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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> 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 DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, 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
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> 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 DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, 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)
> if (nnn <= glob_max_terms) then # if number 13
> ret := array_fact_1[nnn];
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_1`
factorial_1 := proc(nnn)
local ret;
if nnn <= glob_max_terms then ret := array_fact_1[nnn]
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> ret := array_fact_2[mmm,nnn];
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_3`
factorial_3 := proc(mmm, nnn)
local ret;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
ret := array_fact_2[mmm, nnn]
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y := proc(x) 2.0 - cos(x) end proc
> #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
> DEBUGMASSIVE,
> glob_iolevel,
> DEBUGL,
> glob_max_terms,
> INFO,
> ALWAYS,
> #Top Generate Globals Decl
> glob_smallish_float,
> glob_small_float,
> glob_no_eqs,
> glob_max_trunc_err,
> days_in_year,
> djd_debug2,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_iter,
> glob_warned2,
> glob_warned,
> glob_max_hours,
> glob_disp_incr,
> glob_optimal_done,
> djd_debug,
> glob_start,
> glob_log10_relerr,
> glob_hmin,
> glob_max_opt_iter,
> glob_subiter_method,
> glob_optimal_clock_start_sec,
> glob_log10_abserr,
> glob_clock_start_sec,
> sec_in_min,
> glob_dump,
> glob_percent_done,
> glob_last_good_h,
> glob_hmin_init,
> glob_hmax,
> centuries_in_millinium,
> hours_in_day,
> glob_large_float,
> glob_unchanged_h_cnt,
> glob_max_iter,
> glob_relerr,
> glob_look_poles,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> years_in_century,
> glob_h,
> glob_reached_optimal_h,
> glob_almost_1,
> min_in_hour,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_display_flag,
> glob_html_log,
> glob_max_minutes,
> glob_log10relerr,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_optimal_start,
> glob_abserr,
> glob_clock_sec,
> glob_log10normmin,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_dump_analytic,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_m1,
> array_type_pole,
> array_last_rel_error,
> array_y_init,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp1_g,
> array_norms,
> array_y,
> array_x,
> array_fact_1,
> array_complex_pole,
> array_y_set_initial,
> array_y_higher_work2,
> array_y_higher_work,
> array_y_higher,
> array_real_pole,
> array_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> DEBUGL := 3;
> glob_max_terms := 30;
> INFO := 2;
> ALWAYS := 1;
> glob_smallish_float := 0.1e-100;
> glob_small_float := 0.1e-50;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> days_in_year := 365.0;
> djd_debug2 := true;
> glob_optimal_expect_sec := 0.1;
> glob_normmax := 0.0;
> glob_iter := 0;
> glob_warned2 := false;
> glob_warned := false;
> glob_max_hours := 0.0;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> djd_debug := true;
> glob_start := 0;
> glob_log10_relerr := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_max_opt_iter := 10;
> glob_subiter_method := 3;
> glob_optimal_clock_start_sec := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_clock_start_sec := 0.0;
> sec_in_min := 60.0;
> glob_dump := false;
> glob_percent_done := 0.0;
> glob_last_good_h := 0.1;
> glob_hmin_init := 0.001;
> glob_hmax := 1.0;
> centuries_in_millinium := 10.0;
> hours_in_day := 24.0;
> glob_large_float := 9.0e100;
> glob_unchanged_h_cnt := 0;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_look_poles := false;
> glob_not_yet_start_msg := true;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> years_in_century := 100.0;
> glob_h := 0.1;
> glob_reached_optimal_h := false;
> glob_almost_1 := 0.9990;
> min_in_hour := 60.0;
> glob_max_sec := 10000.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_display_flag := true;
> glob_html_log := true;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_log10abserr := 0.0;
> MAX_UNCHANGED := 10;
> glob_orig_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_abserr := 0.1e-10;
> glob_clock_sec := 0.0;
> glob_log10normmin := 0.1;
> glob_current_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_dump_analytic := false;
> #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 := 0.001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#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_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_m1[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_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[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_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[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_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=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 <=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[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #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_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while iiif <= glob_max_terms do # do number 2
> jjjf := 0;
> while jjjf <= glob_max_terms do # do number 3
> temp1 := iiif !;
> temp2 := jjjf !;
> array_fact_1[iiif] := temp1;
> array_fact_2[iiif,jjjf] := temp1/temp2;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> 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 := 0.001 ;
> glob_look_poles := true;
> glob_max_iter := 1000;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := 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)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 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,"2012-06-17T02:56:25-05:00")
> ;
> 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," 091 | ")
> ;
> 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 for speeding factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `iiif` is implicitly declared local to procedure `mainprog`
Warning, `jjjf` is implicitly declared local to procedure `mainprog`
Warning, `temp1` is implicitly declared local to procedure `mainprog`
Warning, `temp2` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, iiif,
jjjf, temp1, temp2;
global DEBUGMASSIVE, glob_iolevel, DEBUGL, glob_max_terms, INFO, ALWAYS,
glob_smallish_float, glob_small_float, glob_no_eqs, glob_max_trunc_err,
days_in_year, djd_debug2, glob_optimal_expect_sec, glob_normmax, glob_iter,
glob_warned2, glob_warned, glob_max_hours, glob_disp_incr,
glob_optimal_done, djd_debug, glob_start, glob_log10_relerr, glob_hmin,
glob_max_opt_iter, glob_subiter_method, glob_optimal_clock_start_sec,
glob_log10_abserr, glob_clock_start_sec, sec_in_min, glob_dump,
glob_percent_done, glob_last_good_h, glob_hmin_init, glob_hmax,
centuries_in_millinium, hours_in_day, glob_large_float,
glob_unchanged_h_cnt, glob_max_iter, glob_relerr, glob_look_poles,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
years_in_century, glob_h, glob_reached_optimal_h, glob_almost_1,
min_in_hour, glob_max_sec, glob_max_rel_trunc_err, glob_display_flag,
glob_html_log, glob_max_minutes, glob_log10relerr, glob_log10abserr,
MAX_UNCHANGED, glob_orig_start_sec, glob_optimal_start, glob_abserr,
glob_clock_sec, glob_log10normmin, glob_current_iter,
glob_curr_iter_when_opt, glob_dump_analytic, array_const_1, array_const_0D0,
array_pole, array_1st_rel_error, array_m1, array_type_pole,
array_last_rel_error, array_y_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp1_g, array_norms, array_y, array_x, array_fact_1,
array_complex_pole, array_y_set_initial, array_y_higher_work2,
array_y_higher_work, array_y_higher, array_real_pole, array_poles,
array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
DEBUGL := 3;
glob_max_terms := 30;
INFO := 2;
ALWAYS := 1;
glob_smallish_float := 0.1*10^(-100);
glob_small_float := 0.1*10^(-50);
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
days_in_year := 365.0;
djd_debug2 := true;
glob_optimal_expect_sec := 0.1;
glob_normmax := 0.;
glob_iter := 0;
glob_warned2 := false;
glob_warned := false;
glob_max_hours := 0.;
glob_disp_incr := 0.1;
glob_optimal_done := false;
djd_debug := true;
glob_start := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_max_opt_iter := 10;
glob_subiter_method := 3;
glob_optimal_clock_start_sec := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_clock_start_sec := 0.;
sec_in_min := 60.0;
glob_dump := false;
glob_percent_done := 0.;
glob_last_good_h := 0.1;
glob_hmin_init := 0.001;
glob_hmax := 1.0;
centuries_in_millinium := 10.0;
hours_in_day := 24.0;
glob_large_float := 0.90*10^101;
glob_unchanged_h_cnt := 0;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_look_poles := false;
glob_not_yet_start_msg := true;
glob_initial_pass := true;
glob_not_yet_finished := true;
years_in_century := 100.0;
glob_h := 0.1;
glob_reached_optimal_h := false;
glob_almost_1 := 0.9990;
min_in_hour := 60.0;
glob_max_sec := 10000.0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_display_flag := true;
glob_html_log := true;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_log10abserr := 0.;
MAX_UNCHANGED := 10;
glob_orig_start_sec := 0.;
glob_optimal_start := 0.;
glob_abserr := 0.1*10^(-10);
glob_clock_sec := 0.;
glob_log10normmin := 0.1;
glob_current_iter := 0;
glob_curr_iter_when_opt := 0;
glob_dump_analytic := false;
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 := 0.001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0 - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#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_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[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_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_fact_1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 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 <= 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[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
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_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
temp1 := iiif!;
temp2 := jjjf!;
array_fact_1[iiif] := temp1;
array_fact_2[iiif, jjjf] := temp1/temp2;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
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 := 0.001;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := 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)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 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, "2012-06-17T02:56:25-05:00");
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, " 091 | ");
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 for speeding factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/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 := 0.001 ;
glob_look_poles := true;
glob_max_iter := 1000;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 - cos(x);
end;
#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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
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 = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 1.000071999136004
y[1] (numeric) = 1.000071999136003
absolute error = 1e-15
relative error = 9.999280060474984e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 1.000084498809965
y[1] (numeric) = 1.000084498809964
absolute error = 1e-15
relative error = 9.999155083294806e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 1.000097998399344
y[1] (numeric) = 1.000097998399343
absolute error = 1e-15
relative error = 9.999020112034012e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.20
NO POLE
x[1] = 0.015
y[1] (analytic) = 1.000112497890641
y[1] (numeric) = 1.00011249789064
absolute error = 1e-15
relative error = 9.998875147637108e-14 %
h = 0.001
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 = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 1.000144496519992
y[1] (numeric) = 1.000144496519991
absolute error = 1e-15
relative error = 9.998555243562357e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 1.000161995626047
y[1] (numeric) = 1.000161995626046
absolute error = 1e-15
relative error = 9.998380306122854e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 1.000180494570024
y[1] (numeric) = 1.000180494570022
absolute error = 2e-15
relative error = 1.999639076004773e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 1.000199993333422
y[1] (numeric) = 1.000199993333421
absolute error = 1e-15
relative error = 9.998000466559138e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 1.000220491896744
y[1] (numeric) = 1.000220491896743
absolute error = 1e-15
relative error = 9.997795567092153e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 1.000241990239491
y[1] (numeric) = 1.00024199023949
absolute error = 1e-15
relative error = 9.997580683056177e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 1.000264488340164
y[1] (numeric) = 1.000264488340163
absolute error = 1e-15
relative error = 9.997355815954209e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 1.000287986176265
y[1] (numeric) = 1.000287986176264
absolute error = 1e-15
relative error = 9.997120967358952e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.025
y[1] (analytic) = 1.000312483724297
y[1] (numeric) = 1.000312483724296
absolute error = 1e-15
relative error = 9.996876138912777e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 1.000337980959762
y[1] (numeric) = 1.000337980959761
absolute error = 1e-15
relative error = 9.996621332327723e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 1.000364477857163
y[1] (numeric) = 1.000364477857162
absolute error = 1e-15
relative error = 9.996356549385443e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 1.000391974390003
y[1] (numeric) = 1.000391974390002
absolute error = 1e-15
relative error = 9.996081791937185e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 1.000420470530784
y[1] (numeric) = 1.000420470530784
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 1.000449966251012
y[1] (numeric) = 1.000449966251012
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 1.000480461521191
y[1] (numeric) = 1.00048046152119
absolute error = 1e-15
relative error = 9.995197692112243e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 1.000511956310825
y[1] (numeric) = 1.000511956310824
absolute error = 1e-15
relative error = 9.994883056543245e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 1.000544450588419
y[1] (numeric) = 1.000544450588418
absolute error = 1e-15
relative error = 9.994558456767225e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 1.000577944321479
y[1] (numeric) = 1.000577944321478
absolute error = 1e-15
relative error = 9.994223895052265e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 1.000612437476511
y[1] (numeric) = 1.000612437476511
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 1.000647930019023
y[1] (numeric) = 1.000647930019023
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 1.000684421913522
y[1] (numeric) = 1.000684421913522
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 1.000721913123515
y[1] (numeric) = 1.000721913123515
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 1.000760403611512
y[1] (numeric) = 1.000760403611512
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=0.45
NO POLE
x[1] = 0.04
y[1] (analytic) = 1.000799893339022
y[1] (numeric) = 1.000799893339022
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.041
y[1] (analytic) = 1.000840382266556
y[1] (numeric) = 1.000840382266555
absolute error = 1e-15
relative error = 9.991603233827828e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 1.000881870353623
y[1] (numeric) = 1.000881870353623
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 1.000924357558738
y[1] (numeric) = 1.000924357558737
absolute error = 1e-15
relative error = 9.990764960890826e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 1.000967843839411
y[1] (numeric) = 1.00096784383941
absolute error = 1e-15
relative error = 9.990330919765628e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 1.001012329152158
y[1] (numeric) = 1.001012329152156
absolute error = 2e-15
relative error = 1.997977389243516e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 1.001057813452492
y[1] (numeric) = 1.00105781345249
absolute error = 2e-15
relative error = 1.997886608668797e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 1.001104296694929
y[1] (numeric) = 1.001104296694927
absolute error = 2e-15
relative error = 1.997793842862178e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 1.001151778832986
y[1] (numeric) = 1.001151778832984
absolute error = 2e-15
relative error = 1.997699092470617e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 1.001200259819182
y[1] (numeric) = 1.001200259819179
absolute error = 3e-15
relative error = 2.996403537232205e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 1.001249739605034
y[1] (numeric) = 1.001249739605031
absolute error = 3e-15
relative error = 2.996255460883734e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 1.001300218141063
y[1] (numeric) = 1.00130021814106
absolute error = 3e-15
relative error = 2.996104410692698e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 1.001351695376791
y[1] (numeric) = 1.001351695376788
absolute error = 3e-15
relative error = 2.995950387711835e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 1.001404171260741
y[1] (numeric) = 1.001404171260737
absolute error = 4e-15
relative error = 3.994391190685882e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 1.001457645740436
y[1] (numeric) = 1.001457645740432
absolute error = 4e-15
relative error = 3.994177903592285e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 1.001512118762402
y[1] (numeric) = 1.001512118762398
absolute error = 4e-15
relative error = 3.993960657154022e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 1.001567590272166
y[1] (numeric) = 1.001567590272162
absolute error = 4e-15
relative error = 3.993739452884093e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.057
y[1] (analytic) = 1.001624060214256
y[1] (numeric) = 1.001624060214253
absolute error = 3e-15
relative error = 2.995135719242082e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 1.001681528532203
y[1] (numeric) = 1.0016815285322
absolute error = 3e-15
relative error = 2.994963882778191e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 1.001739995168539
y[1] (numeric) = 1.001739995168535
absolute error = 4e-15
relative error = 3.993052108623271e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 1.001799460064796
y[1] (numeric) = 1.001799460064792
absolute error = 4e-15
relative error = 3.992815088701766e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 1.00185992316151
y[1] (numeric) = 1.001859923161506
absolute error = 4e-15
relative error = 3.992574118922171e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 1.001921384398217
y[1] (numeric) = 1.001921384398213
absolute error = 4e-15
relative error = 3.992329200960728e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 1.001983843713457
y[1] (numeric) = 1.001983843713453
absolute error = 4e-15
relative error = 3.992080336520778e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 1.00204730104477
y[1] (numeric) = 1.002047301044766
absolute error = 4e-15
relative error = 3.991827527332750e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 1.002111756328699
y[1] (numeric) = 1.002111756328695
absolute error = 4e-15
relative error = 3.991570775154118e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.70
NO POLE
x[1] = 0.066
y[1] (analytic) = 1.002177209500788
y[1] (numeric) = 1.002177209500784
absolute error = 4e-15
relative error = 3.991310081769381e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 1.002243660495585
y[1] (numeric) = 1.002243660495581
absolute error = 4e-15
relative error = 3.991045448990017e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 1.002311109246638
y[1] (numeric) = 1.002311109246634
absolute error = 4e-15
relative error = 3.990776878654473e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 1.002379555686499
y[1] (numeric) = 1.002379555686495
absolute error = 4e-15
relative error = 3.990504372628114e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 1.00244899974672
y[1] (numeric) = 1.002448999746717
absolute error = 3e-15
relative error = 2.992670949602407e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 1.002519441357859
y[1] (numeric) = 1.002519441357856
absolute error = 3e-15
relative error = 2.992460670824159e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 1.002590880449474
y[1] (numeric) = 1.00259088044947
absolute error = 4e-15
relative error = 3.989663259461078e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.073
y[1] (analytic) = 1.002663316950125
y[1] (numeric) = 1.002663316950121
absolute error = 4e-15
relative error = 3.989375029862562e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 1.002736750787376
y[1] (numeric) = 1.002736750787372
absolute error = 4e-15
relative error = 3.989082874302844e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 1.002811181887793
