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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> 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[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := -att(1,array_tmp1,array_x,1);
> #emit pre 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[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := -att(2,array_tmp1,array_x,1);
> #emit pre 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[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := -att(3,array_tmp1,array_x,1);
> #emit pre 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[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := -att(4,array_tmp1,array_x,1);
> #emit pre 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[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_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 DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, 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, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_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)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y := proc(x) 2.0 - cos(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> #Top Generate Globals Decl
> glob_start,
> glob_warned2,
> glob_optimal_start,
> min_in_hour,
> glob_log10normmin,
> MAX_UNCHANGED,
> glob_warned,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_h,
> glob_reached_optimal_h,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10relerr,
> glob_max_hours,
> glob_log10_abserr,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_opt_iter,
> glob_html_log,
> glob_iter,
> glob_max_sec,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_hmin,
> glob_not_yet_start_msg,
> djd_debug,
> glob_max_minutes,
> glob_curr_iter_when_opt,
> glob_small_float,
> glob_max_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_clock_start_sec,
> years_in_century,
> glob_log10abserr,
> glob_normmax,
> glob_orig_start_sec,
> glob_relerr,
> glob_look_poles,
> glob_hmin_init,
> days_in_year,
> glob_dump,
> glob_percent_done,
> glob_current_iter,
> glob_clock_sec,
> glob_almost_1,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_optimal_done,
> glob_subiter_method,
> glob_no_eqs,
> hours_in_day,
> glob_smallish_float,
> glob_log10_relerr,
> glob_last_good_h,
> djd_debug2,
> centuries_in_millinium,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_1st_rel_error,
> array_pole,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_m1,
> array_tmp1_g,
> array_type_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_y_init,
> array_real_pole,
> array_y_higher,
> array_y_set_initial,
> array_complex_pole,
> array_y_higher_work,
> array_y_higher_work2,
> array_poles,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_max_terms := 30;
> INFO := 2;
> glob_start := 0;
> glob_warned2 := false;
> glob_optimal_start := 0.0;
> min_in_hour := 60.0;
> glob_log10normmin := 0.1;
> MAX_UNCHANGED := 10;
> glob_warned := false;
> glob_max_iter := 1000;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_h := 0.1;
> glob_reached_optimal_h := false;
> glob_display_flag := true;
> glob_optimal_expect_sec := 0.1;
> glob_log10relerr := 0.0;
> glob_max_hours := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_disp_incr := 0.1;
> glob_initial_pass := true;
> glob_max_opt_iter := 10;
> glob_html_log := true;
> glob_iter := 0;
> glob_max_sec := 10000.0;
> glob_unchanged_h_cnt := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_not_yet_start_msg := true;
> djd_debug := true;
> glob_max_minutes := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_small_float := 0.1e-50;
> glob_max_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> years_in_century := 100.0;
> glob_log10abserr := 0.0;
> glob_normmax := 0.0;
> glob_orig_start_sec := 0.0;
> glob_relerr := 0.1e-10;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> days_in_year := 365.0;
> glob_dump := false;
> glob_percent_done := 0.0;
> glob_current_iter := 0;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> sec_in_min := 60.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_done := false;
> glob_subiter_method := 3;
> glob_no_eqs := 0;
> hours_in_day := 24.0;
> glob_smallish_float := 0.1e-100;
> glob_log10_relerr := 0.1e-10;
> glob_last_good_h := 0.1;
> djd_debug2 := true;
> centuries_in_millinium := 10.0;
> #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/sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 16;");
> 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 := 0.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.05;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 16;
> 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_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> 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_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.05;
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sin(x);");
> 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,"2012-06-13T19:24:08-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"sin maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO,
glob_start, glob_warned2, glob_optimal_start, min_in_hour,
glob_log10normmin, MAX_UNCHANGED, glob_warned, glob_max_iter,
glob_dump_analytic, glob_large_float, glob_hmax, glob_h,
glob_reached_optimal_h, glob_display_flag, glob_optimal_expect_sec,
glob_log10relerr, glob_max_hours, glob_log10_abserr, glob_disp_incr,
glob_initial_pass, glob_max_opt_iter, glob_html_log, glob_iter,
glob_max_sec, glob_unchanged_h_cnt, glob_max_rel_trunc_err, glob_hmin,
glob_not_yet_start_msg, djd_debug, glob_max_minutes,
glob_curr_iter_when_opt, glob_small_float, glob_max_trunc_err, glob_abserr,
glob_not_yet_finished, glob_clock_start_sec, years_in_century,
glob_log10abserr, glob_normmax, glob_orig_start_sec, glob_relerr,
glob_look_poles, glob_hmin_init, days_in_year, glob_dump, glob_percent_done,
glob_current_iter, glob_clock_sec, glob_almost_1, sec_in_min,
glob_optimal_clock_start_sec, glob_optimal_done, glob_subiter_method,
glob_no_eqs, hours_in_day, glob_smallish_float, glob_log10_relerr,
glob_last_good_h, djd_debug2, centuries_in_millinium, array_const_0D0,
array_const_1, array_1st_rel_error, array_pole, array_norms, array_tmp0,
array_tmp1, array_tmp2, array_m1, array_tmp1_g, array_type_pole, array_y,
array_x, array_last_rel_error, array_y_init, array_real_pole,
array_y_higher, array_y_set_initial, array_complex_pole,
array_y_higher_work, array_y_higher_work2, array_poles, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_max_terms := 30;
INFO := 2;
glob_start := 0;
glob_warned2 := false;
glob_optimal_start := 0.;
min_in_hour := 60.0;
glob_log10normmin := 0.1;
MAX_UNCHANGED := 10;
glob_warned := false;
glob_max_iter := 1000;
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_h := 0.1;
glob_reached_optimal_h := false;
glob_display_flag := true;
glob_optimal_expect_sec := 0.1;
glob_log10relerr := 0.;
glob_max_hours := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_initial_pass := true;
glob_max_opt_iter := 10;
glob_html_log := true;
glob_iter := 0;
glob_max_sec := 10000.0;
glob_unchanged_h_cnt := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_not_yet_start_msg := true;
djd_debug := true;
glob_max_minutes := 0.;
glob_curr_iter_when_opt := 0;
glob_small_float := 0.1*10^(-50);
glob_max_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
years_in_century := 100.0;
glob_log10abserr := 0.;
glob_normmax := 0.;
glob_orig_start_sec := 0.;
glob_relerr := 0.1*10^(-10);
glob_look_poles := false;
glob_hmin_init := 0.001;
days_in_year := 365.0;
glob_dump := false;
glob_percent_done := 0.;
glob_current_iter := 0;
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
sec_in_min := 60.0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_done := false;
glob_subiter_method := 3;
glob_no_eqs := 0;
hours_in_day := 24.0;
glob_smallish_float := 0.1*10^(-100);
glob_log10_relerr := 0.1*10^(-10);
glob_last_good_h := 0.1;
djd_debug2 := true;
centuries_in_millinium := 10.0;
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/sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 16;");
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 := 0.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.05;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0 - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 16;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
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_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_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;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[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_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[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_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_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sin(x);");
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, "2012-06-13T19:24:08-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"sin diffeq.mxt");
logitem_str(html_log_file,
"sin maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/sinpostode.ode#################
diff ( y , x , 1 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits := 16;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.05;
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 - cos(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 1
y[1] (numeric) = 1
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0001
y[1] (analytic) = 1.000000005
y[1] (numeric) = 1.000000005
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0002
y[1] (analytic) = 1.00000002
y[1] (numeric) = 1.00000002
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0003
y[1] (analytic) = 1.000000045
y[1] (numeric) = 1.000000045
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0004
y[1] (analytic) = 1.000000079999999
y[1] (numeric) = 1.000000079999999
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0005
y[1] (analytic) = 1.000000124999997
y[1] (numeric) = 1.000000124999997
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0006
y[1] (analytic) = 1.000000179999995
y[1] (numeric) = 1.000000179999994
absolute error = 1e-15
relative error = 9.999998200000374e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0007
y[1] (analytic) = 1.00000024499999
y[1] (numeric) = 1.000000244999989
absolute error = 1e-15
relative error = 9.999997550000700e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0008
y[1] (analytic) = 1.000000319999983
y[1] (numeric) = 1.000000319999982
absolute error = 1e-15
relative error = 9.999996800001194e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0009
y[1] (analytic) = 1.000000404999973
y[1] (numeric) = 1.000000404999972
absolute error = 1e-15
relative error = 9.999995950001910e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 1.000000499999958
y[1] (numeric) = 1.000000499999958
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0011
y[1] (analytic) = 1.000000604999939
y[1] (numeric) = 1.000000604999939
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0012
y[1] (analytic) = 1.000000719999914
y[1] (numeric) = 1.000000719999914
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0013
y[1] (analytic) = 1.000000844999881
y[1] (numeric) = 1.000000844999881
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0014
y[1] (analytic) = 1.00000097999984
y[1] (numeric) = 1.00000097999984
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0015
y[1] (analytic) = 1.000001124999789
y[1] (numeric) = 1.000001124999789
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.20
NO POLE
x[1] = 0.0016
y[1] (analytic) = 1.000001279999727
y[1] (numeric) = 1.000001279999727
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0017
y[1] (analytic) = 1.000001444999652
y[1] (numeric) = 1.000001444999652
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0018
y[1] (analytic) = 1.000001619999563
y[1] (numeric) = 1.000001619999563
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0019
y[1] (analytic) = 1.000001804999457
y[1] (numeric) = 1.000001804999457
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 1.000001999999333
y[1] (numeric) = 1.000001999999333
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0021
y[1] (analytic) = 1.00000220499919
y[1] (numeric) = 1.000002204999189
absolute error = 1e-15
relative error = 9.999977950056720e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0022
y[1] (analytic) = 1.000002419999024
y[1] (numeric) = 1.000002419999023
absolute error = 1e-15
relative error = 9.999975800068324e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0023
y[1] (analytic) = 1.000002644998834
y[1] (numeric) = 1.000002644998833
absolute error = 1e-15
relative error = 9.999973550081620e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0024
y[1] (analytic) = 1.000002879998618
y[1] (numeric) = 1.000002879998617
absolute error = 1e-15
relative error = 9.999971200096764e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0025
y[1] (analytic) = 1.000003124998372
y[1] (numeric) = 1.000003124998372
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0026
y[1] (analytic) = 1.000003379998096
y[1] (numeric) = 1.000003379998096
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0027
y[1] (analytic) = 1.000003644997786
y[1] (numeric) = 1.000003644997786
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0028
y[1] (analytic) = 1.000003919997439
y[1] (numeric) = 1.000003919997439
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0029
y[1] (analytic) = 1.000004204997053
y[1] (numeric) = 1.000004204997053
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 1.000004499996625
y[1] (numeric) = 1.000004499996625
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0031
y[1] (analytic) = 1.000004804996152
y[1] (numeric) = 1.000004804996152
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0032
y[1] (analytic) = 1.000005119995631
y[1] (numeric) = 1.000005119995631
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0033
y[1] (analytic) = 1.000005444995059
y[1] (numeric) = 1.000005444995059
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0034
y[1] (analytic) = 1.000005779994432
y[1] (numeric) = 1.000005779994432
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0035
y[1] (analytic) = 1.000006124993747
y[1] (numeric) = 1.000006124993747
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0036
y[1] (analytic) = 1.000006479993002
y[1] (numeric) = 1.000006479993001
absolute error = 1e-15
relative error = 9.999935200489880e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0037
y[1] (analytic) = 1.000006844992191
y[1] (numeric) = 1.00000684499219
absolute error = 1e-15
relative error = 9.999931550546626e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0038
y[1] (analytic) = 1.000007219991312
y[1] (numeric) = 1.000007219991311
absolute error = 1e-15
relative error = 9.999927800608159e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=7.6MB, alloc=3.9MB, time=0.45
x[1] = 0.0039
y[1] (analytic) = 1.000007604990361
y[1] (numeric) = 1.00000760499036
absolute error = 1e-15
relative error = 9.999923950674744e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 1.000007999989333
y[1] (numeric) = 1.000007999989333
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0041
y[1] (analytic) = 1.000008404988226
y[1] (numeric) = 1.000008404988226
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0042
y[1] (analytic) = 1.000008819987035
y[1] (numeric) = 1.000008819987035
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0043
y[1] (analytic) = 1.000009244985755
y[1] (numeric) = 1.000009244985755
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0044
y[1] (analytic) = 1.000009679984383
y[1] (numeric) = 1.000009679984383
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0045
y[1] (analytic) = 1.000010124982914
y[1] (numeric) = 1.000010124982914
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0046
y[1] (analytic) = 1.000010579981344
y[1] (numeric) = 1.000010579981344
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0047
y[1] (analytic) = 1.000011044979668
y[1] (numeric) = 1.000011044979668
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0048
y[1] (analytic) = 1.000011519977882
y[1] (numeric) = 1.000011519977882
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0049
y[1] (analytic) = 1.00001200497598
y[1] (numeric) = 1.00001200497598
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 1.000012499973958
y[1] (numeric) = 1.000012499973958
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0051
y[1] (analytic) = 1.000013004971812
y[1] (numeric) = 1.000013004971811
absolute error = 1e-15
relative error = 9.999869951973151e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0052
y[1] (analytic) = 1.000013519969535
y[1] (numeric) = 1.000013519969534
absolute error = 1e-15
relative error = 9.999864802132521e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0053
y[1] (analytic) = 1.000014044967123
y[1] (numeric) = 1.000014044967122
absolute error = 1e-15
relative error = 9.999859552301353e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0054
y[1] (analytic) = 1.000014579964571
y[1] (numeric) = 1.00001457996457
absolute error = 1e-15
relative error = 9.999854202480013e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0055
y[1] (analytic) = 1.000015124961872
y[1] (numeric) = 1.000015124961872
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0056
y[1] (analytic) = 1.000015679959023
y[1] (numeric) = 1.000015679959023
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0057
y[1] (analytic) = 1.000016244956017
y[1] (numeric) = 1.000016244956017
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0058
y[1] (analytic) = 1.000016819952848
y[1] (numeric) = 1.000016819952848
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0059
y[1] (analytic) = 1.000017404949511
y[1] (numeric) = 1.000017404949511
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 1.000017999946
y[1] (numeric) = 1.000017999946
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0061
y[1] (analytic) = 1.000018604942309
y[1] (numeric) = 1.000018604942309
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0062
y[1] (analytic) = 1.000019219938432
y[1] (numeric) = 1.000019219938432
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.70
NO POLE
x[1] = 0.0063
y[1] (analytic) = 1.000019844934363
y[1] (numeric) = 1.000019844934363
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0064
y[1] (analytic) = 1.000020479930095
y[1] (numeric) = 1.000020479930095
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0065
y[1] (analytic) = 1.000021124925622
y[1] (numeric) = 1.000021124925622
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0066
y[1] (analytic) = 1.000021779920939
y[1] (numeric) = 1.000021779920938
absolute error = 1e-15
relative error = 9.999782205534156e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0067
y[1] (analytic) = 1.000022444916037
y[1] (numeric) = 1.000022444916036
absolute error = 1e-15
relative error = 9.999775555877259e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0068
y[1] (analytic) = 1.000023119910911
y[1] (numeric) = 1.00002311991091
absolute error = 1e-15
relative error = 9.999768806236069e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0069
y[1] (analytic) = 1.000023804905554
y[1] (numeric) = 1.000023804905553
absolute error = 1e-15
relative error = 9.999761956611060e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 1.000024499899958
y[1] (numeric) = 1.000024499899958
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0071
y[1] (analytic) = 1.000025204894118
y[1] (numeric) = 1.000025204894118
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0072
y[1] (analytic) = 1.000025919888026
y[1] (numeric) = 1.000025919888026
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0073
y[1] (analytic) = 1.000026644881674
y[1] (numeric) = 1.000026644881674
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0074
y[1] (analytic) = 1.000027379875056
y[1] (numeric) = 1.000027379875056
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0075
y[1] (analytic) = 1.000028124868164
y[1] (numeric) = 1.000028124868164
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0076
y[1] (analytic) = 1.000028879860991
y[1] (numeric) = 1.000028879860991
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0077
y[1] (analytic) = 1.000029644853529
y[1] (numeric) = 1.000029644853529
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0078
y[1] (analytic) = 1.000030419845771
y[1] (numeric) = 1.000030419845771
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0079
y[1] (analytic) = 1.000031204837708
y[1] (numeric) = 1.000031204837708
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 1.000031999829334
y[1] (numeric) = 1.000031999829333
absolute error = 1e-15
relative error = 9.999680011946223e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0081
y[1] (analytic) = 1.000032804820639
y[1] (numeric) = 1.000032804820638
absolute error = 1e-15
relative error = 9.999671962554820e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0082
y[1] (analytic) = 1.000033619811616
y[1] (numeric) = 1.000033619811615
absolute error = 1e-15
relative error = 9.999663813186377e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0083
y[1] (analytic) = 1.000034444802257
y[1] (numeric) = 1.000034444802256
absolute error = 1e-15
relative error = 9.999655563841465e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0084
y[1] (analytic) = 1.000035279792554
y[1] (numeric) = 1.000035279792553
absolute error = 1e-15
relative error = 9.999647214520659e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0085
y[1] (analytic) = 1.000036124782498
y[1] (numeric) = 1.000036124782497
absolute error = 1e-15
relative error = 9.999638765224548e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0086
y[1] (analytic) = 1.00003697977208
y[1] (numeric) = 1.00003697977208
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.94
NO POLE
x[1] = 0.0087
y[1] (analytic) = 1.000037844761293
y[1] (numeric) = 1.000037844761293
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0088
y[1] (analytic) = 1.000038719750128
y[1] (numeric) = 1.000038719750127
absolute error = 1e-15
relative error = 9.999612817490330e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0089
y[1] (analytic) = 1.000039604738575
y[1] (numeric) = 1.000039604738574
absolute error = 1e-15
relative error = 9.999603968298982e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 1.000040499726626
y[1] (numeric) = 1.000040499726625
absolute error = 1e-15
relative error = 9.999595019135354e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0091
y[1] (analytic) = 1.000041404714272
y[1] (numeric) = 1.000041404714271
absolute error = 1e-15
relative error = 9.999585970000074e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0092
y[1] (analytic) = 1.000042319701504
y[1] (numeric) = 1.000042319701503
absolute error = 1e-15
relative error = 9.999576820893773e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0093
y[1] (analytic) = 1.000043244688313
y[1] (numeric) = 1.000043244688312
absolute error = 1e-15
relative error = 9.999567571817092e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0094
y[1] (analytic) = 1.000044179674689
y[1] (numeric) = 1.000044179674688
absolute error = 1e-15
relative error = 9.999558222770684e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0095
y[1] (analytic) = 1.000045124660623
y[1] (numeric) = 1.000045124660623
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0096
y[1] (analytic) = 1.000046079646107
y[1] (numeric) = 1.000046079646106
absolute error = 1e-15
relative error = 9.999539224771289e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0097
y[1] (analytic) = 1.000047044631129
y[1] (numeric) = 1.000047044631128
absolute error = 1e-15
relative error = 9.999529575819642e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0098
y[1] (analytic) = 1.000048019615681
y[1] (numeric) = 1.00004801961568
