolute error = 0.036599264916441835774038994467209
relative error = 3.3835341223482789777823784579494 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.0820837932999392658304452584406
y[1] (numeric) = 1.045264936258430533048490995173
absolute error = 0.036818857041508732781954263267647
relative error = 3.4025883456978302861094508977127 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.0824810264822185512426327970737
y[1] (numeric) = 1.0454420561737699931128326639416
absolute error = 0.037038970308448558129800133132031
relative error = 3.4216738586925228951001639720059 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.082879177183394894524357941723
y[1] (numeric) = 1.0456195737810843219922266073082
absolute error = 0.03725960340231057253213133441479
relative error = 3.4407904581953503110458092568276 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.0832782450053176276785014027179
y[1] (numeric) = 1.0457974899976934178538689509944
absolute error = 0.037480755007624209824632451723478
relative error = 3.4599379411925902016995294649116 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.4MB, time=4.02
x[1] = 0.412
y[1] (analytic) = 1.0836782295489189620379807442877
y[1] (numeric) = 1.045975805740518569603406278597
absolute error = 0.037702423808400392434574465690668
relative error = 3.4791161047956112832487446623669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.084079130414214387333505795996
y[1] (numeric) = 1.0461545219260815399637231360459
absolute error = 0.037924608488132847369782659950154
relative error = 3.4983247462426735357590684768662 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.0844809472003030716780555899898
y[1] (numeric) = 1.0463336394705036489532556855306
absolute error = 0.038147307729799422724799904459249
relative error = 3.5175636629007217274586783598177 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.0848836795053682624676768396186
y[1] (numeric) = 1.046513159289504857764748030505
absolute error = 0.038370520215863404702928809113579
relative error = 3.5368326522671722284962819553265 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.0852873269266776881982030586595
y[1] (numeric) = 1.0466930822984028530453673329375
absolute error = 0.038594244628274835152835725721983
relative error = 3.5561315119716930950697046569448 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.0856918890605839611974925044623
y[1] (numeric) = 1.046873409412112131579093442615
absolute error = 0.038818479648471829618399061847308
relative error = 3.5754600397779774050857003271778 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.0860973655025249812727822128099
y[1] (numeric) = 1.0470541415451430853722983560353
absolute error = 0.039043223957381895900483856774629
relative error = 3.5948180335855098267748468131465 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.0865037558470243402727544771743
y[1] (numeric) = 1.0472352796116010871434304192321
absolute error = 0.03926847623542325312932405794219
relative error = 3.6142052914313264019483192845654 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.0869110596876917275639112103343
y[1] (numeric) = 1.0474168245251855762177177847716
absolute error = 0.039494235162506151346193425562714
relative error = 3.6336216114917675258459265886507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.087319276617223336420850712016
y[1] (numeric) = 1.0475987771991891448278052281419
absolute error = 0.03972049941803419159304548387415
relative error = 3.6530667920842241057870378740336 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.0877284062274022713300404523114
y[1] (numeric) = 1.0477811385464966248212380228215
absolute error = 0.039947267680905646508802429489901
relative error = 3.6725406316688768810979078678222 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.0881384481090989562066785671375
y[1] (numeric) = 1.0479639094795841747757061664678
absolute error = 0.040174538629514781430972400669684
relative error = 3.692042928850428887050418654901 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.088549401852271543524235848908
y[1] (numeric) = 1.0481470909105183675229618429042
absolute error = 0.040402310941753176001274006003844
relative error = 3.7115734823798310458083829376653 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.0889612670459663243562691029099
y[1] (numeric) = 1.0483306837509552780823225959131
absolute error = 0.040630583295011046273946506996717
relative error = 3.7311320911560008676382879523402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.0893740432783181393300958276049
y[1] (numeric) = 1.0485146889121395720046722812558
absolute error = 0.040859354366178567325423546349049
relative error = 3.7507185542275342459016899632113 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.089787730136550790491919265217
y[1] (numeric) = 1.048699107304903594127871452841
absolute error = 0.041088622831647196364047812375954
relative error = 3.7703326707944103296063861009545 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.0902023272069774540829919575135
y[1] (numeric) = 1.0488839398396664577444884275575
absolute error = 0.041318387367310996338503529955998
relative error = 3.7899742402096894575529828826207 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=4.24
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.0906178340750010942264050306518
y[1] (numeric) = 1.0490691874264331341827618609626
absolute error = 0.041548646648567960043643169689236
relative error = 3.8096430619812041383725387502585 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.0910342503251148775240895223366
y[1] (numeric) = 1.0492548509747935428017052527887
absolute error = 0.041779399350321334722384269547818
relative error = 3.8293389357732430610095711691878 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.09145157554090258856361515432
y[1] (numeric) = 1.0494409313939216414012633870873
absolute error = 0.042010644146980947162351767232735
relative error = 3.8490616614082281204628770874593 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.0918698093050390463343710434825
y[1] (numeric) = 1.0496274295925745170484302967777
absolute error = 0.042242379712464529285940746704797
relative error = 3.8688110388683844438543088025454 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.0922889511992905215527119353457
y[1] (numeric) = 1.0498143464790914773202379264082
absolute error = 0.042474604720199044232474008937561
relative error = 3.8885868682974034021528655131999 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.0927090008045151548956526349088
y[1] (numeric) = 1.0500016829613931419645242500637
absolute error = 0.042707317843122012931128384845138
relative error = 3.9083889500020985931381941333091 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.0931299577006633761426924011461
y[1] (numeric) = 1.050189439946980534979389183577
absolute error = 0.042940517753682841163303217569132
relative error = 3.9282170844540547814438314664667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.0935518214667783242253501633781
y[1] (numeric) = 1.0503776183429341771122462115113
absolute error = 0.043174203123844147113103951866796
relative error = 3.9480710722912697817762538177337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.0939745916809962681839905100158
y[1] (numeric) = 1.0505662190559131787793772297883
absolute error = 0.043408372625083089404613280227458
relative error = 3.9679507143197892716610198623462 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.0943982679205470290315194928856
y[1] (numeric) = 1.0507552429921543334068976843289
absolute error = 0.043643024928392695624621808556739
relative error = 3.9878558115153345203219884870033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.0948228497617544025235283834771
y[1] (numeric) = 1.0509446910574712111940386646685
absolute error = 0.043878158704283191329489718808606
relative error = 4.0077861650249230205537558322784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.0952483367800365828344626110016
y[1] (numeric) = 1.0511345641572532532996521891873
absolute error = 0.04411377262278332953481042181434
relative error = 4.0277415761684820107010754368212 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.0956747285499065871393922061318
y[1] (numeric) = 1.0513248631964648664528454953762
absolute error = 0.044349865353441720686546710755579
relative error = 4.0477218464404548741120928354791 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.0961020246449726811009591686834
y[1] (numeric) = 1.0515155890796445179886497244273
absolute error = 0.044586435565328163112309444256084
relative error = 4.067726777511400403684731892522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.0965302246379388052610762723304
y[1] (numeric) = 1.0517067427109038313096279644059
absolute error = 0.044823481927034973951448307924442
relative error = 4.0877561712295849193775053344543 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.0969593281006050023369509146883
y[1] (numeric) = 1.0518983249939266817743271903205
absolute error = 0.045061003106678320562623724367839
relative error = 4.1078098296225672268073772396318 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.0973893346038678454210067167782
y[1] (numeric) = 1.0520903368319682930134782125622
absolute error = 0.045298997771899552407528504215951
relative error = 4.1278875548987764053080715780561 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=4.45
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.0978202437177208670842746719854
y[1] (numeric) = 1.0522827791278543336748473174411
absolute error = 0.045537464589866533409427354544288
relative error = 4.1479891494490824140723892872119 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.0982520550112549893828247411573
y[1] (numeric) = 1.0524756527839800145976428548888
absolute error = 0.045776402227274974785181886268518
relative error = 4.1681144158483595052516579107071 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.0986847680526589547668078874449
y[1] (numeric) = 1.0526689587023091864173795988491
absolute error = 0.046015809350349768349428288595828
relative error = 4.1882631568570424331343836871572 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.0991183824092197578916776418816
y[1] (numeric) = 1.0528626977843734376021032754149
absolute error = 0.046255684624846320289574366466754
relative error = 4.2084351754226754487744974080558 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.0995528976473230783311593885136
y[1] (numeric) = 1.053056870931271192920877222412
absolute error = 0.046496026716051885410282166101602
relative error = 4.2286302746814540696872736957931 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.0999883133324537141915346561489
y[1] (numeric) = 1.0532514790436668123454327118689
absolute error = 0.046736834288786901846101944280009
relative error = 4.2488482579597596144780499967941 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.1004246290291960166268068024775
y[1] (numeric) = 1.0534465230217896903858840336466
absolute error = 0.046978106007406326240922768830905
relative error = 4.2690889287756864925152680301433 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.100861844301234325254313575431
y[1] (numeric) = 1.0536420037654333558614090044374
absolute error = 0.047219840535800969392904570993542
relative error = 4.2893520908405622390050982493341 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.101299958711353404470351136208
y[1] (numeric) = 1.0538379221739545721067951313792
absolute error = 0.047462036537398832363556004828842
relative error = 4.3096375480604602860699787143789 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.1017389718214388806653732283767
y[1] (numeric) = 1.0540342791462724376157512236622
absolute error = 0.047704692675166443049622004714543
relative error = 4.329945104537705460677795364257 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.1021788831924776803383282778904
y[1] (numeric) = 1.0542310755808674871218838087424
absolute error = 0.047947807611610193216444469147972
relative error = 4.3502745645723722005121428367668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.1026196923845584691096963097179
y[1] (numeric) = 1.0544283123757807931182372721108
absolute error = 0.048191380008777675991459037607173
relative error = 4.3706257326637754791171255960816 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.1030613989568720916327866680871
y[1] (numeric) = 1.0546259904286130678162962010021
absolute error = 0.048435408528259023816490467085079
relative error = 4.3909984135119544318924801700876 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.1035040024677120124028566290802
y[1] (numeric) = 1.0548241106365237655453479729673
absolute error = 0.048679891831188246857508656112844
relative error = 4.4113924120191486747564128230784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.1039475024744747574636100964996
y[1] (numeric) = 1.0550226738962301855931031898718
absolute error = 0.048924828578244571870506906627841
relative error = 4.4318075332912673075344451285718 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.104391898533660357010634674543
y[1] (numeric) = 1.0552216811040065754884711166233
absolute error = 0.049170217429653781522163557919649
relative error = 4.4522435826393505943727348767968 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.1048371902008727888913345138855
y[1] (numeric) = 1.0554211331556832347273868417815
absolute error = 0.049416057045189554163947672103984
relative error = 4.4727003655810243137137838476421 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=4.67
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.1052833770308204230009154312754
y[1] (numeric) = 1.0556210309466456189425864341448
absolute error = 0.049662346084174804058328997130561
relative error = 4.4931776878419467706111495794811 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.1057304585773164665739779066934
y[1] (numeric) = 1.0558213753718334445182259254669
absolute error = 0.04990908320548302205575198122659
relative error = 4.5136753553572484643977378253129 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.1061784343932794103712726665209
y[1] (numeric) = 1.0560221673257397936502395046073
absolute error = 0.050156267067539616721033161913622
relative error = 4.5341931742729644049594584492644 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.1066273040307334757611726659979
y[1] (numeric) = 1.0562234077024102198533318626857
absolute error = 0.050403896328323255907840803312124
relative error = 4.5547309509474590711024726990664 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.1070770670408090626954143895363
y[1] (numeric) = 1.0564250973954418539154991821704
absolute error = 0.050651969645367208779915207365925
relative error = 4.5752884919528440047379367952738 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.107527722973743198578660493185
y[1] (numeric) = 1.0566272372979825103009728153069
absolute error = 0.050900485675760688277687677878075
relative error = 4.5958656040763880348430483886377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.1079792713788799880314349197206
y[1] (numeric) = 1.0568298283027297940024792488696
absolute error = 0.051149443076150194028955670851018
relative error = 4.6164620943219201253913215173576 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.1084317118046710635459807234666
y[1] (numeric) = 1.0570328713019302078437095028988
absolute error = 0.051398840502740855702271220567836
relative error = 4.6370777699112248416783451914534 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.1088850437986760370345899490213
y[1] (numeric) = 1.0572363671873782602328906608832
absolute error = 0.051648676611297776801699288138086
relative error = 4.6577124382854304297018136690468 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.1093392669075629522699540156011
y[1] (numeric) = 1.0574403168504155733683517777392
absolute error = 0.051898950057147378901602237861863
relative error = 4.6783659071063895034863459771071 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.1097943806771087382170821666872
y[1] (numeric) = 1.0576447211819299918969759599476
absolute error = 0.052149659495178746320106206739641
relative error = 4.6990379842580523354745314567052 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.1102503846521996632563346530956
y[1] (numeric) = 1.057849581072354692026429959322
absolute error = 0.052400803579844971229904693773558
relative error = 4.7197284778478327453357403508838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.1107072783768317902971164264731
y[1] (numeric) = 1.0580548974116672910920621681044
absolute error = 0.052652380965164499205054258368677
relative error = 4.7404371962079665827735170540258 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.1111650613941114327817762295659
y[1] (numeric) = 1.0582606710893889575793594484153
absolute error = 0.052904390304722475202416781150622
relative error = 4.7611639478968628001408220385532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.1116237332462556115792550793985
y[1] (numeric) = 1.0584669029945835216028527735289
absolute error = 0.053156830251672089976402305869525
relative error = 4.781908541700447110900000182603 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.1120832934745925127680272497516
y[1] (numeric) = 1.0586735940158565858423612019919
absolute error = 0.053409699458735926925666047759613
relative error = 4.8026707866334982301911218369747 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.1125437416195619463078759700387
y[1] (numeric) = 1.058880745041354636937463248269
absolute error = 0.05366299657820730937041272176969
relative error = 4.8234504919409766939982621682422 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=4.88
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.1130050772207158056000451688413
y[1] (numeric) = 1.0590883569587641573410842553688
absolute error = 0.053916720261951648258960913472438
relative error = 4.8442474670993462536283478557717 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.1134672998167185279353077019906
y[1] (numeric) = 1.0592964306553107376330879157902
absolute error = 0.054170869161407790302219786200492
relative error = 4.8650615218178878424414019428734 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.1139304089453475558294896171662
y[1] (numeric) = 1.0595049670177581892947596271213
absolute error = 0.054425441927589366534729990044915
relative error = 4.8858924660400061119943514668485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.1143944041434937992459891195241
y[1] (numeric) = 1.0597139669324076579450689077365
absolute error = 0.054680437211086141300920211787547
relative error = 4.9067401099445285349830224206934 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.1148592849471620987048280158762
y[1] (numeric) = 1.0599234312850967370395976362532
absolute error = 0.054935853662065361665230379623093
relative error = 4.9276042639469970725885267129868 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.1153250508914716892777725284065
y[1] (numeric) = 1.0601333609611985820330204157463
absolute error = 0.055191689930273107244752112660205
relative error = 4.9484847387009524040549402551471 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.115791701510656665469059482842
y[1] (numeric) = 1.0603437568456210250060229001684
absolute error = 0.055447944665035640463036582673577
relative error = 4.9693813450992107165449743607096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.1162592363380664469812629903921
y[1] (numeric) = 1.0605546198228056897575434559804
absolute error = 0.055704616515260757223719534411729
relative error = 4.9902938942751330535392486140683 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.1167276549061662453658358576272
y[1] (numeric) = 1.0607659507767271073632230666792
absolute error = 0.055961704129439138002612790948009
relative error = 5.0112221976038872202627766613819 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.117196956746537531557859073795
y[1] (numeric) = 1.0609777505908918322009479216992
absolute error = 0.056219206155645699356911152095894
relative error = 5.0321660667037022448393714796459 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.1176671413898785042945318408633
y[1] (numeric) = 1.061190020148337558444368664069
absolute error = 0.056477121241540945850163176794324
relative error = 5.0531253134371153940908581572312 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.1181382083660045594169337278386
y[1] (numeric) = 1.0614027603316322370252798032337
absolute error = 0.056735448034372322391653924604953
relative error = 5.0740997499122117431132447166912 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.1186101572038487600545896476376
y[1] (numeric) = 1.0616159720228731930657423305864
absolute error = 0.05699418518097556698884731705125
relative error = 5.0950891884838562979763397546933 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.1190829874314623076923674719854
y[1] (numeric) = 1.0618296561036862437808321055156
absolute error = 0.05725333132777606391153536646984
relative error = 5.1160934417549186711067144708918 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.1195566985760150141192372174827
y[1] (numeric) = 1.0620438134552248168528961091451
absolute error = 0.057512885120790197266341108337605
relative error = 5.1371123225774903091263808936849 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.1200312901637957742584198541208
y[1] (numeric) = 1.0622584449581690692781981914364
absolute error = 0.057772845205626704980221662684423