y[1] (numeric) = 1.002811181887789
absolute error = 4e-15
relative error = 3.988786794808167e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 1.002886610176944
y[1] (numeric) = 1.002886610176941
absolute error = 3e-15
relative error = 2.991365095073605e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 1.002963035579403
y[1] (numeric) = 1.0029630355794
absolute error = 3e-15
relative error = 2.991137154189263e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 1.003040458018743
y[1] (numeric) = 1.00304045801874
absolute error = 3e-15
relative error = 2.990906275032768e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 1.003118877417542
y[1] (numeric) = 1.003118877417539
absolute error = 3e-15
relative error = 2.990672459203725e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 1.003198293697381
y[1] (numeric) = 1.003198293697377
absolute error = 4e-15
relative error = 3.987247611095536e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 1.003278706778842
y[1] (numeric) = 1.003278706778839
absolute error = 3e-15
relative error = 2.990196024025960e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 1.003360116581514
y[1] (numeric) = 1.003360116581511
absolute error = 3e-15
relative error = 2.989953407975906e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 1.003442523023986
y[1] (numeric) = 1.003442523023983
absolute error = 3e-15
relative error = 2.989707861850587e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 1.003525926023852
y[1] (numeric) = 1.003525926023849
absolute error = 3e-15
relative error = 2.989459387348898e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 1.00361032549771
y[1] (numeric) = 1.003610325497706
absolute error = 4e-15
relative error = 3.985610648252669e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 1.003695721361158
y[1] (numeric) = 1.003695721361155
absolute error = 3e-15
relative error = 2.988953660110817e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 1.003782113528802
y[1] (numeric) = 1.003782113528799
absolute error = 3e-15
relative error = 2.988696410870963e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 1.00386950191425
y[1] (numeric) = 1.003869501914247
absolute error = 3e-15
relative error = 2.988436240247747e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.089
y[1] (analytic) = 1.003957886430112
y[1] (numeric) = 1.00395788643011
absolute error = 2e-15
relative error = 1.992115433359091e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 1.004047266988006
y[1] (numeric) = 1.004047266988003
absolute error = 3e-15
relative error = 2.987907142060710e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 1.004137643498549
y[1] (numeric) = 1.004137643498546
absolute error = 3e-15
memory used=15.2MB, alloc=4.2MB, time=0.96
relative error = 2.987638218150652e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 1.004229015871366
y[1] (numeric) = 1.004229015871363
absolute error = 3e-15
relative error = 2.987366380164698e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 1.004321384015084
y[1] (numeric) = 1.004321384015081
absolute error = 3e-15
relative error = 2.987091629978619e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 1.004414747837335
y[1] (numeric) = 1.004414747837332
absolute error = 3e-15
relative error = 2.986813969487682e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 1.004509107244755
y[1] (numeric) = 1.004509107244752
absolute error = 3e-15
relative error = 2.986533400606622e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 1.004604462142985
y[1] (numeric) = 1.004604462142982
absolute error = 3e-15
relative error = 2.986249925269604e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 1.00470081243667
y[1] (numeric) = 1.004700812436667
absolute error = 3e-15
relative error = 2.985963545430198e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 1.004798158029459
y[1] (numeric) = 1.004798158029456
absolute error = 3e-15
relative error = 2.985674263061343e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 1.004896498824008
y[1] (numeric) = 1.004896498824004
absolute error = 4e-15
relative error = 3.980509440207073e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 1.004995834721974
y[1] (numeric) = 1.004995834721971
absolute error = 3e-15
relative error = 2.985086998723663e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.005096165624023
y[1] (numeric) = 1.00509616562402
absolute error = 3e-15
relative error = 2.984789020797252e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.005197491429824
y[1] (numeric) = 1.005197491429821
absolute error = 3e-15
relative error = 2.984488148426144e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.00529981203805
y[1] (numeric) = 1.005299812038047
absolute error = 3e-15
relative error = 2.984184383679614e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.005403127346382
y[1] (numeric) = 1.005403127346378
absolute error = 4e-15
relative error = 3.978503638194789e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.005507437251503
y[1] (numeric) = 1.005507437251499
absolute error = 4e-15
relative error = 3.978090913910862e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.005612741649104
y[1] (numeric) = 1.0056127416491
absolute error = 4e-15
relative error = 3.977674341556573e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.00571904043388
y[1] (numeric) = 1.005719040433876
absolute error = 4e-15
relative error = 3.977253923992877e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.005826333499533
y[1] (numeric) = 1.005826333499529
absolute error = 4e-15
relative error = 3.976829664106082e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.00593462073877
y[1] (numeric) = 1.005934620738766
absolute error = 4e-15
relative error = 3.976401564807814e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.006043902043303
y[1] (numeric) = 1.006043902043299
absolute error = 4e-15
relative error = 3.975969629034965e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.006154177303852
y[1] (numeric) = 1.006154177303847
absolute error = 5e-15
relative error = 4.969417324687042e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.00626544641014
y[1] (numeric) = 1.006265446410135
absolute error = 5e-15
relative error = 4.968867824923871e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.006377709250899
y[1] (numeric) = 1.006377709250894
absolute error = 5e-15
relative error = 4.968313540769667e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.006490965713866
y[1] (numeric) = 1.006490965713861
absolute error = 5e-15
relative error = 4.967754476021242e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.006605215685784
y[1] (numeric) = 1.006605215685779
absolute error = 5e-15
relative error = 4.967190634506677e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.006720459052404
y[1] (numeric) = 1.006720459052399
absolute error = 5e-15
relative error = 4.966622020085249e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=19.0MB, alloc=4.2MB, time=1.22
x[1] = 0.117
y[1] (analytic) = 1.006836695698482
y[1] (numeric) = 1.006836695698477
absolute error = 5e-15
relative error = 4.966048636647380e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.006953925507782
y[1] (numeric) = 1.006953925507777
absolute error = 5e-15
relative error = 4.965470488114561e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.007072148363073
y[1] (numeric) = 1.007072148363068
absolute error = 5e-15
relative error = 4.964887578439299e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.007191364146134
y[1] (numeric) = 1.007191364146128
absolute error = 6e-15
relative error = 5.957159893926033e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.121
y[1] (analytic) = 1.007311572737747
y[1] (numeric) = 1.007311572737741
absolute error = 6e-15
relative error = 5.956448989951291e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.007432774017705
y[1] (numeric) = 1.007432774017699
absolute error = 6e-15
relative error = 5.955732387057078e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.007554967864806
y[1] (numeric) = 1.0075549678648
absolute error = 6e-15
relative error = 5.955010090134439e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.007678154156857
y[1] (numeric) = 1.007678154156851
absolute error = 6e-15
relative error = 5.954282104111219e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.007802332770671
y[1] (numeric) = 1.007802332770665
absolute error = 6e-15
relative error = 5.953548433951999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.007927503582069
y[1] (numeric) = 1.007927503582063
absolute error = 6e-15
relative error = 5.952809084658001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.008053666465882
y[1] (numeric) = 1.008053666465875
absolute error = 7e-15
relative error = 6.944074738144825e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.008180821295944
y[1] (numeric) = 1.008180821295938
absolute error = 6e-15
relative error = 5.951313368853249e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.008308967945104
y[1] (numeric) = 1.008308967945097
absolute error = 7e-15
relative error = 6.942316514615295e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.008438106285212
y[1] (numeric) = 1.008438106285205
absolute error = 7e-15
relative error = 6.941427497009144e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.008568236187132
y[1] (numeric) = 1.008568236187125
absolute error = 7e-15
relative error = 6.940531883557360e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.008699357520732
y[1] (numeric) = 1.008699357520726
absolute error = 6e-15
relative error = 5.948254011727851e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.008831470154893
y[1] (numeric) = 1.008831470154887
absolute error = 6e-15
relative error = 5.947475051584957e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.008964573957501
y[1] (numeric) = 1.008964573957495
absolute error = 6e-15
relative error = 5.946690453626104e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.009098668795452
y[1] (numeric) = 1.009098668795446
absolute error = 6e-15
relative error = 5.945900223178495e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.009233754534652
y[1] (numeric) = 1.009233754534646
absolute error = 6e-15
relative error = 5.945104365605114e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.009369831040015
y[1] (numeric) = 1.009369831040009
absolute error = 6e-15
relative error = 5.944302886304652e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.009506898175464
y[1] (numeric) = 1.009506898175458
absolute error = 6e-15
relative error = 5.943495790711408e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.009644955803933
y[1] (numeric) = 1.009644955803927
absolute error = 6e-15
relative error = 5.942683084295193e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.009784003787363
y[1] (numeric) = 1.009784003787357
absolute error = 6e-15
relative error = 5.941864772561262e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.009924041986707
y[1] (numeric) = 1.009924041986701
absolute error = 6e-15
relative error = 5.941040861050196e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.010065070261926
y[1] (numeric) = 1.01006507026192
absolute error = 6e-15
relative error = 5.940211355337834e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=22.8MB, alloc=4.3MB, time=1.49
x[1] = 0.143
y[1] (analytic) = 1.010207088471993
y[1] (numeric) = 1.010207088471987
absolute error = 6e-15
relative error = 5.939376261035159e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.010350096474888
y[1] (numeric) = 1.010350096474883
absolute error = 5e-15
relative error = 4.948779653156864e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.010494094127605
y[1] (numeric) = 1.0104940941276
absolute error = 5e-15
relative error = 4.948074441065067e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.010639081286145
y[1] (numeric) = 1.01063908128614
absolute error = 5e-15
relative error = 4.947364586017168e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.010785057805522
y[1] (numeric) = 1.010785057805516
absolute error = 6e-15
relative error = 5.935980111366484e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.010932023539758
y[1] (numeric) = 1.010932023539752
absolute error = 6e-15
relative error = 5.935117159501112e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.011079978341888
y[1] (numeric) = 1.011079978341882
absolute error = 6e-15
relative error = 5.934248653444457e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.011228922063958
y[1] (numeric) = 1.011228922063951
absolute error = 7e-15
relative error = 6.922270365559486e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.011378854557023
y[1] (numeric) = 1.011378854557016
absolute error = 7e-15
relative error = 6.921244169244523e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.011529775671151
y[1] (numeric) = 1.011529775671144
absolute error = 7e-15
relative error = 6.920211513650691e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.011681685255421
y[1] (numeric) = 1.011681685255414
absolute error = 7e-15
relative error = 6.919172405728288e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.011834583157923
y[1] (numeric) = 1.011834583157916
absolute error = 7e-15
relative error = 6.918126852467414e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.01198846922576
y[1] (numeric) = 1.011988469225753
absolute error = 7e-15
relative error = 6.917074860897848e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.012143343305046
y[1] (numeric) = 1.012143343305038
absolute error = 8e-15
relative error = 7.904018786387365e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.012299205240905
y[1] (numeric) = 1.012299205240898
absolute error = 7e-15
relative error = 6.914951591149529e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.012456054877477
y[1] (numeric) = 1.01245605487747
absolute error = 7e-15
relative error = 6.913880327227743e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 1.012613892057912
y[1] (numeric) = 1.012613892057905
absolute error = 7e-15
relative error = 6.912802653510965e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.012772716624373
y[1] (numeric) = 1.012772716624366
absolute error = 7e-15
relative error = 6.911718577225682e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.012932528418035
y[1] (numeric) = 1.012932528418028
absolute error = 7e-15
relative error = 6.910628105637373e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.013093327279086
y[1] (numeric) = 1.013093327279079
absolute error = 7e-15
relative error = 6.909531246050391e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.013255113046728
y[1] (numeric) = 1.013255113046721
absolute error = 7e-15
relative error = 6.908428005807835e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.013417885559174
y[1] (numeric) = 1.013417885559167
absolute error = 7e-15
relative error = 6.907318392291456e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.013581644653652
y[1] (numeric) = 1.013581644653646
absolute error = 6e-15
relative error = 5.919602068218434e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.013746390166404
y[1] (numeric) = 1.013746390166398
absolute error = 6e-15
relative error = 5.918640064419973e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.013912121932683
y[1] (numeric) = 1.013912121932677
absolute error = 6e-15
relative error = 5.917672616994671e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.014078839786758
y[1] (numeric) = 1.014078839786752
absolute error = 6e-15
relative error = 5.916699732401170e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=26.7MB, alloc=4.3MB, time=1.75
x[1] = 0.169
y[1] (analytic) = 1.014246543561912
y[1] (numeric) = 1.014246543561905
absolute error = 7e-15
relative error = 6.901674986652497e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.014415233090439
y[1] (numeric) = 1.014415233090433
absolute error = 6e-15
relative error = 5.914737677707051e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.014584908203652
y[1] (numeric) = 1.014584908203645
absolute error = 7e-15
relative error = 6.899373274134025e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.014755568731874
y[1] (numeric) = 1.014755568731867
absolute error = 7e-15
relative error = 6.898212944766396e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.014927214504445
y[1] (numeric) = 1.014927214504438
absolute error = 7e-15
relative error = 6.897046310279369e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.015099845349719
y[1] (numeric) = 1.015099845349713
absolute error = 6e-15
relative error = 5.910748610086625e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.015273461095066
y[1] (numeric) = 1.01527346109506
absolute error = 6e-15
relative error = 5.909737848883046e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.01544806156687
y[1] (numeric) = 1.015448061566864
absolute error = 6e-15
relative error = 5.908721703345222e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.015623646590531
y[1] (numeric) = 1.015623646590524
absolute error = 7e-15
relative error = 6.892316876924972e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.015800215990463
y[1] (numeric) = 1.015800215990456
absolute error = 7e-15
relative error = 6.891118834006746e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.015977769590096
y[1] (numeric) = 1.01597776959009
absolute error = 6e-15
relative error = 5.905641028366936e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.016156307211879
y[1] (numeric) = 1.016156307211872
absolute error = 7e-15
relative error = 6.888703982172330e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.016335828677272
y[1] (numeric) = 1.016335828677265
absolute error = 7e-15
relative error = 6.887487189259354e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.016516333806754
y[1] (numeric) = 1.016516333806747
absolute error = 7e-15
relative error = 6.886264162412114e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.01669782241982
y[1] (numeric) = 1.016697822419814
absolute error = 6e-15
relative error = 5.901458494048441e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.016880294334983
y[1] (numeric) = 1.016880294334976
absolute error = 7e-15
relative error = 6.883799439321266e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.017063749369768
y[1] (numeric) = 1.017063749369762
absolute error = 6e-15
relative error = 5.899335222318119e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.017248187340723
y[1] (numeric) = 1.017248187340717
absolute error = 6e-15
relative error = 5.898265609777219e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.017433608063409
y[1] (numeric) = 1.017433608063402
absolute error = 7e-15
relative error = 6.880055803664530e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.017620011352404
y[1] (numeric) = 1.017620011352397
absolute error = 7e-15
relative error = 6.878795544416515e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.017807397021306
y[1] (numeric) = 1.017807397021299
absolute error = 7e-15
relative error = 6.877529108636914e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.01799576488273
y[1] (numeric) = 1.017995764882722
absolute error = 8e-15
relative error = 7.858578862478446e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.018185114748306
y[1] (numeric) = 1.018185114748299
absolute error = 7e-15
relative error = 6.874977740889868e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.018375446428686
y[1] (numeric) = 1.018375446428679
absolute error = 7e-15
relative error = 6.873692825713852e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.018566759733538
y[1] (numeric) = 1.018566759733531
absolute error = 7e-15
relative error = 6.872401767588836e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.018759054471549
y[1] (numeric) = 1.018759054471541
absolute error = 8e-15
relative error = 7.852690942854748e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.3MB, time=2.00
x[1] = 0.195
y[1] (analytic) = 1.018952330450423
y[1] (numeric) = 1.018952330450415
absolute error = 8e-15
relative error = 7.851201435952983e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.019146587476885
y[1] (numeric) = 1.019146587476877
absolute error = 8e-15
relative error = 7.849704937741791e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.019341825356677
y[1] (numeric) = 1.01934182535667
absolute error = 7e-15
relative error = 6.867176275780341e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.019538043894563
y[1] (numeric) = 1.019538043894556
absolute error = 7e-15
relative error = 6.865854630848788e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.019735242894323
y[1] (numeric) = 1.019735242894316
absolute error = 7e-15
relative error = 6.864526894384705e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.019933422158758
y[1] (numeric) = 1.019933422158751
absolute error = 7e-15
relative error = 6.863193075077417e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.02013258148969
y[1] (numeric) = 1.020132581489683
absolute error = 7e-15
relative error = 6.861853181650140e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.020332720687958
y[1] (numeric) = 1.020332720687951
absolute error = 7e-15
relative error = 6.860507222859872e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.020533839553424
y[1] (numeric) = 1.020533839553417
absolute error = 7e-15