absolute error = 1e-15
relative error = 9.999519826900918e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0099
y[1] (analytic) = 1.000049004599753
y[1] (numeric) = 1.000049004599752
absolute error = 1e-15
relative error = 9.999509978015801e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 1.000049999583335
y[1] (numeric) = 1.000049999583334
absolute error = 1e-15
relative error = 9.999500029164983e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0101
y[1] (analytic) = 1.000051004566416
y[1] (numeric) = 1.000051004566416
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0102
y[1] (analytic) = 1.000052019548988
y[1] (numeric) = 1.000052019548988
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0103
y[1] (analytic) = 1.00005304453104
y[1] (numeric) = 1.000053044531039
absolute error = 1e-15
relative error = 9.999469582825330e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0104
y[1] (analytic) = 1.000054079512561
y[1] (numeric) = 1.00005407951256
absolute error = 1e-15
relative error = 9.999459234118745e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0105
y[1] (analytic) = 1.000055124493541
y[1] (numeric) = 1.00005512449354
absolute error = 1e-15
relative error = 9.999448785450013e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0106
y[1] (analytic) = 1.00005617947397
y[1] (numeric) = 1.000056179473969
absolute error = 1e-15
relative error = 9.999438236819860e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0107
y[1] (analytic) = 1.000057244453837
y[1] (numeric) = 1.000057244453836
absolute error = 1e-15
relative error = 9.999427588229029e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0108
y[1] (analytic) = 1.000058319433132
y[1] (numeric) = 1.000058319433131
absolute error = 1e-15
relative error = 9.999416839678259e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0109
y[1] (analytic) = 1.000059404411843
y[1] (numeric) = 1.000059404411843
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 1.000060499389961
y[1] (numeric) = 1.00006049938996
absolute error = 1e-15
relative error = 9.999395042699938e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.20
NO POLE
x[1] = 0.0111
y[1] (analytic) = 1.000061604367473
y[1] (numeric) = 1.000061604367472
absolute error = 1e-15
relative error = 9.999383994273913e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0112
y[1] (analytic) = 1.00006271934437
y[1] (numeric) = 1.000062719344368
absolute error = 2e-15
relative error = 1.999874569178199e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0113
y[1] (analytic) = 1.000063844320639
y[1] (numeric) = 1.000063844320637
absolute error = 2e-15
relative error = 1.999872319510396e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0114
y[1] (analytic) = 1.00006497929627
y[1] (numeric) = 1.000064979296268
absolute error = 2e-15
relative error = 1.999870049851529e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0115
y[1] (analytic) = 1.000066124271251
y[1] (numeric) = 1.000066124271249
absolute error = 2e-15
relative error = 1.999867760201758e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0116
y[1] (analytic) = 1.00006727924557
y[1] (numeric) = 1.000067279245569
absolute error = 1e-15
relative error = 9.999327252806224e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0117
y[1] (analytic) = 1.000068444219217
y[1] (numeric) = 1.000068444219216
absolute error = 1e-15
relative error = 9.999315604650735e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0118
y[1] (analytic) = 1.00006961919218
y[1] (numeric) = 1.000069619192178
absolute error = 2e-15
relative error = 1.999860771308629e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0119
y[1] (analytic) = 1.000070804164446
y[1] (numeric) = 1.000070804164444
absolute error = 2e-15
relative error = 1.999858401696858e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 1.000071999136004
y[1] (numeric) = 1.000071999136002
absolute error = 2e-15
relative error = 1.999856012094997e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0121
y[1] (analytic) = 1.000073204106842
y[1] (numeric) = 1.00007320410684
absolute error = 2e-15
relative error = 1.999853602503214e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0122
y[1] (analytic) = 1.000074419076948
y[1] (numeric) = 1.000074419076946
absolute error = 2e-15
relative error = 1.999851172921678e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0123
y[1] (analytic) = 1.00007564404631
y[1] (numeric) = 1.000075644046308
absolute error = 2e-15
relative error = 1.999848723350558e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0124
y[1] (analytic) = 1.000076879014916
y[1] (numeric) = 1.000076879014914
absolute error = 2e-15
relative error = 1.999846253790025e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0125
y[1] (analytic) = 1.000078123982753
y[1] (numeric) = 1.000078123982751
absolute error = 2e-15
relative error = 1.999843764240254e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0126
y[1] (analytic) = 1.000079378949808
y[1] (numeric) = 1.000079378949806
absolute error = 2e-15
relative error = 1.999841254701419e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0127
y[1] (analytic) = 1.00008064391607
y[1] (numeric) = 1.000080643916068
absolute error = 2e-15
relative error = 1.999838725173694e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0128
y[1] (analytic) = 1.000081918881525
y[1] (numeric) = 1.000081918881523
absolute error = 2e-15
relative error = 1.999836175657257e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0129
y[1] (analytic) = 1.000083203846161
y[1] (numeric) = 1.000083203846159
absolute error = 2e-15
relative error = 1.999833606152286e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 1.000084498809965
y[1] (numeric) = 1.000084498809963
absolute error = 2e-15
relative error = 1.999831016658961e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0131
y[1] (analytic) = 1.000085803772924
y[1] (numeric) = 1.000085803772922
absolute error = 2e-15
relative error = 1.999828407177464e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0132
y[1] (analytic) = 1.000087118735025
y[1] (numeric) = 1.000087118735023
absolute error = 2e-15
relative error = 1.999825777707976e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0133
y[1] (analytic) = 1.000088443696255
y[1] (numeric) = 1.000088443696253
absolute error = 2e-15
relative error = 1.999823128250681e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0134
y[1] (analytic) = 1.0000897786566
y[1] (numeric) = 1.000089778656598
absolute error = 2e-15
relative error = 1.999820458805767e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=1.45
NO POLE
x[1] = 0.0135
y[1] (analytic) = 1.000091123616048
y[1] (numeric) = 1.000091123616045
absolute error = 3e-15
relative error = 2.999726654060126e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0136
y[1] (analytic) = 1.000092478574584
y[1] (numeric) = 1.000092478574581
absolute error = 3e-15
relative error = 2.999722589930736e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0137
y[1] (analytic) = 1.000093843532195
y[1] (numeric) = 1.000093843532192
absolute error = 3e-15
relative error = 2.999718495820762e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0138
y[1] (analytic) = 1.000095218488868
y[1] (numeric) = 1.000095218488865
absolute error = 3e-15
relative error = 2.999714371730488e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0139
y[1] (analytic) = 1.000096603444589
y[1] (numeric) = 1.000096603444586
absolute error = 3e-15
relative error = 2.999710217660205e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 1.000097998399344
y[1] (numeric) = 1.000097998399341
absolute error = 3e-15
relative error = 2.999706033610204e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0141
y[1] (analytic) = 1.000099403353119
y[1] (numeric) = 1.000099403353116
absolute error = 3e-15
relative error = 2.999701819580777e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0142
y[1] (analytic) = 1.000100818305899
y[1] (numeric) = 1.000100818305897
absolute error = 2e-15
relative error = 1.999798383714814e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0143
y[1] (analytic) = 1.000102243257672
y[1] (numeric) = 1.00010224325767
absolute error = 2e-15
relative error = 1.999795534389886e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0144
y[1] (analytic) = 1.000103678208422
y[1] (numeric) = 1.00010367820842
absolute error = 2e-15
relative error = 1.999792665079269e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0145
y[1] (analytic) = 1.000105123158135
y[1] (numeric) = 1.000105123158133
absolute error = 2e-15
relative error = 1.999789775783164e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0146
y[1] (analytic) = 1.000106578106797
y[1] (numeric) = 1.000106578106795
absolute error = 2e-15
relative error = 1.999786866501771e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0147
y[1] (analytic) = 1.000108043054394
y[1] (numeric) = 1.000108043054391
absolute error = 3e-15
relative error = 2.999675905852940e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0148
y[1] (analytic) = 1.00010951800091
y[1] (numeric) = 1.000109518000907
absolute error = 3e-15
relative error = 2.999671481975907e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0149
y[1] (analytic) = 1.00011100294633
y[1] (numeric) = 1.000111002946328
absolute error = 2e-15
relative error = 1.999778018747913e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 1.000112497890641
y[1] (numeric) = 1.000112497890639
absolute error = 2e-15
relative error = 1.999775029527422e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0151
y[1] (analytic) = 1.000114002833826
y[1] (numeric) = 1.000114002833825
absolute error = 1e-15
relative error = 9.998860101613386e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0152
y[1] (analytic) = 1.000115517775872
y[1] (numeric) = 1.000115517775871
absolute error = 1e-15
relative error = 9.998844955669432e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0153
y[1] (analytic) = 1.000117042716762
y[1] (numeric) = 1.000117042716761
absolute error = 1e-15
relative error = 9.998829709806324e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0154
y[1] (analytic) = 1.000118577656482
y[1] (numeric) = 1.000118577656481
absolute error = 1e-15
relative error = 9.998814364025115e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0155
y[1] (analytic) = 1.000120122595017
y[1] (numeric) = 1.000120122595015
absolute error = 2e-15
relative error = 1.999759783665375e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0156
y[1] (analytic) = 1.00012167753235
y[1] (numeric) = 1.000121677532348
absolute error = 2e-15
relative error = 1.999756674542541e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0157
y[1] (analytic) = 1.000123242468466
y[1] (numeric) = 1.000123242468464
absolute error = 2e-15
relative error = 1.999753545436737e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0158
y[1] (analytic) = 1.00012481740335
y[1] (numeric) = 1.000124817403348
absolute error = 2e-15
relative error = 1.999750396348180e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=4.1MB, time=1.70
x[1] = 0.0159
y[1] (analytic) = 1.000126402336985
y[1] (numeric) = 1.000126402336984
absolute error = 1e-15
relative error = 9.998736136385464e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 1.000127997269357
y[1] (numeric) = 1.000127997269356
absolute error = 1e-15
relative error = 9.998720191118472e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0161
y[1] (analytic) = 1.000129602200448
y[1] (numeric) = 1.000129602200448
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0162
y[1] (analytic) = 1.000131217130244
y[1] (numeric) = 1.000131217130244
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0163
y[1] (analytic) = 1.000132842058727
y[1] (numeric) = 1.000132842058727
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0164
y[1] (analytic) = 1.000134476985882
y[1] (numeric) = 1.000134476985882
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0165
y[1] (analytic) = 1.000136121911692
y[1] (numeric) = 1.000136121911692
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0166
y[1] (analytic) = 1.000137776836141
y[1] (numeric) = 1.000137776836141
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0167
y[1] (analytic) = 1.000139441759212
y[1] (numeric) = 1.000139441759212
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0168
y[1] (analytic) = 1.000141116680889
y[1] (numeric) = 1.000141116680889
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0169
y[1] (analytic) = 1.000142801601154
y[1] (numeric) = 1.000142801601155
absolute error = 1e-15
relative error = 9.998572187882317e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 1.000144496519992
y[1] (numeric) = 1.000144496519993
absolute error = 1e-15
relative error = 9.998555243562357e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0171
y[1] (analytic) = 1.000146201437384
y[1] (numeric) = 1.000146201437386
absolute error = 2e-15
relative error = 1.999707639868703e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0172
y[1] (analytic) = 1.000147916353315
y[1] (numeric) = 1.000147916353317
absolute error = 2e-15
relative error = 1.999704211045394e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0173
y[1] (analytic) = 1.000149641267766
y[1] (numeric) = 1.000149641267768
absolute error = 2e-15
relative error = 1.999700762242785e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0174
y[1] (analytic) = 1.000151376180721
y[1] (numeric) = 1.000151376180723
absolute error = 2e-15
relative error = 1.999697293461118e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0175
y[1] (analytic) = 1.000153121092162
y[1] (numeric) = 1.000153121092164
absolute error = 2e-15
relative error = 1.999693804700635e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0176
y[1] (analytic) = 1.000154876002072
y[1] (numeric) = 1.000154876002074
absolute error = 2e-15
relative error = 1.999690295961579e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0177
y[1] (analytic) = 1.000156640910433
y[1] (numeric) = 1.000156640910435
absolute error = 2e-15
relative error = 1.999686767244198e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0178
y[1] (analytic) = 1.000158415817228
y[1] (numeric) = 1.00015841581723
absolute error = 2e-15
relative error = 1.999683218548736e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0179
y[1] (analytic) = 1.000160200722439
y[1] (numeric) = 1.000160200722441
absolute error = 2e-15
relative error = 1.999679649875443e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 1.000161995626047
y[1] (numeric) = 1.00016199562605
absolute error = 3e-15
relative error = 2.999514091836856e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0181
y[1] (analytic) = 1.000163800528036
y[1] (numeric) = 1.000163800528039
absolute error = 3e-15
relative error = 2.999508678894549e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0182
y[1] (analytic) = 1.000165615428386
y[1] (numeric) = 1.00016561542839
absolute error = 4e-15
relative error = 3.999337647982169e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.1MB, time=1.95
x[1] = 0.0183
y[1] (analytic) = 1.000167440327081
y[1] (numeric) = 1.000167440327084
absolute error = 3e-15
relative error = 2.999497763113466e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0184
y[1] (analytic) = 1.000169275224101
y[1] (numeric) = 1.000169275224104
absolute error = 3e-15
relative error = 2.999492260275453e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0185
y[1] (analytic) = 1.000171120119428
y[1] (numeric) = 1.000171120119431
absolute error = 3e-15
relative error = 2.999486727472972e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0186
y[1] (analytic) = 1.000172975013044
y[1] (numeric) = 1.000172975013047
absolute error = 3e-15
relative error = 2.999481164706410e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0187
y[1] (analytic) = 1.00017483990493
y[1] (numeric) = 1.000174839904933
absolute error = 3e-15
relative error = 2.999475571976156e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0188
y[1] (analytic) = 1.000176714795068
y[1] (numeric) = 1.000176714795071
absolute error = 3e-15
relative error = 2.999469949282600e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0189
y[1] (analytic) = 1.000178599683439
y[1] (numeric) = 1.000178599683442
absolute error = 3e-15
relative error = 2.999464296626136e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 1.000180494570024
y[1] (numeric) = 1.000180494570027
absolute error = 3e-15
relative error = 2.999458614007160e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0191
y[1] (analytic) = 1.000182399454803
y[1] (numeric) = 1.000182399454807
absolute error = 4e-15
relative error = 3.999270535234763e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0192
y[1] (analytic) = 1.000184314337759
y[1] (numeric) = 1.000184314337763
absolute error = 4e-15
relative error = 3.999262878511023e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0193
y[1] (analytic) = 1.000186239218872
y[1] (numeric) = 1.000186239218876
absolute error = 4e-15
relative error = 3.999255181838865e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0194
y[1] (analytic) = 1.000188174098122
y[1] (numeric) = 1.000188174098126
absolute error = 4e-15
relative error = 3.999247445218829e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0195
y[1] (analytic) = 1.00019011897549
y[1] (numeric) = 1.000190118975494
absolute error = 4e-15
relative error = 3.999239668651457e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0196
y[1] (analytic) = 1.000192073850958
y[1] (numeric) = 1.000192073850961
absolute error = 3e-15
relative error = 2.999423889102965e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0197
y[1] (analytic) = 1.000194038724504
y[1] (numeric) = 1.000194038724508
absolute error = 4e-15
relative error = 3.999223995676873e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0198
y[1] (analytic) = 1.00019601359611
y[1] (numeric) = 1.000196013596114
absolute error = 4e-15
relative error = 3.999216099270761e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0199
y[1] (analytic) = 1.000197998465756
y[1] (numeric) = 1.00019799846576
absolute error = 4e-15
relative error = 3.999208162919503e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 1.000199993333422
y[1] (numeric) = 1.000199993333426
absolute error = 4e-15
relative error = 3.999200186623655e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0201
y[1] (analytic) = 1.000201998199088
y[1] (numeric) = 1.000201998199092
absolute error = 4e-15
relative error = 3.999192170383776e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0202
y[1] (analytic) = 1.000204013062734
y[1] (numeric) = 1.000204013062738
absolute error = 4e-15
relative error = 3.999184114200425e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0203
y[1] (analytic) = 1.00020603792434
y[1] (numeric) = 1.000206037924344
absolute error = 4e-15
relative error = 3.999176018074166e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0204
y[1] (analytic) = 1.000208072783886
y[1] (numeric) = 1.00020807278389
absolute error = 4e-15
relative error = 3.999167882005564e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0205
y[1] (analytic) = 1.00021011764135
y[1] (numeric) = 1.000210117641355
absolute error = 5e-15
relative error = 4.998949632493993e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0206
y[1] (analytic) = 1.000212172496714
y[1] (numeric) = 1.000212172496719
absolute error = 5e-15
relative error = 4.998939362554525e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.2MB, time=2.21
x[1] = 0.0207
y[1] (analytic) = 1.000214237349956
y[1] (numeric) = 1.000214237349961
absolute error = 5e-15
relative error = 4.998929042689276e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0208
y[1] (analytic) = 1.000216312201055
y[1] (numeric) = 1.00021631220106
absolute error = 5e-15
relative error = 4.998918672898970e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0209
y[1] (analytic) = 1.000218397049992
y[1] (numeric) = 1.000218397049996
absolute error = 4e-15
relative error = 3.999126602547459e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 1.000220491896744
y[1] (numeric) = 1.000220491896748
absolute error = 4e-15
relative error = 3.999118226836861e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0211
y[1] (analytic) = 1.000222596741292
y[1] (numeric) = 1.000222596741295
absolute error = 3e-15
relative error = 2.999332358390971e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0212
y[1] (analytic) = 1.000224711583613
y[1] (numeric) = 1.000224711583616
absolute error = 3e-15
relative error = 2.999326016701015e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0213
y[1] (analytic) = 1.000226836423687
y[1] (numeric) = 1.00022683642369
absolute error = 3e-15
relative error = 2.999319645058221e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0214
y[1] (analytic) = 1.000228971261493
y[1] (numeric) = 1.000228971261496
absolute error = 3e-15
relative error = 2.999313243463032e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0215
y[1] (analytic) = 1.00023111609701
y[1] (numeric) = 1.000231116097012
absolute error = 2e-15
relative error = 1.999537874610596e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0216
y[1] (analytic) = 1.000233270930215
y[1] (numeric) = 1.000233270930217
absolute error = 2e-15
relative error = 1.999533566944843e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0217
y[1] (analytic) = 1.000235435761087
y[1] (numeric) = 1.000235435761089
absolute error = 2e-15
relative error = 1.999529239311727e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0218
y[1] (analytic) = 1.000237610589605
y[1] (numeric) = 1.000237610589607
absolute error = 2e-15
relative error = 1.999524891711551e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0219
y[1] (analytic) = 1.000239795415747
y[1] (numeric) = 1.000239795415749
absolute error = 2e-15
relative error = 1.999520524144618e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 1.000241990239491
y[1] (numeric) = 1.000241990239493
absolute error = 2e-15
relative error = 1.999516136611235e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0221
y[1] (analytic) = 1.000244195060815
y[1] (numeric) = 1.000244195060817
absolute error = 2e-15
relative error = 1.999511729111709e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0222
y[1] (analytic) = 1.000246409879697
y[1] (numeric) = 1.000246409879699
absolute error = 2e-15
relative error = 1.999507301646348e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0223
y[1] (analytic) = 1.000248634696115
y[1] (numeric) = 1.000248634696117
absolute error = 2e-15
relative error = 1.999502854215461e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0224
y[1] (analytic) = 1.000250869510046
y[1] (numeric) = 1.000250869510049
absolute error = 3e-15
relative error = 2.999247580229041e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0225
y[1] (analytic) = 1.000253114321469
y[1] (numeric) = 1.000253114321472
absolute error = 3e-15
relative error = 2.999240849187536e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0226
y[1] (analytic) = 1.000255369130361
y[1] (numeric) = 1.000255369130364
absolute error = 3e-15
relative error = 2.999234088199148e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0227
y[1] (analytic) = 1.000257633936699
y[1] (numeric) = 1.000257633936702
absolute error = 3e-15
relative error = 2.999227297264351e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0228
y[1] (analytic) = 1.000259908740461
y[1] (numeric) = 1.000259908740464
absolute error = 3e-15
relative error = 2.999220476383618e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0229
y[1] (analytic) = 1.000262193541623
y[1] (numeric) = 1.000262193541627
absolute error = 4e-15
relative error = 3.998951500743242e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 1.000264488340164
y[1] (numeric) = 1.000264488340168
absolute error = 4e-15
relative error = 3.998942326381684e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=38.1MB, alloc=4.2MB, time=2.46
x[1] = 0.0231
y[1] (analytic) = 1.00026679313606