relative error = 5.1581456440540942731310927520923 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.1205067617202130398784529061372
y[1] (numeric) = 1.062473551492725006686835464936
absolute error = 0.058033210227488033191617441201297
relative error = 5.179193219538887571602765535081 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=5.09
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.1209831127697952941846991341835
y[1] (numeric) = 1.0626891339386236031368060251759
absolute error = 0.058293978831171691047893109007559
relative error = 5.2002548626388560463601529476579 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.1214603428361915272908237073372
y[1] (numeric) = 1.0629051931751199213831082035881
absolute error = 0.058555149661071605907715503749061
relative error = 5.2213303872150018121606034213608 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.1219384514421717125697643935207
y[1] (numeric) = 1.0631217300809922336227510837584
absolute error = 0.058816721361179478947013309762381
relative error = 5.2424196073835232507734478490297 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.1224174381096272838837184173962
y[1] (numeric) = 1.0633387455345411427165555359378
absolute error = 0.059078692575086141167162881458341
relative error = 5.263522337516987560552333652523 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.1228973023595716136926687557886
y[1] (numeric) = 1.0635562404135887038886245479366
absolute error = 0.059341061945982909804044207852002
relative error = 5.284638392245495862739616098838 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.1233780437121404920409717621522
y[1] (numeric) = 1.063774215595477546904361152856
absolute error = 0.059603828116662945136610609296213
relative error = 5.3057675864578408659407409750357 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.1238596616865926064215271335312
y[1] (numeric) = 1.0639926719570699987279117755691
absolute error = 0.059866989729522607693615357962084
relative error = 5.326909735302657090410398914102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.1243421558013100225170503558855
y[1] (numeric) = 1.0642116103747472066599123404327
absolute error = 0.060130545426562815857138015452862
relative error = 5.3480646541895636539950965093766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.1248255255737986658179668865485
y[1] (numeric) = 1.0644310317244082619564140024105
absolute error = 0.06039449384939040386155288413801
relative error = 5.3692321587902996217786686195557 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.1253097705206888041164464559633
y[1] (numeric) = 1.0646509368814693239298648826112
absolute error = 0.060658833639219480186581573352192
relative error = 5.3904120650398519216781457825853 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.1257948901577355308760949947039
y[1] (numeric) = 1.0648713267208627445330237071841
absolute error = 0.060923563436872786343071287519816
relative error = 5.4116041891375758284372863358311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.508
y[1] (analytic) = 1.1262808839998192494768208161278
y[1] (numeric) = 1.0650922021170361934266807655877
absolute error = 0.061188681882783056050140050540062
relative error = 5.4328083475483080186639806701054 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.126767751560946158334390809836
y[1] (numeric) = 1.0653135639439517835320611204355
absolute error = 0.061454187616994374802329689400445
relative error = 5.4540243570034721997556310921861 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.1272554923542487368941915264245
y[1] (numeric) = 1.0655354130750851970687845164453
absolute error = 0.061720079279163539825407009979226
relative error = 5.4752520345021773157535011772457 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.1277441058919862324987091598053
y[1] (numeric) = 1.0657577503834248120792559504565
absolute error = 0.061986355508561420419453209348814
relative error = 5.4964911973123083333629094789142 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.1282335916855451481282415596589
y[1] (numeric) = 1.0659805767414708294403603780547
absolute error = 0.062253014944074318687881181604132
relative error = 5.5177416629716096115710103270594 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.1287239492454397310143545333464
y[1] (numeric) = 1.0662038930212344003633345450344
absolute error = 0.062520056224205330651019988312005
relative error = 5.5390032492887608584877555547658 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=5.31
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.1292151780813124621255938238659
y[1] (numeric) = 1.0664277000942367543826884437554
absolute error = 0.062787477987075707742905380110554
relative error = 5.5602757743444456792284618057118 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 1.1297072777019345465249632781811
y[1] (numeric) = 1.0666519988315083278350484053996
absolute error = 0.063055278870426218689914872781512
relative error = 5.5815590564924127188482151064731 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.1302002476152064045986788484863
y[1] (numeric) = 1.0668767901035878928287933492124
absolute error = 0.063323457511618511769885499273886
relative error = 5.6028529143605294045291242463202 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.1306940873281581641557071976931
y[1] (numeric) = 1.0671020747805216867053552190183
absolute error = 0.063592012547636477450351978674734
relative error = 5.6241571668518282914111838664676 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.1311887963469501533975968096429
y[1] (numeric) = 1.0673278537318625419930541456405
absolute error = 0.063860942615087611404542664002435
relative error = 5.6454716331455460166462237734465 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.1316843741768733947581086342535
y[1] (numeric) = 1.0675541278266690168543383813134
absolute error = 0.0641302463502043779037702529401
relative error = 5.6667961326981548664420996843171 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.1321808203223500996121524280115
y[1] (numeric) = 1.0677808979335045260272985587795
absolute error = 0.064399922388845573584853869232014
relative error = 5.6881304852443869610509192866594 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.1326781342869341638535340809147
y[1] (numeric) = 1.06800816492043647226232533348
absolute error = 0.064669969366497691591208747434691
relative error = 5.7094745107982510628406931300474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.1331763155733116643410183521593
y[1] (numeric) = 1.0682359296550353782547789721128
absolute error = 0.064940385918276286086239380046523
relative error = 5.7308280296540420127743495087097 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.1336753636833013562122105685491
y[1] (numeric) = 1.0684641930043740190745389548125
absolute error = 0.065211170678927337137671613736595
relative error = 5.7521908623873428008035532719993 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.1341752781178551710647599717881
y[1] (numeric) = 1.0686929558350265550933011613338
absolute error = 0.0654823222828286159714588104543
relative error = 5.7735628298560192758672176085956 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.1346760583770587160043865334936
y[1] (numeric) = 1.0689222190130676654104897138662
absolute error = 0.065753839363991050593896819627377
relative error = 5.7949437532012075013659925639817 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.135177703960131773559232189945
y[1] (numeric) = 1.0691519834040716817786500504978
absolute error = 0.066025720556060091780582139447184
relative error = 5.8163334538482937621643517138221 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.1356802143654288024600365822581
y[1] (numeric) = 1.0693822498731117230291893038612
absolute error = 0.066297964492317079430847278396896
relative error = 5.8377317535078872293511764464827 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.1361835890904394392856365218521
y[1] (numeric) = 1.0696130192847588299993295591509
absolute error = 0.066570569805680609286306962701122
relative error = 5.8591384741767852891679531967988 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.1366878276317890009732875357502
y[1] (numeric) = 1.0698442925030811009611390644856
absolute error = 0.066843535128707900012148471264613
relative error = 5.8805534381389315426908502833667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.1371929294852389881933049814358
y[1] (numeric) = 1.0700760703916428275535059645121
absolute error = 0.067116859093596160639799016923676
relative error = 5.9019764679663664830290253682458 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=5.53
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.1376988941456875895875213566629
y[1] (numeric) = 1.0703083538135036312179186252061
absolute error = 0.067390540332183958369602731456848
relative error = 5.923407386520170856976529687888 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 1.138205721107170186871055565808
y[1] (numeric) = 1.0705411436312176001389161140162
absolute error = 0.067664577475952586732139451791826
relative error = 5.9448460169514017182291188757277 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.1387134098628598607968890410339
y[1] (numeric) = 1.07077444070683242669007189483
absolute error = 0.067938969156027434106817146203895
relative error = 5.9662921827020211794501502596873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.1392219599050678979827427537335
y[1] (numeric) = 1.071008245901888545386373291706
absolute error = 0.068213714003179352596369462027462
relative error = 5.9877457075058178706415408922517 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.1397313707252442985997482894172
y[1] (numeric) = 1.0712425600774182713438587689199
absolute error = 0.068488810647826027255889520497218
relative error = 6.009206415389321111446477247678 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.1402416418139782849224052974161
y[1] (numeric) = 1.0714773840939449392473745676168
absolute error = 0.068764257720033345675030729799245
relative error = 6.030674130672707805180204561489 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.1407527726609988107393167654858
y[1] (numeric) = 1.0717127188114820428273117312404
absolute error = 0.069040053849516767912005034245376
relative error = 6.0521486779707020625537793227373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.1412647627551750716241927086173
y[1] (numeric) = 1.0719485650895323748461840429306
absolute error = 0.069316197665642696778008665686731
relative error = 6.073629882193467563223140660304 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.1417776115845170160666120010953
y[1] (numeric) = 1.0721849237870871675959068882404
absolute error = 0.06959268779742984847070511285486
relative error = 6.095117568547492663462243560673 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.1422913186361758574620312210822
y[1] (numeric) = 1.0724217957626252339066365458205
absolute error = 0.069869522873550623555394675261742
relative error = 6.1166115625364682584242973551109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.1428058833964445869605285177651
y[1] (numeric) = 1.0726591818741121086680288971617
absolute error = 0.070146701522332478292499620603349
relative error = 6.1381116899621584076193651265304 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.1433213053507584871737696523608
y[1] (numeric) = 1.072897082978999190863776034065
absolute error = 0.070424222371759296309993618295868
relative error = 6.1596177769252637323997020863373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.1438375839836956467396825060591
y[1] (numeric) = 1.0731354999342228861202787292296
absolute error = 0.070702084049472760619403776829488
relative error = 6.1811296498262775944062421030665 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.1443547187789774757443254902696
y[1] (numeric) = 1.0733744335962037497703122212176
absolute error = 0.070980285182773725974013269052011
relative error = 6.2026471353663350640905800389866 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.1448727092194692220004344373497
y[1] (numeric) = 1.0736138848208456304325422500556
absolute error = 0.071258824398623591567892187294065
relative error = 6.2241700605480546885866420468092 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.1453915547871804881821316933069
y[1] (numeric) = 1.0738538544635348141077477638875
absolute error = 0.071537700323645674074383929419417
relative error = 6.2456982526763730683649852417823 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.1459112549632657498152802778119
y[1] (numeric) = 1.0740943433791391687926062003834
absolute error = 0.071816911584126581022674077428451
relative error = 6.2672315393593722522603210070065 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.4MB, time=5.74
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.1464318092280248741229651212096
y[1] (numeric) = 1.0743353524220072896118967290492
absolute error = 0.072096456806017584511068392160362
relative error = 6.2887697485090999606194114902458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 1.1469532170609036397255825330915
y[1] (numeric) = 1.0745768824459676444699763221609
absolute error = 0.072376334614935995255606210930551
relative error = 6.3103127083423826464719455531516 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.1474754779404942571950182023822
y[1] (numeric) = 1.0748189343043277202223830027779
absolute error = 0.072656543636166536972635199604334
relative error = 6.3318602473816314047813575485813 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.1479985913445358904623931748063
y[1] (numeric) = 1.0750615088498731693684200981596
absolute error = 0.072937082494662721093973076646739
relative error = 6.3534121944556407399858089036237 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.1485225567499151790788564000321
y[1] (numeric) = 1.0753046069348669572655748059308
absolute error = 0.073217949815048221813281594101221
relative error = 6.3749683787003802021917077149375 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.1490473736326667613289015877443
y[1] (numeric) = 1.0755482294110485098666238585063
absolute error = 0.073499144221618251462277729237922
relative error = 6.3965286295597789025331946234183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.1495730414679737981956852593716
y[1] (numeric) = 1.0757923771296328619802785485967
absolute error = 0.073780664338340936215406710774866
relative error = 6.4180927767865029183609733954668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.150099559730168498177822030195
y[1] (numeric) = 1.0760370509413098060562208550812
absolute error = 0.074062508788858692121601175113742
relative error = 6.4396606504427255990727112304237 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.1506269278927326429571323050854
y[1] (numeric) = 1.0762822516962430414953818841396
absolute error = 0.074344676196489601461750420945758
relative error = 6.4612320809008907835449762335903 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.1511551454282981139168167201663
y[1] (numeric) = 1.0765279802440693244863133152933
absolute error = 0.074627165184228789430503404873023
relative error = 6.482806898844468940273317200199 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 1.1516842118086474195095308122717
y[1] (numeric) = 1.0767742374338976183685020159145
absolute error = 0.074909974374749801141028796357182
relative error = 6.5043849352687062414726233688784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.1522141265047142234748325481675
y[1] (numeric) = 1.0770210241143082445234774608175
absolute error = 0.07519310239040597895135508735
relative error = 6.5259660214813665825343287069573 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.1527448889865838739054744961337
y[1] (numeric) = 1.0772683411333520337945610657531
absolute error = 0.075476547853231840110913430380557
relative error = 6.5475499891034665583803462296242 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.153276498723493933162011573659
y[1] (numeric) = 1.077516189338549478436106014988
absolute error = 0.075760309384944454725905558671032
relative error = 6.5691366700700034083958325372382 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.1538089551838347086351944566842
y[1] (numeric) = 1.0777645695768898845930756336563
absolute error = 0.076044385606944824042118823027966
relative error = 6.5907258966306759417639909478209 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.1543422578351497843556178880455
y[1] (numeric) = 1.0780134826948305253118078252366
absolute error = 0.076328775140319259043810062808855
relative error = 6.6123175013505984551661231335016 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.1548764061441365534500922755127
y[1] (numeric) = 1.0782629295382957940828125633177
absolute error = 0.076613476605840759367279712195046
relative error = 6.6339113171110076549490339293462 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=5.96
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.1554113995766467514442061230971
y[1] (numeric) = 1.0785129109526763589164488947853
absolute error = 0.076898488623970392527757228311779
relative error = 6.655507177109962595999681919422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 1.1559472375976869904105459931083
y[1] (numeric) = 1.0787634277828283169523273786834
absolute error = 0.077183809814858673458218614424847
relative error = 6.6771049148630376497036495265363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.1564839196714192939620398507875
y[1] (numeric) = 1.0790144808730723496032833512762
absolute error = 0.077469438798346944358756499511344
relative error = 6.6987043642040085134995807064274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.157021445261161633089888798216
y[1] (numeric) = 1.0792660710671928782347658732666
absolute error = 0.077755374193968754855122924949381
relative error = 6.7203053592855312746762021006276 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.1575598138293884628455513596132
y[1] (numeric) = 1.0795181992084372203804866797142
absolute error = 0.078041614620951242465064679899018
relative error = 6.7419077345798145411919048195023 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.158099024837731259866243636084
y[1] (numeric) = 1.0797708661395147464951729169299
absolute error = 0.078328158698216513371070719154101
relative error = 6.7635113248792846524291191508271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.158639077746979060743417804361
y[1] (numeric) = 1.0800240727025960372452669135283
absolute error = 0.078615005044383023498150890832661
relative error = 6.7851159652972439829268637200064 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.1591799720170790012336805911064
y[1] (numeric) = 1.0802778197393120413384156948642
absolute error = 0.07890215227776695989526489624223
relative error = 6.8067214912685223522648943231776 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.1597217071071368563116125119018
y[1] (numeric) = 1.0805321080907532338925924112956
absolute error = 0.079189599016383622419020100606229
relative error = 6.8283277385501215544018162282861 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.1602642824754175810639478221502
y[1] (numeric) = 1.0807869385974687753456913110814
absolute error = 0.079477343877948805718256511068766
relative error = 6.8499345432218530198973576624409 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.1608076975793458524245742857562
y[1] (numeric) = 1.0810423120994656709064373482481
absolute error = 0.079765385479880181518136937508022
relative error = 6.871541741686968624575732003162 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.1613519518755066117498110266296
y[1] (numeric) = 1.0812982294362079305474509744463
absolute error = 0.080053722439298681202360052183257
relative error = 6.8931491706727846583126424487495 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.1618970448196456082334218877795
y[1] (numeric) = 1.0815546914466157295413081216619
absolute error = 0.080342353373029878692113766117598
relative error = 6.9147566672312989677530062964042 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.162442975866669943160820883031
y[1] (numeric) = 1.0818116989690645695404348396525
absolute error = 0.080631276897605373620386043378459
relative error = 6.9363640687398012868898970980892 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.1629897444706486150019254872046
y[1] (numeric) = 1.0820692528413844402016755081445
absolute error = 0.080920491629264174800249979060058
relative error = 6.9579712129014767695575226400438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.16353735008481306534211267195
y[1] (numeric) = 1.0823273539008589813563729991517
absolute error = 0.081209996183954083985739672798236
relative error = 6.9795779377460027380122757028375 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.1640857921615577256507317563242
y[1] (numeric) = 1.0825860029842246457267986192672
absolute error = 0.08149978917733307992393313705701
relative error = 7.0011840816301386618960137589775 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=6.17
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.1646350701524405648866273036464
y[1] (numeric) = 1.0828452009276698621897691154271
absolute error = 0.081789869224770702696858188219306
relative error = 7.0227894832383093819947440615309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 1.165185183508183637940124459152
y[1] (numeric) = 1.0831049485668341995882874804607
absolute error = 0.082080234941349438351836978691325