relative error = 6.859155207497219e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.02073593788497
y[1] (numeric) = 1.020735937884962
absolute error = 8e-15
relative error = 7.837482450727179e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.020939015480495
y[1] (numeric) = 1.020939015480487
absolute error = 8e-15
relative error = 7.835923477010895e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.021143072136923
y[1] (numeric) = 1.021143072136915
absolute error = 8e-15
relative error = 7.834357611865868e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.021348107650198
y[1] (numeric) = 1.02134810765019
absolute error = 8e-15
relative error = 7.832784865490664e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.021554121815284
y[1] (numeric) = 1.021554121815275
absolute error = 9e-15
relative error = 8.810105904136685e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.021761114426166
y[1] (numeric) = 1.021761114426157
absolute error = 9e-15
relative error = 8.808321116286084e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.021969085275852
y[1] (numeric) = 1.021969085275843
absolute error = 9e-15
relative error = 8.806528621725090e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.022178034156371
y[1] (numeric) = 1.022178034156362
absolute error = 9e-15
relative error = 8.804728432095417e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.022387960858775
y[1] (numeric) = 1.022387960858766
absolute error = 9e-15
relative error = 8.802920559080402e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.022598865173136
y[1] (numeric) = 1.022598865173127
absolute error = 9e-15
relative error = 8.801105014404854e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.022810746888551
y[1] (numeric) = 1.022810746888542
absolute error = 9e-15
relative error = 8.799281809834827e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.023023605793138
y[1] (numeric) = 1.023023605793128
absolute error = 1.0e-14
relative error = 9.774945507974979e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.023237441674037
y[1] (numeric) = 1.023237441674027
absolute error = 1.0e-14
relative error = 9.772902742534322e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.023452254317413
y[1] (numeric) = 1.023452254317403
absolute error = 1.0e-14
relative error = 9.770851505593152e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.218
y[1] (analytic) = 1.023668043508454
y[1] (numeric) = 1.023668043508444
absolute error = 1.0e-14
relative error = 9.768791810406275e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.023884809031369
y[1] (numeric) = 1.02388480903136
absolute error = 9e-15
relative error = 8.790051303246032e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.024102550669394
y[1] (numeric) = 1.024102550669385
absolute error = 9e-15
relative error = 8.788182388684847e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=34.3MB, alloc=4.3MB, time=2.25
x[1] = 0.221
y[1] (analytic) = 1.024321268204788
y[1] (numeric) = 1.024321268204778
absolute error = 1.0e-14
relative error = 9.762562108591056e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.024540961418832
y[1] (numeric) = 1.024540961418822
absolute error = 1.0e-14
relative error = 9.760468713863362e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.024761630091833
y[1] (numeric) = 1.024761630091823
absolute error = 1.0e-14
relative error = 9.758366927832632e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.024983274003122
y[1] (numeric) = 1.024983274003113
absolute error = 9e-15
relative error = 8.780631087617715e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.025205892931057
y[1] (numeric) = 1.025205892931047
absolute error = 1.0e-14
relative error = 9.754138235988934e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.025429486653017
y[1] (numeric) = 1.025429486653007
absolute error = 1.0e-14
relative error = 9.752011357348243e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.025654054945409
y[1] (numeric) = 1.025654054945399
absolute error = 1.0e-14
relative error = 9.749876141748648e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.025879597583666
y[1] (numeric) = 1.025879597583655
absolute error = 1.1e-14
relative error = 1.072250586317259e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.026106114342243
y[1] (numeric) = 1.026106114342233
absolute error = 1.0e-14
relative error = 9.745580754491677e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.026333604994625
y[1] (numeric) = 1.026333604994615
absolute error = 1.0e-14
relative error = 9.743420610350541e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.026562069313321
y[1] (numeric) = 1.026562069313311
absolute error = 1.0e-14
relative error = 9.741252184282547e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.026791507069866
y[1] (numeric) = 1.026791507069856
absolute error = 1.0e-14
relative error = 9.739075490151644e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.027021918034824
y[1] (numeric) = 1.027021918034813
absolute error = 1.1e-14
relative error = 1.071057959605008e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.027253301977782
y[1] (numeric) = 1.027253301977771
absolute error = 1.1e-14
relative error = 1.070816708870303e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.027485658667357
y[1] (numeric) = 1.027485658667346
absolute error = 1.1e-14
relative error = 1.070574553251375e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.027718987871192
y[1] (numeric) = 1.027718987871181
absolute error = 1.1e-14
relative error = 1.070331494291577e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.027953289355959
y[1] (numeric) = 1.027953289355948
absolute error = 1.1e-14
relative error = 1.070087533538786e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.028188562887355
y[1] (numeric) = 1.028188562887344
absolute error = 1.1e-14
relative error = 1.069842672545379e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.028424808230107
y[1] (numeric) = 1.028424808230096
absolute error = 1.1e-14
relative error = 1.069596912868207e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.02866202514797
y[1] (numeric) = 1.028662025147959
absolute error = 1.1e-14
relative error = 1.069350256068574e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.028900213403727
y[1] (numeric) = 1.028900213403716
absolute error = 1.1e-14
relative error = 1.069102703712215e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.02913937275919
y[1] (numeric) = 1.029139372759179
absolute error = 1.1e-14
relative error = 1.068854257369270e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.029379502975199
y[1] (numeric) = 1.029379502975188
absolute error = 1.1e-14
relative error = 1.068604918614260e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.029620603811624
y[1] (numeric) = 1.029620603811613
absolute error = 1.1e-14
relative error = 1.068354689026068e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.029862675027365
y[1] (numeric) = 1.029862675027353
absolute error = 1.2e-14
relative error = 1.165203894750447e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.030105716380349
y[1] (numeric) = 1.030105716380338
absolute error = 1.1e-14
relative error = 1.067851563687317e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=38.1MB, alloc=4.3MB, time=2.52
x[1] = 0.247
y[1] (analytic) = 1.030349727627537
y[1] (numeric) = 1.030349727627525
absolute error = 1.2e-14
relative error = 1.164653095763024e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.030594708524916
y[1] (numeric) = 1.030594708524904
absolute error = 1.2e-14
relative error = 1.164376248076756e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.030840658827505
y[1] (numeric) = 1.030840658827494
absolute error = 1.1e-14
relative error = 1.067090234150405e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.031087578289355
y[1] (numeric) = 1.031087578289344
absolute error = 1.1e-14
relative error = 1.066834692960782e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.031335466663546
y[1] (numeric) = 1.031335466663535
absolute error = 1.1e-14
relative error = 1.066578272110227e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.03158432370219
y[1] (numeric) = 1.031584323702179
absolute error = 1.1e-14
relative error = 1.066320973211649e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.031834149156429
y[1] (numeric) = 1.031834149156418
absolute error = 1.1e-14
relative error = 1.066062797882101e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.032084942776438
y[1] (numeric) = 1.032084942776427
absolute error = 1.1e-14
relative error = 1.065803747742760e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.032336704311424
y[1] (numeric) = 1.032336704311413
absolute error = 1.1e-14
relative error = 1.065543824418902e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.032589433509625
y[1] (numeric) = 1.032589433509614
absolute error = 1.1e-14
relative error = 1.065283029539878e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.032843130118312
y[1] (numeric) = 1.032843130118301
absolute error = 1.1e-14
relative error = 1.065021364739092e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.033097793883788
y[1] (numeric) = 1.033097793883777
absolute error = 1.1e-14
relative error = 1.064758831653974e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.03335342455139
y[1] (numeric) = 1.033353424551379
absolute error = 1.1e-14
relative error = 1.064495431925958e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.033610021865487
y[1] (numeric) = 1.033610021865476
absolute error = 1.1e-14
relative error = 1.064231167200460e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.033867585569481
y[1] (numeric) = 1.03386758556947
absolute error = 1.1e-14
relative error = 1.063966039126850e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.034126115405809
y[1] (numeric) = 1.034126115405798
absolute error = 1.1e-14
relative error = 1.063700049358430e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.034385611115941
y[1] (numeric) = 1.03438561111593
absolute error = 1.1e-14
relative error = 1.063433199552410e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.034646072440382
y[1] (numeric) = 1.034646072440371
absolute error = 1.1e-14
relative error = 1.063165491369885e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.03490749911867
y[1] (numeric) = 1.034907499118659
absolute error = 1.1e-14
relative error = 1.062896926475809e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.035169890889378
y[1] (numeric) = 1.035169890889367
absolute error = 1.1e-14
relative error = 1.062627506538973e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.035433247490115
y[1] (numeric) = 1.035433247490104
absolute error = 1.1e-14
relative error = 1.062357233231978e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.035697568657524
y[1] (numeric) = 1.035697568657513
absolute error = 1.1e-14
relative error = 1.062086108231214e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.035962854127284
y[1] (numeric) = 1.035962854127273
absolute error = 1.1e-14
relative error = 1.061814133216834e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.03622910363411
y[1] (numeric) = 1.036229103634099
absolute error = 1.1e-14
relative error = 1.061541309872732e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.036496316911751
y[1] (numeric) = 1.036496316911741
absolute error = 1.0e-14
relative error = 9.647887635331961e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.036764493692996
y[1] (numeric) = 1.036764493692985
absolute error = 1.1e-14
relative error = 1.060993124949483e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=41.9MB, alloc=4.3MB, time=2.77
x[1] = 0.273
y[1] (analytic) = 1.037033633709666
y[1] (numeric) = 1.037033633709655
absolute error = 1.1e-14
relative error = 1.060717766756601e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.037303736692622
y[1] (numeric) = 1.037303736692611
absolute error = 1.1e-14
relative error = 1.060441567006479e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.037574802371762
y[1] (numeric) = 1.037574802371751
absolute error = 1.1e-14
relative error = 1.060164527401342e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.037846830476019
y[1] (numeric) = 1.037846830476008
absolute error = 1.1e-14
relative error = 1.059886649647014e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.038119820733365
y[1] (numeric) = 1.038119820733354
absolute error = 1.1e-14
relative error = 1.059607935452885e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.038393772870811
y[1] (numeric) = 1.038393772870799
absolute error = 1.2e-14
relative error = 1.155630967125700e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.038668686614403
y[1] (numeric) = 1.038668686614391
absolute error = 1.2e-14
relative error = 1.155325095927812e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.038944561689229
y[1] (numeric) = 1.038944561689217
absolute error = 1.2e-14
relative error = 1.155018317867615e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.039221397819413
y[1] (numeric) = 1.039221397819401
absolute error = 1.2e-14
relative error = 1.154710634825213e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.039499194728119
y[1] (numeric) = 1.039499194728107
absolute error = 1.2e-14
relative error = 1.154402048684473e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.03977795213755
y[1] (numeric) = 1.039777952137538
absolute error = 1.2e-14
relative error = 1.154092561332994e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.04005766976895
y[1] (numeric) = 1.040057669768937
absolute error = 1.3e-14
relative error = 1.249930689217259e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.040338347342599
y[1] (numeric) = 1.040338347342586
absolute error = 1.3e-14
relative error = 1.249593464780637e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.040619984577821
y[1] (numeric) = 1.040619984577808
absolute error = 1.3e-14
relative error = 1.249255270191077e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.040902581192978
y[1] (numeric) = 1.040902581192966
absolute error = 1.2e-14
relative error = 1.152845637700966e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.041186136905475
y[1] (numeric) = 1.041186136905462
absolute error = 1.3e-14
relative error = 1.248575978800246e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.041470651431754
y[1] (numeric) = 1.041470651431742
absolute error = 1.2e-14
relative error = 1.152216817968235e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.041756124487303
y[1] (numeric) = 1.04175612448729
absolute error = 1.3e-14
relative error = 1.247892831577823e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.042042555786647
y[1] (numeric) = 1.042042555786634
absolute error = 1.3e-14
relative error = 1.247549817213193e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.042329945043355
y[1] (numeric) = 1.042329945043342
absolute error = 1.3e-14
relative error = 1.247205845118388e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.042618291970039
y[1] (numeric) = 1.042618291970025
absolute error = 1.4e-14
relative error = 1.342773295636972e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.04290759627835
y[1] (numeric) = 1.042907596278337
absolute error = 1.3e-14
relative error = 1.246515036077110e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.043197857678986
y[1] (numeric) = 1.043197857678973
absolute error = 1.3e-14
relative error = 1.246168203309364e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.043489075881684
y[1] (numeric) = 1.043489075881671
absolute error = 1.3e-14
relative error = 1.245820421168837e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.043781250595227
y[1] (numeric) = 1.043781250595214
absolute error = 1.3e-14
relative error = 1.245471691754054e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.04407438152744
y[1] (numeric) = 1.044074381527426
absolute error = 1.4e-14
relative error = 1.340900633872325e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.299
y[1] (analytic) = 1.044368468385191
memory used=45.7MB, alloc=4.3MB, time=3.03
y[1] (numeric) = 1.044368468385177
absolute error = 1.4e-14
relative error = 1.340523045630331e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.044663510874394
y[1] (numeric) = 1.04466351087438
absolute error = 1.4e-14
relative error = 1.340144444049918e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.044959508700007
y[1] (numeric) = 1.044959508699993
absolute error = 1.4e-14
relative error = 1.339764831406420e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.045256461566031
y[1] (numeric) = 1.045256461566017
absolute error = 1.4e-14
relative error = 1.339384209978939e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.045554369175514
y[1] (numeric) = 1.0455543691755
absolute error = 1.4e-14
relative error = 1.339002582050314e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.045853231230549
y[1] (numeric) = 1.045853231230535
absolute error = 1.4e-14
relative error = 1.338619949907085e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.046153047432273
y[1] (numeric) = 1.046153047432259
absolute error = 1.4e-14
relative error = 1.338236315839471e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.04645381748087
y[1] (numeric) = 1.046453817480856
absolute error = 1.4e-14
relative error = 1.337851682141332e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.04675554107557
y[1] (numeric) = 1.046755541075556
absolute error = 1.4e-14
relative error = 1.337466051110139e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.047058217914649
y[1] (numeric) = 1.047058217914635
absolute error = 1.4e-14
relative error = 1.337079425046947e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.047361847695432
y[1] (numeric) = 1.047361847695417
absolute error = 1.5e-14
relative error = 1.432169792417523e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.047666430114287
y[1] (numeric) = 1.047666430114272
absolute error = 1.5e-14
relative error = 1.431753425406949e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.047971964866632
y[1] (numeric) = 1.047971964866618
absolute error = 1.4e-14
relative error = 1.335913599728947e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.048278451646934
y[1] (numeric) = 1.048278451646919
absolute error = 1.5e-14
relative error = 1.430917517805859e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.048585890148704
y[1] (numeric) = 1.048585890148689
absolute error = 1.5e-14
relative error = 1.430497982179866e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.048894280064505
y[1] (numeric) = 1.04889428006449
absolute error = 1.5e-14
relative error = 1.430077395319338e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.049203621085947
y[1] (numeric) = 1.049203621085932
absolute error = 1.5e-14
relative error = 1.429655759715611e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.049513912903688
y[1] (numeric) = 1.049513912903673
absolute error = 1.5e-14
relative error = 1.429233077863592e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.049825155207437
y[1] (numeric) = 1.049825155207422
absolute error = 1.5e-14
relative error = 1.428809352261722e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.050137347685952
y[1] (numeric) = 1.050137347685937
absolute error = 1.5e-14
relative error = 1.428384585411947e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.05045049002704
y[1] (numeric) = 1.050450490027025
absolute error = 1.5e-14
relative error = 1.427958779819683e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.050764581917559
y[1] (numeric) = 1.050764581917544
absolute error = 1.5e-14
relative error = 1.427531937993783e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.051079623043417
y[1] (numeric) = 1.051079623043402
absolute error = 1.5e-14
relative error = 1.427104062446504e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.051395613089573
y[1] (numeric) = 1.051395613089558
absolute error = 1.5e-14
relative error = 1.426675155693472e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.051712551740036
y[1] (numeric) = 1.051712551740022
absolute error = 1.4e-14
relative error = 1.331162205570077e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.052030438677869
y[1] (numeric) = 1.052030438677855
absolute error = 1.4e-14
relative error = 1.330759974739361e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.052349273585184
y[1] (numeric) = 1.05234927358517
absolute error = 1.4e-14
relative error = 1.330356788512265e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=3.29
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.052669056143147
y[1] (numeric) = 1.052669056143133
absolute error = 1.4e-14
relative error = 1.329952649248978e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.052989786031974
y[1] (numeric) = 1.052989786031961
absolute error = 1.3e-14
relative error = 1.234579876504638e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.053311462930937
y[1] (numeric) = 1.053311462930924
absolute error = 1.3e-14
relative error = 1.234202840993137e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.053634086518358
y[1] (numeric) = 1.053634086518345
absolute error = 1.3e-14
relative error = 1.233824927110831e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.053957656471613
y[1] (numeric) = 1.0539576564716
absolute error = 1.3e-14
relative error = 1.233446137060264e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.054282172467133