y[1] (numeric) = 1.000266793136064
absolute error = 4e-15
relative error = 3.998933112094130e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0232
y[1] (analytic) = 1.000269107929288
y[1] (numeric) = 1.000269107929292
absolute error = 4e-15
relative error = 3.998923857881225e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0233
y[1] (analytic) = 1.000271432719824
y[1] (numeric) = 1.000271432719829
absolute error = 5e-15
relative error = 4.998643204679524e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0234
y[1] (analytic) = 1.000273767507647
y[1] (numeric) = 1.000273767507651
absolute error = 4e-15
relative error = 3.998905229681953e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0235
y[1] (analytic) = 1.000276112292731
y[1] (numeric) = 1.000276112292736
absolute error = 5e-15
relative error = 4.998619819621114e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0236
y[1] (analytic) = 1.000278467075055
y[1] (numeric) = 1.00027846707506
absolute error = 5e-15
relative error = 4.998608052236347e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0237
y[1] (analytic) = 1.000280831854594
y[1] (numeric) = 1.000280831854599
absolute error = 5e-15
relative error = 4.998596234948973e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0238
y[1] (analytic) = 1.000283206631324
y[1] (numeric) = 1.00028320663133
absolute error = 6e-15
relative error = 5.998301241311782e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0239
y[1] (analytic) = 1.000285591405223
y[1] (numeric) = 1.000285591405228
absolute error = 5e-15
relative error = 4.998572450669704e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 1.000287986176265
y[1] (numeric) = 1.000287986176271
absolute error = 6e-15
relative error = 5.998272580415371e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0241
y[1] (analytic) = 1.000290390944428
y[1] (numeric) = 1.000290390944434
absolute error = 6e-15
relative error = 5.998258160147952e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0242
y[1] (analytic) = 1.000292805709687
y[1] (numeric) = 1.000292805709693
absolute error = 6e-15
relative error = 5.998243680002401e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0243
y[1] (analytic) = 1.000295230472018
y[1] (numeric) = 1.000295230472024
absolute error = 6e-15
relative error = 5.998229139979732e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0244
y[1] (analytic) = 1.000297665231396
y[1] (numeric) = 1.000297665231402
absolute error = 6e-15
relative error = 5.998214540080964e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0245
y[1] (analytic) = 1.000300109987798
y[1] (numeric) = 1.000300109987804
absolute error = 6e-15
relative error = 5.998199880307111e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0246
y[1] (analytic) = 1.000302564741198
y[1] (numeric) = 1.000302564741205
absolute error = 7e-15
relative error = 6.997882687435742e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0247
y[1] (analytic) = 1.000305029491573
y[1] (numeric) = 1.00030502949158
absolute error = 7e-15
relative error = 6.997865444661319e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0248
y[1] (analytic) = 1.000307504238898
y[1] (numeric) = 1.000307504238905
absolute error = 7e-15
relative error = 6.997848132036234e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0249
y[1] (analytic) = 1.000309988983148
y[1] (numeric) = 1.000309988983155
absolute error = 7e-15
relative error = 6.997830749561702e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 1.000312483724297
y[1] (numeric) = 1.000312483724305
absolute error = 8e-15
relative error = 7.997500911130221e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0251
y[1] (analytic) = 1.000314988462322
y[1] (numeric) = 1.00031498846233
absolute error = 8e-15
relative error = 7.997480885793334e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0252
y[1] (analytic) = 1.000317503197197
y[1] (numeric) = 1.000317503197205
absolute error = 8e-15
relative error = 7.997460780632692e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0253
y[1] (analytic) = 1.000320027928897
y[1] (numeric) = 1.000320027928905
absolute error = 8e-15
relative error = 7.997440595649697e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0254
y[1] (analytic) = 1.000322562657397
y[1] (numeric) = 1.000322562657405
absolute error = 8e-15
relative error = 7.997420330845762e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0255
y[1] (analytic) = 1.000325107382671
y[1] (numeric) = 1.000325107382679
absolute error = 8e-15
memory used=41.9MB, alloc=4.2MB, time=2.71
relative error = 7.997399986222306e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0256
y[1] (analytic) = 1.000327662104694
y[1] (numeric) = 1.000327662104702
absolute error = 8e-15
relative error = 7.997379561780750e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0257
y[1] (analytic) = 1.00033022682344
y[1] (numeric) = 1.000330226823448
absolute error = 8e-15
relative error = 7.997359057522525e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0258
y[1] (analytic) = 1.000332801538884
y[1] (numeric) = 1.000332801538892
absolute error = 8e-15
relative error = 7.997338473449060e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0259
y[1] (analytic) = 1.000335386251
y[1] (numeric) = 1.000335386251008
absolute error = 8e-15
relative error = 7.997317809561796e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 1.000337980959762
y[1] (numeric) = 1.00033798095977
absolute error = 8e-15
relative error = 7.997297065862178e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0261
y[1] (analytic) = 1.000340585665145
y[1] (numeric) = 1.000340585665152
absolute error = 7e-15
relative error = 6.997616712057694e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0262
y[1] (analytic) = 1.000343200367121
y[1] (numeric) = 1.000343200367128
absolute error = 7e-15
relative error = 6.997598421652723e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0263
y[1] (analytic) = 1.000345825065666
y[1] (numeric) = 1.000345825065672
absolute error = 6e-15
relative error = 5.997925766927792e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0264
y[1] (analytic) = 1.000348459760752
y[1] (numeric) = 1.000348459760758
absolute error = 6e-15
relative error = 5.997909969726937e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0265
y[1] (analytic) = 1.000351104452353
y[1] (numeric) = 1.00035110445236
absolute error = 7e-15
relative error = 6.997543131451015e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0266
y[1] (analytic) = 1.000353759140444
y[1] (numeric) = 1.000353759140451
absolute error = 7e-15
relative error = 6.997524561725808e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0267
y[1] (analytic) = 1.000356423824997
y[1] (numeric) = 1.000356423825004
absolute error = 7e-15
relative error = 6.997505922173780e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0268
y[1] (analytic) = 1.000359098505986
y[1] (numeric) = 1.000359098505993
absolute error = 7e-15
relative error = 6.997487212796229e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0269
y[1] (analytic) = 1.000361783183383
y[1] (numeric) = 1.000361783183391
absolute error = 8e-15
relative error = 7.997106781250825e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 1.000364477857163
y[1] (numeric) = 1.000364477857171
absolute error = 8e-15
relative error = 7.997085239508354e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0271
y[1] (analytic) = 1.000367182527298
y[1] (numeric) = 1.000367182527306
absolute error = 8e-15
relative error = 7.997063617969791e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0272
y[1] (analytic) = 1.000369897193761
y[1] (numeric) = 1.000369897193769
absolute error = 8e-15
relative error = 7.997041916636647e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0273
y[1] (analytic) = 1.000372621856526
y[1] (numeric) = 1.000372621856533
absolute error = 7e-15
relative error = 6.997392618571627e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0274
y[1] (analytic) = 1.000375356515564
y[1] (numeric) = 1.000375356515571
absolute error = 7e-15
relative error = 6.997373490268593e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0275
y[1] (analytic) = 1.000378101170848
y[1] (numeric) = 1.000378101170855
absolute error = 7e-15
relative error = 6.997354292149300e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0276
y[1] (analytic) = 1.000380855822352
y[1] (numeric) = 1.000380855822358
absolute error = 6e-15
relative error = 5.997715735041497e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0277
y[1] (analytic) = 1.000383620470046
y[1] (numeric) = 1.000383620470053
absolute error = 7e-15
relative error = 6.997315686467297e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0278
y[1] (analytic) = 1.000386395113905
y[1] (numeric) = 1.000386395113912
absolute error = 7e-15
relative error = 6.997296278907285e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0279
y[1] (analytic) = 1.0003891797539
y[1] (numeric) = 1.000389179753907
absolute error = 7e-15
relative error = 6.997276801536408e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.2MB, time=2.97
NO POLE
x[1] = 0.028
y[1] (analytic) = 1.000391974390003
y[1] (numeric) = 1.00039197439001
absolute error = 7e-15
relative error = 6.997257254356030e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0281
y[1] (analytic) = 1.000394779022186
y[1] (numeric) = 1.000394779022193
absolute error = 7e-15
relative error = 6.997237637367517e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0282
y[1] (analytic) = 1.000397593650421
y[1] (numeric) = 1.000397593650428
absolute error = 7e-15
relative error = 6.997217950572241e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0283
y[1] (analytic) = 1.00040041827468
y[1] (numeric) = 1.000400418274687
absolute error = 7e-15
relative error = 6.997198193971576e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0284
y[1] (analytic) = 1.000403252894936
y[1] (numeric) = 1.000403252894942
absolute error = 6e-15
relative error = 5.997581457914482e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0285
y[1] (analytic) = 1.000406097511158
y[1] (numeric) = 1.000406097511165
absolute error = 7e-15
relative error = 6.997158471359603e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0286
y[1] (analytic) = 1.00040895212332
y[1] (numeric) = 1.000408952123327
absolute error = 7e-15
relative error = 6.997138505351073e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0287
y[1] (analytic) = 1.000411816731392
y[1] (numeric) = 1.000411816731399
absolute error = 7e-15
relative error = 6.997118469542710e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0288
y[1] (analytic) = 1.000414691335346
y[1] (numeric) = 1.000414691335353
absolute error = 7e-15
relative error = 6.997098363935912e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0289
y[1] (analytic) = 1.000417575935153
y[1] (numeric) = 1.00041757593516
absolute error = 7e-15
relative error = 6.997078188532085e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 1.000420470530784
y[1] (numeric) = 1.000420470530791
absolute error = 7e-15
relative error = 6.997057943332641e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0291
y[1] (analytic) = 1.000423375122211
y[1] (numeric) = 1.000423375122218
absolute error = 7e-15
relative error = 6.997037628338987e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0292
y[1] (analytic) = 1.000426289709404
y[1] (numeric) = 1.000426289709411
absolute error = 7e-15
relative error = 6.997017243552551e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0293
y[1] (analytic) = 1.000429214292334
y[1] (numeric) = 1.000429214292341
absolute error = 7e-15
relative error = 6.996996788974757e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0294
y[1] (analytic) = 1.000432148870972
y[1] (numeric) = 1.000432148870979
absolute error = 7e-15
relative error = 6.996976264607032e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0295
y[1] (analytic) = 1.000435093445288
y[1] (numeric) = 1.000435093445295
absolute error = 7e-15
relative error = 6.996955670450816e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0296
y[1] (analytic) = 1.000438048015253
y[1] (numeric) = 1.00043804801526
absolute error = 7e-15
relative error = 6.996935006507545e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0297
y[1] (analytic) = 1.000441012580838
y[1] (numeric) = 1.000441012580845
absolute error = 7e-15
relative error = 6.996914272778660e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0298
y[1] (analytic) = 1.000443987142013
y[1] (numeric) = 1.00044398714202
absolute error = 7e-15
relative error = 6.996893469265611e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0299
y[1] (analytic) = 1.000446971698747
y[1] (numeric) = 1.000446971698755
absolute error = 8e-15
relative error = 7.996425823965558e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 1.000449966251012
y[1] (numeric) = 1.00044996625102
absolute error = 8e-15
relative error = 7.996401889020412e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0301
y[1] (analytic) = 1.000452970798778
y[1] (numeric) = 1.000452970798785
absolute error = 7e-15
relative error = 6.996830640036068e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0302
y[1] (analytic) = 1.000455985342014
y[1] (numeric) = 1.000455985342021
absolute error = 7e-15
relative error = 6.996809557400962e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0303
y[1] (analytic) = 1.000459009880689
y[1] (numeric) = 1.000459009880697
absolute error = 8e-15
relative error = 7.996329605701737e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.2MB, time=3.22
NO POLE
x[1] = 0.0304
y[1] (analytic) = 1.000462044414775
y[1] (numeric) = 1.000462044414783
absolute error = 8e-15
relative error = 7.996305351773378e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0305
y[1] (analytic) = 1.00046508894424
y[1] (numeric) = 1.000465088944248
absolute error = 8e-15
relative error = 7.996281018103444e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0306
y[1] (analytic) = 1.000468143469055
y[1] (numeric) = 1.000468143469062
absolute error = 7e-15
relative error = 6.996724529106922e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0307
y[1] (analytic) = 1.000471207989188
y[1] (numeric) = 1.000471207989195
absolute error = 7e-15
relative error = 6.996703097602433e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0308
y[1] (analytic) = 1.000474282504609
y[1] (numeric) = 1.000474282504616
absolute error = 7e-15
relative error = 6.996681596328542e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0309
y[1] (analytic) = 1.000477367015287
y[1] (numeric) = 1.000477367015294
absolute error = 7e-15
relative error = 6.996660025286751e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 1.000480461521191
y[1] (numeric) = 1.000480461521198
absolute error = 7e-15
relative error = 6.996638384478570e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0311
y[1] (analytic) = 1.000483566022291
y[1] (numeric) = 1.000483566022298
absolute error = 7e-15
relative error = 6.996616673905505e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0312
y[1] (analytic) = 1.000486680518555
y[1] (numeric) = 1.000486680518562
absolute error = 7e-15
relative error = 6.996594893569079e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0313
y[1] (analytic) = 1.000489805009952
y[1] (numeric) = 1.000489805009959
absolute error = 7e-15
relative error = 6.996573043470813e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0314
y[1] (analytic) = 1.000492939496451
y[1] (numeric) = 1.000492939496458
absolute error = 7e-15
relative error = 6.996551123612233e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0315
y[1] (analytic) = 1.000496083978021
y[1] (numeric) = 1.000496083978028
absolute error = 7e-15
relative error = 6.996529133994868e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0316
y[1] (analytic) = 1.00049923845463
y[1] (numeric) = 1.000499238454637
absolute error = 7e-15
relative error = 6.996507074620259e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0317
y[1] (analytic) = 1.000502402926246
y[1] (numeric) = 1.000502402926254
absolute error = 8e-15
relative error = 7.995982794845657e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0318
y[1] (analytic) = 1.000505577392839
y[1] (numeric) = 1.000505577392846
absolute error = 7e-15
relative error = 6.996462746605476e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0319
y[1] (analytic) = 1.000508761854376
y[1] (numeric) = 1.000508761854383
absolute error = 7e-15
relative error = 6.996440477968397e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 1.000511956310825
y[1] (numeric) = 1.000511956310832
absolute error = 7e-15
relative error = 6.996418139580271e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0321
y[1] (analytic) = 1.000515160762154
y[1] (numeric) = 1.000515160762162
absolute error = 8e-15
relative error = 7.995880835934467e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0322
y[1] (analytic) = 1.000518375208332
y[1] (numeric) = 1.00051837520834
absolute error = 8e-15
relative error = 7.995855146922422e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0323
y[1] (analytic) = 1.000521599649326
y[1] (numeric) = 1.000521599649334
absolute error = 8e-15
relative error = 7.995829378200260e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0324
y[1] (analytic) = 1.000524834085104
y[1] (numeric) = 1.000524834085112
absolute error = 8e-15
relative error = 7.995803529769782e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0325
y[1] (analytic) = 1.000528078515634
y[1] (numeric) = 1.000528078515642
absolute error = 8e-15
relative error = 7.995777601632790e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0326
y[1] (analytic) = 1.000531332940883
y[1] (numeric) = 1.000531332940891
absolute error = 8e-15
relative error = 7.995751593791101e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0327
y[1] (analytic) = 1.000534597360819
y[1] (numeric) = 1.000534597360827
absolute error = 8e-15
relative error = 7.995725506246527e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.2MB, time=3.49
NO POLE
x[1] = 0.0328
y[1] (analytic) = 1.000537871775408
y[1] (numeric) = 1.000537871775417
absolute error = 9e-15
relative error = 8.995161756376016e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0329
y[1] (analytic) = 1.000541156184619
y[1] (numeric) = 1.000541156184628
absolute error = 9e-15
relative error = 8.995132228563047e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 1.000544450588419
y[1] (numeric) = 1.000544450588427
absolute error = 8e-15
relative error = 7.995646765413780e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0331
y[1] (analytic) = 1.000547754986774
y[1] (numeric) = 1.000547754986782
absolute error = 8e-15
relative error = 7.995620359075964e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0332
y[1] (analytic) = 1.000551069379651
y[1] (numeric) = 1.000551069379659
absolute error = 8e-15
relative error = 7.995593873044440e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0333
y[1] (analytic) = 1.000554393767017
y[1] (numeric) = 1.000554393767026
absolute error = 9e-15
relative error = 8.995013220736188e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0334
y[1] (analytic) = 1.00055772814884
y[1] (numeric) = 1.000557728148849
absolute error = 9e-15
relative error = 8.994983244646117e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0335
y[1] (analytic) = 1.000561072525085
y[1] (numeric) = 1.000561072525094
absolute error = 9e-15
relative error = 8.994953178906889e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0336
y[1] (analytic) = 1.00056442689572
y[1] (numeric) = 1.000564426895729
absolute error = 9e-15
relative error = 8.994923023520594e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0337
y[1] (analytic) = 1.00056779126071
y[1] (numeric) = 1.000567791260719
absolute error = 9e-15
relative error = 8.994892778489350e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0338
y[1] (analytic) = 1.000571165620023
y[1] (numeric) = 1.000571165620031
absolute error = 8e-15
relative error = 7.995433283391339e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0339
y[1] (analytic) = 1.000574549973624
y[1] (numeric) = 1.000574549973632
absolute error = 8e-15
relative error = 7.995406239555950e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 1.000577944321479
y[1] (numeric) = 1.000577944321487
absolute error = 8e-15
relative error = 7.995379116041812e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0341
y[1] (analytic) = 1.000581348663555
y[1] (numeric) = 1.000581348663563
absolute error = 8e-15
relative error = 7.995351912850812e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0342
y[1] (analytic) = 1.000584762999817
y[1] (numeric) = 1.000584762999825
absolute error = 8e-15
relative error = 7.995324629984859e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0343
y[1] (analytic) = 1.000588187330232
y[1] (numeric) = 1.00058818733024
absolute error = 8e-15
relative error = 7.995297267445850e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0344
y[1] (analytic) = 1.000591621654764
y[1] (numeric) = 1.000591621654773
absolute error = 9e-15
relative error = 8.994678553390173e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0345
y[1] (analytic) = 1.000595065973381
y[1] (numeric) = 1.00059506597339
absolute error = 9e-15
relative error = 8.994647591275878e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0346
y[1] (analytic) = 1.000598520286047
y[1] (numeric) = 1.000598520286056
absolute error = 9e-15
relative error = 8.994616539535874e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0347
y[1] (analytic) = 1.000601984592728
y[1] (numeric) = 1.000601984592737
absolute error = 9e-15
relative error = 8.994585398172324e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0348
y[1] (analytic) = 1.000605458893388
y[1] (numeric) = 1.000605458893398
absolute error = 1.0e-14
relative error = 9.993949074652685e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0349
y[1] (analytic) = 1.000608943187995
y[1] (numeric) = 1.000608943188004
absolute error = 9e-15
relative error = 8.994522846583308e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 1.000612437476511
y[1] (numeric) = 1.000612437476521
absolute error = 1.0e-14
relative error = 9.993879373735794e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0351
y[1] (analytic) = 1.000615941758904
y[1] (numeric) = 1.000615941758913
absolute error = 9e-15
relative error = 8.994459936526304e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.2MB, time=3.74
NO POLE
x[1] = 0.0352
y[1] (analytic) = 1.000619456035137
y[1] (numeric) = 1.000619456035146
absolute error = 9e-15
relative error = 8.994428347077795e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0353
y[1] (analytic) = 1.000622980305175
y[1] (numeric) = 1.000622980305184
absolute error = 9e-15
relative error = 8.994396668018893e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0354
y[1] (analytic) = 1.000626514568984
y[1] (numeric) = 1.000626514568993
absolute error = 9e-15
relative error = 8.994364899351798e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0355
y[1] (analytic) = 1.000630058826527
y[1] (numeric) = 1.000630058826536
absolute error = 9e-15
relative error = 8.994333041078745e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0356
y[1] (analytic) = 1.00063361307777
y[1] (numeric) = 1.000633613077779
absolute error = 9e-15
relative error = 8.994301093201946e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0357
y[1] (analytic) = 1.000637177322677
y[1] (numeric) = 1.000637177322686
absolute error = 9e-15
relative error = 8.994269055723637e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0358
y[1] (analytic) = 1.000640751561212
y[1] (numeric) = 1.000640751561221
absolute error = 9e-15
relative error = 8.994236928646059e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0359
y[1] (analytic) = 1.000644335793339
y[1] (numeric) = 1.000644335793348
absolute error = 9e-15
relative error = 8.994204711971458e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 1.000647930019023