relative error = 7.0443939815831815933238129299283 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.1657361316786736349109282865074
y[1] (numeric) = 1.083365246736807531092043746716
absolute error = 0.082370884941866103818884539791412
relative error = 7.0659974160062336021875234602842 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.1662879141129624312213878253303
y[1] (numeric) = 1.08362609627212919910761140719
absolute error = 0.082661817840833232113776418140281
relative error = 7.0875996261783183719768354413269 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.1668405302592676385645747564985
y[1] (numeric) = 1.0838874980067871807391745538981
absolute error = 0.0829530322524804578254002026004
relative error = 7.1092004521002198725834360589544 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.1673939795649731566866257272142
y[1] (numeric) = 1.0841494527742172538006202726857
absolute error = 0.083244526790755902886005454528472
relative error = 7.1307997341032027484220111891772 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.1679482614766297260027965535271
y[1] (numeric) = 1.0844119614073021633798302823206
absolute error = 0.083536300069327562622966271206547
relative error = 7.1523973128495553201649959280602 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 1.1685033754399554810466756843086
y[1] (numeric) = 1.0846750247383707889560052535039
absolute error = 0.083828350701584692090670430804723
relative error = 7.1739930293331259354054407557513 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.1690593208998365047520034775093
y[1] (numeric) = 1.0849386435991973120708546904075
absolute error = 0.084120677300639192681148787101805
relative error = 7.1955867248798526835738976971064 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.1696160973003273835665430069271
y[1] (numeric) = 1.085202818821000384554484703477
absolute error = 0.084413278479326999012058303450086
relative error = 7.2171782411482864905444103904978 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.1701737040846517633974472856612
y[1] (numeric) = 1.0854675512344422973068154475445
absolute error = 0.084706152850209466090631838116791
relative error = 7.2387674201301076084727845247994 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.1707321406952029063875669609314
y[1] (numeric) = 1.0857328416696281496353594437634
absolute error = 0.084999299025574756752207517167988
relative error = 7.2603541041506355165173221165154 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.1712914065735442485221417040005
y[1] (numeric) = 1.0859986909561050191501914475192
absolute error = 0.085292715617439229371950256481219
relative error = 7.2819381358693322481981260868896 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.1718515011604099580653176885558
y[1] (numeric) = 1.0862650999228611322169399672748
absolute error = 0.085586401237548825848377721280974
relative error = 7.3035193582802991612559221226849 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.172412423895705494825932721079
y[1] (numeric) = 1.0865320693983250349686299812923
absolute error = 0.085880354497380459857302739786703
relative error = 7.3250976147127671659751044714703 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.1729741742185081702520097574644
y[1] (numeric) = 1.0867996002103647648772058403177
absolute error = 0.086174574008143405374803917146655
relative error = 7.3466727488315804280383927869189 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.1735367515670677083533987114403
y[1] (numeric) = 1.0870676931862870228855627846377
absolute error = 0.086469058380780685467835926802624
relative error = 7.3682446046376735620820901024378 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=6.39
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.1741001553788068074520056321979
y[1] (numeric) = 1.0873363491528363461009149434069
absolute error = 0.086763806225970461351090688791062
relative error = 7.3898130264685423322214592190728 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 1.1746643850903217027590475010446
y[1] (numeric) = 1.0876055689361942810503271228095
absolute error = 0.087058816154127421708720378235113
relative error = 7.4113778589987078759151880383157 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.1752294401373827297787700698751
y[1] (numeric) = 1.0878753533619785574992371274547
absolute error = 0.087354086775404172279532942420362
relative error = 7.4329389472401744676362954895998 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.1757953199549348885380653377883
y[1] (numeric) = 1.0881457032552422628337947964137
absolute error = 0.087649616699692625704270541374552
relative error = 7.4544961365428808389141405780668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.1763620239770984086414244362806
y[1] (numeric) = 1.0884166194404730170078433714919
absolute error = 0.087945404536625391633581064788679
relative error = 7.4760492725951450714084396371112 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.1769295516371693151506608681084
y[1] (numeric) = 1.0886881027415921480553682506846
absolute error = 0.088241448895577167095292617423766
relative error = 7.4975982014241030797713730826316 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.177497902367619995288838220145
y[1] (numeric) = 1.0889601539819538681692376143003
absolute error = 0.088537748385666127119600605844705
relative error = 7.5191427693961407011479748457049 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.1780670756000997659678356463513
y[1] (numeric) = 1.0892327739843444503470588449413
absolute error = 0.088834301615755315620776801409969
relative error = 7.5406828232173194082580472644417 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.1786370707654354421389835933405
y[1] (numeric) = 1.0895059635709814056049740954165
absolute error = 0.089131107194454036534009497924031
relative error = 7.5622182099337956630948336436107 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.1792078872936319059662014179512
y[1] (numeric) = 1.089779723563512660760217790723
absolute error = 0.089428163730119245205983627228262
relative error = 7.583748776932233928366612083961 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.1797795246138726768210677237362
y[1] (numeric) = 1.09005405478301573678325828147
absolute error = 0.089725469830856940037809442266142
relative error = 7.6052743719402133538972497255244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.1803519821545204820992534213452
y[1] (numeric) = 1.0903289580499969277203452965351
absolute error = 0.09002302410452355437890812481008
relative error = 7.62679484302662815529057846539 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.1809252593431178288577466964165
y[1] (numeric) = 1.0906044341843904801872842723363
absolute error = 0.090320825158727348670462424080203
relative error = 7.6483100386020817022512237663003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.1814993556063875762722982477992
y[1] (numeric) = 1.0908804840055577734352580648787
absolute error = 0.090618871600829802837040182920517
relative error = 7.6698198074192743340412396741915 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.613
y[1] (analytic) = 1.1820742703702335089145143387088
y[1] (numeric) = 1.0911571083322864999895159786839
absolute error = 0.090917162037947008924998360024928
relative error = 7.6913239985733849196375779568491 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.1826500030597409108480243837716
y[1] (numeric) = 1.0914343079827898468617494738464
absolute error = 0.091215695076951063986274909925148
relative error = 7.7128224615024461802400497481977 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.1832265530991771405431489758368
y[1] (numeric) = 1.0917120837747056773369733387721
absolute error = 0.091514469324471463206175637064708
relative error = 7.7343150459877137918630266586215 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=6.60
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.1838039199119922066094934379379
y[1] (numeric) = 1.0919904365250957133357305416496
absolute error = 0.091813483386896493273762896288281
relative error = 7.7558016021540292858266774551855 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 1.1843821029208193443458911678558
y[1] (numeric) = 1.092269367050444718352438398382
absolute error = 0.092112735870374625993452769473761
relative error = 7.7772819804701767650450486291244 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.1849611015474755931071202253905
y[1] (numeric) = 1.0925488761666596809706931185644
absolute error = 0.092412225380815912136427106826036
relative error = 7.7987560317492334540887749919013 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.1855409152129623744868157956707
y[1] (numeric) = 1.0928289646890689989563492141342
absolute error = 0.092711950523893375530466581536572
relative error = 7.8202236071489141010796524534389 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.1861215433374660713160003456393
y[1] (numeric) = 1.0931096334324216639291896775474
absolute error = 0.093011909905044407386810668091935
relative error = 7.8416845581719092495527219518697 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.1867029853403586074766524752305
y[1] (numeric) = 1.093390883210886446614002257743
absolute error = 0.093312102129472160862650217487454
relative error = 7.8631387366662173984989037750844 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.1872852406401980285297346497202
y[1] (numeric) = 1.0936727148380510826718765827505
absolute error = 0.093612525802146945857858066969678
relative error = 7.8845859948254710688775879285281 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.1878683086547290831570991852689
y[1] (numeric) = 1.0939551291269214591125362975757
absolute error = 0.093913179527807624044562887693238
relative error = 7.9060261851892567949639314849856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 1.1884521888008838054166910457999
y[1] (numeric) = 1.0942381268899208012885198049654
absolute error = 0.094214061910963004128171240834523
relative error = 7.9274591606434290589699407598486 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 1.1890368804947820978104651960589
y[1] (numeric) = 1.0945217089388888604720226148025
absolute error = 0.094515171555893237338442581256388
relative error = 7.9488847744204181874517274839146 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.189622383151732315164435442986
y[1] (numeric) = 1.0948058760850811020152137252208
absolute error = 0.094816507066651213149221717765178
relative error = 7.9703028800995322280876267240774 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.1902086961862318493202708853993
y[1] (numeric) = 1.0950906291391678940948378750554
absolute error = 0.095118067047063955225433010343922
relative error = 7.991713331607252825483152993465 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.1907958190119677146378552804441
y[1] (numeric) = 1.0953759689112336970419149229603
absolute error = 0.09541985010073401759594035748382
relative error = 8.0131159832175251147290526935538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.1913837510418171343082238242947
y[1] (numeric) = 1.0956618962107762532573470234243
absolute error = 0.095721854831040881050876800870393
relative error = 8.034510689552041651507988671783 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.1919724916878481274762910342229
y[1] (numeric) = 1.0959484118467057777142436840119
absolute error = 0.096024079841142349762047350211057
relative error = 8.0558973055805203976136692223823 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.1925620403613200971727826093538
y[1] (numeric) = 1.0962355166273441490477742014361
absolute error = 0.096326523733975948125008407917671
relative error = 8.0772756866209767808135123012002 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
memory used=122.0MB, alloc=4.4MB, time=6.82
y[1] (analytic) = 1.1931523964726844190547833382246
y[1] (numeric) = 1.0965232113604241012333563865436
absolute error = 0.096629185112260317821426951681048
relative error = 8.0986456883399898480522190950756 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.1937435594315850309543123126502
y[1] (numeric) = 1.0968114968530884158539898999555
absolute error = 0.096932062578496615100322412694666
relative error = 8.1200071667529625310589224422116 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 1.1943355286468590232343358993665
y[1] (numeric) = 1.0971003739118891149575419309643
absolute error = 0.097235154734969908276793968402143
relative error = 8.1413599782243760434848780328486 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.1949283035265372299516281134903
y[1] (numeric) = 1.0973898433427866545047923623327
absolute error = 0.097538460183750575446835751157629
relative error = 8.1627039794680384287619829509183 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.1955218834778448208258872309833
y[1] (numeric) = 1.0976799059511491184090449728829
absolute error = 0.097841977526695702416842258100402
relative error = 8.1840390275473272779347400993695 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 1.1961162679072018940145166710524
y[1] (numeric) = 1.0979705625417514131681106381976
absolute error = 0.098145705365450480846406032854739
relative error = 8.2053649798754266367796415666103 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.1967114562202240696924773737563
y[1] (numeric) = 1.0982618139187744630894678973824
absolute error = 0.098449642301449606603009476373891
relative error = 8.2266816942155581215863222507733 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.639
y[1] (analytic) = 1.1973074478217230844366180930148
y[1] (numeric) = 1.0985536608858044061094056606619
absolute error = 0.098753786935918678327212432352893
relative error = 8.2479890286812062630342403032583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.1979042421157073864138892207397
y[1] (numeric) = 1.0988461042458317902069522386005
absolute error = 0.099058137869875596206936982139159
relative error = 8.2692868417363380976570764530482 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.1985018385053827313728449539229
y[1] (numeric) = 1.0991391448012507704133942789503
absolute error = 0.099362693704131960959450674972635
relative error = 8.2905749921956170264445133268531 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.1991002363931527794378378132311
y[1] (numeric) = 1.0994327833538583064181886015422
absolute error = 0.099667453039294473019649211688859
relative error = 8.311853339224610960187561813432 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.1996994351806196927053087189588
y[1] (numeric) = 1.09972702070485336077206932524
absolute error = 0.099972414475766331933239393718857
relative error = 8.333121742339994771229147687318 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.2002994342685847336415750281037
y[1] (numeric) = 1.1000218576548360976881520837842
absolute error = 0.10027757661374863595342294431952
relative error = 8.3543800614097470713362614886576 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.2009002330570488642815181348221
y[1] (numeric) = 1.1003172950038070824418365293548
absolute error = 0.1005829380532417818396816054673
relative error = 8.3756281566533413354636114598146 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.2015018309452133462275714356296
y[1] (numeric) = 1.1006133335511664813703077238828
absolute error = 0.10088849739404686485726371174672
relative error = 8.3968658886419313912314066000191 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.2021042273314803414484086604078
y[1] (numeric) = 1.1009099740957132624724364185438
absolute error = 0.10119425323576707897597224186393
relative error = 8.4180931182985312939916380769018 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.2027074216134535138767317705792
y[1] (numeric) = 1.1012072174356443966098776214654
absolute error = 0.10150020417780911726685414911372
relative error = 8.4393097068981896074080258140962 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=125.8MB, alloc=4.4MB, time=7.04
x[1] = 0.649
y[1] (analytic) = 1.203311413187938631805556826712
y[1] (numeric) = 1.1015050643685540593101662524844
absolute error = 0.10180634881938457249539057422758
relative error = 8.4605155160681581095246565682583 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.2039162014509441710823954293201
y[1] (numeric) = 1.1018035156914328331726080817909
absolute error = 0.10211268575951133790978734752916
relative error = 8.4817104077880549443472637527175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 1.2045217857976819191007285387257
y[1] (numeric) = 1.1021025722006669108777635465022
absolute error = 0.10241921359701500822296499222347
relative error = 8.5028942443900222390090912188069 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.2051281656225675795881686825627
y[1] (numeric) = 1.1024022346920372988013214356163
absolute error = 0.10272593093053028078684724694644
relative error = 8.5240668885588782066403467540402 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.2057353403192213781907057628076
y[1] (numeric) = 1.1027025039607190212331588294044
absolute error = 0.1030328363585023569575469334032
relative error = 8.5452282033322637551063898066337 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.2063433092804686688524308781435
y[1] (numeric) = 1.1030033808012803252023830741176
absolute error = 0.10333992847918834365004780402593
relative error = 8.5663780521007836218250155296067 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.2069520718983405409901317819836
y[1] (numeric) = 1.1033048660076818859091509668973
absolute error = 0.10364720589065865508098081508626
relative error = 8.5875162986081420549174973088556 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.207561627564074427462152801609
y[1] (numeric) = 1.1036069603732760127640597190064
absolute error = 0.10395466719079841469809308260268
relative error = 8.6086428069512730609914361746976 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.2081719756681147133309112496125
y[1] (numeric) = 1.1039096646908058560359036579215
absolute error = 0.104262310977308857295007591691
relative error = 8.6297574415804652398959415939886 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.2087831156001133454184615651814
y[1] (numeric) = 1.1042129797524046141085900204666
absolute error = 0.10457013584770873130987154471478
relative error = 8.6508600672994812268312378203201 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.2093950467489304426544976297072
y[1] (numeric) = 1.1045169063495947413480065800027
absolute error = 0.10487814039933570130649104970443
relative error = 8.6719505492656717622354569845765 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.2100077685026349072161829087698
y[1] (numeric) = 1.1048214452732871565796332407428
absolute error = 0.105186323229347750636549668027
relative error = 8.6930287529900844099111481998035 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 1.2106212802485050364591972807178
y[1] (numeric) = 1.1051265973137804521776891215126
absolute error = 0.10549468293472458428150815920517
relative error = 8.7140945443375669438929049159737 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.2112355813730291356393886208484
y[1] (numeric) = 1.105432363260760103766606039746
absolute error = 0.10580321811226903187278258110244
relative error = 8.7351477895268654245954943950683 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.2118506712619061314244164195866
y[1] (numeric) = 1.1057387439032976805356186941731
absolute error = 0.10611192735860845088879772541347
relative error = 8.7561883551307169848189673079668 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.2124665493000461861947739230711
y[1] (numeric) = 1.1060457400298500561672612315481
absolute error = 0.10642080927019613002751269152294
relative error = 8.7772161080759373462234359243935 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.2130832148715713131335744951767
y[1] (numeric) = 1.1063533524282586203805592688523
absolute error = 0.10672986244331269275301522632444
relative error = 8.7982309156435030869215400371131 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.4MB, time=7.26
x[1] = 0.666
y[1] (analytic) = 1.213700667359815992104487111237
y[1] (numeric) = 1.1066615818857484910897058277151
absolute error = 0.10703908547406750101478128352189
relative error = 8.8192326454686286808710745118591 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.2143189061473277863172051055833
y[1] (numeric) = 1.1069704291889277271790090223123
absolute error = 0.107348476958400059138196083271
relative error = 8.8402211655408383297838350835931 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 1.2149379306158679597798315074841
y[1] (numeric) = 1.1072798951237865418948987257275
absolute error = 0.10765803549208141788493278175661
relative error = 8.8611963442040326082994536440266 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.2155577401464120955375635131482
y[1] (numeric) = 1.1075899804756965168557788227038
absolute error = 0.10796775967071557868178469044437
relative error = 8.8821580501565499432048447188533 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.2161783341191507146970578551619
y[1] (numeric) = 1.1079006860294098166805110388705
absolute error = 0.10827764808974089801654681629143
relative error = 8.9031061524512229475108750670011 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.2167997119134898962358580450436
y[1] (numeric) = 1.1082120125690584042363157178919
absolute error = 0.10858769934443149199954232715171