y[1] (numeric) = 1.05428217246712
absolute error = 1.3e-14
relative error = 1.233066473046643e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.054607634180402
y[1] (numeric) = 1.054607634180389
absolute error = 1.3e-14
relative error = 1.232685937277808e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.054934041285958
y[1] (numeric) = 1.054934041285945
absolute error = 1.3e-14
relative error = 1.232304531964205e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.055261393457393
y[1] (numeric) = 1.055261393457381
absolute error = 1.2e-14
relative error = 1.137159008602025e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.055589690367357
y[1] (numeric) = 1.055589690367345
absolute error = 1.2e-14
relative error = 1.136805342976007e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.055918931687552
y[1] (numeric) = 1.05591893168754
absolute error = 1.2e-14
relative error = 1.136450880828683e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.056249117088736
y[1] (numeric) = 1.056249117088724
absolute error = 1.2e-14
relative error = 1.136095624209821e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.056580246240724
y[1] (numeric) = 1.056580246240712
absolute error = 1.2e-14
relative error = 1.135739575171463e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.056912318812388
y[1] (numeric) = 1.056912318812376
absolute error = 1.2e-14
relative error = 1.135382735767896e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.057245334471654
y[1] (numeric) = 1.057245334471642
absolute error = 1.2e-14
relative error = 1.135025108055630e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.057579292885507
y[1] (numeric) = 1.057579292885495
absolute error = 1.2e-14
relative error = 1.134666694093368e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.057914193719989
y[1] (numeric) = 1.057914193719977
absolute error = 1.2e-14
relative error = 1.134307495941981e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.058250036640198
y[1] (numeric) = 1.058250036640186
absolute error = 1.2e-14
relative error = 1.133947515664482e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.058586821310292
y[1] (numeric) = 1.05858682131028
absolute error = 1.2e-14
relative error = 1.133586755326002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.058924547393487
y[1] (numeric) = 1.058924547393475
absolute error = 1.2e-14
relative error = 1.133225216993757e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.059263214552056
y[1] (numeric) = 1.059263214552044
absolute error = 1.2e-14
relative error = 1.132862902737030e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.059602822447332
y[1] (numeric) = 1.05960282244732
absolute error = 1.2e-14
relative error = 1.132499814627142e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.059943370739707
y[1] (numeric) = 1.059943370739695
absolute error = 1.2e-14
relative error = 1.132135954737423e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.060284859088632
y[1] (numeric) = 1.060284859088621
absolute error = 1.1e-14
relative error = 1.037457048047923e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.060627287152621
y[1] (numeric) = 1.06062728715261
absolute error = 1.1e-14
relative error = 1.037122100594903e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.060970654589244
y[1] (numeric) = 1.060970654589233
absolute error = 1.1e-14
relative error = 1.036786451389521e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=3.55
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.061314961055134
y[1] (numeric) = 1.061314961055123
absolute error = 1.1e-14
relative error = 1.036450102339466e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.061660206205985
y[1] (numeric) = 1.061660206205974
absolute error = 1.1e-14
relative error = 1.036113055354150e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.062006389696552
y[1] (numeric) = 1.062006389696541
absolute error = 1.1e-14
relative error = 1.035775312344687e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.062353511180651
y[1] (numeric) = 1.06235351118064
absolute error = 1.1e-14
relative error = 1.035436875223870e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.06270157031116
y[1] (numeric) = 1.062701570311149
absolute error = 1.1e-14
relative error = 1.035097745906143e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.063050566740021
y[1] (numeric) = 1.06305056674001
absolute error = 1.1e-14
relative error = 1.034757926307578e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.063400500118237
y[1] (numeric) = 1.063400500118226
absolute error = 1.1e-14
relative error = 1.034417418345857e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.063751370095875
y[1] (numeric) = 1.063751370095864
absolute error = 1.1e-14
relative error = 1.034076223940241e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.064103176322065
y[1] (numeric) = 1.064103176322054
absolute error = 1.1e-14
relative error = 1.033734345011550e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.064455918445001
y[1] (numeric) = 1.06445591844499
absolute error = 1.1e-14
relative error = 1.033391783482141e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.06480959611194
y[1] (numeric) = 1.064809596111929
absolute error = 1.1e-14
relative error = 1.033048541275881e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.065164208969205
y[1] (numeric) = 1.065164208969194
absolute error = 1.1e-14
relative error = 1.032704620318126e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.065519756662183
y[1] (numeric) = 1.065519756662172
absolute error = 1.1e-14
relative error = 1.032360022535695e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.065876238835327
y[1] (numeric) = 1.065876238835316
absolute error = 1.1e-14
relative error = 1.032014749856850e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.066233655132154
y[1] (numeric) = 1.066233655132143
absolute error = 1.1e-14
relative error = 1.031668804211269e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.066592005195248
y[1] (numeric) = 1.066592005195237
absolute error = 1.1e-14
relative error = 1.031322187530026e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.066951288666259
y[1] (numeric) = 1.066951288666248
absolute error = 1.1e-14
relative error = 1.030974901745565e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.067311505185904
y[1] (numeric) = 1.067311505185893
absolute error = 1.1e-14
relative error = 1.030626948791677e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.067672654393966
y[1] (numeric) = 1.067672654393955
absolute error = 1.1e-14
relative error = 1.030278330603479e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.068034735929295
y[1] (numeric) = 1.068034735929285
absolute error = 1.0e-14
relative error = 9.362991355612623e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.068397749429811
y[1] (numeric) = 1.068397749429801
absolute error = 1.0e-14
relative error = 9.359810057010005e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.0687616945325
y[1] (numeric) = 1.06876169453249
absolute error = 1.0e-14
relative error = 9.356622763668772e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.069126570873417
y[1] (numeric) = 1.069126570873407
absolute error = 1.0e-14
relative error = 9.353429493226939e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.069492378087686
y[1] (numeric) = 1.069492378087675
absolute error = 1.1e-14
relative error = 1.028525328966685e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.069859115809498
y[1] (numeric) = 1.069859115809488
absolute error = 1.0e-14
relative error = 9.347025091648261e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.070226783672118
y[1] (numeric) = 1.070226783672107
absolute error = 1.1e-14
relative error = 1.027819539542568e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=3.81
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.070595381307876
y[1] (numeric) = 1.070595381307865
absolute error = 1.1e-14
relative error = 1.027465669295343e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.070964908348176
y[1] (numeric) = 1.070964908348165
absolute error = 1.1e-14
relative error = 1.027111151285626e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.38
y[1] (analytic) = 1.07133536442349
y[1] (numeric) = 1.071335364423479
absolute error = 1.1e-14
relative error = 1.026755987460505e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.071706749163362
y[1] (numeric) = 1.071706749163351
absolute error = 1.1e-14
relative error = 1.026400179768137e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.072079062196407
y[1] (numeric) = 1.072079062196396
absolute error = 1.1e-14
relative error = 1.026043730157728e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.072452303150313
y[1] (numeric) = 1.072452303150302
absolute error = 1.1e-14
relative error = 1.025686640579507e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.072826471651839
y[1] (numeric) = 1.072826471651828
absolute error = 1.1e-14
relative error = 1.025328912984708e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.073201567326815
y[1] (numeric) = 1.073201567326805
absolute error = 1.0e-14
relative error = 9.317914084777670e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.073577589800147
y[1] (numeric) = 1.073577589800137
absolute error = 1.0e-14
relative error = 9.314650468683461e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.073954538695812
y[1] (numeric) = 1.073954538695802
absolute error = 1.0e-14
relative error = 9.311381105706571e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.074332413636862
y[1] (numeric) = 1.074332413636851
absolute error = 1.1e-14
relative error = 1.023891661498183e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.07471121424542
y[1] (numeric) = 1.074711214245409
absolute error = 1.1e-14
relative error = 1.023530773122467e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.075090940142687
y[1] (numeric) = 1.075090940142676
absolute error = 1.1e-14
relative error = 1.023169258457342e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.075471590948937
y[1] (numeric) = 1.075471590948926
absolute error = 1.1e-14
relative error = 1.022807119460422e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.075853166283519
y[1] (numeric) = 1.075853166283508
absolute error = 1.1e-14
relative error = 1.022444358090143e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.076235665764857
y[1] (numeric) = 1.076235665764847
absolute error = 1.0e-14
relative error = 9.291645239143065e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.076619089010453
y[1] (numeric) = 1.076619089010443
absolute error = 1.0e-14
relative error = 9.288336146065592e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 1.077003435636883
y[1] (numeric) = 1.077003435636873
absolute error = 1.0e-14
relative error = 9.285021448503112e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.0773887052598
y[1] (numeric) = 1.07738870525979
absolute error = 1.0e-14
relative error = 9.281701164287418e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.077774897493935
y[1] (numeric) = 1.077774897493925
absolute error = 1.0e-14
relative error = 9.278375311256749e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.078162011953096
y[1] (numeric) = 1.078162011953086
absolute error = 1.0e-14
relative error = 9.275043907255598e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.078550048250168
y[1] (numeric) = 1.078550048250158
absolute error = 1.0e-14
relative error = 9.271706970134515e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.078939005997115
y[1] (numeric) = 1.078939005997105
absolute error = 1.0e-14
relative error = 9.268364517749893e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.079328884804979
y[1] (numeric) = 1.079328884804969
absolute error = 1.0e-14
relative error = 9.265016567963779e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.079719684283882
y[1] (numeric) = 1.079719684283872
absolute error = 1.0e-14
relative error = 9.261663138643660e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.080111404043024
y[1] (numeric) = 1.080111404043014
absolute error = 1.0e-14
relative error = 9.258304247662282e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=4.08
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.080504043690685
y[1] (numeric) = 1.080504043690675
absolute error = 1.0e-14
relative error = 9.254939912897440e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.080897602834225
y[1] (numeric) = 1.080897602834216
absolute error = 9e-15
relative error = 8.326413137008604e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.081292081080086
y[1] (numeric) = 1.081292081080077
absolute error = 9e-15
relative error = 8.323375485197338e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.08168747803379
y[1] (numeric) = 1.081687478033781
absolute error = 9e-15
relative error = 8.320332982276472e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.082083793299939
y[1] (numeric) = 1.08208379329993
absolute error = 9e-15
relative error = 8.317285644352426e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.082481026482219
y[1] (numeric) = 1.082481026482209
absolute error = 1.0e-14
relative error = 9.238037208372503e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.082879177183395
y[1] (numeric) = 1.082879177183385
absolute error = 1.0e-14
relative error = 9.234640586598345e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.083278245005318
y[1] (numeric) = 1.083278245005308
absolute error = 1.0e-14
relative error = 9.231238646310033e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.083678229548919
y[1] (numeric) = 1.083678229548909
absolute error = 1.0e-14
relative error = 9.227831405418654e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.084079130414214
y[1] (numeric) = 1.084079130414204
absolute error = 1.0e-14
relative error = 9.224418881838558e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.084480947200303
y[1] (numeric) = 1.084480947200293
absolute error = 1.0e-14
relative error = 9.221001093487174e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.084883679505368
y[1] (numeric) = 1.084883679505358
absolute error = 1.0e-14
relative error = 9.217578058284838e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.085287326926678
y[1] (numeric) = 1.085287326926667
absolute error = 1.1e-14
relative error = 1.013556477357001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.085691889060584
y[1] (numeric) = 1.085691889060573
absolute error = 1.1e-14
relative error = 1.013178795092405e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.086097365502525
y[1] (numeric) = 1.086097365502514
absolute error = 1.1e-14
relative error = 1.012800541589605e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.086503755847024
y[1] (numeric) = 1.086503755847013
absolute error = 1.1e-14
relative error = 1.012421718820893e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.086911059687692
y[1] (numeric) = 1.08691105968768
absolute error = 1.2e-14
relative error = 1.104046176827755e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.087319276617223
y[1] (numeric) = 1.087319276617212
absolute error = 1.1e-14
relative error = 1.011662373375949e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.087728406227402
y[1] (numeric) = 1.087728406227391
absolute error = 1.1e-14
relative error = 1.011281854645279e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.088138448109099
y[1] (numeric) = 1.088138448109088
absolute error = 1.1e-14
relative error = 1.010900774539778e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.088549401852272
y[1] (numeric) = 1.088549401852261
absolute error = 1.1e-14
relative error = 1.010519135032589e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.088961267045966
y[1] (numeric) = 1.088961267045956
absolute error = 1.0e-14
relative error = 9.183063073608743e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.089374043278318
y[1] (numeric) = 1.089374043278308
absolute error = 1.0e-14
relative error = 9.179583506420261e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.089787730136551
y[1] (numeric) = 1.089787730136541
absolute error = 1.0e-14
relative error = 9.176098907579914e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.090202327206978
y[1] (numeric) = 1.090202327206968
absolute error = 1.0e-14
relative error = 9.172609295028107e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.090617834075001
y[1] (numeric) = 1.090617834074992
absolute error = 9e-15
relative error = 8.252203218034922e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=4.33
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.091034250325115
y[1] (numeric) = 1.091034250325106
absolute error = 9e-15
relative error = 8.249053590497373e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.091451575540903
y[1] (numeric) = 1.091451575540894
absolute error = 9e-15
relative error = 8.245899499059102e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.091869809305039
y[1] (numeric) = 1.09186980930503
absolute error = 9e-15
relative error = 8.242740959866253e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.09228895119929
y[1] (numeric) = 1.092288951199281
absolute error = 9e-15
relative error = 8.239577989064484e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.092709000804515
y[1] (numeric) = 1.092709000804506
absolute error = 9e-15
relative error = 8.236410602798809e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.093129957700663
y[1] (numeric) = 1.093129957700654
absolute error = 9e-15
relative error = 8.233238817213454e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.093551821466778
y[1] (numeric) = 1.093551821466769
absolute error = 9e-15
relative error = 8.230062648451653e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.093974591680996
y[1] (numeric) = 1.093974591680987
absolute error = 9e-15
relative error = 8.226882112655509e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.094398267920547
y[1] (numeric) = 1.094398267920538
absolute error = 9e-15
relative error = 8.223697225965819e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.094822849761754
y[1] (numeric) = 1.094822849761745
absolute error = 9e-15
relative error = 8.220508004521922e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.095248336780037
y[1] (numeric) = 1.095248336780027
absolute error = 1.0e-14
relative error = 9.130349404957224e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.095674728549907
y[1] (numeric) = 1.095674728549897
absolute error = 1.0e-14
relative error = 9.126796246578310e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.096102024644973
y[1] (numeric) = 1.096102024644963
absolute error = 1.0e-14
relative error = 9.123238325591996e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.096530224637939
y[1] (numeric) = 1.096530224637929
absolute error = 1.0e-14
relative error = 9.119675659922533e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.096959328100605
y[1] (numeric) = 1.096959328100595
absolute error = 1.0e-14
relative error = 9.116108267491640e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.445
y[1] (analytic) = 1.097389334603868
y[1] (numeric) = 1.097389334603858
absolute error = 1.0e-14
relative error = 9.112536166218316e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.097820243717721
y[1] (numeric) = 1.097820243717711
absolute error = 1.0e-14
relative error = 9.108959374018674e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.098252055011255
y[1] (numeric) = 1.098252055011245
absolute error = 1.0e-14
relative error = 9.105377908805751e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.098684768052659
y[1] (numeric) = 1.098684768052649
absolute error = 1.0e-14
relative error = 9.101791788489334e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.09911838240922
y[1] (numeric) = 1.09911838240921
absolute error = 1.0e-14
relative error = 9.098201030975783e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.099552897647323
y[1] (numeric) = 1.099552897647313
absolute error = 1.0e-14
relative error = 9.094605654167862e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.099988313332454
y[1] (numeric) = 1.099988313332444
absolute error = 1.0e-14
relative error = 9.091005675964540e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.100424629029196
y[1] (numeric) = 1.100424629029186
absolute error = 1.0e-14
relative error = 9.087401114260852e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.100861844301234
y[1] (numeric) = 1.100861844301224
absolute error = 1.0e-14
relative error = 9.083791986947686e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.101299958711353
y[1] (numeric) = 1.101299958711343
absolute error = 1.0e-14
relative error = 9.080178311911629e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.101738971821439
y[1] (numeric) = 1.101738971821428
absolute error = 1.1e-14
relative error = 9.984216117738269e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=4.60
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.102178883192478
y[1] (numeric) = 1.102178883192467
absolute error = 1.1e-14
relative error = 9.980231129214100e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.102619692384558
y[1] (numeric) = 1.102619692384548
absolute error = 1.0e-14
relative error = 9.069310179263808e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.103061398956872
y[1] (numeric) = 1.103061398956862
absolute error = 1.0e-14