y[1] (numeric) = 1.000647930019032
absolute error = 9e-15
relative error = 8.994172405702077e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0361
y[1] (analytic) = 1.000651534238228
y[1] (numeric) = 1.000651534238237
absolute error = 9e-15
relative error = 8.994140009840173e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0362
y[1] (analytic) = 1.000655148450917
y[1] (numeric) = 1.000655148450926
absolute error = 9e-15
relative error = 8.994107524388016e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0363
y[1] (analytic) = 1.000658772657055
y[1] (numeric) = 1.000658772657064
absolute error = 9e-15
relative error = 8.994074949347866e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0364
y[1] (analytic) = 1.000662406856605
y[1] (numeric) = 1.000662406856614
absolute error = 9e-15
relative error = 8.994042284722005e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0365
y[1] (analytic) = 1.000666051049532
y[1] (numeric) = 1.00066605104954
absolute error = 8e-15
relative error = 7.994675138233512e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0366
y[1] (analytic) = 1.000669705235797
y[1] (numeric) = 1.000669705235806
absolute error = 9e-15
relative error = 8.993976686722266e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0367
y[1] (analytic) = 1.000673369415366
y[1] (numeric) = 1.000673369415374
absolute error = 8e-15
relative error = 7.994616669647084e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0368
y[1] (analytic) = 1.0006770435882
y[1] (numeric) = 1.000677043588209
absolute error = 9e-15
relative error = 8.993910730407135e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0369
y[1] (analytic) = 1.000680727754265
y[1] (numeric) = 1.000680727754273
absolute error = 8e-15
relative error = 7.994557882566259e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 1.000684421913522
y[1] (numeric) = 1.00068442191353
absolute error = 8e-15
relative error = 7.994528369595575e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0371
y[1] (analytic) = 1.000688126065935
y[1] (numeric) = 1.000688126065943
absolute error = 8e-15
relative error = 7.994498777007456e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0372
y[1] (analytic) = 1.000691840211466
y[1] (numeric) = 1.000691840211475
absolute error = 9e-15
relative error = 8.993777742904471e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0373
y[1] (analytic) = 1.000695564350079
y[1] (numeric) = 1.000695564350088
absolute error = 9e-15
relative error = 8.993744272110593e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0374
y[1] (analytic) = 1.000699298481737
y[1] (numeric) = 1.000699298481746
absolute error = 9e-15
relative error = 8.993710711754089e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0375
y[1] (analytic) = 1.000703042606401
y[1] (numeric) = 1.000703042606411
absolute error = 1.0e-14
relative error = 9.992974513152574e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.2MB, time=4.00
NO POLE
x[1] = 0.0376
y[1] (analytic) = 1.000706796724035
y[1] (numeric) = 1.000706796724045
absolute error = 1.0e-14
relative error = 9.992937024847350e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0377
y[1] (analytic) = 1.000710560834602
y[1] (numeric) = 1.000710560834611
absolute error = 9e-15
relative error = 8.993609493332333e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0378
y[1] (analytic) = 1.000714334938062
y[1] (numeric) = 1.000714334938071
absolute error = 9e-15
relative error = 8.993575574748856e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0379
y[1] (analytic) = 1.000718119034379
y[1] (numeric) = 1.000718119034388
absolute error = 9e-15
relative error = 8.993541566614535e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 1.000721913123515
y[1] (numeric) = 1.000721913123524
absolute error = 9e-15
relative error = 8.993507468931748e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0381
y[1] (analytic) = 1.000725717205432
y[1] (numeric) = 1.000725717205441
absolute error = 9e-15
relative error = 8.993473281702875e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0382
y[1] (analytic) = 1.000729531280092
y[1] (numeric) = 1.000729531280101
absolute error = 9e-15
relative error = 8.993439004930304e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0383
y[1] (analytic) = 1.000733355347456
y[1] (numeric) = 1.000733355347465
absolute error = 9e-15
relative error = 8.993404638616435e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0384
y[1] (analytic) = 1.000737189407486
y[1] (numeric) = 1.000737189407496
absolute error = 1.0e-14
relative error = 9.992633536404074e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0385
y[1] (analytic) = 1.000741033460145
y[1] (numeric) = 1.000741033460155
absolute error = 1.0e-14
relative error = 9.992595152638212e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0386
y[1] (analytic) = 1.000744887505394
y[1] (numeric) = 1.000744887505403
absolute error = 9e-15
relative error = 8.993301002451027e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0387
y[1] (analytic) = 1.000748751543193
y[1] (numeric) = 1.000748751543203
absolute error = 1.0e-14
relative error = 9.992518086662228e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0388
y[1] (analytic) = 1.000752625573506
y[1] (numeric) = 1.000752625573515
absolute error = 9e-15
relative error = 8.993231464011726e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0389
y[1] (analytic) = 1.000756509596291
y[1] (numeric) = 1.000756509596301
absolute error = 1.0e-14
relative error = 9.992440622778500e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 1.000760403611512
y[1] (numeric) = 1.000760403611522
absolute error = 1.0e-14
relative error = 9.992401741627987e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0391
y[1] (analytic) = 1.000764307619129
y[1] (numeric) = 1.000764307619139
absolute error = 1.0e-14
relative error = 9.992362761008660e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0392
y[1] (analytic) = 1.000768221619102
y[1] (numeric) = 1.000768221619113
absolute error = 1.1e-14
relative error = 1.099155604901557e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0393
y[1] (analytic) = 1.000772145611394
y[1] (numeric) = 1.000772145611404
absolute error = 1.0e-14
relative error = 9.992284501374463e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0394
y[1] (analytic) = 1.000776079595964
y[1] (numeric) = 1.000776079595974
absolute error = 1.0e-14
relative error = 9.992245222365054e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0395
y[1] (analytic) = 1.000780023572773
y[1] (numeric) = 1.000780023572783
absolute error = 1.0e-14
relative error = 9.992205843897760e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0396
y[1] (analytic) = 1.000783977541781
y[1] (numeric) = 1.000783977541792
absolute error = 1.1e-14
relative error = 1.099138300257287e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0397
y[1] (analytic) = 1.00078794150295
y[1] (numeric) = 1.000787941502961
absolute error = 1.1e-14
relative error = 1.099133946746058e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0398
y[1] (analytic) = 1.00079191545624
y[1] (numeric) = 1.000791915456251
absolute error = 1.1e-14
relative error = 1.099129582295370e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0399
y[1] (analytic) = 1.000795899401611
y[1] (numeric) = 1.000795899401621
absolute error = 1.0e-14
relative error = 9.992047335504803e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=64.8MB, alloc=4.2MB, time=4.26
x[1] = 0.04
y[1] (analytic) = 1.000799893339022
y[1] (numeric) = 1.000799893339032
absolute error = 1.0e-14
relative error = 9.992007459789456e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0401
y[1] (analytic) = 1.000803897268435
y[1] (numeric) = 1.000803897268445
absolute error = 1.0e-14
relative error = 9.991967484632812e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0402
y[1] (analytic) = 1.000807911189808
y[1] (numeric) = 1.000807911189819
absolute error = 1.1e-14
relative error = 1.099112015104145e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0403
y[1] (analytic) = 1.000811935103103
y[1] (numeric) = 1.000811935103113
absolute error = 1.0e-14
relative error = 9.991887236006839e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0404
y[1] (analytic) = 1.000815969008278
y[1] (numeric) = 1.000815969008288
absolute error = 1.0e-14
relative error = 9.991846962543108e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0405
y[1] (analytic) = 1.000820012905293
y[1] (numeric) = 1.000820012905303
absolute error = 1.0e-14
relative error = 9.991806589649296e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0406
y[1] (analytic) = 1.000824066794108
y[1] (numeric) = 1.000824066794118
absolute error = 1.0e-14
relative error = 9.991766117328216e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0407
y[1] (analytic) = 1.000828130674683
y[1] (numeric) = 1.000828130674693
absolute error = 1.0e-14
relative error = 9.991725545582689e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0408
y[1] (analytic) = 1.000832204546976
y[1] (numeric) = 1.000832204546986
absolute error = 1.0e-14
relative error = 9.991684874415560e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0409
y[1] (analytic) = 1.000836288410947
y[1] (numeric) = 1.000836288410957
absolute error = 1.0e-14
relative error = 9.991644103829660e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 1.000840382266556
y[1] (numeric) = 1.000840382266565
absolute error = 9e-15
relative error = 8.992442910445045e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0411
y[1] (analytic) = 1.00084448611376
y[1] (numeric) = 1.000844486113769
absolute error = 9e-15
relative error = 8.992406037971641e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0412
y[1] (analytic) = 1.00084859995252
y[1] (numeric) = 1.000848599952529
absolute error = 9e-15
relative error = 8.992369076029039e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0413
y[1] (analytic) = 1.000852723782793
y[1] (numeric) = 1.000852723782803
absolute error = 1.0e-14
relative error = 9.991480027355373e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0414
y[1] (analytic) = 1.00085685760454
y[1] (numeric) = 1.000856857604549
absolute error = 9e-15
relative error = 8.992294883746596e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0415
y[1] (analytic) = 1.000861001417717
y[1] (numeric) = 1.000861001417727
absolute error = 1.0e-14
relative error = 9.991397392679929e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0416
y[1] (analytic) = 1.000865155222285
y[1] (numeric) = 1.000865155222295
absolute error = 1.0e-14
relative error = 9.991355926242703e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0417
y[1] (analytic) = 1.000869319018201
y[1] (numeric) = 1.000869319018211
absolute error = 1.0e-14
relative error = 9.991314360409671e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0418
y[1] (analytic) = 1.000873492805424
y[1] (numeric) = 1.000873492805434
absolute error = 1.0e-14
relative error = 9.991272695183728e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0419
y[1] (analytic) = 1.000877676583912
y[1] (numeric) = 1.000877676583922
absolute error = 1.0e-14
relative error = 9.991230930567783e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 1.000881870353623
y[1] (numeric) = 1.000881870353633
absolute error = 1.0e-14
relative error = 9.991189066564754e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0421
y[1] (analytic) = 1.000886074114516
y[1] (numeric) = 1.000886074114526
absolute error = 1.0e-14
relative error = 9.991147103177553e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0422
y[1] (analytic) = 1.000890287866548
y[1] (numeric) = 1.000890287866558
absolute error = 1.0e-14
relative error = 9.991105040409117e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0423
y[1] (analytic) = 1.000894511609677
y[1] (numeric) = 1.000894511609687
absolute error = 1.0e-14
relative error = 9.991062878262381e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=68.6MB, alloc=4.2MB, time=4.51
x[1] = 0.0424
y[1] (analytic) = 1.00089874534386
y[1] (numeric) = 1.000898745343871
absolute error = 1.1e-14
relative error = 1.099012267841432e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0425
y[1] (analytic) = 1.000902989069057
y[1] (numeric) = 1.000902989069067
absolute error = 1.0e-14
relative error = 9.990978255845785e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0426
y[1] (analytic) = 1.000907242785223
y[1] (numeric) = 1.000907242785233
absolute error = 1.0e-14
relative error = 9.990935795581832e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0427
y[1] (analytic) = 1.000911506492317
y[1] (numeric) = 1.000911506492327
absolute error = 1.0e-14
relative error = 9.990893235951384e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0428
y[1] (analytic) = 1.000915780190296
y[1] (numeric) = 1.000915780190306
absolute error = 1.0e-14
relative error = 9.990850576957415e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0429
y[1] (analytic) = 1.000920063879117
y[1] (numeric) = 1.000920063879127
absolute error = 1.0e-14
relative error = 9.990807818602904e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 1.000924357558738
y[1] (numeric) = 1.000924357558747
absolute error = 9e-15
relative error = 8.991688464801743e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0431
y[1] (analytic) = 1.000928661229115
y[1] (numeric) = 1.000928661229124
absolute error = 9e-15
relative error = 8.991649803441764e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0432
y[1] (analytic) = 1.000932974890205
y[1] (numeric) = 1.000932974890214
absolute error = 9e-15
relative error = 8.991611052665373e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0433
y[1] (analytic) = 1.000937298541965
y[1] (numeric) = 1.000937298541975
absolute error = 1.0e-14
relative error = 9.990635791639193e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0434
y[1] (analytic) = 1.000941632184353
y[1] (numeric) = 1.000941632184363
absolute error = 1.0e-14
relative error = 9.990592536526849e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0435
y[1] (analytic) = 1.000945975817324
y[1] (numeric) = 1.000945975817334
absolute error = 1.0e-14
relative error = 9.990549182071974e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0436
y[1] (analytic) = 1.000950329440835
y[1] (numeric) = 1.000950329440845
absolute error = 1.0e-14
relative error = 9.990505728277587e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0437
y[1] (analytic) = 1.000954693054844
y[1] (numeric) = 1.000954693054853
absolute error = 9e-15
relative error = 8.991415957632035e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0438
y[1] (analytic) = 1.000959066659305
y[1] (numeric) = 1.000959066659314
absolute error = 9e-15
relative error = 8.991376670414153e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0439
y[1] (analytic) = 1.000963450254175
y[1] (numeric) = 1.000963450254184
absolute error = 9e-15
relative error = 8.991337293798916e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 1.000967843839411
y[1] (numeric) = 1.00096784383942
absolute error = 9e-15
relative error = 8.991297827789065e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0441
y[1] (analytic) = 1.000972247414969
y[1] (numeric) = 1.000972247414978
absolute error = 9e-15
relative error = 8.991258272387353e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0442
y[1] (analytic) = 1.000976660980804
y[1] (numeric) = 1.000976660980813
absolute error = 9e-15
relative error = 8.991218627596548e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0443
y[1] (analytic) = 1.000981084536872
y[1] (numeric) = 1.000981084536881
absolute error = 9e-15
relative error = 8.991178893419416e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0444
y[1] (analytic) = 1.00098551808313
y[1] (numeric) = 1.000985518083139
absolute error = 9e-15
relative error = 8.991139069858718e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0445
y[1] (analytic) = 1.000989961619532
y[1] (numeric) = 1.000989961619541
absolute error = 9e-15
relative error = 8.991099156917245e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0446
y[1] (analytic) = 1.000994415146035
y[1] (numeric) = 1.000994415146044
absolute error = 9e-15
relative error = 8.991059154597771e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0447
y[1] (analytic) = 1.000998878662594
y[1] (numeric) = 1.000998878662603
absolute error = 9e-15
relative error = 8.991019062903090e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0448
y[1] (analytic) = 1.001003352169163
y[1] (numeric) = 1.001003352169173
absolute error = 1.0e-14
memory used=72.4MB, alloc=4.2MB, time=4.76
relative error = 9.989976535373346e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0449
y[1] (analytic) = 1.0010078356657
y[1] (numeric) = 1.001007835665709
absolute error = 9e-15
relative error = 8.990938611399313e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 1.001012329152158
y[1] (numeric) = 1.001012329152167
absolute error = 9e-15
relative error = 8.990898251595823e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0451
y[1] (analytic) = 1.001016832628492
y[1] (numeric) = 1.001016832628502
absolute error = 1.0e-14
relative error = 9.989842002698177e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0452
y[1] (analytic) = 1.001021346094658
y[1] (numeric) = 1.001021346094668
absolute error = 1.0e-14
relative error = 9.989796959888591e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0453
y[1] (analytic) = 1.001025869550611
y[1] (numeric) = 1.001025869550621
absolute error = 1.0e-14
relative error = 9.989751817791966e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0454
y[1] (analytic) = 1.001030402996305
y[1] (numeric) = 1.001030402996315
absolute error = 1.0e-14
relative error = 9.989706576411458e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0455
y[1] (analytic) = 1.001034946431696
y[1] (numeric) = 1.001034946431705
absolute error = 9e-15
relative error = 8.990695112175188e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0456
y[1] (analytic) = 1.001039499856736
y[1] (numeric) = 1.001039499856746
absolute error = 1.0e-14
relative error = 9.989615795811406e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0457
y[1] (analytic) = 1.001044063271382
y[1] (numeric) = 1.001044063271392
absolute error = 1.0e-14
relative error = 9.989570256598196e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0458
y[1] (analytic) = 1.001048636675587
y[1] (numeric) = 1.001048636675597
absolute error = 1.0e-14
relative error = 9.989524618113767e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0459
y[1] (analytic) = 1.001053220069305
y[1] (numeric) = 1.001053220069316
absolute error = 1.1e-14
relative error = 1.098842676839744e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 1.001057813452492
y[1] (numeric) = 1.001057813452502
absolute error = 1.0e-14
relative error = 9.989433043343983e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0461
y[1] (analytic) = 1.0010624168251
y[1] (numeric) = 1.00106241682511
absolute error = 1.0e-14
relative error = 9.989387107065017e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0462
y[1] (analytic) = 1.001067030187084
y[1] (numeric) = 1.001067030187094
absolute error = 1.0e-14
relative error = 9.989341071527602e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0463
y[1] (analytic) = 1.001071653538398
y[1] (numeric) = 1.001071653538408
absolute error = 1.0e-14
relative error = 9.989294936734947e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0464
y[1] (analytic) = 1.001076286878995
y[1] (numeric) = 1.001076286879005
absolute error = 1.0e-14
relative error = 9.989248702690277e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0465
y[1] (analytic) = 1.001080930208829
y[1] (numeric) = 1.001080930208839
absolute error = 1.0e-14
relative error = 9.989202369396813e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0466
y[1] (analytic) = 1.001085583527854
y[1] (numeric) = 1.001085583527864
absolute error = 1.0e-14
relative error = 9.989155936857782e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0467
y[1] (analytic) = 1.001090246836023
y[1] (numeric) = 1.001090246836033
absolute error = 1.0e-14
relative error = 9.989109405076428e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0468
y[1] (analytic) = 1.00109492013329
y[1] (numeric) = 1.0010949201333
absolute error = 1.0e-14
relative error = 9.989062774055988e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0469
y[1] (analytic) = 1.001099603419607
y[1] (numeric) = 1.001099603419617
absolute error = 1.0e-14
relative error = 9.989016043799729e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 1.001104296694929
y[1] (numeric) = 1.001104296694938
absolute error = 9e-15
relative error = 8.990072292879800e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0471
y[1] (analytic) = 1.001108999959207
y[1] (numeric) = 1.001108999959216
absolute error = 9e-15
relative error = 8.990030057033480e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0472
y[1] (analytic) = 1.001113713212396
y[1] (numeric) = 1.001113713212404
absolute error = 8e-15
relative error = 7.991100206118865e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=5.03
NO POLE
x[1] = 0.0473
y[1] (analytic) = 1.001118436454447
y[1] (numeric) = 1.001118436454455
absolute error = 8e-15
relative error = 7.991062504385331e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0474
y[1] (analytic) = 1.001123169685314
y[1] (numeric) = 1.001123169685322
absolute error = 8e-15
relative error = 7.991024723276221e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0475
y[1] (analytic) = 1.001127912904949
y[1] (numeric) = 1.001127912904957
absolute error = 8e-15
relative error = 7.990986862794177e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0476
y[1] (analytic) = 1.001132666113305
y[1] (numeric) = 1.001132666113313
absolute error = 8e-15
relative error = 7.990948922941833e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0477
y[1] (analytic) = 1.001137429310335
y[1] (numeric) = 1.001137429310342
absolute error = 7e-15
relative error = 6.992047040756602e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0478
y[1] (analytic) = 1.00114220249599
y[1] (numeric) = 1.001142202495997
absolute error = 7e-15
relative error = 6.992013704494730e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0479
y[1] (analytic) = 1.001146985670223
y[1] (numeric) = 1.00114698567023
absolute error = 7e-15
relative error = 6.991980298790805e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 1.001151778832986
y[1] (numeric) = 1.001151778832993
absolute error = 7e-15
relative error = 6.991946823647160e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0481
y[1] (analytic) = 1.001156581984232
y[1] (numeric) = 1.001156581984238
absolute error = 6e-15
relative error = 5.993068524913817e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0482
y[1] (analytic) = 1.001161395123911
y[1] (numeric) = 1.001161395123918
absolute error = 7e-15
relative error = 6.991879665050038e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0483
y[1] (analytic) = 1.001166218251977
y[1] (numeric) = 1.001166218251984
absolute error = 7e-15
relative error = 6.991845981601245e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0484
y[1] (analytic) = 1.00117105136838
y[1] (numeric) = 1.001171051368387
absolute error = 7e-15
relative error = 6.991812228722099e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0485
y[1] (analytic) = 1.001175894473073
y[1] (numeric) = 1.00117589447308
absolute error = 7e-15
relative error = 6.991778406414946e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0486
y[1] (analytic) = 1.001180747566007
y[1] (numeric) = 1.001180747566014
absolute error = 7e-15
relative error = 6.991744514682146e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0487
y[1] (analytic) = 1.001185610647134
y[1] (numeric) = 1.00118561064714
absolute error = 6e-15
relative error = 5.992894760165195e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0488
y[1] (analytic) = 1.001190483716404