relative error = 8.9240405204954296302280023164182 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.2174218729080518975962636795423
y[1] (numeric) = 1.108523960878153256506874298576
absolute error = 0.10889791202989864108938938096632
relative error = 8.9449610240511395027119102659099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.2180448164806757760630212168607
y[1] (numeric) = 1.1088365317395835810814176237714
absolute error = 0.10920828474109219498160359308932
relative error = 8.9658675332349546024786019309363 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.2186685420084180109242148451658
y[1] (numeric) = 1.1091497259356160332655835919023
absolute error = 0.1095188160728019776586312532635
relative error = 8.9867599185181454554160006093678 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.219293048867553126414735282546
y[1] (numeric) = 1.109463544247893933814827040216
absolute error = 0.10982950461965919259990824232999
relative error = 9.0076380507266819973458582227181 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.2199183364335743154417035649992
y[1] (numeric) = 1.1097779874574364872911641262692
absolute error = 0.11014034897613782815053943872991
relative error = 9.0285018010412594759156829960643 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.2205444040811940640912260970796
y[1] (numeric) = 1.1100930563446380010440328508439
absolute error = 0.11045134773655606304719324623574
relative error = 9.0493510409973193538254792371792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.2211712511843447769158564585004
y[1] (numeric) = 1.1104087516892671048160507413653
absolute error = 0.11076249949507767209980571713506
relative error = 9.0701856424850652344183446380974 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.221798877116179403002138679282
y[1] (numeric) = 1.1107250742704659709744500900023
absolute error = 0.11107380284571343202768858927966
relative error = 9.0910054777494738306873992401658 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.2224272812490720628176059159557
y[1] (numeric) = 1.1110420248667495353689705149466
absolute error = 0.11138525638232252744863540100906
relative error = 9.1118104193903009987741290799784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.2230564629546186758366076818755
y[1] (numeric) = 1.1113596042560047188169879869159
absolute error = 0.11169685869861395701961969495963
relative error = 9.1326003403620828570550206851156 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.223686421603637588944338005864
y[1] (numeric) = 1.1116778132154896492166588356858
absolute error = 0.11200860838814793972767917017813
relative error = 9.1533751139741320119343441449203 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.4MB, time=7.48
x[1] = 0.683
y[1] (analytic) = 1.2243171565661702056184361152149
y[1] (numeric) = 1.111996652521832884288856623442
absolute error = 0.11232050404433732132957949177289
relative error = 9.1741346138905289114811165848303 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.2249486672114816158875304615069
y[1] (numeric) = 1.112316122951032634948679142951
absolute error = 0.11263254426044898093885131855584
relative error = 9.1948787141301083480676486775243 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 1.2255809529080612270660961307334
y[1] (numeric) = 1.1126362252784559893073021689778
absolute error = 0.11294472762960523775879396175567
relative error = 9.2156072890664411311856484966754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.2262140130236233952649949029474
y[1] (numeric) = 1.1129569602788381373049559610317
absolute error = 0.11325705274478525796003894191571
relative error = 9.236320213427810951633633737414 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.2268478469251080576770664509304
y[1] (numeric) = 1.1132783287262815959757998844002
absolute error = 0.11356951819882646170126656653017
relative error = 9.2570173622971864582863892808538 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.2274824539786813656371383923497
y[1] (numeric) = 1.1136003313942554353454698845303
absolute error = 0.1138821225844259302916685078194
relative error = 9.2776986111121885686734064683401 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.2281178335497363184558221354451
y[1] (numeric) = 1.1139229690555945049620729171461
absolute error = 0.11419486449414181349374921829894
relative error = 9.2983638356650530346086574851121 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.2287539850028933980264606845022
y[1] (numeric) = 1.1142462424824986610614018030442
absolute error = 0.11450774252039473696505888145807
relative error = 9.3190129121025882841286971537524 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.2293909077020012042045937982186
y[1] (numeric) = 1.1145701524465319943671433422862
absolute error = 0.1148207552554692098374504559324
relative error = 9.3396457169261285610099494359686 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.2300286010101370909593051215486
y[1] (numeric) = 1.1148946997186220585268518875181
absolute error = 0.11513390129151503243245323403053
relative error = 9.3602621269914823831491312773473 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.2306670642896078032958151397345
y[1] (numeric) = 1.1152198850690590991844599403758
absolute error = 0.11544717922054870411135519935873
relative error = 9.3808620195088763411030963534397 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.2313062969019501149486830319832
y[1] (numeric) = 1.1155457092674952836900966984047
absolute error = 0.11576058763445483125858633357849
relative error = 9.4014452720428942580959500455305 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.2319462982079314668449797316401
y[1] (numeric) = 1.1158721730829439314479848426092
absolute error = 0.11607412512498753539699488903092
relative error = 9.4220117625124117328120988579777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.2325870675675506063367937297397
y[1] (numeric) = 1.1161992772837787449031852176704
absolute error = 0.11638779028377186143360851206929
relative error = 9.4425613691905260863039567616709 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.2332286043400382272024303894814
y[1] (numeric) = 1.1165270226377330411679584180258
absolute error = 0.11670158170230518603447197145562
relative error = 9.4630939707044817343523418935148 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.2338709078838576104156647704838
y[1] (numeric) = 1.1168554099118989842885116533825
absolute error = 0.11701549797195862612715311710128
relative error = 9.4836094460355910066261639511443 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.234513977556705265682407193618
y[1] (numeric) = 1.1171844398727268181528986268552
absolute error = 0.11732953768397844752950856676276
relative error = 9.5041076745191504339958297939395 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=137.3MB, alloc=4.4MB, time=7.69
x[1] = 0.7
y[1] (analytic) = 1.2351578127155115737441400098081
y[1] (numeric) = 1.1175141132860241000408395177637
absolute error = 0.11764369942948747370330049204445
relative error = 9.5245885358443525253618865014922 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.2358024127164414294474832694162
y[1] (numeric) = 1.1178444309169549348162275192071
absolute error = 0.11795798179948649463125575020904
relative error = 9.5450519100541930553667817614012 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 1.2364477769148948855792462226979
y[1] (numeric) = 1.1181753935300392097630877378442
absolute error = 0.11827238338485567581615848485369
relative error = 9.5654976775453738843632552784895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.2370939046655077974663208163335
y[1] (numeric) = 1.1185070018891518300657536198565
absolute error = 0.11858690277635596740056719647696
relative error = 9.5859257190682013320177862422351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.2377407953221524683397725861917
y[1] (numeric) = 1.118839256757521954934025422855
absolute error = 0.11890153856463051340574716333673
relative error = 9.6063359157264801259317150892147 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.2383884482379382954624835822915
y[1] (numeric) = 1.1191721588977322343740746085074
absolute error = 0.11921628934020606108840897378415
relative error = 9.6267281489774029466661371890252 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.2390368627652124170197011983717
y[1] (numeric) = 1.1195057090717180466058573849191
absolute error = 0.11953115369349437041384381345263
relative error = 9.6471023006314355905594360070736 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.2396860382555603597718460155734
y[1] (numeric) = 1.1198399080407667361277999812896
absolute error = 0.11984613021479362364404603428383
relative error = 9.6674582528521977717283881023387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.2403359740598066874689310074817
y[1] (numeric) = 1.1201747565655168524295175900959
absolute error = 0.12016121749428983503941341738577
relative error = 9.6877958881563395846451363538876 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.709
y[1] (analytic) = 1.2409866695280156500259436921618
y[1] (numeric) = 1.1205102554059573893533282640216
absolute error = 0.12047641412205826067261542814018
relative error = 9.7081150894134136486829954321121 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.2416381240094918334585420558604
y[1] (numeric) = 1.1208464053214270251053224060522
absolute error = 0.12079171868806480835321964980827
relative error = 9.7284157398457429560240290989273 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.2422903368527808105784143127322
y[1] (numeric) = 1.1211832070706133629167478416062
absolute error = 0.12110712978216744766166647112604
relative error = 9.7486977230282844443206267989241 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.2429433074056697924476518052839
y[1] (numeric) = 1.121520661411552172356469811252
absolute error = 0.12142264599411762009118199403194
relative error = 9.7689609228884883155019115575564 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.2435970350151882805914835912195
y[1] (numeric) = 1.121858769101626631295264571488
absolute error = 0.1217382659135616492962190197315
relative error = 9.7892052237061531221137368029394 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.2442515190276087199687205040045
y[1] (numeric) = 1.1221975308975665685227046392291
absolute error = 0.12205398813004215144601586477539
relative error = 9.8094305101132766425782807477453 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.2449067587884471526992557167609
y[1] (numeric) = 1.1225369475554477070173930630512
absolute error = 0.12236981123299944568186265370973
relative error = 9.8296366670939025667558277826464 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.2455627536424638725479680820458
y[1] (numeric) = 1.122877019830690907871303450896
absolute error = 0.12268573381177296467666463114978
relative error = 9.8498235799839630131872413207973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=141.1MB, alloc=4.4MB, time=7.91
x[1] = 0.717
y[1] (analytic) = 1.2462195029336640801643737636656
y[1] (numeric) = 1.1232177484780614148689818298342
absolute error = 0.12300175445560266529539193383137
relative error = 9.8699911344711168993908860740773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.2468770060052985390773709209283
y[1] (numeric) = 1.1235591342516680997223657586206
absolute error = 0.12331787175363043935500516230771
relative error = 9.8901392165945841865823542181614 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 1.2475352621998642324444214506443
y[1] (numeric) = 1.1239011779049627079619754581605
absolute error = 0.12363408429490152448244599248374
relative error = 9.9102677127449760201792936984507 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.2481942708591050205545130377481
y[1] (numeric) = 1.1242438801907391054852310686332
absolute error = 0.12395039066836591506928196911483
relative error = 9.9303765096641207874469324272299 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.2488540313240122990842440116342
y[1] (numeric) = 1.1245872418611325257626494848915
absolute error = 0.12426678946287977332159452674267
relative error = 9.950465494444886113632543709919 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.249514542934825658106372752177
y[1] (numeric) = 1.124931263667618817702673563879
absolute error = 0.12458327926720684040369918829794
relative error = 9.9705345545309968179291103014921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.2501758050310335418501726369398
y[1] (numeric) = 1.1252759463610136941758858391726
absolute error = 0.12489985867001984767428679776716
relative error = 9.9905835777168488505998214200643 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.2508378169513739092129327692739
y[1] (numeric) = 1.1256212906914719811993582183739
absolute error = 0.12521652625990192801357455090003
relative error = 10.010612452147319232585783220566 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.2515005780338348950219439758613
y[1] (numeric) = 1.1259672974084868677818884789374
absolute error = 0.12553328062534802724005549692389
relative error = 10.030621066317572018909443044557 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.2521640876156554720463088117698
y[1] (numeric) = 1.1263139672608891564308737171364
absolute error = 0.12585012035476631561543509463344
relative error = 10.050609309072860307175725599511 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.2528283450333261137579135612673
y[1] (numeric) = 1.1266613009968465143215702432306
absolute error = 0.12616704403647959943634331803668
relative error = 10.07057706960832431246175946877 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.2534933496225894578408994734763
y[1] (numeric) = 1.1270092993638627251294887535136
absolute error = 0.12648405025872673271141071996274
relative error = 10.090524237468785529874339397387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.2541591007184409704489697234547
y[1] (numeric) = 1.1273579631087769415266729467816
absolute error = 0.12680113760966402892229677667309
relative error = 10.11045070254853700604192802387 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.2548255976551296112098678414497
y[1] (numeric) = 1.1277072929777629383426090888842
absolute error = 0.12711830467736667286725875256543
relative error = 10.130356355091129740795054516685 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.2554928397661584989763626059028
y[1] (numeric) = 1.1280572897163283663905133643838
absolute error = 0.12743555004983013258584924151907
relative error = 10.150241085689155240275421309004 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.2561608263842855783230736492765
y[1] (numeric) = 1.1284079540693140069597431889745
absolute error = 0.12775287231497157136333046030195
relative error = 10.170104785284024242699888185669 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 1.2568295568415242867884712799312
y[1] (numeric) = 1.1287592867808930269750779901885
absolute error = 0.12807027006063125981339328974262
relative error = 10.189947345165741637990769740474 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.4MB, time=8.13
x[1] = 0.734
y[1] (analytic) = 1.2574990304691442228613832781104
y[1] (numeric) = 1.1291112885945702348236142970445
absolute error = 0.12838774187457398803776898106582
relative error = 10.209768656972677602468562065629 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.2581692465976718147113406795812
y[1] (numeric) = 1.1294639602531813368500193116835
absolute error = 0.12870528634449047786132136789766
relative error = 10.229568612691334969787311831589 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 1.2588402045568909896620938166407
y[1] (numeric) = 1.1298173024988921945208864676749
absolute error = 0.12902290205799879514120734896585
relative error = 10.249347104656112859276360035042 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.2595119036758438444076291430284
y[1] (numeric) = 1.1301713160731980822589358105762
absolute error = 0.12934058760264576214869333245227
relative error = 10.269104025549066582835138003191 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.2601843432828313159700166267826
y[1] (numeric) = 1.1305260017169229459478013664837
absolute error = 0.12965834156590837002221526029891
relative error = 10.288839268399663851510069107857 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.2608575227054138533984167532507
y[1] (numeric) = 1.1308813601702186621081469937255
absolute error = 0.12997616253519519129026975952523
relative error = 10.308552726584537302864440424418 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.2615314412704120902085754393012
y[1] (numeric) = 1.1312373921725642977458515415181
absolute error = 0.13029404909784779246272389778306
relative error = 10.328244293827233370233358625382 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.2622060983039075175621344192991
y[1] (numeric) = 1.1315940984627653708730034673417
absolute error = 0.1306119998411421466891309519574
relative error = 10.347913864197957514936598079956 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.2628814931312431581850839235906
y[1] (numeric) = 1.1319514797789531117024443919758
absolute error = 0.1309300133522900464826395316148
relative error = 10.367561332113315842502290788614 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.2635576250770242410246837310994
y[1] (numeric) = 1.1323095368585837245166003975913
absolute error = 0.13124808821844051650808333350808
relative error = 10.387186592336053123934001760527 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.744
y[1] (analytic) = 1.2642344934651188766441779391716
y[1] (numeric) = 1.1326682704384376502113392000064
absolute error = 0.13156622302668122643283873916522
relative error = 10.40678953997478724303278408213 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.2649120976186587333546280560096
y[1] (numeric) = 1.1330276812546188295155906511868
absolute error = 0.1318844163640399038390374048228
relative error = 10.426370070483740090764319563065 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.2655904368600397140831882839174
y[1] (numeric) = 1.1333877700425539668874673523086
absolute error = 0.13220266681748574719572093160881
relative error = 10.445928079662464927639227811854 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.2662695105109226339771461251409
y[1] (numeric) = 1.1337485375369917950876214812027
absolute error = 0.13252097297393083888952464393824
relative error = 10.465463463655570235052073213782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.2669493178922338987430507063167
y[1] (numeric) = 1.1341099844720023404305732607616
absolute error = 0.13283933342023155831247744555517
relative error = 10.484976118952440076501519877726 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.2676298583241661837202504824584
y[1] (numeric) = 1.134472111580976188714745816919
absolute error = 0.13315774674318999500550466553945
relative error = 10.504465942386950989590483501904 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.2683111311261791136881612469999
y[1] (numeric) = 1.1348349195966237518319404961072
absolute error = 0.13347621152955536185622075089274
relative error = 10.523932831137185429681010589524 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=148.7MB, alloc=4.4MB, time=8.34
x[1] = 0.751
y[1] (analytic) = 1.2689931356169999434065846406836
y[1] (numeric) = 1.1351984092509745350569860326545
absolute error = 0.13379472636602540834959860802904
relative error = 10.54337668272514178605398382719 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.2696758711146242388883966190315
y[1] (numeric) = 1.1355625812753764050182942764133
absolute error = 0.13411328983924783387010234261821
relative error = 10.56279739501644099139861201825 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 1.270359336936316559403924605769
y[1] (numeric) = 1.1359274364004948583500545100017
absolute error = 0.13443190053582170105387009576736
relative error = 10.582194866220029745431018030561 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.2710435323986111402163313278786
y[1] (numeric) = 1.1362929753563122910267977034034
absolute error = 0.13475055704229884918953362447523
relative error = 10.601568994887880373415093057121 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.2717284568173125760473225969591
y[1] (numeric) = 1.1366591988721272683810613713015
absolute error = 0.13506925794518530766626122565761
relative error = 10.620919679914687340332144375679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.2724141095074965052724955712377
y[1] (numeric) = 1.137026107676553795804885015419
absolute error = 0.13538800183094270946761055581874
relative error = 10.640246820537560441418730999905 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 1.2731004897835102948456433029448
y[1] (numeric) = 1.1373937024975205901358654503111
absolute error = 0.1357067872859897047097778526337
relative error = 10.659550316335714689764461402764 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.2737875969589737259513306468032
y[1] (numeric) = 1.137761984062270351728500626493
absolute error = 0.13602561289670337422283002031024
relative error = 10.678830067230156921633424118059 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.274475430346779680385055877114
y[1] (numeric) = 1.1381309530973590372115498794981
absolute error = 0.13634447724942064317350599761589
relative error = 10.698085973483369140144339736614 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.275163989259094827660311633333