relative error = 9.065678492109925e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.103504002467712
y[1] (numeric) = 1.103504002467702
absolute error = 1.0e-14
relative error = 9.062042346595472e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.103947502474475
y[1] (numeric) = 1.103947502474465
absolute error = 1.0e-14
relative error = 9.058401760577574e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.10439189853366
y[1] (numeric) = 1.104391898533651
absolute error = 9e-15
relative error = 8.149281076717076e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.104837190200873
y[1] (numeric) = 1.104837190200863
absolute error = 1.0e-14
relative error = 9.051107338432260e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.10528337703082
y[1] (numeric) = 1.105283377030811
absolute error = 9e-15
relative error = 8.142708184191792e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.105730458577316
y[1] (numeric) = 1.105730458577307
absolute error = 9e-15
relative error = 8.139415831576003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.106178434393279
y[1] (numeric) = 1.10617843439327
absolute error = 9e-15
relative error = 8.136119562786771e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.106627304030734
y[1] (numeric) = 1.106627304030724
absolute error = 1.0e-14
relative error = 9.036465993181633e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.107077067040809
y[1] (numeric) = 1.1070770670408
absolute error = 9e-15
relative error = 8.129515340839630e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.107527722973743
y[1] (numeric) = 1.107527722973734
absolute error = 9e-15
relative error = 8.126207419742729e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.10797927137888
y[1] (numeric) = 1.107979271378871
absolute error = 9e-15
relative error = 8.122895646594093e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.108431711804671
y[1] (numeric) = 1.108431711804662
absolute error = 9e-15
relative error = 8.119580037408736e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.108885043798676
y[1] (numeric) = 1.108885043798667
absolute error = 9e-15
relative error = 8.116260608195197e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.109339266907563
y[1] (numeric) = 1.109339266907554
absolute error = 9e-15
relative error = 8.112937374955407e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.109794380677109
y[1] (numeric) = 1.1097943806771
absolute error = 9e-15
relative error = 8.109610353684536e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.1102503846522
y[1] (numeric) = 1.110250384652191
absolute error = 9e-15
relative error = 8.106279560370847e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.110707278376832
y[1] (numeric) = 1.110707278376823
absolute error = 9e-15
relative error = 8.102945010995553e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.111165061394111
y[1] (numeric) = 1.111165061394103
absolute error = 8e-15
relative error = 7.199650419140148e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.111623733246256
y[1] (numeric) = 1.111623733246247
absolute error = 9e-15
relative error = 8.096264707948842e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.112083293474592
y[1] (numeric) = 1.112083293474584
absolute error = 8e-15
relative error = 7.193705765514027e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.112543741619562
y[1] (numeric) = 1.112543741619553
absolute error = 9e-15
relative error = 8.089569572247506e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.113005077220716
y[1] (numeric) = 1.113005077220707
absolute error = 9e-15
relative error = 8.086216482025304e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.113467299816718
y[1] (numeric) = 1.11346729981671
absolute error = 8e-15
relative error = 7.184764205753360e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.3MB, time=4.86
x[1] = 0.482
y[1] (analytic) = 1.113930408945348
y[1] (numeric) = 1.113930408945339
absolute error = 9e-15
relative error = 8.079499336516955e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.114394404143494
y[1] (numeric) = 1.114394404143485
absolute error = 9e-15
relative error = 8.076135313078190e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.114859284947162
y[1] (numeric) = 1.114859284947153
absolute error = 9e-15
relative error = 8.072767677067469e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.115325050891472
y[1] (numeric) = 1.115325050891463
absolute error = 9e-15
relative error = 8.069396444387543e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.115791701510657
y[1] (numeric) = 1.115791701510648
absolute error = 9e-15
relative error = 8.066021630932555e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.116259236338066
y[1] (numeric) = 1.116259236338058
absolute error = 8e-15
relative error = 7.166794002300332e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.116727654906166
y[1] (numeric) = 1.116727654906158
absolute error = 8e-15
relative error = 7.163787844648843e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.117196956746538
y[1] (numeric) = 1.117196956746529
absolute error = 9e-15
relative error = 8.055875864726204e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.117667141389878
y[1] (numeric) = 1.11766714138987
absolute error = 8e-15
relative error = 7.157766121719905e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.118138208366005
y[1] (numeric) = 1.118138208365996
absolute error = 9e-15
relative error = 8.049094407704912e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.118610157203849
y[1] (numeric) = 1.11861015720384
absolute error = 9e-15
relative error = 8.045698442875745e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.119082987431462
y[1] (numeric) = 1.119082987431454
absolute error = 8e-15
relative error = 7.148710229579786e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.119556698576015
y[1] (numeric) = 1.119556698576007
absolute error = 8e-15
relative error = 7.145685439759638e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.120031290163796
y[1] (numeric) = 1.120031290163788
absolute error = 8e-15
relative error = 7.142657593816027e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.120506761720213
y[1] (numeric) = 1.120506761720205
absolute error = 8e-15
relative error = 7.139626705793655e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.120983112769795
y[1] (numeric) = 1.120983112769787
absolute error = 8e-15
relative error = 7.136592789728206e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.121460342836192
y[1] (numeric) = 1.121460342836183
absolute error = 9e-15
relative error = 8.025250342102021e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.121938451442172
y[1] (numeric) = 1.121938451442163
absolute error = 9e-15
relative error = 8.021830420760730e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 1.122417438109627
y[1] (numeric) = 1.122417438109619
absolute error = 8e-15
relative error = 7.127473013492718e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 1.122897302359572
y[1] (numeric) = 1.122897302359563
absolute error = 9e-15
relative error = 8.014980516106038e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.502
y[1] (analytic) = 1.12337804371214
y[1] (numeric) = 1.123378043712132
absolute error = 8e-15
relative error = 7.121378279358609e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.503
y[1] (analytic) = 1.123859661686593
y[1] (numeric) = 1.123859661686584
absolute error = 9e-15
relative error = 8.008117300423049e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.504
y[1] (analytic) = 1.12434215580131
y[1] (numeric) = 1.124342155801301
absolute error = 9e-15
relative error = 8.004680740255416e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.505
y[1] (analytic) = 1.124825525573799
y[1] (numeric) = 1.12482552557379
absolute error = 9e-15
relative error = 8.001240899479851e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.506
y[1] (analytic) = 1.125309770520689
y[1] (numeric) = 1.12530977052068
absolute error = 9e-15
relative error = 7.997797793789380e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.507
y[1] (analytic) = 1.125794890157736
y[1] (numeric) = 1.125794890157727
absolute error = 9e-15
relative error = 7.994351438865567e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=76.2MB, alloc=4.3MB, time=5.12
x[1] = 0.508
y[1] (analytic) = 1.126280883999819
y[1] (numeric) = 1.126280883999811
absolute error = 8e-15
relative error = 7.103023867003043e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.509
y[1] (analytic) = 1.126767751560946
y[1] (numeric) = 1.126767751560938
absolute error = 8e-15
relative error = 7.099954705765544e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.51
y[1] (analytic) = 1.127255492354249
y[1] (numeric) = 1.127255492354241
absolute error = 8e-15
relative error = 7.096882698075989e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.511
y[1] (analytic) = 1.127744105891986
y[1] (numeric) = 1.127744105891978
absolute error = 8e-15
relative error = 7.093807857831740e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.512
y[1] (analytic) = 1.128233591685545
y[1] (numeric) = 1.128233591685537
absolute error = 8e-15
relative error = 7.090730198919406e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.513
y[1] (analytic) = 1.12872394924544
y[1] (numeric) = 1.128723949245432
absolute error = 8e-15
relative error = 7.087649735214759e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.514
y[1] (analytic) = 1.129215178081312
y[1] (numeric) = 1.129215178081305
absolute error = 7e-15
relative error = 6.198995670509795e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.515
y[1] (analytic) = 1.129707277701934
y[1] (numeric) = 1.129707277701927
absolute error = 7e-15
relative error = 6.196295392767139e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.516
y[1] (analytic) = 1.130200247615206
y[1] (numeric) = 1.130200247615199
absolute error = 7e-15
relative error = 6.193592697197194e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.517
y[1] (analytic) = 1.130694087328158
y[1] (numeric) = 1.130694087328151
absolute error = 7e-15
relative error = 6.190887595902331e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.518
y[1] (analytic) = 1.13118879634695
y[1] (numeric) = 1.131188796346943
absolute error = 7e-15
relative error = 6.188180100974949e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.519
y[1] (analytic) = 1.131684374176873
y[1] (numeric) = 1.131684374176866
absolute error = 7e-15
relative error = 6.185470224497380e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.52
y[1] (analytic) = 1.13218082032235
y[1] (numeric) = 1.132180820322343
absolute error = 7e-15
relative error = 6.182757978541792e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.521
y[1] (analytic) = 1.132678134286934
y[1] (numeric) = 1.132678134286927
absolute error = 7e-15
relative error = 6.180043375170104e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.522
y[1] (analytic) = 1.133176315573312
y[1] (numeric) = 1.133176315573305
absolute error = 7e-15
relative error = 6.177326426433882e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.523
y[1] (analytic) = 1.133675363683301
y[1] (numeric) = 1.133675363683295
absolute error = 6e-15
relative error = 5.292520409463653e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.524
y[1] (analytic) = 1.134175278117855
y[1] (numeric) = 1.134175278117849
absolute error = 6e-15
relative error = 5.290187606590138e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.525
y[1] (analytic) = 1.134676058377059
y[1] (numeric) = 1.134676058377053
absolute error = 6e-15
relative error = 5.287852824339903e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.526
y[1] (analytic) = 1.135177703960132
y[1] (numeric) = 1.135177703960126
absolute error = 6e-15
relative error = 5.285516073006595e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.527
y[1] (analytic) = 1.135680214365429
y[1] (numeric) = 1.135680214365423
absolute error = 6e-15
relative error = 5.283177362874593e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.528
y[1] (analytic) = 1.136183589090439
y[1] (numeric) = 1.136183589090434
absolute error = 5e-15
relative error = 4.400697253515783e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.529
y[1] (analytic) = 1.136687827631789
y[1] (numeric) = 1.136687827631784
absolute error = 5e-15
relative error = 4.398745089421039e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.53
y[1] (analytic) = 1.137192929485239
y[1] (numeric) = 1.137192929485234
absolute error = 5e-15
relative error = 4.396791318658037e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.531
y[1] (analytic) = 1.137698894145688
y[1] (numeric) = 1.137698894145683
absolute error = 5e-15
relative error = 4.394835949765567e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.532
y[1] (analytic) = 1.13820572110717
y[1] (numeric) = 1.138205721107166
absolute error = 4e-15
relative error = 3.514303193019509e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.533
y[1] (analytic) = 1.13871340986286
y[1] (numeric) = 1.138713409862856
absolute error = 4e-15
relative error = 3.512736361365707e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.534
y[1] (analytic) = 1.139221959905068
y[1] (numeric) = 1.139221959905064
absolute error = 4e-15
relative error = 3.511168271662637e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=5.38
NO POLE
x[1] = 0.535
y[1] (analytic) = 1.139731370725244
y[1] (numeric) = 1.13973137072524
absolute error = 4e-15
relative error = 3.509598930715300e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.536
y[1] (analytic) = 1.140241641813978
y[1] (numeric) = 1.140241641813974
absolute error = 4e-15
relative error = 3.508028345322062e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.537
y[1] (analytic) = 1.140752772660999
y[1] (numeric) = 1.140752772660995
absolute error = 4e-15
relative error = 3.506456522274605e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.538
y[1] (analytic) = 1.141264762755175
y[1] (numeric) = 1.141264762755171
absolute error = 4e-15
relative error = 3.504883468357888e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.539
y[1] (analytic) = 1.141777611584517
y[1] (numeric) = 1.141777611584513
absolute error = 4e-15
relative error = 3.503309190350078e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.54
y[1] (analytic) = 1.142291318636176
y[1] (numeric) = 1.142291318636172
absolute error = 4e-15
relative error = 3.501733695022517e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.541
y[1] (analytic) = 1.142805883396445
y[1] (numeric) = 1.142805883396441
absolute error = 4e-15
relative error = 3.500156989139668e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.542
y[1] (analytic) = 1.143321305350758
y[1] (numeric) = 1.143321305350755
absolute error = 3e-15
relative error = 2.623934309594304e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.543
y[1] (analytic) = 1.143837583983696
y[1] (numeric) = 1.143837583983692
absolute error = 4e-15
relative error = 3.496999972731282e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.544
y[1] (analytic) = 1.144354718778978
y[1] (numeric) = 1.144354718778974
absolute error = 4e-15
relative error = 3.495419675699843e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.545
y[1] (analytic) = 1.144872709219469
y[1] (numeric) = 1.144872709219466
absolute error = 3e-15
relative error = 2.620378646325919e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.546
y[1] (analytic) = 1.14539155478718
y[1] (numeric) = 1.145391554787177
absolute error = 3e-15
relative error = 2.619191653248584e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.547
y[1] (analytic) = 1.145911254963266
y[1] (numeric) = 1.145911254963262
absolute error = 4e-15
relative error = 3.490671710112688e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.548
y[1] (analytic) = 1.146431809228025
y[1] (numeric) = 1.146431809228021
absolute error = 4e-15
relative error = 3.489086719159937e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.549
y[1] (analytic) = 1.146953217060904
y[1] (numeric) = 1.1469532170609
absolute error = 4e-15
relative error = 3.487500571514241e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.55
y[1] (analytic) = 1.147475477940494
y[1] (numeric) = 1.147475477940491
absolute error = 3e-15
relative error = 2.614434955407016e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.551
y[1] (analytic) = 1.147998591344536
y[1] (numeric) = 1.147998591344533
absolute error = 3e-15
relative error = 2.613243624703755e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.552
y[1] (analytic) = 1.148522556749915
y[1] (numeric) = 1.148522556749912
absolute error = 3e-15
relative error = 2.612051441540155e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.553
y[1] (analytic) = 1.149047373632667
y[1] (numeric) = 1.149047373632664
absolute error = 3e-15
relative error = 2.610858410924887e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.554
y[1] (analytic) = 1.149573041467974
y[1] (numeric) = 1.149573041467971
absolute error = 3e-15
relative error = 2.609664537861013e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.555
y[1] (analytic) = 1.150099559730168
y[1] (numeric) = 1.150099559730166
absolute error = 2e-15
relative error = 1.738979884897297e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.556
y[1] (analytic) = 1.150626927892733
y[1] (numeric) = 1.15062692789273
absolute error = 3e-15
relative error = 2.607274284371411e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.557
y[1] (analytic) = 1.151155145428298
y[1] (numeric) = 1.151155145428295
absolute error = 3e-15
relative error = 2.606077913923429e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.558
y[1] (analytic) = 1.151684211808647
y[1] (numeric) = 1.151684211808644
absolute error = 3e-15
relative error = 2.604880720982265e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.559
y[1] (analytic) = 1.152214126504714
y[1] (numeric) = 1.152214126504711
absolute error = 3e-15
relative error = 2.603682710522406e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.56
y[1] (analytic) = 1.152744888986584
y[1] (numeric) = 1.152744888986581
absolute error = 3e-15
relative error = 2.602483887512526e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.3MB, time=5.64
NO POLE
x[1] = 0.561
y[1] (analytic) = 1.153276498723494
y[1] (numeric) = 1.153276498723491
absolute error = 3e-15
relative error = 2.601284256915453e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.562
y[1] (analytic) = 1.153808955183835
y[1] (numeric) = 1.153808955183832
absolute error = 3e-15
relative error = 2.600083823688137e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.563
y[1] (analytic) = 1.15434225783515
y[1] (numeric) = 1.154342257835147
absolute error = 3e-15
relative error = 2.598882592781617e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.564
y[1] (analytic) = 1.154876406144137
y[1] (numeric) = 1.154876406144134
absolute error = 3e-15
relative error = 2.597680569140987e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.565
y[1] (analytic) = 1.155411399576647
y[1] (numeric) = 1.155411399576644
absolute error = 3e-15
relative error = 2.596477757705374e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.566
y[1] (analytic) = 1.155947237597687
y[1] (numeric) = 1.155947237597684
absolute error = 3e-15
relative error = 2.595274163407891e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.567
y[1] (analytic) = 1.156483919671419
y[1] (numeric) = 1.156483919671416
absolute error = 3e-15
relative error = 2.594069791175620e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.568
y[1] (analytic) = 1.157021445261162
y[1] (numeric) = 1.157021445261158
absolute error = 4e-15
relative error = 3.457152861239424e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.569
y[1] (analytic) = 1.157559813829388
y[1] (numeric) = 1.157559813829385
absolute error = 3e-15
relative error = 2.591658732584654e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.57
y[1] (analytic) = 1.158099024837731
y[1] (numeric) = 1.158099024837728
absolute error = 3e-15
relative error = 2.590452056049654e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.571
y[1] (analytic) = 1.158639077746979
y[1] (numeric) = 1.158639077746976
absolute error = 3e-15
relative error = 2.589244621227192e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.572
y[1] (analytic) = 1.159179972017079
y[1] (numeric) = 1.159179972017076
absolute error = 3e-15
relative error = 2.588036433013699e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.573
y[1] (analytic) = 1.159721707107137
y[1] (numeric) = 1.159721707107134
absolute error = 3e-15
relative error = 2.586827496299382e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.574
y[1] (analytic) = 1.160264282475418
y[1] (numeric) = 1.160264282475415
absolute error = 3e-15
relative error = 2.585617815968199e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.575
y[1] (analytic) = 1.160807697579346
y[1] (numeric) = 1.160807697579343
absolute error = 3e-15
relative error = 2.584407396897829e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.576
y[1] (analytic) = 1.161351951875507
y[1] (numeric) = 1.161351951875504
absolute error = 3e-15
relative error = 2.583196243959635e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.577
y[1] (analytic) = 1.161897044819646
y[1] (numeric) = 1.161897044819643
absolute error = 3e-15