y[1] (numeric) = 1.00119048371641
absolute error = 6e-15
relative error = 5.992865591099199e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0489
y[1] (analytic) = 1.00119536677377
y[1] (numeric) = 1.001195366773776
absolute error = 6e-15
relative error = 5.992836362531589e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 1.001200259819182
y[1] (numeric) = 1.001200259819188
absolute error = 6e-15
relative error = 5.992807074464411e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0491
y[1] (analytic) = 1.001205162852591
y[1] (numeric) = 1.001205162852597
absolute error = 6e-15
relative error = 5.992777726899706e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0492
y[1] (analytic) = 1.001210075873948
y[1] (numeric) = 1.001210075873955
absolute error = 7e-15
relative error = 6.991539706479440e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0493
y[1] (analytic) = 1.001214998883205
y[1] (numeric) = 1.001214998883212
absolute error = 7e-15
relative error = 6.991505328833545e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0494
y[1] (analytic) = 1.001219931880312
y[1] (numeric) = 1.001219931880319
absolute error = 7e-15
relative error = 6.991470881781042e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0495
y[1] (analytic) = 1.00122487486522
y[1] (numeric) = 1.001224874865227
absolute error = 7e-15
relative error = 6.991436365324329e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0496
y[1] (analytic) = 1.001229827837878
y[1] (numeric) = 1.001229827837886
absolute error = 8e-15
relative error = 7.990173462246655e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.31
NO POLE
x[1] = 0.0497
y[1] (analytic) = 1.001234790798239
y[1] (numeric) = 1.001234790798246
absolute error = 7e-15
relative error = 6.991367124207917e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0498
y[1] (analytic) = 1.001239763746251
y[1] (numeric) = 1.001239763746259
absolute error = 8e-15
relative error = 7.990094170917765e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0499
y[1] (analytic) = 1.001244746681866
y[1] (numeric) = 1.001244746681874
absolute error = 8e-15
relative error = 7.990054406289842e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 1.001249739605034
y[1] (numeric) = 1.001249739605041
absolute error = 7e-15
relative error = 6.991262742062046e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0501
y[1] (analytic) = 1.001254742515704
y[1] (numeric) = 1.001254742515711
absolute error = 7e-15
relative error = 6.991227809230786e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0502
y[1] (analytic) = 1.001259755413826
y[1] (numeric) = 1.001259755413834
absolute error = 8e-15
relative error = 7.989934636585446e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0503
y[1] (analytic) = 1.001264778299351
y[1] (numeric) = 1.001264778299359
absolute error = 8e-15
relative error = 7.989894554753046e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0504
y[1] (analytic) = 1.001269811172229
y[1] (numeric) = 1.001269811172236
absolute error = 7e-15
relative error = 6.991122594423179e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0505
y[1] (analytic) = 1.001274854032408
y[1] (numeric) = 1.001274854032415
absolute error = 7e-15
relative error = 6.991087384057518e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0506
y[1] (analytic) = 1.001279906879838
y[1] (numeric) = 1.001279906879846
absolute error = 8e-15
relative error = 7.989773833502151e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0507
y[1] (analytic) = 1.00128496971447
y[1] (numeric) = 1.001284969714478
absolute error = 8e-15
relative error = 7.989733434509966e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0508
y[1] (analytic) = 1.001290042536252
y[1] (numeric) = 1.00129004253626
absolute error = 8e-15
relative error = 7.989692956234864e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0509
y[1] (analytic) = 1.001295125345133
y[1] (numeric) = 1.001295125345141
absolute error = 8e-15
relative error = 7.989652398679667e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 1.001300218141063
y[1] (numeric) = 1.001300218141071
absolute error = 8e-15
relative error = 7.989611761847196e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0511
y[1] (analytic) = 1.001305320923991
y[1] (numeric) = 1.001305320923999
absolute error = 8e-15
relative error = 7.989571045740283e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0512
y[1] (analytic) = 1.001310433693866
y[1] (numeric) = 1.001310433693874
absolute error = 8e-15
relative error = 7.989530250361764e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0513
y[1] (analytic) = 1.001315556450636
y[1] (numeric) = 1.001315556450644
absolute error = 8e-15
relative error = 7.989489375714491e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0514
y[1] (analytic) = 1.001320689194251
y[1] (numeric) = 1.001320689194259
absolute error = 8e-15
relative error = 7.989448421801301e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0515
y[1] (analytic) = 1.001325831924659
y[1] (numeric) = 1.001325831924667
absolute error = 8e-15
relative error = 7.989407388625054e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0516
y[1] (analytic) = 1.001330984641808
y[1] (numeric) = 1.001330984641817
absolute error = 9e-15
relative error = 8.988037060712191e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0517
y[1] (analytic) = 1.001336147345648
y[1] (numeric) = 1.001336147345657
absolute error = 9e-15
relative error = 8.987990720056687e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0518
y[1] (analytic) = 1.001341320036126
y[1] (numeric) = 1.001341320036135
absolute error = 9e-15
relative error = 8.987944290239917e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0519
y[1] (analytic) = 1.001346502713191
y[1] (numeric) = 1.0013465027132
absolute error = 9e-15
relative error = 8.987897771265108e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 1.001351695376791
y[1] (numeric) = 1.0013516953768
absolute error = 9e-15
relative error = 8.987851163135504e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=5.58
NO POLE
x[1] = 0.0521
y[1] (analytic) = 1.001356898026874
y[1] (numeric) = 1.001356898026883
absolute error = 9e-15
relative error = 8.987804465854353e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0522
y[1] (analytic) = 1.001362110663388
y[1] (numeric) = 1.001362110663397
absolute error = 9e-15
relative error = 8.987757679424908e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0523
y[1] (analytic) = 1.001367333286281
y[1] (numeric) = 1.00136733328629
absolute error = 9e-15
relative error = 8.987710803850428e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0524
y[1] (analytic) = 1.001372565895501
y[1] (numeric) = 1.00137256589551
absolute error = 9e-15
relative error = 8.987663839134177e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0525
y[1] (analytic) = 1.001377808490995
y[1] (numeric) = 1.001377808491004
absolute error = 9e-15
relative error = 8.987616785279433e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0526
y[1] (analytic) = 1.00138306107271
y[1] (numeric) = 1.00138306107272
absolute error = 1.0e-14
relative error = 9.986188491432755e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0527
y[1] (analytic) = 1.001388323640596
y[1] (numeric) = 1.001388323640605
absolute error = 9e-15
relative error = 8.987522410167578e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0528
y[1] (analytic) = 1.001393596194598
y[1] (numeric) = 1.001393596194607
absolute error = 9e-15
relative error = 8.987475088917041e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0529
y[1] (analytic) = 1.001398878734664
y[1] (numeric) = 1.001398878734673
absolute error = 9e-15
relative error = 8.987427678541158e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 1.001404171260741
y[1] (numeric) = 1.00140417126075
absolute error = 9e-15
relative error = 8.987380179043234e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0531
y[1] (analytic) = 1.001409473772776
y[1] (numeric) = 1.001409473772785
absolute error = 9e-15
relative error = 8.987332590426579e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0532
y[1] (analytic) = 1.001414786270717
y[1] (numeric) = 1.001414786270726
absolute error = 9e-15
relative error = 8.987284912694498e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0533
y[1] (analytic) = 1.00142010875451
y[1] (numeric) = 1.001420108754519
absolute error = 9e-15
relative error = 8.987237145850320e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0534
y[1] (analytic) = 1.001425441224101
y[1] (numeric) = 1.001425441224111
absolute error = 1.0e-14
relative error = 9.985765877663757e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0535
y[1] (analytic) = 1.001430783679439
y[1] (numeric) = 1.001430783679448
absolute error = 9e-15
relative error = 8.987141344838993e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0536
y[1] (analytic) = 1.001436136120468
y[1] (numeric) = 1.001436136120477
absolute error = 9e-15
relative error = 8.987093310678518e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0537
y[1] (analytic) = 1.001441498547136
y[1] (numeric) = 1.001441498547145
absolute error = 9e-15
relative error = 8.987045187419290e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0538
y[1] (analytic) = 1.001446870959389
y[1] (numeric) = 1.001446870959398
absolute error = 9e-15
relative error = 8.986996975064662e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0539
y[1] (analytic) = 1.001452253357174
y[1] (numeric) = 1.001452253357182
absolute error = 8e-15
relative error = 7.988398820993767e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 1.001457645740436
y[1] (numeric) = 1.001457645740444
absolute error = 8e-15
relative error = 7.988355807184570e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0541
y[1] (analytic) = 1.001463048109121
y[1] (numeric) = 1.001463048109129
absolute error = 8e-15
relative error = 7.988312714188439e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0542
y[1] (analytic) = 1.001468460463176
y[1] (numeric) = 1.001468460463184
absolute error = 8e-15
relative error = 7.988269542008368e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0543
y[1] (analytic) = 1.001473882802546
y[1] (numeric) = 1.001473882802554
absolute error = 8e-15
relative error = 7.988226290647369e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0544
y[1] (analytic) = 1.001479315127178
y[1] (numeric) = 1.001479315127185
absolute error = 7e-15
relative error = 6.989660090094890e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=87.7MB, alloc=4.3MB, time=5.85
x[1] = 0.0545
y[1] (analytic) = 1.001484757437016
y[1] (numeric) = 1.001484757437023
absolute error = 7e-15
relative error = 6.989622106595301e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0546
y[1] (analytic) = 1.001490209732007
y[1] (numeric) = 1.001490209732014
absolute error = 7e-15
relative error = 6.989584053820316e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0547
y[1] (analytic) = 1.001495672012095
y[1] (numeric) = 1.001495672012103
absolute error = 8e-15
relative error = 7.988052493454395e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0548
y[1] (analytic) = 1.001501144277227
y[1] (numeric) = 1.001501144277235
absolute error = 8e-15
relative error = 7.988008846234037e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0549
y[1] (analytic) = 1.001506626527347
y[1] (numeric) = 1.001506626527355
absolute error = 8e-15
relative error = 7.987965119850910e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 1.001512118762402
y[1] (numeric) = 1.001512118762409
absolute error = 7e-15
relative error = 6.989431150019538e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0551
y[1] (analytic) = 1.001517620982334
y[1] (numeric) = 1.001517620982342
absolute error = 8e-15
relative error = 7.987877429608514e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0552
y[1] (analytic) = 1.001523133187091
y[1] (numeric) = 1.001523133187099
absolute error = 8e-15
relative error = 7.987833465755352e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0553
y[1] (analytic) = 1.001528655376617
y[1] (numeric) = 1.001528655376624
absolute error = 7e-15
relative error = 6.989315744907673e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0554
y[1] (analytic) = 1.001534187550856
y[1] (numeric) = 1.001534187550863
absolute error = 7e-15
relative error = 6.989277138025359e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0555
y[1] (analytic) = 1.001539729709752
y[1] (numeric) = 1.00153972970976
absolute error = 8e-15
relative error = 7.987701099304782e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0556
y[1] (analytic) = 1.001545281853252
y[1] (numeric) = 1.00154528185326
absolute error = 8e-15
relative error = 7.987656818867799e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0557
y[1] (analytic) = 1.001550843981299
y[1] (numeric) = 1.001550843981307
absolute error = 8e-15
relative error = 7.987612459292557e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0558
y[1] (analytic) = 1.001556416093837
y[1] (numeric) = 1.001556416093845
absolute error = 8e-15
relative error = 7.987568020582148e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0559
y[1] (analytic) = 1.001561998190811
y[1] (numeric) = 1.001561998190819
absolute error = 8e-15
relative error = 7.987523502739660e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 1.001567590272166
y[1] (numeric) = 1.001567590272173
absolute error = 7e-15
relative error = 6.989044042547163e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0561
y[1] (analytic) = 1.001573192337844
y[1] (numeric) = 1.001573192337851
absolute error = 7e-15
relative error = 6.989004950961993e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0562
y[1] (analytic) = 1.00157880438779
y[1] (numeric) = 1.001578804387797
absolute error = 7e-15
relative error = 6.988965790144406e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0563
y[1] (analytic) = 1.001584426421949
y[1] (numeric) = 1.001584426421955
absolute error = 6e-15
relative error = 5.990508480083247e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0564
y[1] (analytic) = 1.001590058440263
y[1] (numeric) = 1.001590058440269
absolute error = 6e-15
relative error = 5.990474794991042e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0565
y[1] (analytic) = 1.001595700442676
y[1] (numeric) = 1.001595700442682
absolute error = 6e-15
relative error = 5.990441050563791e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0566
y[1] (analytic) = 1.001601352429132
y[1] (numeric) = 1.001601352429138
absolute error = 6e-15
relative error = 5.990407246803841e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0567
y[1] (analytic) = 1.001607014399575
y[1] (numeric) = 1.001607014399581
absolute error = 6e-15
relative error = 5.990373383713542e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0568
y[1] (analytic) = 1.001612686353948
y[1] (numeric) = 1.001612686353954
absolute error = 6e-15
relative error = 5.990339461295253e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.3MB, time=6.11
x[1] = 0.0569
y[1] (analytic) = 1.001618368292194
y[1] (numeric) = 1.0016183682922
absolute error = 6e-15
relative error = 5.990305479551338e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 1.001624060214256
y[1] (numeric) = 1.001624060214262
absolute error = 6e-15
relative error = 5.990271438484164e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0571
y[1] (analytic) = 1.001629762120078
y[1] (numeric) = 1.001629762120084
absolute error = 6e-15
relative error = 5.990237338096094e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0572
y[1] (analytic) = 1.001635474009602
y[1] (numeric) = 1.001635474009608
absolute error = 6e-15
relative error = 5.990203178389509e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0573
y[1] (analytic) = 1.001641195882771
y[1] (numeric) = 1.001641195882777
absolute error = 6e-15
relative error = 5.990168959366785e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0574
y[1] (analytic) = 1.001646927739528
y[1] (numeric) = 1.001646927739534
absolute error = 6e-15
relative error = 5.990134681030302e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0575
y[1] (analytic) = 1.001652669579816
y[1] (numeric) = 1.001652669579822
absolute error = 6e-15
relative error = 5.990100343382446e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0576
y[1] (analytic) = 1.001658421403577
y[1] (numeric) = 1.001658421403583
absolute error = 6e-15
relative error = 5.990065946425610e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0577
y[1] (analytic) = 1.001664183210754
y[1] (numeric) = 1.00166418321076
absolute error = 6e-15
relative error = 5.990031490162184e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0578
y[1] (analytic) = 1.00166995500129
y[1] (numeric) = 1.001669955001295
absolute error = 5e-15
relative error = 4.991664145495470e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0579
y[1] (analytic) = 1.001675736775125
y[1] (numeric) = 1.001675736775131
absolute error = 6e-15
relative error = 5.989962399725165e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 1.001681528532203
y[1] (numeric) = 1.001681528532209
absolute error = 6e-15
relative error = 5.989927765556382e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0581
y[1] (analytic) = 1.001687330272466
y[1] (numeric) = 1.001687330272472
absolute error = 6e-15
relative error = 5.989893072090627e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0582
y[1] (analytic) = 1.001693141995856
y[1] (numeric) = 1.001693141995862
absolute error = 6e-15
relative error = 5.989858319330314e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0583
y[1] (analytic) = 1.001698963702314
y[1] (numeric) = 1.00169896370232
absolute error = 6e-15
relative error = 5.989823507277868e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0584
y[1] (analytic) = 1.001704795391783
y[1] (numeric) = 1.001704795391789
absolute error = 6e-15
relative error = 5.989788635935703e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0585
y[1] (analytic) = 1.001710637064203
y[1] (numeric) = 1.00171063706421
absolute error = 7e-15
relative error = 6.988045989523965e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0586
y[1] (analytic) = 1.001716488719518
y[1] (numeric) = 1.001716488719524
absolute error = 6e-15
relative error = 5.989718715391944e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0587
y[1] (analytic) = 1.001722350357667
y[1] (numeric) = 1.001722350357673
absolute error = 6e-15
relative error = 5.989683666195216e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0588
y[1] (analytic) = 1.001728221978593
y[1] (numeric) = 1.001728221978599
absolute error = 6e-15
relative error = 5.989648557718503e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0589
y[1] (analytic) = 1.001734103582236
y[1] (numeric) = 1.001734103582243
absolute error = 7e-15
relative error = 6.987882288291630e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 1.001739995168539
y[1] (numeric) = 1.001739995168546
absolute error = 7e-15
relative error = 6.987841190090724e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0591
y[1] (analytic) = 1.001745896737441
y[1] (numeric) = 1.001745896737449
absolute error = 8e-15
relative error = 7.986057168843898e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0592
y[1] (analytic) = 1.001751808288885
y[1] (numeric) = 1.001751808288893
absolute error = 8e-15
relative error = 7.986010041414332e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0593
y[1] (analytic) = 1.00175772982281
y[1] (numeric) = 1.001757729822819
absolute error = 9e-15
memory used=95.3MB, alloc=4.3MB, time=6.36
relative error = 8.984208189331279e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0594
y[1] (analytic) = 1.001763661339159
y[1] (numeric) = 1.001763661339167
absolute error = 8e-15
relative error = 7.985915549487580e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0595
y[1] (analytic) = 1.00176960283787
y[1] (numeric) = 1.001769602837879
absolute error = 9e-15
relative error = 8.984101708121595e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0596
y[1] (analytic) = 1.001775554318886
y[1] (numeric) = 1.001775554318895
absolute error = 9e-15
relative error = 8.984048334179168e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0597
y[1] (analytic) = 1.001781515782146
y[1] (numeric) = 1.001781515782155
absolute error = 9e-15
relative error = 8.983994871349971e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0598
y[1] (analytic) = 1.001787487227591
y[1] (numeric) = 1.0017874872276
absolute error = 9e-15
relative error = 8.983941319637721e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0599
y[1] (analytic) = 1.001793468655161
y[1] (numeric) = 1.00179346865517
absolute error = 9e-15
relative error = 8.983887679046144e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 1.001799460064796
y[1] (numeric) = 1.001799460064805
absolute error = 9e-15
relative error = 8.983833949578974e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0601
y[1] (analytic) = 1.001805461456436
y[1] (numeric) = 1.001805461456446
absolute error = 1.0e-14
relative error = 9.981977923599945e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0602
y[1] (analytic) = 1.001811472830022
y[1] (numeric) = 1.001811472830032
absolute error = 1.0e-14
relative error = 9.981918026703120e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0603
y[1] (analytic) = 1.001817494185494
y[1] (numeric) = 1.001817494185503
absolute error = 9e-15
relative error = 8.983672227961296e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0604
y[1] (analytic) = 1.00182352552279
y[1] (numeric) = 1.001823525522799
absolute error = 9e-15
relative error = 8.983618143029187e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0605
y[1] (analytic) = 1.001829566841851
y[1] (numeric) = 1.00182956684186
absolute error = 9e-15
relative error = 8.983563969240231e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0606
y[1] (analytic) = 1.001835618142617
y[1] (numeric) = 1.001835618142625
absolute error = 8e-15
relative error = 7.985341961420615e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0607
y[1] (analytic) = 1.001841679425026
y[1] (numeric) = 1.001841679425034
absolute error = 8e-15
relative error = 7.985293648983876e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0608
y[1] (analytic) = 1.001847750689018
y[1] (numeric) = 1.001847750689026
absolute error = 8e-15
relative error = 7.985245257573341e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0609
y[1] (analytic) = 1.001853831934533
y[1] (numeric) = 1.001853831934541
absolute error = 8e-15
relative error = 7.985196787192372e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 1.00185992316151
y[1] (numeric) = 1.001859923161518
absolute error = 8e-15
relative error = 7.985148237844343e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0611
y[1] (analytic) = 1.001866024369887
y[1] (numeric) = 1.001866024369895
absolute error = 8e-15
relative error = 7.985099609532637e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0612
y[1] (analytic) = 1.001872135559604
y[1] (numeric) = 1.001872135559612
absolute error = 8e-15
relative error = 7.985050902260630e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0613
y[1] (analytic) = 1.0018782567306
y[1] (numeric) = 1.001878256730608
absolute error = 8e-15
relative error = 7.985002116031708e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0614
y[1] (analytic) = 1.001884387882813
y[1] (numeric) = 1.001884387882821
absolute error = 8e-15
relative error = 7.984953250849271e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0615
y[1] (analytic) = 1.001890529016182
y[1] (numeric) = 1.00189052901619
absolute error = 8e-15
relative error = 7.984904306716715e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0616
y[1] (analytic) = 1.001896680130646
y[1] (numeric) = 1.001896680130654
absolute error = 8e-15
relative error = 7.984855283637441e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0617
y[1] (analytic) = 1.001902841226143
y[1] (numeric) = 1.001902841226151
absolute error = 8e-15