y[1] (numeric) = 1.1385006103286551329321378474463
absolute error = 0.13666337893043969472817378588671
relative error = 10.717317935698988617915465849598 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.2758532730073603128418580871366
y[1] (numeric) = 1.1388709564813389290873286129581
absolute error = 0.13698231652602138375452947417846
relative error = 10.736525854821484779250759085473 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.2765432809022924451045204977583
y[1] (numeric) = 1.1392419922799017945438959377793
absolute error = 0.13730128862239065056062455997904
relative error = 10.755709632135832882413804763302 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.2772340122538833870168225968583
y[1] (numeric) = 1.1396137184481454523470147702857
absolute error = 0.13762029380573793466980782657261
relative error = 10.774869169267184522505569059727 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.277925466371401844548766519348
y[1] (numeric) = 1.1399861357091812559185985171166
absolute error = 0.13793933066222058863016800223132
relative error = 10.794004368180534975431115167555 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.2786176425633937578030692724491
y[1] (numeric) = 1.1403592447854294659460058805392
absolute error = 0.13825839777796429185706339190995
relative error = 10.813115131180387403409057909563 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.2793105401376829924691650118068
y[1] (numeric) = 1.1407330463986185279618403727754
absolute error = 0.13857749373906446450732463903142
relative error = 10.83220136091041394244571485216 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.2800041584013720319992816707128
y[1] (numeric) = 1.1411075412697843506155649274343
absolute error = 0.13889661713158768138371674327848
relative error = 10.851262960353113692163650321271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=152.5MB, alloc=4.4MB, time=8.55
x[1] = 0.768
y[1] (analytic) = 1.2806984966608426705058997664195
y[1] (numeric) = 1.1414827301192695846376533363724
absolute error = 0.13921576654157308586824643004715
relative error = 10.870299832829467628341606029484 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.2813935542217567063799004861449
y[1] (numeric) = 1.1418586136667229024969995477723
absolute error = 0.13953494055503380388290093837259
relative error = 10.889311881998590458489672442029 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
y[1] (analytic) = 1.2820893303890566366287094346757
y[1] (numeric) = 1.1422351926310982787523051679694
absolute error = 0.13985413775795835787640426670624
relative error = 10.908299011857379440749982693181 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.2827858244669663519337417054856
y[1] (numeric) = 1.1426124677306542710981648155796
absolute error = 0.14017335673631208083557688990597
relative error = 10.927261126740160186379209957997 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.2834830357589918324264532179796
y[1] (numeric) = 1.1429904396829533021065682817824
absolute error = 0.14049259607603853031988493619728
relative error = 10.946198131318329466034723821168 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.2841809635679218441823025448716
y[1] (numeric) = 1.1433691092048609416645377551974
absolute error = 0.14081185436306090251776478967426
relative error = 10.965109930599995040051415489441 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.2848796071958286364319267357915
y[1] (numeric) = 1.1437484770125451901086176736581
absolute error = 0.14113113018328344632330906213341
relative error = 10.983996429929612532860939780716 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.2855789659440686394888339260045
y[1] (numeric) = 1.1441285438214757620569340683321
absolute error = 0.14145042212259287743189985767244
relative error = 11.002857534987619371669447795519 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 1.2862790391132831633929148026071
y[1] (numeric) = 1.1445093103464233709395395680688
absolute error = 0.14176972876685979245337523453835
relative error = 11.021693151790065809473802128737 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.2869798260033990972690742847478
y[1] (numeric) = 1.1448907773014590142277595335715
absolute error = 0.14208904870194008304131475117639
relative error = 11.040503186688243052459780494282 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.2876813259136296094002840592981
y[1] (numeric) = 1.1452729453999532593632540919861
absolute error = 0.14240838051367635003702996731203
relative error = 11.059287546368308511788887785245 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.28838353814247484801435589898
y[1] (numeric) = 1.1456558153545755303875101427866
absolute error = 0.14272772278789931762684575619343
relative error = 11.078046137850908199743114938552 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.2890864619877226427837349762354
y[1] (numeric) = 1.1460393878772933952724767054046
absolute error = 0.14304707411042924751125827083083
relative error = 11.096778868490796290159309566976 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 1.289790096746449207037611673102
y[1] (numeric) = 1.1464236636793718539530562779092
absolute error = 0.1433664330670773530845553951928
relative error = 11.115485645976451863046762201955 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.2904944417150198406856496750424
y[1] (numeric) = 1.1468086434713726270621641741857
absolute error = 0.14368579824364721362348550085673
relative error = 11.134166378329692853243167186436 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.2911994961890896338526274250576
y[1] (numeric) = 1.147194327963153445369067104495
absolute error = 0.14400516822593618848356032056267
relative error = 11.152820973905287222925292784822 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.2919052594636041712232893035015
y[1] (numeric) = 1.147580717863867339921711561016
absolute error = 0.14432454159973683130157774248546
relative error = 11.171449341390561377751494942438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=156.4MB, alloc=4.4MB, time=8.77
x[1] = 0.785
y[1] (analytic) = 1.2926117308328002370967021888034
y[1] (numeric) = 1.1479678138819619328937518659831
absolute error = 0.14464391695083830420295032282026
relative error = 11.190051389805005846373637323532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 1.2933189095902065211494123448021
y[1] (numeric) = 1.1483556167251787291369870353313
absolute error = 0.14496329286502779201242530947075
relative error = 11.208627028499878243016040766787 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 1.2940267950286443249066968715924
y[1] (numeric) = 1.1487441271005524084399149053545
absolute error = 0.14528266792809191646678196623785
relative error = 11.227176167157803532778782090587 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 1.2947353864402282689212032486917
y[1] (numeric) = 1.149133345714410118493111263762
absolute error = 0.14560204072581815042809198492962
relative error = 11.245698715792371619281999215087 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 1.2954446831163670006582697919461
y[1] (numeric) = 1.1495232732723707685621410196967
absolute error = 0.14592140984399623209612877224946
relative error = 11.264194584747732274226840790274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 1.296154684347763903087219138915
y[1] (numeric) = 1.1499139104793443238687077397435
absolute error = 0.14624077386841957921851139917155
relative error = 11.282663684698187428407327862404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 1.2968653894244178039779161714986
y[1] (numeric) = 1.1503052580395311006807471687215
absolute error = 0.14656013138488670329716900277716
relative error = 11.301105926647780843665676496618 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 1.2975767976356236859018810793109
y[1] (numeric) = 1.1506973166564210621121696451055
absolute error = 0.14687948097920262378971143420543
relative error = 11.319521221929885185241567609933 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 1.2982889082699733969372475627432
y[1] (numeric) = 1.1510900870327931146329556112775
absolute error = 0.14719882123718028230429195146569
relative error = 11.337909482206786513923447452235 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 1.2990017206153563620768554708199
y[1] (numeric) = 1.1514835698707144052903077084532
absolute error = 0.14751815074464195678654776236662
relative error = 11.356270619469266217367203086626 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 1.2997152339589602953387664658126
y[1] (numeric) = 1.1518777658715396196415622350731
absolute error = 0.14783746808742067569720423073948
relative error = 11.374604546036180399904485735074 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 1.3004294475872719125784906041565
y[1] (numeric) = 1.1522726757359102803995620356875
absolute error = 0.14815677185136163217892856846903
relative error = 11.392911174554036750119554828008 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.797
y[1] (analytic) = 1.3011443607860776450022110215024
y[1] (numeric) = 1.1526683001637540467911921749061
absolute error = 0.14847606062232359821101884659632
relative error = 11.411190417996568905429790871929 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 1.3018599728404643533802932087375
y[1] (numeric) = 1.1530646398542840146297790378152
absolute error = 0.14879533298618033875051417092227
relative error = 11.429442189664308332860979658164 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 1.3025762830348200429603646655274
y[1] (numeric) = 1.1534616955059980171020527844079
absolute error = 0.14911458752882202585831188111952
relative error = 11.447666403184153745164107696599 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 1.3032932906528345790792500183577
y[1] (numeric) = 1.1538594678166779262703723710043
absolute error = 0.14943382283615665280887764735338
relative error = 11.465862972508938071375732874921 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 1.3040109949775004034730459911998
y[1] (numeric) = 1.1542579574833889552909116363803
absolute error = 0.14975303749411144818213435481951
relative error = 11.484031811916993000879009007501 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=160.2MB, alloc=4.4MB, time=8.98
x[1] = 0.802
y[1] (analytic) = 1.3047293952911132512846199187868
y[1] (numeric) = 1.1546571652024789613485042343594
absolute error = 0.15007223008863428993611568442738
relative error = 11.502172836011711119977151925877 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 1.3054484908752728687678147950589
y[1] (numeric) = 1.1550570916695777493088444779652
absolute error = 0.15039139920569511945897031709364
relative error = 11.520285959721105659945541838322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 1.3061682810108837316876431526351
y[1] (numeric) = 1.1554577375795963760887404428759
absolute error = 0.15071054343128735559890270975917
relative error = 11.538371098297367875482765599056 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 1.3068887649781557644157513731752
y[1] (numeric) = 1.1558591036267264557451149598684
absolute error = 0.15102966135142930867063641330677
relative error = 11.556428167316422072434717013993 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 1.3076099420566050597204353332294
y[1] (numeric) = 1.1562611905044394652834494071953
absolute error = 0.15134875155216559443698592603412
relative error = 11.574457082677478303619397091396 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 1.3083318115250545992504875956188
y[1] (numeric) = 1.156663998905486051186364494391
absolute error = 0.15166781261956854806412310122776
relative error = 11.592457760602582751533292930106 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 1.3090543726616349747121556625597
y[1] (numeric) = 1.1570675295218953366630315088699
absolute error = 0.15198684313973963804912415368985
relative error = 11.610430117636165816673167418582 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 1.3097776247437851097384901136345
y[1] (numeric) = 1.1574717830449742296201067758463
absolute error = 0.15230584169881088011838333778821
relative error = 11.628374070644587930159765774188 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 1.3105015670482529824503607593199
y[1] (numeric) = 1.1578767601653067313548813605859
absolute error = 0.152624806882946251095479398734
relative error = 11.646289536815683109302342848667 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 1.311226198851096348708418249117
y[1] (numeric) = 1.1582824615727532459713373197788
absolute error = 0.15294373727834310273708092933825
relative error = 11.664176433658300274695040713045 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 1.3119515194276834660552778823829
y[1] (numeric) = 1.1586888879564498905198010859229
absolute error = 0.15326263147123357553547679645993
relative error = 11.682034679001842347388002949138 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 1.3126775280526938183472016797382
y[1] (numeric) = 1.1590960400048078058608838450056
absolute error = 0.15358148804788601248631783473261
relative error = 11.699864190995803144627703936569 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 1.3134042240001188410745540834315
y[1] (numeric) = 1.1595039184055124682543980434852
absolute error = 0.15390030559460637282015603994623
relative error = 11.717664888109302092612301840262 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 1.3141316065432626473703059662622
y[1] (numeric) = 1.1599125238455230016739384355999
absolute error = 0.15421908269773964569636753066224
relative error = 11.735436689130616774658896565496 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 1.314859674954742754705860940622
y[1] (numeric) = 1.1603218570110714908478153563648
absolute error = 0.15453781794367126385804558425722
relative error = 11.753179513166713333130392232607 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 1.315588428506490812273477271886
y[1] (numeric) = 1.1607319185876622950270271792665
absolute error = 0.15485650991882851724645009261953
relative error = 11.770893279642774743420231293223 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 1.316317866469753329054558013794
y[1] (numeric) = 1.1611427092600713624809581906264
absolute error = 0.15517515720968196657359982316757
relative error = 11.788577908301726978243587811445 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=164.0MB, alloc=4.4MB, time=9.20
x[1] = 0.819
y[1] (analytic) = 1.3170479881150924025730812975917
y[1] (numeric) = 1.1615542297123455457214873848768
absolute error = 0.15549375840274685685159391271495
relative error = 11.806233319203763080433684198368 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 1.3177787927123864483334420215631
y[1] (numeric) = 1.161966480627801917456192956584
absolute error = 0.15581231208458453087724906497905
relative error = 11.823859432725865162391732333492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 1.3185102795308309299419755031717
y[1] (numeric) = 1.1623794626890270872713365359582
absolute error = 0.15613081684180384267063896721349
relative error = 11.841456169561324350288600033285 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 1.3192424478389390899114329723498
y[1] (numeric) = 1.162793176577876519045310484807
absolute error = 0.15644927126106257086612248754284
relative error = 11.859023450719258691065670721547 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.823
y[1] (analytic) = 1.3199752969045426811476781015192
y[1] (numeric) = 1.1632076229754738490932308394299
absolute error = 0.15676767392906883205444726208926
relative error = 11.876561197524129040231501388991 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 1.3207088259947926991178730857087
y[1] (numeric) = 1.1636228025622102050433577558035
absolute error = 0.15708602343258249407451532990514
relative error = 11.894069331615252948399794956059 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 1.3214430343761601146994221046441
y[1] (numeric) = 1.1640387160177435254460245805801
absolute error = 0.15740431835841658925339752406402
relative error = 11.911547774946316564462891413079 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 1.3221779213144366077089393179268
y[1] (numeric) = 1.1644553640209978801157559389138
absolute error = 0.15772255729343872759318337901299
relative error = 11.928996449784884573243451029871 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 1.3229134860747353011105078643946
y[1] (numeric) = 1.16487274725016279120725449694
absolute error = 0.15804073882457250990325336745462
relative error = 11.94641527871190818541525591139 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 1.3236497279214914959024956574681
y[1] (numeric) = 1.1652908663826925550259353228643
absolute error = 0.15835886153879894087656033460378
relative error = 11.963804184621231197432096619997 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 1.3243866461184634066821930897261
y[1] (numeric) = 1.1657097220953055645736860360703
absolute error = 0.15867692402315784210850705365583
relative error = 11.981163090719094139151541865709 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 1.3251242399287328978875370821355
y[1] (numeric) = 1.1661293150639836328305301984294
absolute error = 0.15899492486474926505700688370617
relative error = 11.998491920523636526788014744744 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 1.3258625086147062207151852362717
y[1] (numeric) = 1.1665496459639713167728706660932
absolute error = 0.15931286265073490394231457017849
relative error = 12.01579059786439723877702202957 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 1.3266014514381147507142031715169
y[1] (numeric) = 1.1669707154697752421289888834685
absolute error = 0.15963073596833950858521428804842
relative error = 12.033059046881813032079606910073 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 1.3273410676600157260546274536119
y[1] (numeric) = 1.1673925242551634288724753638195
absolute error = 0.15994854340485229718215208979245
relative error = 12.050297192026715216403123669365 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 1.3280813565407929864701658460576
y[1] (numeric) = 1.1678150729931646174542658630102
absolute error = 0.16026628354762836901589998304734
relative error = 12.067504958059824503761268346801 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 1.3288223173401577128742959417292
y[1] (numeric) = 1.1682383623560675957739570142956
absolute error = 0.16058395498409011710033892743361
relative error = 12.084682270051244050742945776786 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=167.8MB, alloc=4.4MB, time=9.41
x[1] = 0.836
y[1] (analytic) = 1.3295639493171491676490225586661
y[1] (numeric) = 1.1686623930154205268910744527882
absolute error = 0.16090155630172864075794810587791
relative error = 12.101829053379950710806013760677 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 1.3303062517301354356055536113409
y[1] (numeric) = 1.1690871656420302774769657182781
absolute error = 0.16121908608810515812858789306278
relative error = 12.118945233733284513858222779894 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 1.3310492238368141656161534967937
y[1] (numeric) = 1.1695126809059617470079894844554
absolute error = 0.16153654293085241860816401233827
relative error = 12.136030737106436390333767824799 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 1.3317928648942133129164323638407
y[1] (numeric) = 1.1699389394765371977006719212914
absolute error = 0.16185392541767611521576044254935
relative error = 12.153085489801934156919790812975 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 1.3325371741586918820773289631291
y[1] (numeric) = 1.1703659420223355851895002553656
absolute error = 0.16217123213635629688782870776356
relative error = 12.170109418429126781032920903234 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 1.3332821508859406706460441061175
y[1] (numeric) = 1.17079368921119188994802285029
absolute error = 0.16248846167474878069802125582747
relative error = 12.187102449903666941091518962502 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 1.3340277943309830134551810921098
y[1] (numeric) = 1.1712221817101964494539243860735
absolute error = 0.16280561262078656400125670603631
relative error = 12.204064511446991899574704679971 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 1.334774103748175527599348794266
y[1] (numeric) = 1.171651420185694291098743972297
absolute error = 0.16312268356248123650060482196897
relative error = 12.22099553058580270580449349846 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 1.3355210783912088580784824280462
y[1] (numeric) = 1.1720814053032844658429032853248
absolute error = 0.16343967308792439223557914272136
relative error = 12.237895435151541745332458782114 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 1.3362687175131084241071363588314
y[1] (numeric) = 1.1725121377278193826167110744685
absolute error = 0.16375657978528904149042528436295
relative error = 12.254764153279868652757265581659 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 1.3370170203662351660890026394896
y[1] (numeric) = 1.1729436181234041434680096360437
absolute error = 0.16407340224283102262099300344593
relative error = 12.271601613410134604744199095673 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 1.3377659862022862932559083034306
y[1] (numeric) = 1.1733758471533958794571281076181
absolute error = 0.16439013904889041379878019581254