relative error = 2.581984362018643e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.578
y[1] (analytic) = 1.16244297586667
y[1] (numeric) = 1.162442975866667
absolute error = 3e-15
relative error = 2.580771755933509e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.579
y[1] (analytic) = 1.162989744470649
y[1] (numeric) = 1.162989744470646
absolute error = 3e-15
relative error = 2.579558430556489e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.58
y[1] (analytic) = 1.163537350084813
y[1] (numeric) = 1.16353735008481
absolute error = 3e-15
relative error = 2.578344390733416e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.581
y[1] (analytic) = 1.164085792161558
y[1] (numeric) = 1.164085792161555
absolute error = 3e-15
relative error = 2.577129641303658e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.582
y[1] (analytic) = 1.164635070152441
y[1] (numeric) = 1.164635070152438
absolute error = 3e-15
relative error = 2.575914187100106e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.583
y[1] (analytic) = 1.165185183508184
y[1] (numeric) = 1.165185183508181
absolute error = 3e-15
relative error = 2.574698032949137e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.584
y[1] (analytic) = 1.165736131678674
y[1] (numeric) = 1.165736131678671
absolute error = 3e-15
relative error = 2.573481183670583e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.585
y[1] (analytic) = 1.166287914112962
y[1] (numeric) = 1.16628791411296
absolute error = 2e-15
relative error = 1.714842429385141e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.586
y[1] (analytic) = 1.166840530259268
y[1] (numeric) = 1.166840530259265
absolute error = 3e-15
relative error = 2.571045418977185e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=5.90
NO POLE
x[1] = 0.587
y[1] (analytic) = 1.167393979564973
y[1] (numeric) = 1.167393979564971
absolute error = 2e-15
relative error = 1.713217675446036e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.588
y[1] (analytic) = 1.16794826147663
y[1] (numeric) = 1.167948261476628
absolute error = 2e-15
relative error = 1.712404620964470e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.589
y[1] (analytic) = 1.168503375439956
y[1] (numeric) = 1.168503375439954
absolute error = 2e-15
relative error = 1.711591119064569e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.59
y[1] (analytic) = 1.169059320899836
y[1] (numeric) = 1.169059320899835
absolute error = 1e-15
relative error = 8.553885864665024e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.591
y[1] (analytic) = 1.169616097300327
y[1] (numeric) = 1.169616097300326
absolute error = 1e-15
relative error = 8.549813928759789e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.592
y[1] (analytic) = 1.170173704084652
y[1] (numeric) = 1.17017370408465
absolute error = 2e-15
relative error = 1.709147960699104e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.593
y[1] (analytic) = 1.170732140695203
y[1] (numeric) = 1.170732140695201
absolute error = 2e-15
relative error = 1.708332700947598e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.594
y[1] (analytic) = 1.171291406573544
y[1] (numeric) = 1.171291406573542
absolute error = 2e-15
relative error = 1.707517009666050e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.595
y[1] (analytic) = 1.17185150116041
y[1] (numeric) = 1.171851501160408
absolute error = 2e-15
relative error = 1.706700890018511e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.596
y[1] (analytic) = 1.172412423895706
y[1] (numeric) = 1.172412423895704
absolute error = 2e-15
relative error = 1.705884345164457e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.597
y[1] (analytic) = 1.172974174218508
y[1] (numeric) = 1.172974174218507
absolute error = 1e-15
relative error = 8.525336891293862e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.598
y[1] (analytic) = 1.173536751567068
y[1] (numeric) = 1.173536751567067
absolute error = 1e-15
relative error = 8.521249962258636e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.599
y[1] (analytic) = 1.174100155378807
y[1] (numeric) = 1.174100155378806
absolute error = 1e-15
relative error = 8.517160954444844e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.6
y[1] (analytic) = 1.174664385090322
y[1] (numeric) = 1.174664385090321
absolute error = 1e-15
relative error = 8.513069883557492e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.601
y[1] (analytic) = 1.175229440137383
y[1] (numeric) = 1.175229440137382
absolute error = 1e-15
relative error = 8.508976765278286e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.602
y[1] (analytic) = 1.175795319954935
y[1] (numeric) = 1.175795319954934
absolute error = 1e-15
relative error = 8.504881615265548e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.603
y[1] (analytic) = 1.176362023977098
y[1] (numeric) = 1.176362023977098
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.604
y[1] (analytic) = 1.176929551637169
y[1] (numeric) = 1.176929551637169
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.605
y[1] (analytic) = 1.17749790236762
y[1] (numeric) = 1.17749790236762
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.606
y[1] (analytic) = 1.1780670756001
y[1] (numeric) = 1.1780670756001
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.607
y[1] (analytic) = 1.178637070765435
y[1] (numeric) = 1.178637070765436
absolute error = 1e-15
relative error = 8.484375935592932e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.608
y[1] (analytic) = 1.179207887293632
y[1] (numeric) = 1.179207887293632
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.609
y[1] (analytic) = 1.179779524613873
y[1] (numeric) = 1.179779524613873
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.61
y[1] (analytic) = 1.18035198215452
y[1] (numeric) = 1.180351982154521
absolute error = 1e-15
relative error = 8.472049143973818e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.611
y[1] (analytic) = 1.180925259343118
y[1] (numeric) = 1.180925259343118
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.612
y[1] (analytic) = 1.181499355606388
y[1] (numeric) = 1.181499355606388
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=6.16
NO POLE
x[1] = 0.613
y[1] (analytic) = 1.182074270370234
y[1] (numeric) = 1.182074270370234
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.614
y[1] (analytic) = 1.182650003059741
y[1] (numeric) = 1.182650003059741
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.615
y[1] (analytic) = 1.183226553099177
y[1] (numeric) = 1.183226553099177
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.616
y[1] (analytic) = 1.183803919911992
y[1] (numeric) = 1.183803919911992
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.617
y[1] (analytic) = 1.184382102920819
y[1] (numeric) = 1.184382102920819
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.618
y[1] (analytic) = 1.184961101547476
y[1] (numeric) = 1.184961101547475
absolute error = 1e-15
relative error = 8.439095584606703e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.619
y[1] (analytic) = 1.185540915212962
y[1] (numeric) = 1.185540915212962
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.62
y[1] (analytic) = 1.186121543337466
y[1] (numeric) = 1.186121543337466
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.621
y[1] (analytic) = 1.186702985340359
y[1] (numeric) = 1.186702985340359
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.622
y[1] (analytic) = 1.187285240640198
y[1] (numeric) = 1.187285240640198
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.623
y[1] (analytic) = 1.187868308654729
y[1] (numeric) = 1.187868308654729
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.624
y[1] (analytic) = 1.188452188800884
y[1] (numeric) = 1.188452188800884
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.625
y[1] (analytic) = 1.189036880494782
y[1] (numeric) = 1.189036880494782
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.626
y[1] (analytic) = 1.189622383151732
y[1] (numeric) = 1.189622383151732
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.627
y[1] (analytic) = 1.190208696186232
y[1] (numeric) = 1.190208696186232
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.628
y[1] (analytic) = 1.190795819011968
y[1] (numeric) = 1.190795819011968
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.629
y[1] (analytic) = 1.191383751041817
y[1] (numeric) = 1.191383751041817
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.63
y[1] (analytic) = 1.191972491687848
y[1] (numeric) = 1.191972491687848
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.631
y[1] (analytic) = 1.19256204036132
y[1] (numeric) = 1.19256204036132
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.632
y[1] (analytic) = 1.193152396472684
y[1] (numeric) = 1.193152396472684
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.633
y[1] (analytic) = 1.193743559431585
y[1] (numeric) = 1.193743559431585
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.634
y[1] (analytic) = 1.194335528646859
y[1] (numeric) = 1.194335528646859
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.635
y[1] (analytic) = 1.194928303526537
y[1] (numeric) = 1.194928303526537
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.636
y[1] (analytic) = 1.195521883477845
y[1] (numeric) = 1.195521883477845
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.637
y[1] (analytic) = 1.196116267907202
y[1] (numeric) = 1.196116267907202
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.638
y[1] (analytic) = 1.196711456220224
y[1] (numeric) = 1.196711456220224
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=95.3MB, alloc=4.4MB, time=6.42
x[1] = 0.639
y[1] (analytic) = 1.197307447821723
y[1] (numeric) = 1.197307447821723
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.64
y[1] (analytic) = 1.197904242115707
y[1] (numeric) = 1.197904242115707
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.641
y[1] (analytic) = 1.198501838505383
y[1] (numeric) = 1.198501838505382
absolute error = 1e-15
relative error = 8.343750237772443e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.642
y[1] (analytic) = 1.199100236393153
y[1] (numeric) = 1.199100236393152
absolute error = 1e-15
relative error = 8.339586380267601e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.643
y[1] (analytic) = 1.19969943518062
y[1] (numeric) = 1.199699435180619
absolute error = 1e-15
relative error = 8.335421111950808e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.644
y[1] (analytic) = 1.200299434268585
y[1] (numeric) = 1.200299434268584
absolute error = 1e-15
relative error = 8.331254447431781e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.645
y[1] (analytic) = 1.200900233057049
y[1] (numeric) = 1.200900233057048
absolute error = 1e-15
relative error = 8.327086401293877e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.646
y[1] (analytic) = 1.201501830945213
y[1] (numeric) = 1.201501830945212
absolute error = 1e-15
relative error = 8.322916988094034e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.647
y[1] (analytic) = 1.20210422733148
y[1] (numeric) = 1.202104227331479
absolute error = 1e-15
relative error = 8.318746222362715e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.648
y[1] (analytic) = 1.202707421613454
y[1] (numeric) = 1.202707421613452
absolute error = 2e-15
relative error = 1.662914823720771e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.649
y[1] (analytic) = 1.203311413187939
y[1] (numeric) = 1.203311413187937
absolute error = 2e-15
relative error = 1.662080138258965e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.65
y[1] (analytic) = 1.203916201450944
y[1] (numeric) = 1.203916201450943
absolute error = 1e-15
relative error = 8.306225954886338e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.651
y[1] (analytic) = 1.204521785797682
y[1] (numeric) = 1.204521785797681
absolute error = 1e-15
relative error = 8.302049923802419e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.652
y[1] (analytic) = 1.205128165622568
y[1] (numeric) = 1.205128165622567
absolute error = 1e-15
relative error = 8.297872612440362e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.653
y[1] (analytic) = 1.205735340319221
y[1] (numeric) = 1.205735340319221
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.654
y[1] (analytic) = 1.206343309280469
y[1] (numeric) = 1.206343309280468
absolute error = 1e-15
relative error = 8.289514206336969e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.655
y[1] (analytic) = 1.20695207189834
y[1] (numeric) = 1.20695207189834
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.656
y[1] (analytic) = 1.207561627564074
y[1] (numeric) = 1.207561627564074
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.657
y[1] (analytic) = 1.208171975668115
y[1] (numeric) = 1.208171975668114
absolute error = 1e-15
relative error = 8.276967353484618e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.658
y[1] (analytic) = 1.208783115600113
y[1] (numeric) = 1.208783115600113
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.659
y[1] (analytic) = 1.20939504674893
y[1] (numeric) = 1.20939504674893
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.66
y[1] (analytic) = 1.210007768502635
y[1] (numeric) = 1.210007768502634
absolute error = 1e-15
relative error = 8.264409750339734e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.661
y[1] (analytic) = 1.210621280248505
y[1] (numeric) = 1.210621280248504
absolute error = 1e-15
relative error = 8.260221559914504e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.662
y[1] (analytic) = 1.211235581373029
y[1] (numeric) = 1.211235581373028
absolute error = 1e-15
relative error = 8.256032231701969e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.663
y[1] (analytic) = 1.211850671261906
y[1] (numeric) = 1.211850671261905
absolute error = 1e-15
relative error = 8.251841779801922e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.664
y[1] (analytic) = 1.212466549300046
y[1] (numeric) = 1.212466549300045
absolute error = 1e-15
relative error = 8.247650218286827e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.665
y[1] (analytic) = 1.213083214871571
y[1] (numeric) = 1.21308321487157
absolute error = 1e-15
relative error = 8.243457561201767e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=6.68
NO POLE
x[1] = 0.666
y[1] (analytic) = 1.213700667359816
y[1] (numeric) = 1.213700667359815
absolute error = 1e-15
relative error = 8.239263822564399e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.667
y[1] (analytic) = 1.214318906147328
y[1] (numeric) = 1.214318906147327
absolute error = 1e-15
relative error = 8.235069016364918e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.668
y[1] (analytic) = 1.214937930615868
y[1] (numeric) = 1.214937930615867
absolute error = 1e-15
relative error = 8.230873156566005e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.669
y[1] (analytic) = 1.215557740146412
y[1] (numeric) = 1.215557740146411
absolute error = 1e-15
relative error = 8.226676257102781e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.67
y[1] (analytic) = 1.216178334119151
y[1] (numeric) = 1.21617833411915
absolute error = 1e-15
relative error = 8.222478331882768e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.671
y[1] (analytic) = 1.21679971191349
y[1] (numeric) = 1.216799711913489
absolute error = 1e-15
relative error = 8.218279394785856e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.672
y[1] (analytic) = 1.217421872908052
y[1] (numeric) = 1.217421872908051
absolute error = 1e-15
relative error = 8.214079459664241e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.673
y[1] (analytic) = 1.218044816480676
y[1] (numeric) = 1.218044816480675
absolute error = 1e-15
relative error = 8.209878540342401e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.674
y[1] (analytic) = 1.218668542008418
y[1] (numeric) = 1.218668542008417
absolute error = 1e-15
relative error = 8.205676650617051e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.675
y[1] (analytic) = 1.219293048867553
y[1] (numeric) = 1.219293048867552
absolute error = 1e-15
relative error = 8.201473804257093e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.676
y[1] (analytic) = 1.219918336433574
y[1] (numeric) = 1.219918336433573
absolute error = 1e-15
relative error = 8.197270015003592e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.677
y[1] (analytic) = 1.220544404081194
y[1] (numeric) = 1.220544404081193
absolute error = 1e-15
relative error = 8.193065296569720e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.678
y[1] (analytic) = 1.221171251184345
y[1] (numeric) = 1.221171251184344
absolute error = 1e-15
relative error = 8.188859662640735e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.679
y[1] (analytic) = 1.221798877116179
y[1] (numeric) = 1.221798877116179
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.68
y[1] (analytic) = 1.222427281249072
y[1] (numeric) = 1.222427281249072
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.681
y[1] (analytic) = 1.223056462954619
y[1] (numeric) = 1.223056462954619
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.682
y[1] (analytic) = 1.223686421603638
y[1] (numeric) = 1.223686421603638
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.683
y[1] (analytic) = 1.22431715656617
y[1] (numeric) = 1.224317156566171
absolute error = 1e-15
relative error = 8.167818237593680e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.684
y[1] (analytic) = 1.224948667211482
y[1] (numeric) = 1.224948667211482
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.685
y[1] (analytic) = 1.225580952908061
y[1] (numeric) = 1.225580952908062
absolute error = 1e-15
relative error = 8.159395734954904e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.686
y[1] (analytic) = 1.226214013023623
y[1] (numeric) = 1.226214013023624
absolute error = 1e-15
relative error = 8.155183266371096e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.687
y[1] (analytic) = 1.226847846925108
y[1] (numeric) = 1.226847846925109
absolute error = 1e-15
relative error = 8.150970004196814e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.688
y[1] (analytic) = 1.227482453978681
y[1] (numeric) = 1.227482453978682
absolute error = 1e-15
relative error = 8.146755961836079e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.689
y[1] (analytic) = 1.228117833549736
y[1] (numeric) = 1.228117833549737
absolute error = 1e-15
relative error = 8.142541152664585e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.69
y[1] (analytic) = 1.228753985002893
y[1] (numeric) = 1.228753985002894
absolute error = 1e-15
relative error = 8.138325590029688e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.691
y[1] (analytic) = 1.229390907702001
y[1] (numeric) = 1.229390907702002
absolute error = 1e-15
relative error = 8.134109287250363e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.4MB, time=6.95
NO POLE
x[1] = 0.692
y[1] (analytic) = 1.230028601010137
y[1] (numeric) = 1.230028601010138
absolute error = 1e-15
relative error = 8.129892257617177e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.693
y[1] (analytic) = 1.230667064289608
y[1] (numeric) = 1.230667064289609
absolute error = 1e-15
relative error = 8.125674514392253e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.694
y[1] (analytic) = 1.23130629690195
y[1] (numeric) = 1.231306296901951
absolute error = 1e-15
relative error = 8.121456070809251e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.695
y[1] (analytic) = 1.231946298207932
y[1] (numeric) = 1.231946298207932
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.696
y[1] (analytic) = 1.232587067567551
y[1] (numeric) = 1.232587067567551
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.697
y[1] (analytic) = 1.233228604340038
y[1] (numeric) = 1.233228604340039
absolute error = 1e-15
relative error = 8.108796669820595e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.698
y[1] (analytic) = 1.233870907883858
y[1] (numeric) = 1.233870907883858
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.699
y[1] (analytic) = 1.234513977556705
y[1] (numeric) = 1.234513977556706
absolute error = 1e-15
relative error = 8.100353808704178e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.7
y[1] (analytic) = 1.235157812715512
y[1] (numeric) = 1.235157812715512
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.701
y[1] (analytic) = 1.235802412716441
y[1] (numeric) = 1.235802412716442
absolute error = 1e-15
relative error = 8.091908461336314e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.702
y[1] (analytic) = 1.236447776914895
y[1] (numeric) = 1.236447776914895
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.703
y[1] (analytic) = 1.237093904665508
y[1] (numeric) = 1.237093904665508
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.704
y[1] (analytic) = 1.237740795322152
y[1] (numeric) = 1.237740795322153
absolute error = 1e-15
relative error = 8.079236006273234e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.705
y[1] (analytic) = 1.238388448237938
y[1] (numeric) = 1.238388448237939
absolute error = 1e-15
relative error = 8.075010724000752e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.706
y[1] (analytic) = 1.239036862765212
y[1] (numeric) = 1.239036862765213
absolute error = 1e-15
relative error = 8.070784897942882e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.707