relative error = 7.984806181614862e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.3MB, time=6.62
NO POLE
x[1] = 0.0618
y[1] (analytic) = 1.001909012302612
y[1] (numeric) = 1.00190901230262
absolute error = 8e-15
relative error = 7.984757000652387e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0619
y[1] (analytic) = 1.00191519335999
y[1] (numeric) = 1.001915193359999
absolute error = 9e-15
relative error = 8.982796208347629e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 1.001921384398217
y[1] (numeric) = 1.001921384398226
absolute error = 9e-15
relative error = 8.982740702161638e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0621
y[1] (analytic) = 1.00192758541723
y[1] (numeric) = 1.001927585417239
absolute error = 9e-15
relative error = 8.982685107179831e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0622
y[1] (analytic) = 1.001933796416967
y[1] (numeric) = 1.001933796416976
absolute error = 9e-15
relative error = 8.982629423406075e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0623
y[1] (analytic) = 1.001940017397366
y[1] (numeric) = 1.001940017397375
absolute error = 9e-15
relative error = 8.982573650844241e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0624
y[1] (analytic) = 1.001946248358365
y[1] (numeric) = 1.001946248358374
absolute error = 9e-15
relative error = 8.982517789498205e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0625
y[1] (analytic) = 1.001952489299901
y[1] (numeric) = 1.00195248929991
absolute error = 9e-15
relative error = 8.982461839371857e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0626
y[1] (analytic) = 1.001958740221912
y[1] (numeric) = 1.001958740221921
absolute error = 9e-15
relative error = 8.982405800469086e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0627
y[1] (analytic) = 1.001965001124336
y[1] (numeric) = 1.001965001124345
absolute error = 9e-15
relative error = 8.982349672793781e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0628
y[1] (analytic) = 1.00197127200711
y[1] (numeric) = 1.001971272007119
absolute error = 9e-15
relative error = 8.982293456349850e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0629
y[1] (analytic) = 1.001977552870171
y[1] (numeric) = 1.00197755287018
absolute error = 9e-15
relative error = 8.982237151141204e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 1.001983843713457
y[1] (numeric) = 1.001983843713466
absolute error = 9e-15
relative error = 8.982180757171750e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0631
y[1] (analytic) = 1.001990144536904
y[1] (numeric) = 1.001990144536913
absolute error = 9e-15
relative error = 8.982124274445420e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0632
y[1] (analytic) = 1.00199645534045
y[1] (numeric) = 1.001996455340459
absolute error = 9e-15
relative error = 8.982067702966130e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0633
y[1] (analytic) = 1.002002776124031
y[1] (numeric) = 1.00200277612404
absolute error = 9e-15
relative error = 8.982011042737822e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0634
y[1] (analytic) = 1.002009106887585
y[1] (numeric) = 1.002009106887593
absolute error = 8e-15
relative error = 7.983959372235044e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0635
y[1] (analytic) = 1.002015447631047
y[1] (numeric) = 1.002015447631055
absolute error = 8e-15
relative error = 7.983908849822131e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0636
y[1] (analytic) = 1.002021798354355
y[1] (numeric) = 1.002021798354363
absolute error = 8e-15
relative error = 7.983858248531715e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0637
y[1] (analytic) = 1.002028159057445
y[1] (numeric) = 1.002028159057453
absolute error = 8e-15
relative error = 7.983807568367318e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0638
y[1] (analytic) = 1.002034529740253
y[1] (numeric) = 1.002034529740261
absolute error = 8e-15
relative error = 7.983756809332466e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0639
y[1] (analytic) = 1.002040910402716
y[1] (numeric) = 1.002040910402724
absolute error = 8e-15
relative error = 7.983705971430681e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 1.00204730104477
y[1] (numeric) = 1.002047301044778
absolute error = 8e-15
relative error = 7.983655054665500e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0641
y[1] (analytic) = 1.002053701666351
y[1] (numeric) = 1.002053701666359
absolute error = 8e-15
relative error = 7.983604059040462e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.3MB, time=6.88
NO POLE
x[1] = 0.0642
y[1] (analytic) = 1.002060112267395
y[1] (numeric) = 1.002060112267403
absolute error = 8e-15
relative error = 7.983552984559112e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0643
y[1] (analytic) = 1.002066532847838
y[1] (numeric) = 1.002066532847846
absolute error = 8e-15
relative error = 7.983501831224999e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0644
y[1] (analytic) = 1.002072963407615
y[1] (numeric) = 1.002072963407623
absolute error = 8e-15
relative error = 7.983450599041685e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0645
y[1] (analytic) = 1.002079403946663
y[1] (numeric) = 1.002079403946671
absolute error = 8e-15
relative error = 7.983399288012720e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0646
y[1] (analytic) = 1.002085854464916
y[1] (numeric) = 1.002085854464925
absolute error = 9e-15
relative error = 8.981266385409394e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0647
y[1] (analytic) = 1.002092314962311
y[1] (numeric) = 1.00209231496232
absolute error = 9e-15
relative error = 8.981208483111152e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0648
y[1] (analytic) = 1.002098785438783
y[1] (numeric) = 1.002098785438792
absolute error = 9e-15
relative error = 8.981150492123612e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0649
y[1] (analytic) = 1.002105265894268
y[1] (numeric) = 1.002105265894276
absolute error = 8e-15
relative error = 7.983193255511821e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 1.002111756328699
y[1] (numeric) = 1.002111756328707
absolute error = 8e-15
relative error = 7.983141550308237e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0651
y[1] (analytic) = 1.002118256742013
y[1] (numeric) = 1.002118256742021
absolute error = 8e-15
relative error = 7.983089766280481e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0652
y[1] (analytic) = 1.002124767134144
y[1] (numeric) = 1.002124767134152
absolute error = 8e-15
relative error = 7.983037903432162e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0653
y[1] (analytic) = 1.002131287505028
y[1] (numeric) = 1.002131287505036
absolute error = 8e-15
relative error = 7.982985961766872e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0654
y[1] (analytic) = 1.002137817854598
y[1] (numeric) = 1.002137817854607
absolute error = 9e-15
relative error = 8.980800683949267e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0655
y[1] (analytic) = 1.002144358182791
y[1] (numeric) = 1.0021443581828
absolute error = 9e-15
relative error = 8.980742072249836e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0656
y[1] (analytic) = 1.00215090848954
y[1] (numeric) = 1.002150908489549
absolute error = 9e-15
relative error = 8.980683371893524e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0657
y[1] (analytic) = 1.00215746877478
y[1] (numeric) = 1.002157468774789
absolute error = 9e-15
relative error = 8.980624582884405e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0658
y[1] (analytic) = 1.002164039038445
y[1] (numeric) = 1.002164039038454
absolute error = 9e-15
relative error = 8.980565705226569e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0659
y[1] (analytic) = 1.00217061928047
y[1] (numeric) = 1.002170619280479
absolute error = 9e-15
relative error = 8.980506738924101e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 1.002177209500788
y[1] (numeric) = 1.002177209500798
absolute error = 1.0e-14
relative error = 9.978275204423452e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0661
y[1] (analytic) = 1.002183809699335
y[1] (numeric) = 1.002183809699344
absolute error = 9e-15
relative error = 8.980388540401674e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0662
y[1] (analytic) = 1.002190419876043
y[1] (numeric) = 1.002190419876052
absolute error = 9e-15
relative error = 8.980329308189929e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0663
y[1] (analytic) = 1.002197040030847
y[1] (numeric) = 1.002197040030856
absolute error = 9e-15
relative error = 8.980269987349978e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0664
y[1] (analytic) = 1.002203670163681
y[1] (numeric) = 1.00220367016369
absolute error = 9e-15
relative error = 8.980210577885940e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0665
y[1] (analytic) = 1.002210310274478
y[1] (numeric) = 1.002210310274487
absolute error = 9e-15
relative error = 8.980151079801949e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.3MB, time=7.13
NO POLE
x[1] = 0.0666
y[1] (analytic) = 1.002216960363172
y[1] (numeric) = 1.002216960363181
absolute error = 9e-15
relative error = 8.980091493102135e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0667
y[1] (analytic) = 1.002223620429696
y[1] (numeric) = 1.002223620429705
absolute error = 9e-15
relative error = 8.980031817790641e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0668
y[1] (analytic) = 1.002230290473984
y[1] (numeric) = 1.002230290473993
absolute error = 9e-15
relative error = 8.979972053871608e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0669
y[1] (analytic) = 1.002236970495969
y[1] (numeric) = 1.002236970495978
absolute error = 9e-15
relative error = 8.979912201349190e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 1.002243660495585
y[1] (numeric) = 1.002243660495593
absolute error = 8e-15
relative error = 7.982090897980034e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0671
y[1] (analytic) = 1.002250360472764
y[1] (numeric) = 1.002250360472772
absolute error = 8e-15
relative error = 7.982037538231845e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0672
y[1] (analytic) = 1.002257070427439
y[1] (numeric) = 1.002257070427447
absolute error = 8e-15
relative error = 7.981984099736197e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0673
y[1] (analytic) = 1.002263790359544
y[1] (numeric) = 1.002263790359552
absolute error = 8e-15
relative error = 7.981930582496794e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0674
y[1] (analytic) = 1.00227052026901
y[1] (numeric) = 1.002270520269019
absolute error = 9e-15
relative error = 8.979611609832039e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0675
y[1] (analytic) = 1.002277260155772
y[1] (numeric) = 1.00227726015578
absolute error = 8e-15
relative error = 7.981823311801622e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0676
y[1] (analytic) = 1.00228401001976
y[1] (numeric) = 1.002284010019769
absolute error = 9e-15
relative error = 8.979490753147469e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0677
y[1] (analytic) = 1.002290769860909
y[1] (numeric) = 1.002290769860918
absolute error = 9e-15
relative error = 8.979430191948149e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0678
y[1] (analytic) = 1.00229753967915
y[1] (numeric) = 1.002297539679159
absolute error = 9e-15
relative error = 8.979369542183083e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0679
y[1] (analytic) = 1.002304319474416
y[1] (numeric) = 1.002304319474425
absolute error = 9e-15
relative error = 8.979308803856478e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 1.002311109246638
y[1] (numeric) = 1.002311109246647
absolute error = 9e-15
relative error = 8.979247976972563e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0681
y[1] (analytic) = 1.002317908995749
y[1] (numeric) = 1.002317908995758
absolute error = 9e-15
relative error = 8.979187061535554e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0682
y[1] (analytic) = 1.002324718721681
y[1] (numeric) = 1.00232471872169
absolute error = 9e-15
relative error = 8.979126057549681e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0683
y[1] (analytic) = 1.002331538424366
y[1] (numeric) = 1.002331538424375
absolute error = 9e-15
relative error = 8.979064965019179e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0684
y[1] (analytic) = 1.002338368103736
y[1] (numeric) = 1.002338368103745
absolute error = 9e-15
relative error = 8.979003783948290e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0685
y[1] (analytic) = 1.002345207759722
y[1] (numeric) = 1.002345207759731
absolute error = 9e-15
relative error = 8.978942514341269e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0686
y[1] (analytic) = 1.002352057392256
y[1] (numeric) = 1.002352057392265
absolute error = 9e-15
relative error = 8.978881156202366e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0687
y[1] (analytic) = 1.002358917001269
y[1] (numeric) = 1.002358917001278
absolute error = 9e-15
relative error = 8.978819709535847e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0688
y[1] (analytic) = 1.002365786586693
y[1] (numeric) = 1.002365786586702
absolute error = 9e-15
relative error = 8.978758174345972e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0689
y[1] (analytic) = 1.002372666148459
y[1] (numeric) = 1.002372666148468
absolute error = 9e-15
relative error = 8.978696550637018e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.3MB, time=7.39
x[1] = 0.069
y[1] (analytic) = 1.002379555686499
y[1] (numeric) = 1.002379555686508
absolute error = 9e-15
relative error = 8.978634838413256e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0691
y[1] (analytic) = 1.002386455200742
y[1] (numeric) = 1.002386455200752
absolute error = 1.0e-14
relative error = 9.976192264087766e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0692
y[1] (analytic) = 1.002393364691122
y[1] (numeric) = 1.002393364691131
absolute error = 9e-15
relative error = 8.978511148438482e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0693
y[1] (analytic) = 1.002400284157568
y[1] (numeric) = 1.002400284157577
absolute error = 9e-15
relative error = 8.978449170696049e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0694
y[1] (analytic) = 1.00240721360001
y[1] (numeric) = 1.00240721360002
absolute error = 1.0e-14
relative error = 9.975985671617777e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0695
y[1] (analytic) = 1.002414153018381
y[1] (numeric) = 1.002414153018391
absolute error = 1.0e-14
relative error = 9.975916610802913e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0696
y[1] (analytic) = 1.00242110241261
y[1] (numeric) = 1.00242110241262
absolute error = 1.0e-14
relative error = 9.975847451666940e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0697
y[1] (analytic) = 1.002428061782629
y[1] (numeric) = 1.002428061782638
absolute error = 9e-15
relative error = 8.978200374793179e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0698
y[1] (analytic) = 1.002435031128366
y[1] (numeric) = 1.002435031128376
absolute error = 1.0e-14
relative error = 9.975708838450856e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0699
y[1] (analytic) = 1.002442010449753
y[1] (numeric) = 1.002442010449763
absolute error = 1.0e-14
relative error = 9.975639384380376e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 1.00244899974672
y[1] (numeric) = 1.00244899974673
absolute error = 1.0e-14
relative error = 9.975569832008025e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0701
y[1] (analytic) = 1.002455999019198
y[1] (numeric) = 1.002455999019207
absolute error = 9e-15
relative error = 8.977950163204761e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0702
y[1] (analytic) = 1.002463008267115
y[1] (numeric) = 1.002463008267124
absolute error = 9e-15
relative error = 8.977887389139322e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0703
y[1] (analytic) = 1.002470027490402
y[1] (numeric) = 1.002470027490411
absolute error = 9e-15
relative error = 8.977824526615255e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0704
y[1] (analytic) = 1.002477056688988
y[1] (numeric) = 1.002477056688998
absolute error = 1.0e-14
relative error = 9.975290639596588e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0705
y[1] (analytic) = 1.002484095862804
y[1] (numeric) = 1.002484095862814
absolute error = 1.0e-14
relative error = 9.975220595787447e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0706
y[1] (analytic) = 1.00249114501178
y[1] (numeric) = 1.002491145011789
absolute error = 9e-15
relative error = 8.977635408334947e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0707
y[1] (analytic) = 1.002498204135843
y[1] (numeric) = 1.002498204135853
absolute error = 1.0e-14
relative error = 9.975080213355629e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0708
y[1] (analytic) = 1.002505273234925
y[1] (numeric) = 1.002505273234935
absolute error = 1.0e-14
relative error = 9.975009874742695e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0709
y[1] (analytic) = 1.002512352308954
y[1] (numeric) = 1.002512352308964
absolute error = 1.0e-14
relative error = 9.974939437871587e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 1.002519441357859
y[1] (numeric) = 1.002519441357869
absolute error = 1.0e-14
relative error = 9.974868902747197e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0711
y[1] (analytic) = 1.00252654038157
y[1] (numeric) = 1.00252654038158
absolute error = 1.0e-14
relative error = 9.974798269374411e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0712
y[1] (analytic) = 1.002533649380016
y[1] (numeric) = 1.002533649380026
absolute error = 1.0e-14
relative error = 9.974727537758131e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0713
y[1] (analytic) = 1.002540768353125
y[1] (numeric) = 1.002540768353135
absolute error = 1.0e-14
relative error = 9.974656707903273e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=114.4MB, alloc=4.3MB, time=7.66
x[1] = 0.0714
y[1] (analytic) = 1.002547897300826
y[1] (numeric) = 1.002547897300836
absolute error = 1.0e-14
relative error = 9.974585779814753e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0715
y[1] (analytic) = 1.002555036223049
y[1] (numeric) = 1.002555036223058
absolute error = 9e-15
relative error = 8.977063278147730e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0716
y[1] (analytic) = 1.002562185119721
y[1] (numeric) = 1.00256218511973
absolute error = 9e-15
relative error = 8.976999266060753e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0717
y[1] (analytic) = 1.002569343990771
y[1] (numeric) = 1.00256934399078
absolute error = 9e-15
relative error = 8.976935165576784e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0718
y[1] (analytic) = 1.002576512836128
y[1] (numeric) = 1.002576512836137
absolute error = 9e-15
relative error = 8.976870976700267e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0719
y[1] (analytic) = 1.002583691655719
y[1] (numeric) = 1.002583691655729
absolute error = 1.0e-14
relative error = 9.974229666039628e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 1.002590880449474
y[1] (numeric) = 1.002590880449484
absolute error = 1.0e-14
relative error = 9.974158148652694e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0721
y[1] (analytic) = 1.00259807921732
y[1] (numeric) = 1.00259807921733
absolute error = 1.0e-14
relative error = 9.974086533066688e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0722
y[1] (analytic) = 1.002605287959185
y[1] (numeric) = 1.002605287959195
absolute error = 1.0e-14
relative error = 9.974014819286580e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0723
y[1] (analytic) = 1.002612506674997
y[1] (numeric) = 1.002612506675007
absolute error = 1.0e-14
relative error = 9.973943007317344e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0724
y[1] (analytic) = 1.002619735364684
y[1] (numeric) = 1.002619735364694
absolute error = 1.0e-14
relative error = 9.973871097163960e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0725
y[1] (analytic) = 1.002626974028174
y[1] (numeric) = 1.002626974028184
absolute error = 1.0e-14
relative error = 9.973799088831414e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0726
y[1] (analytic) = 1.002634222665394
y[1] (numeric) = 1.002634222665404
absolute error = 1.0e-14
relative error = 9.973726982324709e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0727
y[1] (analytic) = 1.002641481276271
y[1] (numeric) = 1.002641481276282
absolute error = 1.1e-14
relative error = 1.097102025541373e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0728
y[1] (analytic) = 1.002648749860734
y[1] (numeric) = 1.002648749860745
absolute error = 1.1e-14
relative error = 1.097094072228971e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0729
y[1] (analytic) = 1.00265602841871
y[1] (numeric) = 1.00265602841872
absolute error = 1.0e-14
relative error = 9.973510073809671e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 1.002663316950125
y[1] (numeric) = 1.002663316950135
absolute error = 1.0e-14
relative error = 9.973437574656404e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0731
y[1] (analytic) = 1.002670615454907
y[1] (numeric) = 1.002670615454917
absolute error = 1.0e-14
relative error = 9.973364977354050e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0732
y[1] (analytic) = 1.002677923932982
y[1] (numeric) = 1.002677923932993
absolute error = 1.1e-14
relative error = 1.097062151009842e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0733
y[1] (analytic) = 1.002685242384279
y[1] (numeric) = 1.00268524238429
absolute error = 1.1e-14
relative error = 1.097054143715446e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0734
y[1] (analytic) = 1.002692570808723
y[1] (numeric) = 1.002692570808734
absolute error = 1.1e-14
relative error = 1.097046125626316e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0735
y[1] (analytic) = 1.002699909206241
y[1] (numeric) = 1.002699909206252
absolute error = 1.1e-14
relative error = 1.097038096743006e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0736
y[1] (analytic) = 1.002707257576761
y[1] (numeric) = 1.002707257576771
absolute error = 1.0e-14
relative error = 9.973000518782485e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0737
y[1] (analytic) = 1.002714615920207
y[1] (numeric) = 1.002714615920218
absolute error = 1.1e-14
relative error = 1.097022006596077e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0738
y[1] (analytic) = 1.002721984236508
y[1] (numeric) = 1.002721984236519
absolute error = 1.1e-14
relative error = 1.097013945333573e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=7.93
NO POLE
x[1] = 0.0739
y[1] (analytic) = 1.002729362525589
y[1] (numeric) = 1.0027293625256
absolute error = 1.1e-14
relative error = 1.097005873279121e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 1.002736750787376
y[1] (numeric) = 1.002736750787387
absolute error = 1.1e-14
relative error = 1.096997790433282e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0741
y[1] (analytic) = 1.002744149021795
y[1] (numeric) = 1.002744149021807
absolute error = 1.2e-14
relative error = 1.196716032869036e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0742
y[1] (analytic) = 1.002751557228773
y[1] (numeric) = 1.002751557228785
absolute error = 1.2e-14
relative error = 1.196707191676019e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0743
y[1] (analytic) = 1.002758975408236
y[1] (numeric) = 1.002758975408247
absolute error = 1.1e-14
relative error = 1.096973477153048e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0744
y[1] (analytic) = 1.002766403560108
y[1] (numeric) = 1.00276640356012
absolute error = 1.2e-14
relative error = 1.196689473978841e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0745
y[1] (analytic) = 1.002773841684317
y[1] (numeric) = 1.002773841684329
absolute error = 1.2e-14
relative error = 1.196680597475908e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0746