relative error = 12.288407744284855009962436544969 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 1.3385156142722960319705437742155
y[1] (numeric) = 1.1738088254804030872998066874412
absolute error = 0.16470678879189294467073708677434
relative error = 12.30518247494918061260028874663 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.849
y[1] (analytic) = 1.3392659038266363746921740890535
y[1] (numeric) = 1.1742425537662849667587551360768
absolute error = 0.16502335006035140793341895297665
relative error = 12.321925734750367026062970247392 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 1.3400168541150178296045839705385
y[1] (numeric) = 1.1746770326721507587845081686252
absolute error = 0.16533982144286707082007580191329
relative error = 12.338637453337242713401647489288 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 1.3407684643864901709055071187423
y[1] (numeric) = 1.1751122628583590844062395966229
absolute error = 0.1656562015281310864992675221194
relative error = 12.355317560659675430966566153499 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 1.3415207338894431897567894342973
y[1] (numeric) = 1.1755482449845172843731963287523
absolute error = 0.16597248890492590538359310554495
relative error = 12.371965986968037151720974564151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=171.6MB, alloc=4.4MB, time=9.63
x[1] = 0.853
y[1] (analytic) = 1.3422736618716074458945352223685
y[1] (numeric) = 1.1759849797094807595474125888713
absolute error = 0.16628868216212668634712263349713
relative error = 12.388582662812667484596342818888 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 1.3430272475800550198984847674315
y[1] (numeric) = 1.1764224676913523120483639585941
absolute error = 0.16660477988870270785012080883749
relative error = 12.405167519043335606213030117003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 1.3437814902612002661198710095412
y[1] (numeric) = 1.1768607095874814871502200997135
absolute error = 0.16692078067371877896965090982769
relative error = 12.421720486808700721234078531827 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 1.3445363891608005662670023942965
y[1] (numeric) = 1.177299706054463915932354259159
absolute error = 0.16723668310633665033464813513751
relative error = 12.438241497555771067563213158104 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 1.3452919435239570836478183109831
y[1] (numeric) = 1.1777394577481406586837669059236
absolute error = 0.16755248577581642496405140505953
relative error = 12.454730483029361482541409076841 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 1.3460481525951155180686628763995
y[1] (numeric) = 1.1781799653235975490620800954835
absolute error = 0.16786818727151796900658278091598
relative error = 12.471187375271549546239547822225 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 1.3468050156180668613885221656564
y[1] (numeric) = 1.1786212294351645390077584026603
absolute error = 0.16818378618290232238076376299616
relative error = 12.487612106621130317887732893707 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 1.3475625318359481537279693357761
y[1] (numeric) = 1.1790632507364150444142115086506
absolute error = 0.1684992810995331093137578271255
relative error = 12.504004609713069681424768200332 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 1.3483207004912432403320614332074
y[1] (numeric) = 1.1795060298801652915544327720661
absolute error = 0.16881467061107794877762866114134
relative error = 12.520364817477956316094128006242 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 1.3490795208257835290864310224247
y[1] (numeric) = 1.1799495675184736642648273572899
absolute error = 0.16912995330730986482160366513475
relative error = 12.536692663141452307955464801458 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 1.3498389920807487486858151195816
y[1] (numeric) = 1.1803938643026400518868827362692
absolute error = 0.16944512777810869679893238331241
relative error = 12.552988080223742418123315369274 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 1.3505991134966677074542632627533
y[1] (numeric) = 1.1808389208832051979673336220157
absolute error = 0.16976019261346250948692964073755
relative error = 12.569251002538982023487177962672 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 1.3513598843134190528162658986232
y[1] (numeric) = 1.1812847379099500497174726335987
absolute error = 0.17007514640346900309879326502447
relative error = 12.585481364194743745609547722053 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 1.3521213037702320314180436145485
y[1] (numeric) = 1.1817313160318951082322572332622
absolute error = 0.17038998773833692318578638128631
relative error = 12.601679099591462783440816033432 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 1.3528833711056872498982370947791
y[1] (numeric) = 1.1821786558972997794698627165078
absolute error = 0.17070471520838747042837437827129
relative error = 12.617844143421880965432165191218 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 1.3536460855577174363072370302028
y[1] (numeric) = 1.1826267581536617259923302755348
absolute error = 0.17101932740405571031490675466799
relative error = 12.633976430670489536569725227246 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 1.3544094463636082021743925623505
y[1] (numeric) = 1.1830756234477162194679583953353
absolute error = 0.17133382291589198270643416701518
relative error = 12.650075896612970695795307815214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=175.4MB, alloc=4.4MB, time=9.85
x[1] = 0.87
y[1] (analytic) = 1.3551734527599988052223361945172
y[1] (numeric) = 1.1835252524254354939360850800004
absolute error = 0.17164820033456331128625111451678
relative error = 12.66614247681563789922099545782 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 1.3559381039828829127276624557363
y[1] (numeric) = 1.1839756457320280998349076443997
absolute error = 0.17196245825085481289275481133654
relative error = 12.682176107134874944486745396271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 1.3567033992676093655271969569926
y[1] (numeric) = 1.1844268040119382587929860433614
absolute error = 0.17227659525567110673421091363117
relative error = 12.698176723716573851551969515358 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 1.3574693378488829426690918334692
y[1] (numeric) = 1.1848787279088452191850749467957
absolute error = 0.17259060994003772348401688667354
relative error = 12.714144262995571555153776601824 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 1.3582359189607651267079829217956
y[1] (numeric) = 1.1853314180656626124529290048756
absolute error = 0.17290450089510251425505391691999
relative error = 12.73007866169508542410621428238 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.875
y[1] (analytic) = 1.359003141836674869643443377204
y[1] (numeric) = 1.1857848751245378101917249824166
absolute error = 0.17321826671213705945171839478734
relative error = 12.745979856826147622556427436548 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 1.3597710057093893595009677922045
y[1] (numeric) = 1.1862390997268512820027436759791
absolute error = 0.17353190598253807749822411622541
relative error = 12.761847785687038328255160447848 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 1.3605395098110447875547202358586
y[1] (numeric) = 1.1866940925132159541129537609581
absolute error = 0.17384541729782883344176647490041
relative error = 12.777682385862717822840474907049 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 1.3613086533731371161912789909657
y[1] (numeric) = 1.1871498541234765687621389490235
absolute error = 0.17415879924966054742914004194214
relative error = 12.793483595224257469074934878807 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 1.3620784356265228474136101254846
y[1] (numeric) = 1.1876063851967090443582090687296
absolute error = 0.17447205042981380305540105675503
relative error = 12.809251351928269589917831136655 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 1.3628488558014197919845013942779
y[1] (numeric) = 1.1880636863712198364013349139301
absolute error = 0.17478516943019995558316648034781
relative error = 12.824985594416336264255276392773 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 1.3636199131274078392086873278103
y[1] (numeric) = 1.1885217582845452991775459358103
absolute error = 0.17509815484286254003114139200003
relative error = 12.840686261414437054052208013186 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 1.3643916068334297273528957257406
y[1] (numeric) = 1.1889806015734510482224290848851
absolute error = 0.17541100525997867913046664085549
relative error = 12.856353291932375677631485514097 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 1.3651639361477918147030451354242
y[1] (numeric) = 1.189440216873931323555566339212
absolute error = 0.17572371927386049114747879621219
relative error = 12.871986625263205643726369762189 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 1.3659369002981648512578222581931
y[1] (numeric) = 1.1899006048212083536863476843268
absolute error = 0.17603629547695649757147457386622
relative error = 12.887586200982654860893721715435 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 1.3667104985115847510578675899006
y[1] (numeric) = 1.1903617660497317203917955390382
absolute error = 0.17634873246185303066607205086236
relative error = 12.903151958948549236816263188697 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 1.3674847300144533651497969666091
y[1] (numeric) = 1.1908237011931777242670358492015
absolute error = 0.17666102882127564088276111740765
relative error = 12.918683839300235281963202941169 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=179.2MB, alloc=4.5MB, time=10.07
x[1] = 0.887
y[1] (analytic) = 1.3682595940325392551842860514642
y[1] (numeric) = 1.1912864108844487510490502989496
absolute error = 0.17697318314809050413523575251458
relative error = 12.934181782458001732019450774412 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 1.3690350897909784676474441647341
y[1] (numeric) = 1.1917498957556726387143433155751
absolute error = 0.17728519403530582893310084915903
relative error = 12.949645729122500203434522697679 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 1.369811216514275308724703225707
y[1] (numeric) = 1.1922141564382020453511567703437
absolute error = 0.17759706007607326337354645536334
relative error = 12.965075620274164896383083941879 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 1.3705879734263031197964469426197
y[1] (numeric) = 1.1926791935626138178068645029723
absolute error = 0.17790877986368930198958243964748
relative error = 12.98047139717263135936988604873 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 1.3713653597503050535646047550548
y[1] (numeric) = 1.1931450077587083611111780223238
absolute error = 0.17822035199159669245342673273097
relative error = 12.995833001356154329652631774293 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 1.3721433747088948508094344022757
y[1] (numeric) = 1.1936115996555090086757939600612
absolute error = 0.17853177505338584213364044221454
relative error = 13.011160374641024663597049456689 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 1.3729220175240576177757163607833
y[1] (numeric) = 1.1940789698812613932711130775599
absolute error = 0.17884304764279622450460328322348
relative error = 13.026453459120985371019179119841 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 1.373701287417150604187582764963
y[1] (numeric) = 1.1945471190634328187806598493083
absolute error = 0.17915416835371778540692291565467
relative error = 13.041712197166646767510568215657 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 1.3744811836089039818912027960585
y[1] (numeric) = 1.1950160478287116327338308683236
absolute error = 0.17946513578019234915737192773495
relative error = 13.056936531424900758682747826486 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 1.3752617053194216241245458968532
y[1] (numeric) = 1.195485756803006599617599540782
absolute error = 0.17977594851641502450694635607116
relative error = 13.07212640481833427020801262163 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 1.3760428517681818854134435423582
y[1] (numeric) = 1.1959562466114462749678037581078
absolute error = 0.18008660515673561044563978425035
relative error = 13.087281760544641837474162133309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 1.3768246221740383820931696705131
y[1] (numeric) = 1.1964275178783783802406424551797
absolute error = 0.18039710429566000185252721533343
relative error = 13.102402542076037368611479219292 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 1.3776070157552207734547592513822
y[1] (numeric) = 1.1968995712273691784650061831069
absolute error = 0.18070744452785159498975306827522
relative error = 13.117488693158665094590826125419 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 1.3783900317293355435152838485929
y[1] (numeric) = 1.1973724072812028506762660441925
absolute error = 0.18101762444813269283901780440038
relative error = 13.132540157812009720032331548863 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 1.3791736693133667834113024028072
y[1] (numeric) = 1.1978460266618808731321445552418
absolute error = 0.18132764265148591027915784756537
relative error = 13.147556880328305788304725713186 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.902
y[1] (analytic) = 1.3799579277236769744147048438388
y[1] (numeric) = 1.1983204299906213953112912232949
absolute error = 0.18163749773305557910341362054385
relative error = 13.162538805271946274435956863522 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 1.380742806176007771570165515639
y[1] (numeric) = 1.1987956178878586186951848351545
absolute error = 0.18194718828814915287498068048448
relative error = 13.17748587747889041929629392256 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=183.1MB, alloc=4.5MB, time=10.29
x[1] = 0.904
y[1] (analytic) = 1.3815283038854807879534227767624
y[1] (numeric) = 1.1992715909732421763339836787553
absolute error = 0.18225671291223861161943909800709
relative error = 13.192398042056070818455688446973 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 1.3823144200665983795496005180982
y[1] (numeric) = 1.1997483498656365131969441304734
absolute error = 0.18256607020096186635265638762479
relative error = 13.207275244380799779057736604884 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 1.3831011539332444307507867196122
y[1] (numeric) = 1.2002258951831202673080272579059
absolute error = 0.18287525875012416344275946170632
relative error = 13.222117430100174957993150756478 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 1.3838885046986851404720835485838
y[1] (numeric) = 1.2007042275429856516673123024602
absolute error = 0.18318427715569948880477124612354
relative error = 13.23692454513048429459622244475 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 1.3846764715755698088853428833566
y[1] (numeric) = 1.201183347561737836958835120292
absolute error = 0.1834931240138319719265077630646
relative error = 13.251696535656610251028336257546 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 1.3854650537759316247698005289301
y[1] (numeric) = 1.2016632558550943350454688736976
absolute error = 0.18380179792083728972433165523256
relative error = 13.266433348131433373453179155676 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 1.3862542505111884534788217738253
y[1] (numeric) = 1.2021439530379843832514634780322
absolute error = 0.18411029747320407022735829579309
relative error = 13.281134929275235187048884508438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 1.3870440609921436255219703215436
y[1] (numeric) = 1.2026254397245483294332595215616
absolute error = 0.18441862126759529608871079998199
relative error = 13.295801226075100437842956255048 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 1.387834484428986725761612014616
y[1] (numeric) = 1.2031077165281370178391915873815
absolute error = 0.18472676790084970792242042723453
relative error = 13.310432185784318694296438319373 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 1.3886255200312943832232641547054
y[1] (numeric) = 1.2035907840613111757586951176523
absolute error = 0.18503473596998320746456903705313
relative error = 13.325027755921785321504429631299 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 1.3894171670080310615189006084766
y[1] (numeric) = 1.2040746429358408009616301708887
absolute error = 0.18534252407219026055727043758787
relative error = 13.339587884271401840820697820033 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 1.390209424567549849882422275997
y[1] (numeric) = 1.2045592937627045499283346329315
absolute error = 0.18565013080484529995408764306545
relative error = 13.354112518881475687654816795637 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 1.3910022919175932548165018862618
y[1] (numeric) = 1.2050447371520891268710186514958
absolute error = 0.18595755476550412794548323476604
relative error = 13.368601608064119380130946962098 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 1.3917957682652939923500114730661
y[1] (numeric) = 1.2055309737133886735471112728512
absolute error = 0.18626479455190531880290020021488
relative error = 13.383055100394649111238093629204 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 1.3925898528171757809052402738607
y[1] (numeric) = 1.2060180040552041598651694672363
absolute error = 0.18657184876197162104007080662432
relative error = 13.397472944710982777042421216441 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 1.3933845447791541347741101844421
y[1] (numeric) = 1.2065058287853427752839589370476
absolute error = 0.18687871599381135949015124739452
relative error = 13.411855090113037453472969959084 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 1.3941798433565371582025952933256
y[1] (numeric) = 1.2069944485108173210053153086708
absolute error = 0.18718539484571983719727998465485
relative error = 13.426201485962126334132919907937 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=10.50
NO POLE
x[1] = 0.921
y[1] (analytic) = 1.3949757477540263400825514114488
y[1] (numeric) = 1.2074838638378456029613935150442
absolute error = 0.18749188391618073712115789640463
relative error = 13.440512081880355141529375916986 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 1.3957722571757173492501609054418
y[1] (numeric) = 1.2079740753718498255969123816521
absolute error = 0.18779818180386752365324852378966
relative error = 13.454786827750018024055508879283 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 1.3965693708251008303901975360864
y[1] (numeric) = 1.2084650837174559864470006336551
absolute error = 0.18810428710764484394319690243135
relative error = 13.469025673712992950999784526359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 1.3973670879050632005453153977649
y[1] (numeric) = 1.2089568894784932715112497462588
absolute error = 0.18841019842656992903406565150608
relative error = 13.483228570170136617797943460485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 1.3981654076178874462295654496762
y[1] (numeric) = 1.2094494932579934514245782642204
absolute error = 0.18871591435989399480498718545579
relative error = 13.497395467780678873684366536579 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 1.3989643291652539211453425253694
y[1] (numeric) = 1.2099428956581902784255114195752
absolute error = 0.18902143350706364271983110579412
relative error = 13.511526317461616683840470030193 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 1.3997638517482411445029651037137
y[1] (numeric) = 1.2104370972805188841224790792562
absolute error = 0.18932675446772226038048602445743
relative error = 13.525621070387107638078826983021 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.928
y[1] (analytic) = 1.4005639745673265999420895217925
y[1] (numeric) = 1.2109320987256151780587342562568
absolute error = 0.18963187584171142188335526553576
relative error = 13.539679677987863018042806455346 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 1.4013646968223875350541597083728
y[1] (numeric) = 1.2114279005933152470764936193682
absolute error = 0.18993679622907228797766608900456
relative error = 13.553702091950540434842662867866 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 1.402166017712701761505092915567
y[1] (numeric) = 1.2119245034826547554809006373023
absolute error = 0.19024151423004700602419227826471
relative error = 13.567688264217136048990194900081 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 1.4029679364369484557574013260696
y[1] (numeric) = 1.2124219079918683460044111931847
absolute error = 0.19054602844508010975299013288488
relative error = 13.581638146984376384435329230109 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 1.4037704521932089603909488139114
y[1] (numeric) = 1.2129201147183890415722007049844
absolute error = 0.19085033747481991881874810892698
relative error = 13.595551692703109748449270437202 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 1.4045735641789675860215415380431
y[1] (numeric) = 1.2134191242588476478691909864216
absolute error = 0.19115443992011993815235055162154
relative error = 13.609428854077697269040196314039 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 1.4053772715911124138165504502244
y[1] (numeric) = 1.2139189372090721567092942812784
absolute error = 0.19145833438204025710725616894596
relative error = 13.623269584065403561528869306102 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 1.4061815736259360986067632016613