y[1] (analytic) = 1.23968603825556
y[1] (numeric) = 1.239686038255561
absolute error = 1e-15
relative error = 8.066558540960603e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.708
y[1] (analytic) = 1.240335974059807
y[1] (numeric) = 1.240335974059807
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.709
y[1] (analytic) = 1.240986669528016
y[1] (numeric) = 1.240986669528016
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.71
y[1] (analytic) = 1.241638124009492
y[1] (numeric) = 1.241638124009492
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.711
y[1] (analytic) = 1.242290336852781
y[1] (numeric) = 1.242290336852781
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.712
y[1] (analytic) = 1.24294330740567
y[1] (numeric) = 1.24294330740567
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.713
y[1] (analytic) = 1.243597035015188
y[1] (numeric) = 1.243597035015188
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.714
y[1] (analytic) = 1.244251519027609
y[1] (numeric) = 1.244251519027608
absolute error = 1e-15
relative error = 8.036960250460508e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.715
y[1] (analytic) = 1.244906758788447
y[1] (numeric) = 1.244906758788446
absolute error = 1e-15
relative error = 8.032730105612149e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.716
y[1] (analytic) = 1.245562753642464
y[1] (numeric) = 1.245562753642463
absolute error = 1e-15
relative error = 8.028499544287495e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.717
y[1] (analytic) = 1.246219502933664
y[1] (numeric) = 1.246219502933663
absolute error = 1e-15
relative error = 8.024268579058097e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=7.22
NO POLE
x[1] = 0.718
y[1] (analytic) = 1.246877006005298
y[1] (numeric) = 1.246877006005297
absolute error = 1e-15
relative error = 8.020037222466439e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.719
y[1] (analytic) = 1.247535262199864
y[1] (numeric) = 1.247535262199863
absolute error = 1e-15
relative error = 8.015805487025928e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.72
y[1] (analytic) = 1.248194270859105
y[1] (numeric) = 1.248194270859104
absolute error = 1e-15
relative error = 8.011573385220890e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.721
y[1] (analytic) = 1.248854031324012
y[1] (numeric) = 1.248854031324011
absolute error = 1e-15
relative error = 8.007340929506537e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.722
y[1] (analytic) = 1.249514542934826
y[1] (numeric) = 1.249514542934824
absolute error = 2e-15
relative error = 1.600621626461789e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.723
y[1] (analytic) = 1.250175805031034
y[1] (numeric) = 1.250175805031032
absolute error = 2e-15
relative error = 1.599775001205013e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.724
y[1] (analytic) = 1.250837816951374
y[1] (numeric) = 1.250837816951372
absolute error = 2e-15
relative error = 1.598928312604534e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.725
y[1] (analytic) = 1.251500578033835
y[1] (numeric) = 1.251500578033833
absolute error = 2e-15
relative error = 1.598081563128075e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.726
y[1] (analytic) = 1.252164087615656
y[1] (numeric) = 1.252164087615654
absolute error = 2e-15
relative error = 1.597234755237516e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.727
y[1] (analytic) = 1.252828345033326
y[1] (numeric) = 1.252828345033325
absolute error = 1e-15
relative error = 7.981939456944514e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.728
y[1] (analytic) = 1.25349334962259
y[1] (numeric) = 1.253493349622588
absolute error = 2e-15
relative error = 1.595540974032430e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.729
y[1] (analytic) = 1.254159100718441
y[1] (numeric) = 1.25415910071844
absolute error = 1e-15
relative error = 7.973470028062255e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.73
y[1] (analytic) = 1.25482559765513
y[1] (numeric) = 1.254825597655129
absolute error = 1e-15
relative error = 7.969234942837331e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.731
y[1] (analytic) = 1.255492839766158
y[1] (numeric) = 1.255492839766158
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.732
y[1] (analytic) = 1.256160826384286
y[1] (numeric) = 1.256160826384285
absolute error = 1e-15
relative error = 7.960764091636137e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.733
y[1] (analytic) = 1.256829556841524
y[1] (numeric) = 1.256829556841524
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.734
y[1] (analytic) = 1.257499030469144
y[1] (numeric) = 1.257499030469144
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.735
y[1] (analytic) = 1.258169246597672
y[1] (numeric) = 1.258169246597672
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.736
y[1] (analytic) = 1.258840204556891
y[1] (numeric) = 1.258840204556891
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.737
y[1] (analytic) = 1.259511903675844
y[1] (numeric) = 1.259511903675844
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.738
y[1] (analytic) = 1.260184343282831
y[1] (numeric) = 1.260184343282831
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.739
y[1] (analytic) = 1.260857522705414
y[1] (numeric) = 1.260857522705414
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.74
y[1] (analytic) = 1.261531441270412
y[1] (numeric) = 1.261531441270412
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.741
y[1] (analytic) = 1.262206098303908
y[1] (numeric) = 1.262206098303907
absolute error = 1e-15
relative error = 7.922636416855789e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.742
y[1] (analytic) = 1.262881493131243
y[1] (numeric) = 1.262881493131243
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.743
y[1] (analytic) = 1.263557625077024
y[1] (numeric) = 1.263557625077024
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=110.6MB, alloc=4.4MB, time=7.48
x[1] = 0.744
y[1] (analytic) = 1.264234493465119
y[1] (numeric) = 1.264234493465119
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.745
y[1] (analytic) = 1.264912097618659
y[1] (numeric) = 1.264912097618659
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.746
y[1] (analytic) = 1.26559043686004
y[1] (numeric) = 1.26559043686004
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.747
y[1] (analytic) = 1.266269510510923
y[1] (numeric) = 1.266269510510923
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.748
y[1] (analytic) = 1.266949317892234
y[1] (numeric) = 1.266949317892234
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.749
y[1] (analytic) = 1.267629858324166
y[1] (numeric) = 1.267629858324166
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.75
y[1] (analytic) = 1.268311131126179
y[1] (numeric) = 1.268311131126179
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.751
y[1] (analytic) = 1.268993135617
y[1] (numeric) = 1.268993135617
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.752
y[1] (analytic) = 1.269675871114624
y[1] (numeric) = 1.269675871114624
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.753
y[1] (analytic) = 1.270359336936317
y[1] (numeric) = 1.270359336936316
absolute error = 1e-15
relative error = 7.871788484757915e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.754
y[1] (analytic) = 1.271043532398611
y[1] (numeric) = 1.271043532398611
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.755
y[1] (analytic) = 1.271728456817313
y[1] (numeric) = 1.271728456817312
absolute error = 1e-15
relative error = 7.863313859490466e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.756
y[1] (analytic) = 1.272414109507496
y[1] (numeric) = 1.272414109507496
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.757
y[1] (analytic) = 1.27310048978351
y[1] (numeric) = 1.27310048978351
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.758
y[1] (analytic) = 1.273787596958974
y[1] (numeric) = 1.273787596958973
absolute error = 1e-15
relative error = 7.850602426867624e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.759
y[1] (analytic) = 1.27447543034678
y[1] (numeric) = 1.274475430346779
absolute error = 1e-15
relative error = 7.846365462909738e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.76
y[1] (analytic) = 1.275163989259095
y[1] (numeric) = 1.275163989259094
absolute error = 1e-15
relative error = 7.842128607952827e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.761
y[1] (analytic) = 1.27585327300736
y[1] (numeric) = 1.275853273007359
absolute error = 1e-15
relative error = 7.837891873278373e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.762
y[1] (analytic) = 1.276543280902292
y[1] (numeric) = 1.276543280902291
absolute error = 1e-15
relative error = 7.833655270138397e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.763
y[1] (analytic) = 1.277234012253883
y[1] (numeric) = 1.277234012253882
absolute error = 1e-15
relative error = 7.829418809755470e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.764
y[1] (analytic) = 1.277925466371402
y[1] (numeric) = 1.2779254663714
absolute error = 2e-15
relative error = 1.565036500664541e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.765
y[1] (analytic) = 1.278617642563394
y[1] (numeric) = 1.278617642563392
absolute error = 2e-15
relative error = 1.564189272400752e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.766
y[1] (analytic) = 1.279310540137683
y[1] (numeric) = 1.279310540137681
absolute error = 2e-15
relative error = 1.563342079386569e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.767
y[1] (analytic) = 1.280004158401372
y[1] (numeric) = 1.28000415840137
absolute error = 2e-15
relative error = 1.562494923842941e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.768
y[1] (analytic) = 1.280698496660843
y[1] (numeric) = 1.280698496660841
absolute error = 2e-15
relative error = 1.561647807984929e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.769
y[1] (analytic) = 1.281393554221757
y[1] (numeric) = 1.281393554221755
absolute error = 2e-15
relative error = 1.560800734021705e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.77
memory used=114.4MB, alloc=4.4MB, time=7.74
y[1] (analytic) = 1.282089330389057
y[1] (numeric) = 1.282089330389055
absolute error = 2e-15
relative error = 1.559953704156550e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.771
y[1] (analytic) = 1.282785824466966
y[1] (numeric) = 1.282785824466965
absolute error = 1e-15
relative error = 7.795533602934289e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.772
y[1] (analytic) = 1.283483035758992
y[1] (numeric) = 1.28348303575899
absolute error = 2e-15
relative error = 1.558259785504133e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.773
y[1] (analytic) = 1.284180963567922
y[1] (numeric) = 1.28418096356792
absolute error = 2e-15
relative error = 1.557412901093996e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.774
y[1] (analytic) = 1.284879607195829
y[1] (numeric) = 1.284879607195827
absolute error = 2e-15
relative error = 1.556566069536178e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.775
y[1] (analytic) = 1.285578965944069
y[1] (numeric) = 1.285578965944067
absolute error = 2e-15
relative error = 1.555719293004529e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.776
y[1] (analytic) = 1.286279039113283
y[1] (numeric) = 1.286279039113282
absolute error = 1e-15
relative error = 7.774362868335054e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.777
y[1] (analytic) = 1.286979826003399
y[1] (numeric) = 1.286979826003398
absolute error = 1e-15
relative error = 7.770129568428518e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.778
y[1] (analytic) = 1.28768132591363
y[1] (numeric) = 1.287681325913629
absolute error = 1e-15
relative error = 7.765896576084028e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.779
y[1] (analytic) = 1.288383538142475
y[1] (numeric) = 1.288383538142474
absolute error = 1e-15
relative error = 7.761663902053176e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.78
y[1] (analytic) = 1.289086461987723
y[1] (numeric) = 1.289086461987722
absolute error = 1e-15
relative error = 7.757431557058147e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.781
y[1] (analytic) = 1.289790096746449
y[1] (numeric) = 1.289790096746449
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.782
y[1] (analytic) = 1.29049444171502
y[1] (numeric) = 1.29049444171502
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.783
y[1] (analytic) = 1.29119949618909
y[1] (numeric) = 1.29119949618909
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.784
y[1] (analytic) = 1.291905259463604
y[1] (numeric) = 1.291905259463605
absolute error = 1e-15
relative error = 7.740505680851533e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.785
y[1] (analytic) = 1.2926117308328
y[1] (numeric) = 1.292611730832801
absolute error = 1e-15
relative error = 7.736275140840034e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.786
y[1] (analytic) = 1.293318909590206
y[1] (numeric) = 1.293318909590207
absolute error = 1e-15
relative error = 7.732044993580544e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.787
y[1] (analytic) = 1.294026795028644
y[1] (numeric) = 1.294026795028645
absolute error = 1e-15
relative error = 7.727815249589669e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.788
y[1] (analytic) = 1.294735386440228
y[1] (numeric) = 1.294735386440229
absolute error = 1e-15
relative error = 7.723585919354691e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.789
y[1] (analytic) = 1.295444683116367
y[1] (numeric) = 1.295444683116368
absolute error = 1e-15
relative error = 7.719357013333561e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.79
y[1] (analytic) = 1.296154684347764
y[1] (numeric) = 1.296154684347765
absolute error = 1e-15
relative error = 7.715128541954917e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.791
y[1] (analytic) = 1.296865389424418
y[1] (numeric) = 1.296865389424419
absolute error = 1e-15
relative error = 7.710900515618090e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.792
y[1] (analytic) = 1.297576797635624
y[1] (numeric) = 1.297576797635625
absolute error = 1e-15
relative error = 7.706672944693118e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.793
y[1] (analytic) = 1.298288908269973
y[1] (numeric) = 1.298288908269975
absolute error = 2e-15
relative error = 1.540489167904152e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.794
y[1] (analytic) = 1.299001720615356
y[1] (numeric) = 1.299001720615358
absolute error = 2e-15
relative error = 1.539643842082496e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.795
y[1] (analytic) = 1.29971523395896
y[1] (numeric) = 1.299715233958962
absolute error = 2e-15
relative error = 1.538798613530102e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.796
y[1] (analytic) = 1.300429447587272
y[1] (numeric) = 1.300429447587274
absolute error = 2e-15
relative error = 1.537953484297563e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=8.00
NO POLE
x[1] = 0.797
y[1] (analytic) = 1.301144360786078
y[1] (numeric) = 1.30114436078608
absolute error = 2e-15
relative error = 1.537108456429625e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.798
y[1] (analytic) = 1.301859972840464
y[1] (numeric) = 1.301859972840467
absolute error = 3e-15
relative error = 2.304395297947788e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.799
y[1] (analytic) = 1.30257628303482
y[1] (numeric) = 1.302576283034823
absolute error = 3e-15
relative error = 2.303128069405978e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.8
y[1] (analytic) = 1.303293290652835
y[1] (numeric) = 1.303293290652838
absolute error = 3e-15
relative error = 2.301861002059839e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.801
y[1] (analytic) = 1.3040109949775
y[1] (numeric) = 1.304010994977504
absolute error = 4e-15
relative error = 3.067458798588595e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.802
y[1] (analytic) = 1.304729395291113
y[1] (numeric) = 1.304729395291117
absolute error = 4e-15
relative error = 3.065769817432154e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.803
y[1] (analytic) = 1.305448490875273
y[1] (numeric) = 1.305448490875277
absolute error = 4e-15
relative error = 3.064081063296563e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.804
y[1] (analytic) = 1.306168281010884
y[1] (numeric) = 1.306168281010888
absolute error = 4e-15
relative error = 3.062392540189597e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.805
y[1] (analytic) = 1.306888764978156
y[1] (numeric) = 1.30688876497816
absolute error = 4e-15
relative error = 3.060704252107377e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.806
y[1] (analytic) = 1.307609942056605
y[1] (numeric) = 1.307609942056609
absolute error = 4e-15
relative error = 3.059016203034379e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.807
y[1] (analytic) = 1.308331811525055
y[1] (numeric) = 1.308331811525059
absolute error = 4e-15
relative error = 3.057328396943437e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.808
y[1] (analytic) = 1.309054372661635
y[1] (numeric) = 1.309054372661639
absolute error = 4e-15
relative error = 3.055640837795759e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.809
y[1] (analytic) = 1.309777624743785
y[1] (numeric) = 1.309777624743789
absolute error = 4e-15
relative error = 3.053953529540916e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.81
y[1] (analytic) = 1.310501567048253
y[1] (numeric) = 1.310501567048257
absolute error = 4e-15
relative error = 3.052266476116864e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.811
y[1] (analytic) = 1.311226198851096
y[1] (numeric) = 1.3112261988511
absolute error = 4e-15
relative error = 3.050579681449946e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.812
y[1] (analytic) = 1.311951519427684
y[1] (numeric) = 1.311951519427687
absolute error = 3e-15
relative error = 2.286669862091168e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.813
y[1] (analytic) = 1.312677528052694
y[1] (numeric) = 1.312677528052697
absolute error = 3e-15
relative error = 2.285405163026127e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.814
y[1] (analytic) = 1.313404224000119
y[1] (numeric) = 1.313404224000122
absolute error = 3e-15
relative error = 2.284140666810988e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.815
y[1] (analytic) = 1.314131606543263
y[1] (numeric) = 1.314131606543266
absolute error = 3e-15
relative error = 2.282876376355716e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.816
y[1] (analytic) = 1.314859674954743
y[1] (numeric) = 1.314859674954746
absolute error = 3e-15
relative error = 2.281612294561592e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.817
y[1] (analytic) = 1.315588428506491
y[1] (numeric) = 1.315588428506494
absolute error = 3e-15
relative error = 2.280348424321215e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.818
y[1] (analytic) = 1.316317866469753
y[1] (numeric) = 1.316317866469757
absolute error = 4e-15
relative error = 3.038779691358017e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.819
y[1] (analytic) = 1.317047988115092
y[1] (numeric) = 1.317047988115096
absolute error = 4e-15
relative error = 3.037095106704992e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.82
y[1] (analytic) = 1.317778792712386
y[1] (numeric) = 1.31777879271239
absolute error = 4e-15
relative error = 3.035410815624673e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.821
y[1] (analytic) = 1.318510279530831
y[1] (numeric) = 1.318510279530834
absolute error = 3e-15
relative error = 2.275295116445734e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.822
y[1] (analytic) = 1.319242447838939
y[1] (numeric) = 1.319242447838942
absolute error = 3e-15
relative error = 2.274032347059726e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=8.25
NO POLE
x[1] = 0.823
y[1] (analytic) = 1.319975296904543
y[1] (numeric) = 1.319975296904546
absolute error = 3e-15
relative error = 2.272769806401121e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.824
y[1] (analytic) = 1.320708825994793
y[1] (numeric) = 1.320708825994796
absolute error = 3e-15
relative error = 2.271507497301928e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.825
y[1] (analytic) = 1.32144303437616
y[1] (numeric) = 1.321443034376163
absolute error = 3e-15
relative error = 2.270245422585522e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.826
y[1] (analytic) = 1.322177921314437
y[1] (numeric) = 1.322177921314439
absolute error = 2e-15
relative error = 1.512655723377765e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.827
y[1] (analytic) = 1.322913486074735
y[1] (numeric) = 1.322913486074738
absolute error = 3e-15
relative error = 2.267721987551438e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.828
y[1] (analytic) = 1.323649727921492
y[1] (numeric) = 1.323649727921494
absolute error = 2e-15
relative error = 1.510973755224935e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.829
y[1] (analytic) = 1.324386646118463
y[1] (numeric) = 1.324386646118466
absolute error = 3e-15
relative error = 2.265199523713453e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.83
y[1] (analytic) = 1.325124239928733
y[1] (numeric) = 1.325124239928735
absolute error = 2e-15