y[1] (analytic) = 1.002781289780787
y[1] (numeric) = 1.002781289780799
absolute error = 1.2e-14
relative error = 1.196671709204233e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0747
y[1] (analytic) = 1.002788747849444
y[1] (numeric) = 1.002788747849456
absolute error = 1.2e-14
relative error = 1.196662809164433e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0748
y[1] (analytic) = 1.002796215890214
y[1] (numeric) = 1.002796215890226
absolute error = 1.2e-14
relative error = 1.196653897357123e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0749
y[1] (analytic) = 1.002803693903022
y[1] (numeric) = 1.002803693903034
absolute error = 1.2e-14
relative error = 1.196644973782923e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 1.002811181887793
y[1] (numeric) = 1.002811181887805
absolute error = 1.2e-14
relative error = 1.196636038442450e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0751
y[1] (analytic) = 1.002818679844451
y[1] (numeric) = 1.002818679844464
absolute error = 1.3e-14
relative error = 1.296346015614353e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0752
y[1] (analytic) = 1.002826187772924
y[1] (numeric) = 1.002826187772936
absolute error = 1.2e-14
relative error = 1.196618132465168e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0753
y[1] (analytic) = 1.002833705673134
y[1] (numeric) = 1.002833705673146
absolute error = 1.2e-14
relative error = 1.196609161829599e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0754
y[1] (analytic) = 1.002841233545007
y[1] (numeric) = 1.002841233545019
absolute error = 1.2e-14
relative error = 1.196600179430241e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0755
y[1] (analytic) = 1.002848771388468
y[1] (numeric) = 1.00284877138848
absolute error = 1.2e-14
relative error = 1.196591185267716e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0756
y[1] (analytic) = 1.002856319203441
y[1] (numeric) = 1.002856319203453
absolute error = 1.2e-14
relative error = 1.196582179342648e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0757
y[1] (analytic) = 1.00286387698985
y[1] (numeric) = 1.002863876989863
absolute error = 1.3e-14
relative error = 1.296287591793634e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0758
y[1] (analytic) = 1.002871444747622
y[1] (numeric) = 1.002871444747634
absolute error = 1.2e-14
relative error = 1.196564132207380e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0759
y[1] (analytic) = 1.002879022476678
y[1] (numeric) = 1.002879022476691
absolute error = 1.3e-14
relative error = 1.296268015248301e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 1.002886610176944
y[1] (numeric) = 1.002886610176957
absolute error = 1.3e-14
relative error = 1.296258207865229e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0761
y[1] (analytic) = 1.002894207848345
y[1] (numeric) = 1.002894207848357
absolute error = 1.2e-14
relative error = 1.196536973301037e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0762
y[1] (analytic) = 1.002901815490803
y[1] (numeric) = 1.002901815490815
absolute error = 1.2e-14
relative error = 1.196527896813848e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.3MB, time=8.19
NO POLE
x[1] = 0.0763
y[1] (analytic) = 1.002909433104243
y[1] (numeric) = 1.002909433104255
absolute error = 1.2e-14
relative error = 1.196518808568501e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0764
y[1] (analytic) = 1.002917060688589
y[1] (numeric) = 1.002917060688601
absolute error = 1.2e-14
relative error = 1.196509708565628e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0765
y[1] (analytic) = 1.002924698243764
y[1] (numeric) = 1.002924698243776
absolute error = 1.2e-14
relative error = 1.196500596805859e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0766
y[1] (analytic) = 1.002932345769692
y[1] (numeric) = 1.002932345769704
absolute error = 1.2e-14
relative error = 1.196491473289826e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0767
y[1] (analytic) = 1.002940003266296
y[1] (numeric) = 1.002940003266309
absolute error = 1.3e-14
relative error = 1.296189199519675e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0768
y[1] (analytic) = 1.002947670733501
y[1] (numeric) = 1.002947670733514
absolute error = 1.3e-14
relative error = 1.296179290240787e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0769
y[1] (analytic) = 1.002955348171229
y[1] (numeric) = 1.002955348171242
absolute error = 1.3e-14
relative error = 1.296169368228004e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 1.002963035579403
y[1] (numeric) = 1.002963035579416
absolute error = 1.3e-14
relative error = 1.296159433482014e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0771
y[1] (analytic) = 1.002970732957947
y[1] (numeric) = 1.00297073295796
absolute error = 1.3e-14
relative error = 1.296149486003503e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0772
y[1] (analytic) = 1.002978440306784
y[1] (numeric) = 1.002978440306797
absolute error = 1.3e-14
relative error = 1.296139525793162e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0773
y[1] (analytic) = 1.002986157625836
y[1] (numeric) = 1.002986157625849
absolute error = 1.3e-14
relative error = 1.296129552851681e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0774
y[1] (analytic) = 1.002993884915027
y[1] (numeric) = 1.00299388491504
absolute error = 1.3e-14
relative error = 1.296119567179749e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0775
y[1] (analytic) = 1.003001622174279
y[1] (numeric) = 1.003001622174292
absolute error = 1.3e-14
relative error = 1.296109568778061e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0776
y[1] (analytic) = 1.003009369403514
y[1] (numeric) = 1.003009369403528
absolute error = 1.4e-14
relative error = 1.395799523620178e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0777
y[1] (analytic) = 1.003017126602656
y[1] (numeric) = 1.00301712660267
absolute error = 1.4e-14
relative error = 1.395788728694967e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0778
y[1] (analytic) = 1.003024893771627
y[1] (numeric) = 1.003024893771641
absolute error = 1.4e-14
relative error = 1.395777920063027e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0779
y[1] (analytic) = 1.003032670910348
y[1] (numeric) = 1.003032670910363
absolute error = 1.5e-14
relative error = 1.495464747562616e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 1.003040458018743
y[1] (numeric) = 1.003040458018758
absolute error = 1.5e-14
relative error = 1.495453137516384e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0781
y[1] (analytic) = 1.003048255096734
y[1] (numeric) = 1.003048255096748
absolute error = 1.4e-14
relative error = 1.395745411934328e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0782
y[1] (analytic) = 1.003056062144241
y[1] (numeric) = 1.003056062144256
absolute error = 1.5e-14
relative error = 1.495429873374613e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0783
y[1] (analytic) = 1.003063879161188
y[1] (numeric) = 1.003063879161203
absolute error = 1.5e-14
relative error = 1.495418219280685e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0784
y[1] (analytic) = 1.003071706147497
y[1] (numeric) = 1.003071706147511
absolute error = 1.4e-14
relative error = 1.395712780472084e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0785
y[1] (analytic) = 1.003079543103088
y[1] (numeric) = 1.003079543103102
absolute error = 1.4e-14
relative error = 1.395701875914062e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0786
y[1] (analytic) = 1.003087390027884
y[1] (numeric) = 1.003087390027898
absolute error = 1.4e-14
relative error = 1.395690957655327e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.3MB, time=8.46
NO POLE
x[1] = 0.0787
y[1] (analytic) = 1.003095246921806
y[1] (numeric) = 1.00309524692182
absolute error = 1.4e-14
relative error = 1.395680025696636e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0788
y[1] (analytic) = 1.003103113784776
y[1] (numeric) = 1.003103113784789
absolute error = 1.3e-14
relative error = 1.295978431464550e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0789
y[1] (analytic) = 1.003110990616714
y[1] (numeric) = 1.003110990616727
absolute error = 1.3e-14
relative error = 1.295968254919387e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 1.003118877417542
y[1] (numeric) = 1.003118877417555
absolute error = 1.3e-14
relative error = 1.295958065654947e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0791
y[1] (analytic) = 1.003126774187182
y[1] (numeric) = 1.003126774187195
absolute error = 1.3e-14
relative error = 1.295947863671937e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0792
y[1] (analytic) = 1.003134680925554
y[1] (numeric) = 1.003134680925567
absolute error = 1.3e-14
relative error = 1.295937648971063e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0793
y[1] (analytic) = 1.003142597632579
y[1] (numeric) = 1.003142597632592
absolute error = 1.3e-14
relative error = 1.295927421553033e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0794
y[1] (analytic) = 1.003150524308178
y[1] (numeric) = 1.003150524308191
absolute error = 1.3e-14
relative error = 1.295917181418555e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0795
y[1] (analytic) = 1.003158460952272
y[1] (numeric) = 1.003158460952285
absolute error = 1.3e-14
relative error = 1.295906928568338e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0796
y[1] (analytic) = 1.003166407564781
y[1] (numeric) = 1.003166407564794
absolute error = 1.3e-14
relative error = 1.295896663003093e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0797
y[1] (analytic) = 1.003174364145626
y[1] (numeric) = 1.003174364145639
absolute error = 1.3e-14
relative error = 1.295886384723529e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0798
y[1] (analytic) = 1.003182330694727
y[1] (numeric) = 1.00318233069474
absolute error = 1.3e-14
relative error = 1.295876093730359e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0799
y[1] (analytic) = 1.003190307212006
y[1] (numeric) = 1.003190307212018
absolute error = 1.2e-14
relative error = 1.196183806176271e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 1.003198293697381
y[1] (numeric) = 1.003198293697393
absolute error = 1.2e-14
relative error = 1.196174283328661e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0801
y[1] (analytic) = 1.003206290150773
y[1] (numeric) = 1.003206290150785
absolute error = 1.2e-14
relative error = 1.196164748747389e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0802
y[1] (analytic) = 1.003214296572102
y[1] (numeric) = 1.003214296572114
absolute error = 1.2e-14
relative error = 1.196155202433117e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0803
y[1] (analytic) = 1.003222312961288
y[1] (numeric) = 1.0032223129613
absolute error = 1.2e-14
relative error = 1.196145644386505e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0804
y[1] (analytic) = 1.003230339318251
y[1] (numeric) = 1.003230339318263
absolute error = 1.2e-14
relative error = 1.196136074608215e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0805
y[1] (analytic) = 1.003238375642911
y[1] (numeric) = 1.003238375642923
absolute error = 1.2e-14
relative error = 1.196126493098908e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0806
y[1] (analytic) = 1.003246421935187
y[1] (numeric) = 1.003246421935199
absolute error = 1.2e-14
relative error = 1.196116899859249e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0807
y[1] (analytic) = 1.003254478194999
y[1] (numeric) = 1.003254478195011
absolute error = 1.2e-14
relative error = 1.196107294889902e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0808
y[1] (analytic) = 1.003262544422266
y[1] (numeric) = 1.003262544422278
absolute error = 1.2e-14
relative error = 1.196097678191531e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0809
y[1] (analytic) = 1.003270620616907
y[1] (numeric) = 1.003270620616919
absolute error = 1.2e-14
relative error = 1.196088049764803e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 1.003278706778842
y[1] (numeric) = 1.003278706778854
absolute error = 1.2e-14
relative error = 1.196078409610384e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.3MB, time=8.73
NO POLE
x[1] = 0.0811
y[1] (analytic) = 1.00328680290799
y[1] (numeric) = 1.003286802908002
absolute error = 1.2e-14
relative error = 1.196068757728941e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0812
y[1] (analytic) = 1.003294909004271
y[1] (numeric) = 1.003294909004282
absolute error = 1.1e-14
relative error = 1.096387502944378e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0813
y[1] (analytic) = 1.003303025067602
y[1] (numeric) = 1.003303025067613
absolute error = 1.1e-14
relative error = 1.096378633888682e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0814
y[1] (analytic) = 1.003311151097902
y[1] (numeric) = 1.003311151097914
absolute error = 1.2e-14
relative error = 1.196039731729151e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0815
y[1] (analytic) = 1.003319287095092
y[1] (numeric) = 1.003319287095103
absolute error = 1.1e-14
relative error = 1.096360863534107e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0816
y[1] (analytic) = 1.003327433059088
y[1] (numeric) = 1.003327433059099
absolute error = 1.1e-14
relative error = 1.096351962236458e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0817
y[1] (analytic) = 1.00333558898981
y[1] (numeric) = 1.003335588989821
absolute error = 1.1e-14
relative error = 1.096343050192722e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0818
y[1] (analytic) = 1.003343754887176
y[1] (numeric) = 1.003343754887187
absolute error = 1.1e-14
relative error = 1.096334127403517e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0819
y[1] (analytic) = 1.003351930751105
y[1] (numeric) = 1.003351930751116
absolute error = 1.1e-14
relative error = 1.096325193869458e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 1.003360116581514
y[1] (numeric) = 1.003360116581525
absolute error = 1.1e-14
relative error = 1.096316249591165e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0821
y[1] (analytic) = 1.003368312378322
y[1] (numeric) = 1.003368312378333
absolute error = 1.1e-14
relative error = 1.096307294569258e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0822
y[1] (analytic) = 1.003376518141447
y[1] (numeric) = 1.003376518141458
absolute error = 1.1e-14
relative error = 1.096298328804354e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0823
y[1] (analytic) = 1.003384733870807
y[1] (numeric) = 1.003384733870818
absolute error = 1.1e-14
relative error = 1.096289352297075e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0824
y[1] (analytic) = 1.003392959566319
y[1] (numeric) = 1.00339295956633
absolute error = 1.1e-14
relative error = 1.096280365048043e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0825
y[1] (analytic) = 1.003401195227902
y[1] (numeric) = 1.003401195227913
absolute error = 1.1e-14
relative error = 1.096271367057877e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0826
y[1] (analytic) = 1.003409440855473
y[1] (numeric) = 1.003409440855484
absolute error = 1.1e-14
relative error = 1.096262358327202e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0827
y[1] (analytic) = 1.00341769644895
y[1] (numeric) = 1.00341769644896
absolute error = 1.0e-14
relative error = 9.965939444151273e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0828
y[1] (analytic) = 1.003425962008249
y[1] (numeric) = 1.003425962008259
absolute error = 1.0e-14
relative error = 9.965857351334698e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0829
y[1] (analytic) = 1.003434237533289
y[1] (numeric) = 1.003434237533299
absolute error = 1.0e-14
relative error = 9.965775160894138e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 1.003442523023986
y[1] (numeric) = 1.003442523023996
absolute error = 1.0e-14
relative error = 9.965692872835291e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0831
y[1] (analytic) = 1.003450818480259
y[1] (numeric) = 1.003450818480268
absolute error = 9e-15
relative error = 8.969049438447449e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0832
y[1] (analytic) = 1.003459123902023
y[1] (numeric) = 1.003459123902032
absolute error = 9e-15
relative error = 8.968975203496932e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0833
y[1] (analytic) = 1.003467439289195
y[1] (numeric) = 1.003467439289205
absolute error = 1.0e-14
relative error = 9.965445423005941e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0834
y[1] (analytic) = 1.003475764641694
y[1] (numeric) = 1.003475764641703
absolute error = 9e-15
relative error = 8.968826470077814e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=133.5MB, alloc=4.3MB, time=9.00
x[1] = 0.0835
y[1] (analytic) = 1.003484099959434
y[1] (numeric) = 1.003484099959444
absolute error = 1.0e-14
relative error = 9.965279968466119e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0836
y[1] (analytic) = 1.003492445242334
y[1] (numeric) = 1.003492445242344
absolute error = 1.0e-14
relative error = 9.965197094817285e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0837
y[1] (analytic) = 1.00350080049031
y[1] (numeric) = 1.003500800490319
absolute error = 9e-15
relative error = 8.968602711231126e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0838
y[1] (analytic) = 1.003509165703277
y[1] (numeric) = 1.003509165703286
absolute error = 9e-15
relative error = 8.968527949311395e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0839
y[1] (analytic) = 1.003517540881152
y[1] (numeric) = 1.003517540881162
absolute error = 1.0e-14
relative error = 9.964947888423920e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 1.003525926023852
y[1] (numeric) = 1.003525926023862
absolute error = 1.0e-14
relative error = 9.964864624496326e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0841
y[1] (analytic) = 1.003534321131293
y[1] (numeric) = 1.003534321131303
absolute error = 1.0e-14
relative error = 9.964781263013419e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0842
y[1] (analytic) = 1.003542726203391
y[1] (numeric) = 1.003542726203401
absolute error = 1.0e-14
relative error = 9.964697803980964e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0843
y[1] (analytic) = 1.003551141240061
y[1] (numeric) = 1.003551141240071
absolute error = 1.0e-14
relative error = 9.964614247404742e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0844
y[1] (analytic) = 1.00355956624122
y[1] (numeric) = 1.00355956624123
absolute error = 1.0e-14
relative error = 9.964530593290519e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0845
y[1] (analytic) = 1.003568001206784
y[1] (numeric) = 1.003568001206793
absolute error = 9e-15
relative error = 8.968002157479671e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0846
y[1] (analytic) = 1.003576446136667
y[1] (numeric) = 1.003576446136676
absolute error = 9e-15
relative error = 8.967926693224106e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0847
y[1] (analytic) = 1.003584901030786
y[1] (numeric) = 1.003584901030795
absolute error = 9e-15
relative error = 8.967851141199977e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0848
y[1] (analytic) = 1.003593365889056
y[1] (numeric) = 1.003593365889065
absolute error = 9e-15
relative error = 8.967775501412512e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0849
y[1] (analytic) = 1.003601840711392
y[1] (numeric) = 1.003601840711401
absolute error = 9e-15
relative error = 8.967699773866945e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 1.00361032549771
y[1] (numeric) = 1.003610325497719
absolute error = 9e-15
relative error = 8.967623958568505e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0851
y[1] (analytic) = 1.003618820247924
y[1] (numeric) = 1.003618820247933
absolute error = 9e-15
relative error = 8.967548055522444e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0852
y[1] (analytic) = 1.00362732496195
y[1] (numeric) = 1.003627324961959
absolute error = 9e-15
relative error = 8.967472064734001e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0853
y[1] (analytic) = 1.003635839639703
y[1] (numeric) = 1.003635839639712
absolute error = 9e-15
relative error = 8.967395986208430e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0854
y[1] (analytic) = 1.003644364281098
y[1] (numeric) = 1.003644364281107
absolute error = 9e-15
relative error = 8.967319819950988e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0855
y[1] (analytic) = 1.003652898886049
y[1] (numeric) = 1.003652898886058
absolute error = 9e-15
relative error = 8.967243565966949e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0856
y[1] (analytic) = 1.003661443454471
y[1] (numeric) = 1.00366144345448
absolute error = 9e-15
relative error = 8.967167224261581e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0857
y[1] (analytic) = 1.003669997986278
y[1] (numeric) = 1.003669997986287
absolute error = 9e-15
relative error = 8.967090794840165e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0858
y[1] (analytic) = 1.003678562481386
y[1] (numeric) = 1.003678562481395
absolute error = 9e-15
relative error = 8.967014277707971e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=137.3MB, alloc=4.3MB, time=9.27
x[1] = 0.0859
y[1] (analytic) = 1.003687136939708
y[1] (numeric) = 1.003687136939717
absolute error = 9e-15
relative error = 8.966937672870301e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 1.003695721361158
y[1] (numeric) = 1.003695721361167
absolute error = 9e-15
relative error = 8.966860980332451e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0861
y[1] (analytic) = 1.003704315745651
y[1] (numeric) = 1.00370431574566
absolute error = 9e-15
relative error = 8.966784200099716e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0862
y[1] (analytic) = 1.003712920093102
y[1] (numeric) = 1.00371292009311
absolute error = 8e-15
relative error = 7.970406517491016e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0863
y[1] (analytic) = 1.003721534403422
y[1] (numeric) = 1.003721534403431
absolute error = 9e-15
relative error = 8.966630376570823e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0864
y[1] (analytic) = 1.003730158676528
y[1] (numeric) = 1.003730158676537
absolute error = 9e-15
relative error = 8.966553333285295e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0865
y[1] (analytic) = 1.003738792912332
y[1] (numeric) = 1.003738792912341
absolute error = 9e-15
relative error = 8.966476202326149e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0866
y[1] (analytic) = 1.003747437110748
y[1] (numeric) = 1.003747437110757
absolute error = 9e-15
relative error = 8.966398983698714e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0867
y[1] (analytic) = 1.00375609127169
y[1] (numeric) = 1.003756091271699
absolute error = 9e-15
relative error = 8.966321677408322e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0868
y[1] (analytic) = 1.00376475539507
y[1] (numeric) = 1.00376475539508
absolute error = 1.0e-14
relative error = 9.962493648289252e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0869
y[1] (analytic) = 1.003773429480803
y[1] (numeric) = 1.003773429480813
absolute error = 1.0e-14
relative error = 9.962407557622293e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 1.003782113528802
y[1] (numeric) = 1.003782113528812
absolute error = 1.0e-14
relative error = 9.962321369569876e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0871
y[1] (analytic) = 1.00379080753898
y[1] (numeric) = 1.00379080753899
absolute error = 1.0e-14
relative error = 9.962235084137959e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0872
y[1] (analytic) = 1.00379951151125
y[1] (numeric) = 1.00379951151126
absolute error = 1.0e-14
relative error = 9.962148701332503e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0873
y[1] (analytic) = 1.003808225445524
y[1] (numeric) = 1.003808225445534
absolute error = 1.0e-14
relative error = 9.962062221159487e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0874