y[1] (numeric) = 1.2144195541640871502074711018174
absolute error = 0.19176201946184894839929209984386
relative error = 13.637073835875787035852981450311 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 1.4069864694791366725936623366093
y[1] (numeric) = 1.2149209757181132057551976992014
absolute error = 0.19206549376102346683846463740786
relative error = 13.650841562970089856110553649278 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 1.4077919583458183496513260657285
y[1] (numeric) = 1.2154232024645663017999381903968
absolute error = 0.19236875588125204785138787533171
relative error = 13.664572719060627563794272000799 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=10.72
NO POLE
x[1] = 0.938
y[1] (analytic) = 1.4085980394204923302221473173594
y[1] (numeric) = 1.2159262349960572244292155620397
absolute error = 0.19267180442443510579293175531976
relative error = 13.678267258110178376110265799096 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 1.409404711897077606805566171065
y[1] (numeric) = 1.216430073904390974759874967143
absolute error = 0.19297463799268663204569120392203
relative error = 13.691925134331372170716515314407 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 1.410211974968901770039010184776
y[1] (numeric) = 1.2169347197805661771331319253335
absolute error = 0.19327725518833559290587825944252
relative error = 13.705546302186079168157824105356 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 1.4110198278287018153702365346646
y[1] (numeric) = 1.2174401732147744881159972315197
absolute error = 0.19357965461392732725423930314484
relative error = 13.719130716384798323216101973726 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 1.4118282696686249503202692954725
y[1] (numeric) = 1.2179464347964000063096695715178
absolute error = 0.19388183487222494401059972395468
relative error = 13.73267833188604543633658226856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 1.4126372996802294023361245984231
y[1] (numeric) = 1.2184535051140186829654860361924
absolute error = 0.19418379456621071937063856223068
relative error = 13.746189103895740996232542605728 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 1.41344691705448522723251581406
y[1] (numeric) = 1.2189613847553977334090199181144
absolute error = 0.19448553229908749382349589594561
relative error = 13.759662987866597764713112695422 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 1.4142571209817751182217303183736
y[1] (numeric) = 1.2194700743074950492729143665867
absolute error = 0.1947870466742800689488159517869
relative error = 13.773099939497508114720838353692 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 1.4150679106518952155308688124071
y[1] (numeric) = 1.2199795743564586115390396681573
absolute error = 0.19508833629543660399182914424977
relative error = 13.786499914732931132507828390926 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 1.4158792852540559166056375781701
y[1] (numeric) = 1.2204898854876259043905611104128
absolute error = 0.19538939976643001221507646775726
relative error = 13.799862869762279494821542380923 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 1.4166912439768826868998834671338
y[1] (numeric) = 1.2210010082855233298745035769346
absolute error = 0.19569023569135935702537989019923
relative error = 13.813188761019306131913583765608 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 1.4175037860084168712500608318425
y[1] (numeric) = 1.2215129433338656233753982108062
absolute error = 0.19599084267455124787466262103627
relative error = 13.826477545181490687127245774091 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 1.4183169105361165058338190262395
y[1] (numeric) = 1.2220256912155552699005956729751
absolute error = 0.1962912193205612359332233532644
relative error = 13.839729179169425783762018648426 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 1.4191306167468571307118985161905
y[1] (numeric) = 1.2225392525126819211778297101076
absolute error = 0.19659136423417520953406880608293
relative error = 13.852943620146203109855807074784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 1.419944903826932602952523058373
y[1] (numeric) = 1.223053627806521813565613934324
absolute error = 0.19689127602041078938690912404893
relative error = 13.866120825516799331468227906671 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 1.4207597709620559103374748232099
y[1] (numeric) = 1.2235688176775371867770539043705
absolute error = 0.19719095328451872356042091883937
relative error = 13.879260752927461844991061610497 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.954
y[1] (analytic) = 1.4215752173373599856490387558386
y[1] (numeric) = 1.2240848227053757034176557843646
absolute error = 0.19749039463198428223138297147407
relative error = 13.892363360265094378954717723314 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=10.94
NO POLE
x[1] = 0.955
y[1] (analytic) = 1.4223912421373985215370018882395
y[1] (numeric) = 1.2246016434688698693377120422595
absolute error = 0.19778959866852865219928984597993
relative error = 13.905428605656642455742446333715 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 1.4232078445461467859648927355918
y[1] (numeric) = 1.2251192805460364547998438355926
absolute error = 0.19808856400011033116504889999919
relative error = 13.918456447468478723566985511492 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 1.4240250237470024382346453306867
y[1] (numeric) = 1.2256377345140759164622789169259
absolute error = 0.19838728923292652177236641376071
relative error = 13.931446844305788169007380037159 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 1.4248427789227863455888718718004
y[1] (numeric) = 1.226157005949371820178443075656
absolute error = 0.1986857729734145254104287961445
relative error = 13.944399755011953220346841022531 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 1.4256611092557434003899273818234
y[1] (numeric) = 1.2266770954274902646134423165492
absolute error = 0.19898401382825313577648506527422
relative error = 13.957315138667938751895740357687 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 1.4264800139275433378749491996481
y[1] (numeric) = 1.2271980035231793056780121584765
absolute error = 0.1992820104043640321969370411716
relative error = 13.970192954591676999427149643586 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 1.4272994921192815544860535488458
y[1] (numeric) = 1.2277197308103683817805096193475
absolute error = 0.19957976130891317270554392949835
relative error = 13.983033162337452396795741634974 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 1.4281195430114799267748708535018
y[1] (numeric) = 1.2282422778621677398975226352045
absolute error = 0.19987726514931218687734821829738
relative error = 13.995835721695286343754374473133 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 1.4289401657840876308806008967442
y[1] (numeric) = 1.2287656452508678624636708428209
absolute error = 0.20017452053321976841693005392329
relative error = 14.008600592690321914926276366557 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 1.4297613596164819625807683439772
y[1] (numeric) = 1.2292898335479388950811708359532
absolute error = 0.20047152606854306749959750802391
relative error = 14.021327735582208519834442100372 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 1.4305831236874691579138585801337
y[1] (numeric) = 1.2298148433240300750497381856351
absolute error = 0.20076828036343908286412039449859
relative error = 14.034017110864486523833644029069 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 1.4314054571752852143730132383785
y[1] (numeric) = 1.230340675148969160717397694563
absolute error = 0.20106478202631605365561554381551
relative error = 14.046668679263971839734350225166 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 1.4322283592575967126699642266353
y[1] (numeric) = 1.2308673295917618616527725347167
absolute error = 0.20136102966583485101719169191862
relative error = 14.059282401740140499851832398574 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 1.4330518291115016390683844880724
y[1] (numeric) = 1.231394807220591269639422095877
absolute error = 0.20165702189091036942896239219538
relative error = 14.071858239484513218157837233856 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 1.4338758659135302082858331622636
y[1] (numeric) = 1.2319231086028172904927975506554
absolute error = 0.20195275731071291779303561160826
relative error = 14.084396153920039952156388068304 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 1.4347004688396456869634722451501
y[1] (numeric) = 1.2324522343049760767003833190338
absolute error = 0.20224823453466961026308892611638
relative error = 14.096896106700484474049580492171 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 1.4355256370652452177027312781524
y[1] (numeric) = 1.2329821848927794608855917922244
absolute error = 0.20254345217246575681713948592802
relative error = 14.109358059709808960703636619847 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=11.16
NO POLE
x[1] = 0.972
y[1] (analytic) = 1.4363513697651606436680960298383
y[1] (numeric) = 1.2335129609311143900959778519086
absolute error = 0.20283840883404625357211817792975
relative error = 14.121781975061558611869989570187 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 1.4371776661136593337551965674268
y[1] (numeric) = 1.2340445629840423609163388965926
absolute error = 0.20313310312961697283885767083415
relative error = 14.134167815098246306060783205493 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 1.4380045252844450083233695501071
y[1] (numeric) = 1.2345769916147988554072652619334
absolute error = 0.20342753366964615291610428817368
relative error = 14.146515542390737303422893498505 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 1.4388319464506585654918690116816
y[1] (numeric) = 1.2351102473857927778697050964369
absolute error = 0.2037216990648657876221639152447
relative error = 14.158825119737634004899408098845 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 1.4396599287848789079988993363885
y[1] (numeric) = 1.2356443308586058924361069279168
absolute error = 0.20401559792627301556279240847166
relative error = 14.171096510164660776912440815437 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 1.4404884714591237706226435689417
y[1] (numeric) = 1.2361792425939922614887023295251
absolute error = 0.20430922886513150913394123941658
relative error = 14.183329676924048850746208867175 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 1.4413175736448505481634596378282
y[1] (numeric) = 1.2367149831518776849054902670239
absolute error = 0.20460259049297286325796937080421
relative error = 14.195524583493921305754463915454 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 1.4421472345129571239864165097351
y[1] (numeric) = 1.2372515530913591401344838812686
absolute error = 0.20489568142159798385193262846644
relative error = 14.207681193577678145461644101264 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.98
y[1] (analytic) = 1.4429774532337826991233417326401
y[1] (numeric) = 1.2377889529707042230967796316075
absolute error = 0.20518850026307847602656210103254
relative error = 14.219799471103381475572504575584 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 1.4438082289771086219335512655861
y[1] (numeric) = 1.2383271833473505899190078970838
absolute error = 0.20548104562975803201454336850229
relative error = 14.231879380223140792850489331581 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 1.4446395609121592183224319344801
y[1] (numeric) = 1.2388662447779053994957233029414
absolute error = 0.20577331613425381882670863153869
relative error = 14.243920885312498393770728504588 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 1.4454714482076026225170462954026
y[1] (numeric) = 1.2394061378181447568822922099991
absolute error = 0.20606531038945786563475408540345
relative error = 14.255923950969814911799283672472 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 1.4463038900315516083979291298914
y[1] (numeric) = 1.2399468630230131575188339739576
absolute error = 0.20635702700853845087909515593381
relative error = 14.267888542015654992096120023777 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 1.4471368855515644213862442404742
y[1] (numeric) = 1.2404884209466229322857717506535
absolute error = 0.20664846460494148910047248982077
relative error = 14.279814623492173112385259510505 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 1.4479704339346456108854696593607
y[1] (numeric) = 1.2410308121422536933915477916621
absolute error = 0.20693962179239191749392186769859
relative error = 14.291702160662499558681664200684 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 1.4488045343472468632767788286789
y[1] (numeric) = 1.2415740371623517810930573424881
absolute error = 0.20723049718489508218372148619088
relative error = 14.303551119010126564510614914779 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 1.4496391859552678354672847569453
y[1] (numeric) = 1.2421180965585297112493544228635
absolute error = 0.20752108939673812421793033408181
relative error = 14.315361464238294622201687779251 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=11.37
NO POLE
x[1] = 0.989
y[1] (analytic) = 1.4504743879240569889903136035916
y[1] (numeric) = 1.2426629908815656237091819354023
absolute error = 0.20781139704249136528113166818939
relative error = 14.327133162269378974785891457319 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 1.4513101394184124246568735913464
y[1] (numeric) = 1.2432087206814027315328777150336
absolute error = 0.20810141873700969312399587631282
relative error = 14.338866179244276296971111406771 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 1.4521464396025827177574845950707
y[1] (numeric) = 1.243755286507148771049207297264
absolute error = 0.20839115309543394670827729780668
relative error = 14.350560481521791573617715440438 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 1.4529832876402677538135332052885
y[1] (numeric) = 1.2443026889070754527476733483882
absolute error = 0.20868059873319230106585985690028
relative error = 14.362216035678025184083007988093 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 1.4538206826946195648773175151265
y[1] (numeric) = 1.2448509284286179130068508652943
absolute error = 0.20896975426600165187046664983219
relative error = 14.373832808505760200750179628194 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 1.4546586239282431663799453306873
y[1] (numeric) = 1.2454000056183741666592964164817
absolute error = 0.20925861830986899972064891420564
relative error = 14.385410767013849910004484511489 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 1.4554971105031973945262489570286
y[1] (numeric) = 1.2459499210221045603935788593375
absolute error = 0.20954718948109283413267009769116
relative error = 14.396949878426605563866592061593 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 1.4563361415809957442358791649033
y[1] (numeric) = 1.2465006751847312269939781315955
absolute error = 0.20983546639626451724190103330778
relative error = 14.40845011018318437044040162404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 1.4571757163226072076297403972349
y[1] (numeric) = 1.2470522686503375404183978772321
absolute error = 0.21012344767226966721134252000289
relative error = 14.419911429936977731280080347151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 1.4580158338884571130609287289657
y[1] (numeric) = 1.2476047019621675717150368288423
absolute error = 0.21041113192628954134589190012342
relative error = 14.431333805554999733728686305799 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 1.4588564934384279646893335494061
y[1] (numeric) = 1.248157975662625545778363029779
absolute error = 0.21069851777580241891097051962719
relative error = 14.44271720511727590622847150179 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 1.459697694131860282599063392557
y[1] (numeric) = 1.2487120902932752989449341400351
absolute error = 0.21098560383858498365412925252194
relative error = 14.4540615969162322445508236595 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.001
y[1] (analytic) = 1.4605394351275534434578557980465
y[1] (numeric) = 1.2492670463948397374296062300045
absolute error = 0.21127238873271370602824956804198
relative error = 14.46536694945608451684180243863 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.002
y[1] (analytic) = 1.4613817155837665217176305433427
y[1] (numeric) = 1.2498228445072002966026726258663
absolute error = 0.21155887107656622511495791747643
relative error = 14.476633231452227855327355552125 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.003
y[1] (analytic) = 1.4622245346582191313553450467597
y[1] (numeric) = 1.2503794851693964011084735294098
absolute error = 0.21184504948882273024687151734982
relative error = 14.487860411830626642470564039723 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.004
y[1] (analytic) = 1.4630678915080922681533102004696
y[1] (numeric) = 1.250936968919624925826016293645
absolute error = 0.21213092258846734232729390682456
relative error = 14.499048459727204699321664328357 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.005
memory used=206.0MB, alloc=4.5MB, time=11.59
y[1] (analytic) = 1.4639117852900291525181243532775
y[1] (numeric) = 1.2514952962952396576721453935329
absolute error = 0.21241648899478949484597895974458
relative error = 14.510197344487235783750128420636 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.006
y[1] (analytic) = 1.4647562151601360728373826242936
y[1] (numeric) = 1.2520544678327507582478002886221
absolute error = 0.21270174732738531458958233567145
relative error = 14.521307035664734406196753291616 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.007
y[1] (analytic) = 1.4656011802739832293733181908644
y[1] (numeric) = 1.252614484067824227327898531288
absolute error = 0.21298669620615900204541965957645
relative error = 14.532377503021846970532517030812 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.008
y[1] (analytic) = 1.4664466797866055786925316571923
y[1] (numeric) = 1.2531753455352813671953806306468
absolute error = 0.21327133425132421149715102654548
relative error = 14.543408716528243247559903118574 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.009
y[1] (analytic) = 1.467292712852503678630964073983
y[1] (numeric) = 1.2537370527690982478199523380557
absolute error = 0.21355566008340543081101173592732
relative error = 14.554400646360508188641476140418 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.01
y[1] (analytic) = 1.4681392786256445337932686442208
y[1] (numeric) = 1.2542996063024051728820591754113
absolute error = 0.21383967232323936091120946880949
relative error = 14.565353262901534086889712875534 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.011
y[1] (analytic) = 1.4689863762594624415857356157674
y[1] (numeric) = 1.254863006667486146642627182228
absolute error = 0.21412336959197629494310843353947
relative error = 14.576266536739913093301452691719 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.012
y[1] (analytic) = 1.4698340049068598387819243279326
y[1] (numeric) = 1.2554272543957783416591030117105
absolute error = 0.2144067505110814971228213162221
relative error = 14.587140438669330095169831172698 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.013
y[1] (analytic) = 1.4706821637202081486201558464535
y[1] (numeric) = 1.2559923500178715673483256597374
absolute error = 0.21468981370233658127183018671606
relative error = 14.597974939687955964056201519049 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.014
y[1] (analytic) = 1.4715308518513486284320190894609
y[1] (numeric) = 1.2565582940635077393967612638375
absolute error = 0.21497255778784088903525782562344
relative error = 14.608770010997841180554330113751 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.015
y[1] (analytic) = 1.472380068451593217801042815998
y[1] (numeric) = 1.2571250870615803500186315618821
absolute error = 0.21525498139001286778241125411595
relative error = 14.619525624004309843029076330384 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.016
y[1] (analytic) = 1.4732298126717253872506853184886
y[1] (numeric) = 1.2576927295401339390624657523197
absolute error = 0.21553708313159144818821956616897
relative error = 14.630241750315354067461832778297 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.017
y[1] (analytic) = 1.4740800836620009874607931312371
y[1] (numeric) = 1.2582612220263635659666046493565
absolute error = 0.21581886163563742149418848188055
relative error = 14.64091836174102878548521130624 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.018
y[1] (analytic) = 1.4749308805721490990116795385718
y[1] (numeric) = 1.2588305650466142825641851775364
absolute error = 0.21610031552553481644749436103541
relative error = 14.651555430292846947639812795512 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.019
y[1] (analytic) = 1.4757822025513728826549731386242
y[1] (numeric) = 1.2594007591263806067381324006894
absolute error = 0.21638144342499227591684073793482
relative error = 14.662152928183175138836415626397 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.02
y[1] (analytic) = 1.4766340487483504301103861919662
y[1] (numeric) = 1.2599718047903059969266854302157
absolute error = 0.21666224395804443318370076175046
relative error = 14.672710827824629612957559248623 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.021
y[1] (analytic) = 1.4774864183112356153875519584076
y[1] (numeric) = 1.260543702562182327479982707133
absolute error = 0.21694271574905328790756925127452
relative error = 14.683229101829472753483286068174 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=11.80
NO POLE
x[1] = 1.022
y[1] (analytic) = 1.4783393103876589466320797001881
y[1] (numeric) = 1.2611164529649493648682313012594
absolute error = 0.21722285742270958176384839892871
relative error = 14.693707723009009966976737409734 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.023
y[1] (analytic) = 1.4791927241247284184949755055798
y[1] (numeric) = 1.2616900565206942447419840193189
absolute error = 0.21750266760403417375299148626097
relative error = 14.704146664372987016216378146755 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.024
y[1] (analytic) = 1.4800466586690303650245765635492
y[1] (numeric) = 1.2622645137506509498450472616482
absolute error = 0.21778214491837941517952930190098
relative error = 14.714545899128987799712850220151 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.025
y[1] (analytic) = 1.4809011131666303130801459976169
y[1] (numeric) = 1.2628398251751997887805417145545
absolute error = 0.21806128799143052429960428306244
relative error = 14.724905400681832584299828192617 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.026
y[1] (analytic) = 1.4817560867630738362662748453913
y[1] (numeric) = 1.2634159913138668756306371122187
absolute error = 0.21834009544920696063563773317262
relative error = 14.735225142632976697439770699202 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.027
y[1] (analytic) = 1.4826115786033874093872372494439
y[1] (numeric) = 1.2639930126853236104304814483673
absolute error = 0.21861856591806379895675580107655
relative error = 14.74550509877990968583713063716 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.028
y[1] (analytic) = 1.4834675878320792634204444052437
y[1] (numeric) = 1.2645708898073861604968441637395
absolute error = 0.21889669802469310292360024150419
relative error = 14.755745243115554946903404660431 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.029
y[1] (analytic) = 1.4843241135931402410081422927682
y[1] (numeric) = 1.2651496231970149426119919806637
absolute error = 0.21917449039612529839615031210453
relative error = 14.765945549827669839570369468003 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.03
y[1] (analytic) = 1.4851811550300446524664977001626
y[1] (numeric) = 1.2657292133703141060633152008238
absolute error = 0.21945194165973054640318249933889
relative error = 14.776105993298246280899968952903 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.031
y[1] (analytic) = 1.4860387112857511323112165304354
y[1] (numeric) = 1.266309660842531016539221426547
absolute error = 0.21972905044322011577199510388841
relative error = 14.78622654810291183489158295217 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.032
y[1] (analytic) = 1.4868967815027034962988378656402
y[1] (numeric) = 1.266890966128055740881812809675
absolute error = 0.22000581537464775541702505596524
relative error = 14.796307189010331299839825540825 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.033
y[1] (analytic) = 1.4877553648228315989828467473245
y[1] (numeric) = 1.2674731297404205326968620752993
absolute error = 0.22028223508241106628598467202517
relative error = 14.80634789098160880054858896825 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.034
y[1] (analytic) = 1.4886144603875521917837481172009
y[1] (numeric) = 1.2680561521922993188216017103416
absolute error = 0.22055830819525287296214640685925
relative error = 14.816348629169690391659768857775 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.035
y[1] (analytic) = 1.4894740673377697815722438480409
y[1] (numeric) = 1.2686400339955071866508398491471
absolute error = 0.22083403334226259492140399889381
relative error = 14.826309378918767178307977584638 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.036
y[1] (analytic) = 1.4903341848138774897646542816843
y[1] (numeric) = 1.2692247756609998723219155299322
absolute error = 0.22110940915287761744273875175215
relative error = 14.836230115763678960265576209556 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.037
y[1] (analytic) = 1.4911948119557579119297251788145
y[1] (numeric) = 1.2698103776988732497590051370887
absolute error = 0.22138443425688466217072004172586
relative error = 14.846110815429318405695531361683 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=12.01
NO POLE
x[1] = 1.038
y[1] (analytic) = 1.4920559479027839779059604737648
y[1] (numeric) = 1.2703968406183628205772909849955
absolute error = 0.22165910728442115732866948876936
relative error = 14.85595145383003576058293241306 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.039
y[1] (analytic) = 1.4929175917938198124286207170946
y[1] (numeric) = 1.2709841649278432048475021391268
absolute error = 0.22193342686597660758111857796775
relative error = 14.865752007069044099869486535494 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.04
y[1] (analytic) = 1.4937797427672215962655265790078
y[1] (numeric) = 1.2715723511348276327213367098733
absolute error = 0.22220739163239396354418986913456
relative error = 14.875512451437825126268945139499 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.041
y[1] (analytic) = 1.4946423999608384278608062778836
y[1] (numeric) = 1.2721613997459674369182739936114
absolute error = 0.22248100021487099094253228427219
relative error = 14.885232763415535522695205114226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.042
y[1] (analytic) = 1.4955055625120131854857252902416
y[1] (numeric) = 1.2727513112670515460742839741677
absolute error = 0.22275425124496163941144131607394
relative error = 14.89491291966841386418877255895 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.043
y[1] (analytic) = 1.4963692295575833898957361913855
y[1] (numeric) = 1.2733420862030059789529408359241
absolute error = 0.22302714335457741094279535546142
relative error = 14.904552897049188095181375653659 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.044
y[1] (analytic) = 1.4972334002338820674928859697465
y[1] (numeric) = 1.2739337250578933395194462774113
absolute error = 0.2232996751759887279734396923352
relative error = 14.914152672596483577892767282918 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.045
y[1] (analytic) = 1.4980980736767386139927176525903
y[1] (numeric) = 1.2745262283349123128780675513219
absolute error = 0.22357184534182630111465010126844
relative error = 14.923712223534231717608167319076 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.046
y[1] (analytic) = 1.4989632490214796585948025762604
y[1] (numeric) = 1.2751195965363971620734942934662
absolute error = 0.2238436524850824965213082827942
relative error = 14.933231527271079170539359395083 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.047
y[1] (analytic) = 1.499828925402929928656039130494
y[1] (numeric) = 1.2757138301638172257566173392693
absolute error = 0.22411509523911270289942179122465
relative error = 14.942710561399797639927177852148 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.048
y[1] (analytic) = 1.5006951019554131148658533035871
y[1] (numeric) = 1.2763089297177764167152318619906
absolute error = 0.22438617223763669815062144159645
relative error = 14.952149303696694265997997623322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.049
y[1] (analytic) = 1.5015617778127527369224358532785
y[1] (numeric) = 1.27690489569801272127016630192
absolute error = 0.22465688211474001565226955135848
relative error = 14.961547732121022615341873392309 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.05
y[1] (analytic) = 1.5024289521082730097091504271879
y[1] (numeric) = 1.2775017286033976995373376903801
absolute error = 0.22492722350487531017181273680779
relative error = 14.970905824814394275235164720808 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.051
y[1] (analytic) = 1.5032966239747997099702464564727
y[1] (numeric) = 1.278099428931935986556233106438
absolute error = 0.22519719504286372341401335003472
relative error = 14.980223560100191058385831232295 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.052
y[1] (analytic) = 1.5041647925446610434850101470624
y[1] (numeric) = 1.2786979971807647942853161378029
absolute error = 0.22546679536389624919969400925941
relative error = 14.989500916482977823535086632272 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.053
y[1] (analytic) = 1.5050334569496885127394863943916
y[1] (numeric) = 1.2792974338461534144648563504624
absolute error = 0.22573602310353509827463004392916
relative error = 14.998737872647915917304762583059 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.5MB, time=12.23
NO POLE
x[1] = 1.054
y[1] (analytic) = 1.5059026163212177850949039499833
y[1] (numeric) = 1.2798977394235027223476789041855
absolute error = 0.22600487689771506274722504579779
relative error = 15.007934407460177242635553475813 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.055
y[1] (analytic) = 1.5067722697900895614519356715277
y[1] (numeric) = 1.2804989144073446812983305831025
absolute error = 0.22627335538274488015360508842518
relative error = 15.017090499964358959117291185938 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.056
y[1] (analytic) = 1.5076424164866504454099251922705
y[1] (numeric) = 1.2811009592913418482611576421541
absolute error = 0.22654145719530859714876755011643
relative error = 15.0262061293838988204685351849 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.057
y[1] (analytic) = 1.508513055540753812920210850555
y[1] (numeric) = 1.2817038745682868800977900012895
absolute error = 0.2268091809724669328224208492655
relative error = 15.035281275120491154379058128201 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.058
y[1] (analytic) = 1.5093841860817606824326772262677
y[1] (numeric) = 1.2823076607301020407945254498905
absolute error = 0.22707652535165864163815177637717
relative error = 15.044315916753503489885260454517 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.059
y[1] (analytic) = 1.5102558072385405855346641377078
y[1] (numeric) = 1.2829123182678387095401066539942
absolute error = 0.22734348897070187599455748371357
relative error = 15.053310034039393837405159815645 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.06
y[1] (analytic) = 1.5111279181394724380813624600436
y[1] (numeric) = 1.2835178476716768896743828884967
absolute error = 0.22761007046779554840697957154685
relative error = 15.062263606911128626516372504031 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.061
y[1] (analytic) = 1.5120005179124454118168256350344
y[1] (numeric) = 1.284124249430924718508347545637
absolute error = 0.22787626848152069330847808939738
relative error = 15.07117661547760130651743463965 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.062
y[1] (analytic) = 1.5128736056848598064847252510766
y[1] (numeric) = 1.2847315240340179780160415996795
absolute error = 0.22814208165084182846868365139706
relative error = 15.080049040023051614769900898703 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.063
y[1] (analytic) = 1.513747180583627922427978582893
y[1] (numeric) = 1.2853396719685196063988123358541
absolute error = 0.22840750861510831602916624703894
relative error = 15.088880861006485517775908183226 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.064
y[1] (analytic) = 1.5146212417351749336763754913097
y[1] (numeric) = 1.2859486937211192105224157792519
absolute error = 0.22867254801405572315395971205787
relative error = 15.097672059061095829903301005899 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.065
y[1] (analytic) = 1.5154957882654397615213315955666
y[1] (numeric) = 1.2865585897776325792274503865355
absolute error = 0.22893719848780718229388120903102
relative error = 15.10642261499368351462798465349 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.066
y[1] (analytic) = 1.5163708192998759485768941434805
y[1] (numeric) = 1.2871693606230011975136086899883
absolute error = 0.22920145867687475106328545349221
relative error = 15.11513250978407967312090154322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.067
y[1] (analytic) = 1.5172463339634525333261265185295
y[1] (numeric) = 1.2877810067412917615982327096104
absolute error = 0.22946532722216077172789380891911
relative error = 15.123801724584568224964915739551 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.068
y[1] (analytic) = 1.5181223313806549251519968375448
y[1] (numeric) = 1.2883935286156956948496580746673
absolute error = 0.2297288027649592303023387628775
relative error = 15.132430240719309285744940487656 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.069
y[1] (analytic) = 1.5189988106754857798518956081959
y[1] (numeric) = 1.2890069267285286645958309213045
absolute error = 0.2299918839469571152560646868914
relative error = 15.14101803968376324621285397024 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=221.2MB, alloc=4.5MB, time=12.45
x[1] = 1.07
y[1] (analytic) = 1.5198757709714658756349069318241
y[1] (numeric) = 1.2896212015612300998086807575726
absolute error = 0.2302545694102357758262261742515
relative error = 15.149565103144115557687119425355 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.071
y[1] (analytic) = 1.5207532113916349896009572544251
y[1] (numeric) = 1.2902363535943627096647316114483
absolute error = 0.23051685779727227993622564297678
relative error = 15.15807141293670222830555738613 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.072
y[1] (analytic) = 1.521631131058552774700965186707
y[1] (numeric) = 1.2908523833076120029824329012021
absolute error = 0.23077874775094077171853228550486
relative error = 15.166536951067436034708410223754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.073
y[1] (analytic) = 1.5225095290942996371771154331449
y[1] (numeric) = 1.2914692911797858085366905907397
absolute error = 0.23104023791451382864042484240525
relative error = 15.174961699711233453687692490375 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.074
y[1] (analytic) = 1.5233884046204776144823793898327
y[1] (numeric) = 1.2920870776888137962510783153468
absolute error = 0.23130132693166381823130107448583
relative error = 15.183345641211442318297834859586 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.075
y[1] (analytic) = 1.5242677567582112536784044916836
y[1] (numeric) = 1.2927057433117469992682072855874
absolute error = 0.23156201344646425441019720609617
relative error = 15.191688758079270202881804832999 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.076
y[1] (analytic) = 1.5251475846281484903108939111643
y[1] (numeric) = 1.2933252885247573368987328989431
absolute error = 0.2318222961033911534121610122212
relative error = 15.199991032993213541426223899074 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.077
y[1] (analytic) = 1.5260278873504615277615977332555
y[1] (numeric) = 1.2939457138031371384494751101503
absolute error = 0.23208217354732438931212262310525
relative error = 15.208252448798487483618498565448 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.078
y[1] (analytic) = 1.5269086640448477170760362547213
y[1] (numeric) = 1.2945670196212986679311287320728
absolute error = 0.23234164442354904914490752264851
relative error = 15.216472988506456492938641702061 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.079
y[1] (analytic) = 1.527789913830530437266075580037
y[1] (numeric) = 1.2951892064527736496460389593611
absolute error = 0.23260070737775678762003662067589
relative error = 15.224652635294065691078280986709 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.08
y[1] (analytic) = 1.528671635826259976086475211474
y[1] (numeric) = 1.2958122747702127946565165270828
absolute error = 0.23285936105604718142995868439113
relative error = 15.232791372503272952939332987505 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.081
y[1] (analytic) = 1.5295538291503144112845268568664
y[1] (numeric) = 1.2964362250453853281341660359699
absolute error = 0.23311760410492908315036082089645
relative error = 15.240889183640481756424964592339 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.082
y[1] (analytic) = 1.5304364929205004923219032054952
y[1] (numeric) = 1.2970610577491785175907000949149
absolute error = 0.23337543517132197473120311058033
relative error = 15.248946052375974791195768141076 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.083
y[1] (analytic) = 1.5313196262541545225678349503138
y[1] (numeric) = 1.2976867733515972019907110498625
absolute error = 0.2336328529025573205771239004513
relative error = 15.256961962543348330524542763201 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.084
y[1] (analytic) = 1.5322032282681432419627338634115
y[1] (numeric) = 1.2983133723217633217468711862861
absolute error = 0.2338898559463799202158626771254
relative error = 15.264936898138947370343702096449 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.085
y[1] (analytic) = 1.533087298078864710151379261166
y[1] (numeric) = 1.2989408551279154495980314100089
absolute error = 0.23414644295094926055334785115708
relative error = 15.272870843321301539540117779271 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=225.0MB, alloc=4.5MB, time=12.67
x[1] = 1.086
y[1] (analytic) = 1.5339718348022491900847847259714
y[1] (numeric) = 1.299569222237408322370687528233
absolute error = 0.23440261256484086771409719773844
relative error = 15.280763782410561785513158883754 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.087
y[1] (analytic) = 1.5348568375537600320898614827493
y[1] (numeric) = 1.3001984741167123736242823692702
absolute error = 0.23465836343704765846557911347907
relative error = 15.288615699887937838972799792015 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.088
y[1] (analytic) = 1.5357423054483945584059943606521
y[1] (numeric) = 1.3008286112314132671808110956343
absolute error = 0.23491369421698129122518326501778
relative error = 15.296426580395136461915942917792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.089
y[1] (analytic) = 1.5366282376006849481876458034578
y[1] (numeric) = 1.3014596340462114315391961808496
absolute error = 0.23516860355447351664844962260826
relative error = 15.30419640873380048268053812983 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.09
y[1] (analytic) = 1.5375146331246991229721029261249
y[1] (numeric) = 1.3020915430249215951748976355628
absolute error = 0.23542309009977752779720529056204
relative error = 15.311925169864948621938677732404 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.091
y[1] (analytic) = 1.5384014911340416326114821498343
y[1] (numeric) = 1.3027243386304723227252231833097
absolute error = 0.23567715250356930988625896652456
relative error = 15.319612848908416113451604382639 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.092
y[1] (analytic) = 1.5392888107418545416681054835882
y[1] (numeric) = 1.3033580213249055520608022005858
absolute error = 0.23593078941694898960730328300236
relative error = 15.327259431142296123371489350086 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.093
y[1] (analytic) = 1.5401765910608183162723620570624
y[1] (numeric) = 1.3039925915693761322436863497111
absolute error = 0.23618399949144218402867570735138
relative error = 15.334864902002381971836920021165 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.094
y[1] (analytic) = 1.5410648312031527114421680469252
y[1] (numeric) = 1.3046280498241513623725389463472
absolute error = 0.236436781379001349069629100578
relative error = 15.342429247081610160571278483848 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.095
y[1] (analytic) = 1.5419535302806176588631376772364
y[1] (numeric) = 1.3052643965486105313153742164418
absolute error = 0.23668913373200712754776346079462
relative error = 15.349952452129504210155597354536 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.096
y[1] (analytic) = 1.5428426874045141551285775138303
y[1] (numeric) = 1.3059016322012444583303067098201
absolute error = 0.23694105520326969679827080401024
relative error = 15.357434503051619310610044682408 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.097
y[1] (analytic) = 1.5437323016856851504384158127608
y[1] (numeric) = 1.3065397572396550345747702496371
absolute error = 0.23719254444603011586364556312369
relative error = 15.364875385908987788880916733322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.098
y[1] (analytic) = 1.5446223722345164377561782239551
y[1] (numeric) = 1.3071787721205547655036649084339
absolute error = 0.23744360011396167225251331552117
relative error = 15.372275086917565396792905657314 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.099
y[1] (analytic) = 1.5455128981609375424231206931733
y[1] (numeric) = 1.3078186772997663141568896126116
absolute error = 0.2376942208611712282662310805617
relative error = 15.379633592447678422989458416529 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1.1
y[1] (analytic) = 1.5464038785744226122286299482153
y[1] (numeric) = 1.3084594732322220453367170877529
absolute error = 0.23794440534220056689191286046237
relative error = 15.386950889023471632347253824546 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 2 ) = sin(x);
Iterations = 1000
Total Elapsed Time = 12 Seconds
Elapsed Time(since restart) = 12 Seconds
Expected Time Remaining = 49 Seconds
Optimized Time Remaining = 49 Seconds
Time to Timeout = 14 Minutes 47 Seconds
Percent Done = 20.43 %
> quit
memory used=228.5MB, alloc=4.5MB, time=12.85