y[1] (analytic) = 1.003816949341716
y[1] (numeric) = 1.003816949341726
absolute error = 1.0e-14
relative error = 9.961975643624875e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0875
y[1] (analytic) = 1.003825683199739
y[1] (numeric) = 1.003825683199749
absolute error = 1.0e-14
relative error = 9.961888968734647e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0876
y[1] (analytic) = 1.003834427019505
y[1] (numeric) = 1.003834427019515
absolute error = 1.0e-14
relative error = 9.961802196494796e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0877
y[1] (analytic) = 1.003843180800926
y[1] (numeric) = 1.003843180800937
absolute error = 1.1e-14
relative error = 1.095788685960246e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0878
y[1] (analytic) = 1.003851944543916
y[1] (numeric) = 1.003851944543927
absolute error = 1.1e-14
relative error = 1.095779119598924e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0879
y[1] (analytic) = 1.003860718248387
y[1] (numeric) = 1.003860718248397
absolute error = 1.0e-14
relative error = 9.961541295737486e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 1.00386950191425
y[1] (numeric) = 1.00386950191426
absolute error = 1.0e-14
relative error = 9.961454134159158e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0881
y[1] (analytic) = 1.003878295541418
y[1] (numeric) = 1.003878295541428
absolute error = 1.0e-14
relative error = 9.961366875261245e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0882
y[1] (analytic) = 1.003887099129803
y[1] (numeric) = 1.003887099129813
absolute error = 1.0e-14
relative error = 9.961279519049777e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0883
y[1] (analytic) = 1.003895912679317
y[1] (numeric) = 1.003895912679327
absolute error = 1.0e-14
relative error = 9.961192065530787e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.3MB, time=9.54
NO POLE
x[1] = 0.0884
y[1] (analytic) = 1.003904736189872
y[1] (numeric) = 1.003904736189882
absolute error = 1.0e-14
relative error = 9.961104514710313e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0885
y[1] (analytic) = 1.00391356966138
y[1] (numeric) = 1.00391356966139
absolute error = 1.0e-14
relative error = 9.961016866594402e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0886
y[1] (analytic) = 1.003922413093752
y[1] (numeric) = 1.003922413093762
absolute error = 1.0e-14
relative error = 9.960929121189112e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0887
y[1] (analytic) = 1.0039312664869
y[1] (numeric) = 1.00393126648691
absolute error = 1.0e-14
relative error = 9.960841278500501e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0888
y[1] (analytic) = 1.003940129840735
y[1] (numeric) = 1.003940129840745
absolute error = 1.0e-14
relative error = 9.960753338534639e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0889
y[1] (analytic) = 1.003949003155169
y[1] (numeric) = 1.003949003155179
absolute error = 1.0e-14
relative error = 9.960665301297593e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 1.003957886430112
y[1] (numeric) = 1.003957886430123
absolute error = 1.1e-14
relative error = 1.095663488347500e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0891
y[1] (analytic) = 1.003966779665477
y[1] (numeric) = 1.003966779665488
absolute error = 1.1e-14
relative error = 1.095653782853773e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0892
y[1] (analytic) = 1.003975682861174
y[1] (numeric) = 1.003975682861185
absolute error = 1.1e-14
relative error = 1.095644066662224e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0893
y[1] (analytic) = 1.003984596017115
y[1] (numeric) = 1.003984596017125
absolute error = 1.0e-14
relative error = 9.960312179759309e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0894
y[1] (analytic) = 1.003993519133209
y[1] (numeric) = 1.003993519133219
absolute error = 1.0e-14
relative error = 9.960223656257694e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0895
y[1] (analytic) = 1.004002452209368
y[1] (numeric) = 1.004002452209378
absolute error = 1.0e-14
relative error = 9.960135035521473e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0896
y[1] (analytic) = 1.004011395245503
y[1] (numeric) = 1.004011395245513
absolute error = 1.0e-14
relative error = 9.960046317556763e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0897
y[1] (analytic) = 1.004020348241523
y[1] (numeric) = 1.004020348241534
absolute error = 1.1e-14
relative error = 1.095595325260667e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0898
y[1] (analytic) = 1.004029311197341
y[1] (numeric) = 1.004029311197351
absolute error = 1.0e-14
relative error = 9.959868589966403e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0899
y[1] (analytic) = 1.004038284112865
y[1] (numeric) = 1.004038284112875
absolute error = 1.0e-14
relative error = 9.959779580353023e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 1.004047266988006
y[1] (numeric) = 1.004047266988016
absolute error = 1.0e-14
relative error = 9.959690473535701e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0901
y[1] (analytic) = 1.004056259822674
y[1] (numeric) = 1.004056259822684
absolute error = 1.0e-14
relative error = 9.959601269520591e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0902
y[1] (analytic) = 1.00406526261678
y[1] (numeric) = 1.00406526261679
absolute error = 1.0e-14
relative error = 9.959511968313841e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0903
y[1] (analytic) = 1.004074275370233
y[1] (numeric) = 1.004074275370243
absolute error = 1.0e-14
relative error = 9.959422569921626e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0904
y[1] (analytic) = 1.004083298082944
y[1] (numeric) = 1.004083298082953
absolute error = 9e-15
relative error = 8.963399766915095e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0905
y[1] (analytic) = 1.004092330754821
y[1] (numeric) = 1.00409233075483
absolute error = 9e-15
relative error = 8.963319133444928e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0906
y[1] (analytic) = 1.004101373385776
y[1] (numeric) = 1.004101373385784
absolute error = 8e-15
relative error = 7.967323033355117e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0907
y[1] (analytic) = 1.004110425975716
y[1] (numeric) = 1.004110425975724
absolute error = 8e-15
relative error = 7.967251203697268e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.3MB, time=9.81
NO POLE
x[1] = 0.0908
y[1] (analytic) = 1.004119488524552
y[1] (numeric) = 1.00411948852456
absolute error = 8e-15
relative error = 7.967179296315779e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0909
y[1] (analytic) = 1.004128561032193
y[1] (numeric) = 1.004128561032201
absolute error = 8e-15
relative error = 7.967107311215615e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 1.004137643498549
y[1] (numeric) = 1.004137643498557
absolute error = 8e-15
relative error = 7.967035248401740e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0911
y[1] (analytic) = 1.004146735923528
y[1] (numeric) = 1.004146735923536
absolute error = 8e-15
relative error = 7.966963107879135e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0912
y[1] (analytic) = 1.00415583830704
y[1] (numeric) = 1.004155838307048
absolute error = 8e-15
relative error = 7.966890889652773e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0913
y[1] (analytic) = 1.004164950648994
y[1] (numeric) = 1.004164950649001
absolute error = 7e-15
relative error = 6.970966269511682e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0914
y[1] (analytic) = 1.004174072949297
y[1] (numeric) = 1.004174072949305
absolute error = 8e-15
relative error = 7.966746220108730e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0915
y[1] (analytic) = 1.004183205207861
y[1] (numeric) = 1.004183205207868
absolute error = 7e-15
relative error = 6.970839547700894e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0916
y[1] (analytic) = 1.004192347424592
y[1] (numeric) = 1.004192347424599
absolute error = 7e-15
relative error = 6.970776084833341e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0917
y[1] (analytic) = 1.004201499599399
y[1] (numeric) = 1.004201499599407
absolute error = 8e-15
relative error = 7.966528633139265e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0918
y[1] (analytic) = 1.004210661732192
y[1] (numeric) = 1.0042106617322
absolute error = 8e-15
relative error = 7.966455948795215e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0919
y[1] (analytic) = 1.004219833822878
y[1] (numeric) = 1.004219833822886
absolute error = 8e-15
relative error = 7.966383186782409e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 1.004229015871366
y[1] (numeric) = 1.004229015871374
absolute error = 8e-15
relative error = 7.966310347105862e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0921
y[1] (analytic) = 1.004238207877563
y[1] (numeric) = 1.004238207877572
absolute error = 9e-15
relative error = 8.962017108491935e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0922
y[1] (analytic) = 1.004247409841379
y[1] (numeric) = 1.004247409841387
absolute error = 8e-15
relative error = 7.966164434781665e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0923
y[1] (analytic) = 1.00425662176272
y[1] (numeric) = 1.004256621762728
absolute error = 8e-15
relative error = 7.966091362144082e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0924
y[1] (analytic) = 1.004265843641495
y[1] (numeric) = 1.004265843641503
absolute error = 8e-15
relative error = 7.966018211862891e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0925
y[1] (analytic) = 1.004275075477612
y[1] (numeric) = 1.00427507547762
absolute error = 8e-15
relative error = 7.965944983943138e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0926
y[1] (analytic) = 1.004284317270978
y[1] (numeric) = 1.004284317270986
absolute error = 8e-15
relative error = 7.965871678389880e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0927
y[1] (analytic) = 1.0042935690215
y[1] (numeric) = 1.004293569021509
absolute error = 9e-15
relative error = 8.961523082109199e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0928
y[1] (analytic) = 1.004302830729087
y[1] (numeric) = 1.004302830729096
absolute error = 9e-15
relative error = 8.961440438703464e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0929
y[1] (analytic) = 1.004312102393646
y[1] (numeric) = 1.004312102393655
absolute error = 9e-15
relative error = 8.961357707977114e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 1.004321384015084
y[1] (numeric) = 1.004321384015093
absolute error = 9e-15
relative error = 8.961274889935858e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0931
y[1] (analytic) = 1.004330675593308
y[1] (numeric) = 1.004330675593317
absolute error = 9e-15
relative error = 8.961191984585409e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.3MB, time=10.08
NO POLE
x[1] = 0.0932
y[1] (analytic) = 1.004339977128225
y[1] (numeric) = 1.004339977128234
absolute error = 9e-15
relative error = 8.961108991931486e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0933
y[1] (analytic) = 1.004349288619742
y[1] (numeric) = 1.004349288619751
absolute error = 9e-15
relative error = 8.961025911979813e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0934
y[1] (analytic) = 1.004358610067766
y[1] (numeric) = 1.004358610067775
absolute error = 9e-15
relative error = 8.960942744736118e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0935
y[1] (analytic) = 1.004367941472204
y[1] (numeric) = 1.004367941472213
absolute error = 9e-15
relative error = 8.960859490206136e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0936
y[1] (analytic) = 1.004377282832963
y[1] (numeric) = 1.004377282832972
absolute error = 9e-15
relative error = 8.960776148395604e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0937
y[1] (analytic) = 1.004386634149949
y[1] (numeric) = 1.004386634149958
absolute error = 9e-15
relative error = 8.960692719310274e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0938
y[1] (analytic) = 1.004395995423069
y[1] (numeric) = 1.004395995423078
absolute error = 9e-15
relative error = 8.960609202955896e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0939
y[1] (analytic) = 1.004405366652229
y[1] (numeric) = 1.004405366652238
absolute error = 9e-15
relative error = 8.960525599338231e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 1.004414747837335
y[1] (numeric) = 1.004414747837344
absolute error = 9e-15
relative error = 8.960441908463047e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0941
y[1] (analytic) = 1.004424138978293
y[1] (numeric) = 1.004424138978303
absolute error = 1.0e-14
relative error = 9.955953478151239e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0942
y[1] (analytic) = 1.00443354007501
y[1] (numeric) = 1.00443354007502
absolute error = 1.0e-14
relative error = 9.955860294403561e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0943
y[1] (analytic) = 1.004442951127392
y[1] (numeric) = 1.004442951127402
absolute error = 1.0e-14
relative error = 9.955767013722330e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0944
y[1] (analytic) = 1.004452372135344
y[1] (numeric) = 1.004452372135354
absolute error = 1.0e-14
relative error = 9.955673636113987e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0945
y[1] (analytic) = 1.004461803098773
y[1] (numeric) = 1.004461803098782
absolute error = 9e-15
relative error = 8.960022145426462e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0946
y[1] (analytic) = 1.004471244017583
y[1] (numeric) = 1.004471244017592
absolute error = 9e-15
relative error = 8.959937931127531e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0947
y[1] (analytic) = 1.004480694891681
y[1] (numeric) = 1.00448069489169
absolute error = 9e-15
relative error = 8.959853629611590e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0948
y[1] (analytic) = 1.004490155720972
y[1] (numeric) = 1.004490155720981
absolute error = 9e-15
relative error = 8.959769240884454e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0949
y[1] (analytic) = 1.004499626505362
y[1] (numeric) = 1.00449962650537
absolute error = 8e-15
relative error = 7.964164235512830e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 1.004509107244755
y[1] (numeric) = 1.004509107244763
absolute error = 8e-15
relative error = 7.964089068284325e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0951
y[1] (analytic) = 1.004518597939057
y[1] (numeric) = 1.004518597939065
absolute error = 8e-15
relative error = 7.964013823550284e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0952
y[1] (analytic) = 1.004528098588173
y[1] (numeric) = 1.004528098588181
absolute error = 8e-15
relative error = 7.963938501315895e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0953
y[1] (analytic) = 1.004537609192008
y[1] (numeric) = 1.004537609192016
absolute error = 8e-15
relative error = 7.963863101586348e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0954
y[1] (analytic) = 1.004547129750467
y[1] (numeric) = 1.004547129750475
absolute error = 8e-15
relative error = 7.963787624366841e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0955
y[1] (analytic) = 1.004556660263455
y[1] (numeric) = 1.004556660263463
absolute error = 8e-15
relative error = 7.963712069662572e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.3MB, time=10.34
NO POLE
x[1] = 0.0956
y[1] (analytic) = 1.004566200730876
y[1] (numeric) = 1.004566200730884
absolute error = 8e-15
relative error = 7.963636437478754e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0957
y[1] (analytic) = 1.004575751152635
y[1] (numeric) = 1.004575751152643
absolute error = 8e-15
relative error = 7.963560727820596e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0958
y[1] (analytic) = 1.004585311528637
y[1] (numeric) = 1.004585311528645
absolute error = 8e-15
relative error = 7.963484940693312e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0959
y[1] (analytic) = 1.004594881858785
y[1] (numeric) = 1.004594881858793
absolute error = 8e-15
relative error = 7.963409076102134e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 1.004604462142985
y[1] (numeric) = 1.004604462142993
absolute error = 8e-15
relative error = 7.963333134052278e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0961
y[1] (analytic) = 1.00461405238114
y[1] (numeric) = 1.004614052381148
absolute error = 8e-15
relative error = 7.963257114548985e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0962
y[1] (analytic) = 1.004623652573154
y[1] (numeric) = 1.004623652573162
absolute error = 8e-15
relative error = 7.963181017597494e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0963
y[1] (analytic) = 1.004633262718932
y[1] (numeric) = 1.00463326271894
absolute error = 8e-15
relative error = 7.963104843203041e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0964
y[1] (analytic) = 1.004642882818377
y[1] (numeric) = 1.004642882818385
absolute error = 8e-15
relative error = 7.963028591370879e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0965
y[1] (analytic) = 1.004652512871394
y[1] (numeric) = 1.004652512871401
absolute error = 7e-15
relative error = 6.967583229342973e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0966
y[1] (analytic) = 1.004662152877885
y[1] (numeric) = 1.004662152877892
absolute error = 7e-15
relative error = 6.967516373487634e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0967
y[1] (analytic) = 1.004671802837755
y[1] (numeric) = 1.004671802837762
absolute error = 7e-15
relative error = 6.967449449888098e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0968
y[1] (analytic) = 1.004681462750907
y[1] (numeric) = 1.004681462750914
absolute error = 7e-15
relative error = 6.967382458548980e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0969
y[1] (analytic) = 1.004691132617244
y[1] (numeric) = 1.004691132617251
absolute error = 7e-15
relative error = 6.967315399474897e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 1.00470081243667
y[1] (numeric) = 1.004700812436677
absolute error = 7e-15
relative error = 6.967248272670463e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0971
y[1] (analytic) = 1.004710502209087
y[1] (numeric) = 1.004710502209095
absolute error = 8e-15
relative error = 7.962492660731784e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0972
y[1] (analytic) = 1.0047202019344
y[1] (numeric) = 1.004720201934408
absolute error = 8e-15
relative error = 7.962415789587492e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0973
y[1] (analytic) = 1.00472991161251
y[1] (numeric) = 1.004729911612519
absolute error = 9e-15
relative error = 8.957631196184585e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0974
y[1] (analytic) = 1.004739631243322
y[1] (numeric) = 1.00473963124333
absolute error = 8e-15
relative error = 7.962261815133484e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0975
y[1] (analytic) = 1.004749360826737
y[1] (numeric) = 1.004749360826745
absolute error = 8e-15
relative error = 7.962184711834370e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0976
y[1] (analytic) = 1.004759100362658
y[1] (numeric) = 1.004759100362667
absolute error = 9e-15
relative error = 8.957370972556046e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0977
y[1] (analytic) = 1.004768849850989
y[1] (numeric) = 1.004768849850998
absolute error = 9e-15
relative error = 8.957284057258278e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0978
y[1] (analytic) = 1.004778609291631
y[1] (numeric) = 1.00477860929164
absolute error = 9e-15
relative error = 8.957197054926359e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0979
y[1] (analytic) = 1.004788378684487
y[1] (numeric) = 1.004788378684496
absolute error = 9e-15
relative error = 8.957109965566276e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=156.4MB, alloc=4.3MB, time=10.59
x[1] = 0.098
y[1] (analytic) = 1.004798158029459
y[1] (numeric) = 1.004798158029468
absolute error = 9e-15
relative error = 8.957022789184029e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0981
y[1] (analytic) = 1.00480794732645
y[1] (numeric) = 1.004807947326459
absolute error = 9e-15
relative error = 8.956935525785614e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0982
y[1] (analytic) = 1.00481774657536
y[1] (numeric) = 1.00481774657537
absolute error = 1.0e-14
relative error = 9.952053528196731e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0983
y[1] (analytic) = 1.004827555776094
y[1] (numeric) = 1.004827555776104
absolute error = 1.0e-14
relative error = 9.951956375515942e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0984
y[1] (analytic) = 1.004837374928552
y[1] (numeric) = 1.004837374928562
absolute error = 1.0e-14
relative error = 9.951859126170581e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0985
y[1] (analytic) = 1.004847204032636
y[1] (numeric) = 1.004847204032646
absolute error = 1.0e-14
relative error = 9.951761780167340e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0986
y[1] (analytic) = 1.004857043088248
y[1] (numeric) = 1.004857043088258
absolute error = 1.0e-14
relative error = 9.951664337512919e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0987
y[1] (analytic) = 1.00486689209529
y[1] (numeric) = 1.0048668920953
absolute error = 1.0e-14
relative error = 9.951566798214022e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0988
y[1] (analytic) = 1.004876751053663
y[1] (numeric) = 1.004876751053673
absolute error = 1.0e-14
relative error = 9.951469162277369e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0989
y[1] (analytic) = 1.004886619963268
y[1] (numeric) = 1.004886619963278
absolute error = 1.0e-14
relative error = 9.951371429709686e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 1.004896498824008
y[1] (numeric) = 1.004896498824017
absolute error = 9e-15
relative error = 8.956146240465915e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0991
y[1] (analytic) = 1.004906387635782
y[1] (numeric) = 1.004906387635791
absolute error = 9e-15
relative error = 8.956058107237306e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0992
y[1] (analytic) = 1.004916286398492
y[1] (numeric) = 1.004916286398501
absolute error = 9e-15
relative error = 8.955969887058948e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0993
y[1] (analytic) = 1.004926195112039
y[1] (numeric) = 1.004926195112048
absolute error = 9e-15
relative error = 8.955881579936915e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0994
y[1] (analytic) = 1.004936113776324
y[1] (numeric) = 1.004936113776333
absolute error = 9e-15
relative error = 8.955793185877283e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0995
y[1] (analytic) = 1.004946042391249
y[1] (numeric) = 1.004946042391257
absolute error = 8e-15
relative error = 7.960626404343222e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0996
y[1] (analytic) = 1.004955980956713
y[1] (numeric) = 1.004955980956721
absolute error = 8e-15
relative error = 7.960547677306264e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0997
y[1] (analytic) = 1.004965929472616
y[1] (numeric) = 1.004965929472625
absolute error = 9e-15
relative error = 8.955527482133650e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0998
y[1] (analytic) = 1.004975887938861
y[1] (numeric) = 1.00497588793887
absolute error = 9e-15
relative error = 8.955438740384512e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0999
y[1] (analytic) = 1.004985856355347
y[1] (numeric) = 1.004985856355356
absolute error = 9e-15
relative error = 8.955349911728253e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 1.004995834721974
y[1] (numeric) = 1.004995834721983
absolute error = 9e-15
relative error = 8.955260996170989e-13 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sin(x);
Iterations = 1000
Total Elapsed Time = 10 Seconds
Elapsed Time(since restart) = 10 Seconds
Expected Time Remaining = 8 Minutes 46 Seconds
Optimized Time Remaining = 8 Minutes 46 Seconds
Time to Timeout = 14 Minutes 49 Seconds
Percent Done = 2.002 %
> quit
memory used=159.6MB, alloc=4.3MB, time=10.81