relative error = 1.509292441973262e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.831
y[1] (analytic) = 1.325862508614706
y[1] (numeric) = 1.325862508614708
absolute error = 2e-15
relative error = 1.508452035565626e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.832
y[1] (analytic) = 1.326601451438115
y[1] (numeric) = 1.326601451438117
absolute error = 2e-15
relative error = 1.507611798428142e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.833
y[1] (analytic) = 1.327341067660016
y[1] (numeric) = 1.327341067660018
absolute error = 2e-15
relative error = 1.506771732397176e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.834
y[1] (analytic) = 1.328081356540793
y[1] (numeric) = 1.328081356540795
absolute error = 2e-15
relative error = 1.505931839303377e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.835
y[1] (analytic) = 1.328822317340158
y[1] (numeric) = 1.32882231734016
absolute error = 2e-15
relative error = 1.505092120971679e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.836
y[1] (analytic) = 1.329563949317149
y[1] (numeric) = 1.329563949317151
absolute error = 2e-15
relative error = 1.504252579221316e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.837
y[1] (analytic) = 1.330306251730135
y[1] (numeric) = 1.330306251730137
absolute error = 2e-15
relative error = 1.503413215865814e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.838
y[1] (analytic) = 1.331049223836814
y[1] (numeric) = 1.331049223836816
absolute error = 2e-15
relative error = 1.502574032713007e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.839
y[1] (analytic) = 1.331792864894213
y[1] (numeric) = 1.331792864894215
absolute error = 2e-15
relative error = 1.501735031565035e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.84
y[1] (analytic) = 1.332537174158692
y[1] (numeric) = 1.332537174158694
absolute error = 2e-15
relative error = 1.500896214218351e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.841
y[1] (analytic) = 1.333282150885941
y[1] (numeric) = 1.333282150885943
absolute error = 2e-15
relative error = 1.500057582463725e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.842
y[1] (analytic) = 1.334027794330983
y[1] (numeric) = 1.334027794330985
absolute error = 2e-15
relative error = 1.499219138086252e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.843
y[1] (analytic) = 1.334774103748176
y[1] (numeric) = 1.334774103748178
absolute error = 2e-15
relative error = 1.498380882865351e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.844
y[1] (analytic) = 1.335521078391209
y[1] (numeric) = 1.335521078391211
absolute error = 2e-15
relative error = 1.497542818574779e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.845
y[1] (analytic) = 1.336268717513108
y[1] (numeric) = 1.336268717513111
absolute error = 3e-15
relative error = 2.245057420473941e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.846
y[1] (analytic) = 1.337017020366235
y[1] (numeric) = 1.337017020366238
absolute error = 3e-15
relative error = 2.243800904776995e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.847
y[1] (analytic) = 1.337765986202286
y[1] (numeric) = 1.337765986202289
absolute error = 3e-15
relative error = 2.242544683406508e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.848
y[1] (analytic) = 1.338515614272296
y[1] (numeric) = 1.338515614272299
absolute error = 3e-15
relative error = 2.241288758989184e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=8.51
NO POLE
x[1] = 0.849
y[1] (analytic) = 1.339265903826636
y[1] (numeric) = 1.339265903826639
absolute error = 3e-15
relative error = 2.240033134143271e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.85
y[1] (analytic) = 1.340016854115018
y[1] (numeric) = 1.34001685411502
absolute error = 2e-15
relative error = 1.492518540985704e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.851
y[1] (analytic) = 1.34076846438649
y[1] (numeric) = 1.340768464386492
absolute error = 2e-15
relative error = 1.491681862397593e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.852
y[1] (analytic) = 1.341520733889443
y[1] (numeric) = 1.341520733889445
absolute error = 2e-15
relative error = 1.490845388726451e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.853
y[1] (analytic) = 1.342273661871607
y[1] (numeric) = 1.342273661871609
absolute error = 2e-15
relative error = 1.490009121695265e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.854
y[1] (analytic) = 1.343027247580055
y[1] (numeric) = 1.343027247580057
absolute error = 2e-15
relative error = 1.489173063021407e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.855
y[1] (analytic) = 1.3437814902612
y[1] (numeric) = 1.343781490261202
absolute error = 2e-15
relative error = 1.488337214416643e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.856
y[1] (analytic) = 1.344536389160801
y[1] (numeric) = 1.344536389160802
absolute error = 1e-15
relative error = 7.437507887935669e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.857
y[1] (analytic) = 1.345291943523957
y[1] (numeric) = 1.345291943523959
absolute error = 2e-15
relative error = 1.486666154233446e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.858
y[1] (analytic) = 1.346048152595116
y[1] (numeric) = 1.346048152595117
absolute error = 1e-15
relative error = 7.429154730252764e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.859
y[1] (analytic) = 1.346805015618067
y[1] (numeric) = 1.346805015618068
absolute error = 1e-15
relative error = 7.424979773639219e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.86
y[1] (analytic) = 1.347562531835948
y[1] (numeric) = 1.347562531835949
absolute error = 1e-15
relative error = 7.420805909745640e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.861
y[1] (analytic) = 1.348320700491243
y[1] (numeric) = 1.348320700491244
absolute error = 1e-15
relative error = 7.416633146963205e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.862
y[1] (analytic) = 1.349079520825784
y[1] (numeric) = 1.349079520825784
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.863
y[1] (analytic) = 1.349838992080749
y[1] (numeric) = 1.349838992080749
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.864
y[1] (analytic) = 1.350599113496668
y[1] (numeric) = 1.350599113496668
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.865
y[1] (analytic) = 1.351359884313419
y[1] (numeric) = 1.351359884313419
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.866
y[1] (analytic) = 1.352121303770232
y[1] (numeric) = 1.352121303770232
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.867
y[1] (analytic) = 1.352883371105687
y[1] (numeric) = 1.352883371105687
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.868
y[1] (analytic) = 1.353646085557717
y[1] (numeric) = 1.353646085557717
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.869
y[1] (analytic) = 1.354409446363608
y[1] (numeric) = 1.354409446363608
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.87
y[1] (analytic) = 1.355173452759999
y[1] (numeric) = 1.355173452759999
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.871
y[1] (analytic) = 1.355938103982883
y[1] (numeric) = 1.355938103982883
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.872
y[1] (analytic) = 1.356703399267609
y[1] (numeric) = 1.356703399267609
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.873
y[1] (analytic) = 1.357469337848883
y[1] (numeric) = 1.357469337848883
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.874
y[1] (analytic) = 1.358235918960765
y[1] (numeric) = 1.358235918960765
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=129.7MB, alloc=4.4MB, time=8.77
x[1] = 0.875
y[1] (analytic) = 1.359003141836675
y[1] (numeric) = 1.359003141836675
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.876
y[1] (analytic) = 1.359771005709389
y[1] (numeric) = 1.359771005709389
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.877
y[1] (analytic) = 1.360539509811045
y[1] (numeric) = 1.360539509811044
absolute error = 1e-15
relative error = 7.350025433211288e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.878
y[1] (analytic) = 1.361308653373137
y[1] (numeric) = 1.361308653373136
absolute error = 1e-15
relative error = 7.345872646310861e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.879
y[1] (analytic) = 1.362078435626523
y[1] (numeric) = 1.362078435626522
absolute error = 1e-15
relative error = 7.341721106832033e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.88
y[1] (analytic) = 1.36284885580142
y[1] (numeric) = 1.362848855801419
absolute error = 1e-15
relative error = 7.337570822642342e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.881
y[1] (analytic) = 1.363619913127408
y[1] (numeric) = 1.363619913127407
absolute error = 1e-15
relative error = 7.333421801582083e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.882
y[1] (analytic) = 1.36439160683343
y[1] (numeric) = 1.364391606833429
absolute error = 1e-15
relative error = 7.329274051464344e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.883
y[1] (analytic) = 1.365163936147792
y[1] (numeric) = 1.365163936147791
absolute error = 1e-15
relative error = 7.325127580075046e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.884
y[1] (analytic) = 1.365936900298165
y[1] (numeric) = 1.365936900298164
absolute error = 1e-15
relative error = 7.320982395172968e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.885
y[1] (analytic) = 1.366710498511585
y[1] (numeric) = 1.366710498511584
absolute error = 1e-15
relative error = 7.316838504489789e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.886
y[1] (analytic) = 1.367484730014453
y[1] (numeric) = 1.367484730014453
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.887
y[1] (analytic) = 1.368259594032539
y[1] (numeric) = 1.368259594032539
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.888
y[1] (analytic) = 1.369035089790978
y[1] (numeric) = 1.369035089790978
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.889
y[1] (analytic) = 1.369811216514275
y[1] (numeric) = 1.369811216514275
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.89
y[1] (analytic) = 1.370587973426303
y[1] (numeric) = 1.370587973426303
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.891
y[1] (analytic) = 1.371365359750305
y[1] (numeric) = 1.371365359750305
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.892
y[1] (analytic) = 1.372143374708895
y[1] (numeric) = 1.372143374708895
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.893
y[1] (analytic) = 1.372922017524058
y[1] (numeric) = 1.372922017524058
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.894
y[1] (analytic) = 1.373701287417151
y[1] (numeric) = 1.373701287417151
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.895
y[1] (analytic) = 1.374481183608904
y[1] (numeric) = 1.374481183608904
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.896
y[1] (analytic) = 1.375261705319422
y[1] (numeric) = 1.375261705319422
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.897
y[1] (analytic) = 1.376042851768182
y[1] (numeric) = 1.376042851768182
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.898
y[1] (analytic) = 1.376824622174038
y[1] (numeric) = 1.376824622174038
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.899
y[1] (analytic) = 1.377607015755221
y[1] (numeric) = 1.37760701575522
absolute error = 1e-15
relative error = 7.258964193440811e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.9
y[1] (analytic) = 1.378390031729336
y[1] (numeric) = 1.378390031729335
absolute error = 1e-15
relative error = 7.254840625518702e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.901
y[1] (analytic) = 1.379173669313367
y[1] (numeric) = 1.379173669313366
absolute error = 1e-15
relative error = 7.250718471864811e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=9.04
NO POLE
x[1] = 0.902
y[1] (analytic) = 1.379957927723677
y[1] (numeric) = 1.379957927723676
absolute error = 1e-15
relative error = 7.246597739755441e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.903
y[1] (analytic) = 1.380742806176008
y[1] (numeric) = 1.380742806176007
absolute error = 1e-15
relative error = 7.242478436440440e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.904
y[1] (analytic) = 1.381528303885481
y[1] (numeric) = 1.38152830388548
absolute error = 1e-15
relative error = 7.238360569143236e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.905
y[1] (analytic) = 1.382314420066598
y[1] (numeric) = 1.382314420066598
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.906
y[1] (analytic) = 1.383101153933244
y[1] (numeric) = 1.383101153933244
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.907
y[1] (analytic) = 1.383888504698685
y[1] (numeric) = 1.383888504698685
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.908
y[1] (analytic) = 1.38467647157557
y[1] (numeric) = 1.38467647157557
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.909
y[1] (analytic) = 1.385465053775932
y[1] (numeric) = 1.385465053775932
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.91
y[1] (analytic) = 1.386254250511188
y[1] (numeric) = 1.386254250511189
absolute error = 1e-15
relative error = 7.213683922925720e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.911
y[1] (analytic) = 1.387044060992144
y[1] (numeric) = 1.387044060992144
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.912
y[1] (analytic) = 1.387834484428987
y[1] (numeric) = 1.387834484428987
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.913
y[1] (analytic) = 1.388625520031294
y[1] (numeric) = 1.388625520031295
absolute error = 1e-15
relative error = 7.201365563103464e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.914
y[1] (analytic) = 1.389417167008031
y[1] (numeric) = 1.389417167008032
absolute error = 1e-15
relative error = 7.197262447486514e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.915
y[1] (analytic) = 1.39020942456755
y[1] (numeric) = 1.390209424567551
absolute error = 1e-15
relative error = 7.193160845611935e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.916
y[1] (analytic) = 1.391002291917593
y[1] (numeric) = 1.391002291917594
absolute error = 1e-15
relative error = 7.189060764389042e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.917
y[1] (analytic) = 1.391795768265294
y[1] (numeric) = 1.391795768265295
absolute error = 1e-15
relative error = 7.184962210701213e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.918
y[1] (analytic) = 1.392589852817176
y[1] (numeric) = 1.392589852817177
absolute error = 1e-15
relative error = 7.180865191405954e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.919
y[1] (analytic) = 1.393384544779154
y[1] (numeric) = 1.393384544779155
absolute error = 1e-15
relative error = 7.176769713334922e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.92
y[1] (analytic) = 1.394179843356537
y[1] (numeric) = 1.394179843356538
absolute error = 1e-15
relative error = 7.172675783293960e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.921
y[1] (analytic) = 1.394975747754026
y[1] (numeric) = 1.394975747754027
absolute error = 1e-15
relative error = 7.168583408063152e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.922
y[1] (analytic) = 1.395772257175717
y[1] (numeric) = 1.395772257175718
absolute error = 1e-15
relative error = 7.164492594396850e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.923
y[1] (analytic) = 1.396569370825101
y[1] (numeric) = 1.396569370825101
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.924
y[1] (analytic) = 1.397367087905063
y[1] (numeric) = 1.397367087905063
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.925
y[1] (analytic) = 1.398165407617887
y[1] (numeric) = 1.398165407617887
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.926
y[1] (analytic) = 1.398964329165254
y[1] (numeric) = 1.398964329165253
absolute error = 1e-15
relative error = 7.148145089565568e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.927
y[1] (analytic) = 1.399763851748241
y[1] (numeric) = 1.39976385174824
absolute error = 1e-15
relative error = 7.144062184139459e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=9.29
NO POLE
x[1] = 0.928
y[1] (analytic) = 1.400563974567327
y[1] (numeric) = 1.400563974567325
absolute error = 2e-15
relative error = 1.427996176053190e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.929
y[1] (analytic) = 1.401364696822388
y[1] (numeric) = 1.401364696822386
absolute error = 2e-15
relative error = 1.427180236904087e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.93
y[1] (analytic) = 1.402166017712702
y[1] (numeric) = 1.4021660177127
absolute error = 2e-15
relative error = 1.426364620690581e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.931
y[1] (analytic) = 1.402967936436948
y[1] (numeric) = 1.402967936436947
absolute error = 1e-15
relative error = 7.127746643587972e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.932
y[1] (analytic) = 1.403770452193209
y[1] (numeric) = 1.403770452193208
absolute error = 1e-15
relative error = 7.123671811424937e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.933
y[1] (analytic) = 1.404573564178968
y[1] (numeric) = 1.404573564178967
absolute error = 1e-15
relative error = 7.119598613437822e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.934
y[1] (analytic) = 1.405377271591112
y[1] (numeric) = 1.405377271591112
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.935
y[1] (analytic) = 1.406181573625936
y[1] (numeric) = 1.406181573625936
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.936
y[1] (analytic) = 1.406986469479137
y[1] (numeric) = 1.406986469479137
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.937
y[1] (analytic) = 1.407791958345818
y[1] (numeric) = 1.407791958345819
absolute error = 1e-15
relative error = 7.103322291846437e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.938
y[1] (analytic) = 1.408598039420492
y[1] (numeric) = 1.408598039420493
absolute error = 1e-15
relative error = 7.099257360967275e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.939
y[1] (analytic) = 1.409404711897078
y[1] (numeric) = 1.409404711897078
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.94
y[1] (analytic) = 1.410211974968902
y[1] (numeric) = 1.410211974968902
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.941
y[1] (analytic) = 1.411019827828702
y[1] (numeric) = 1.411019827828702
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.942
y[1] (analytic) = 1.411828269668625
y[1] (numeric) = 1.411828269668625
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.943
y[1] (analytic) = 1.412637299680229
y[1] (numeric) = 1.412637299680229
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.944
y[1] (analytic) = 1.413446917054485
y[1] (numeric) = 1.413446917054485
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.945
y[1] (analytic) = 1.414257120981775
y[1] (numeric) = 1.414257120981775
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.946
y[1] (analytic) = 1.415067910651895
y[1] (numeric) = 1.415067910651895
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.947
y[1] (analytic) = 1.415879285254056
y[1] (numeric) = 1.415879285254056
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.948
y[1] (analytic) = 1.416691243976883
y[1] (numeric) = 1.416691243976883
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.949
y[1] (analytic) = 1.417503786008417
y[1] (numeric) = 1.417503786008417
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.95
y[1] (analytic) = 1.418316910536116
y[1] (numeric) = 1.418316910536117
absolute error = 1e-15
relative error = 7.050610428257571e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.951
y[1] (analytic) = 1.419130616746857
y[1] (numeric) = 1.419130616746858
absolute error = 1e-15
relative error = 7.046567723923463e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.952
y[1] (analytic) = 1.419944903826933
y[1] (numeric) = 1.419944903826933
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.953
y[1] (analytic) = 1.420759770962056
y[1] (numeric) = 1.420759770962056
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=9.55
NO POLE
x[1] = 0.954
y[1] (analytic) = 1.42157521733736
y[1] (numeric) = 1.42157521733736
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.955
y[1] (analytic) = 1.422391242137398
y[1] (numeric) = 1.422391242137399
absolute error = 1e-15
relative error = 7.030414490582216e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.956
y[1] (analytic) = 1.423207844546147
y[1] (numeric) = 1.423207844546147
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.957
y[1] (analytic) = 1.424025023747002
y[1] (numeric) = 1.424025023747003
absolute error = 1e-15
relative error = 7.022348507392971e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.958
y[1] (analytic) = 1.424842778922786
y[1] (numeric) = 1.424842778922787
absolute error = 1e-15
relative error = 7.018318194769693e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.959
y[1] (analytic) = 1.425661109255743
y[1] (numeric) = 1.425661109255744
absolute error = 1e-15
relative error = 7.014289675910732e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.96
y[1] (analytic) = 1.426480013927543
y[1] (numeric) = 1.426480013927544
absolute error = 1e-15
relative error = 7.010262956623480e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.961
y[1] (analytic) = 1.427299492119282
y[1] (numeric) = 1.427299492119282
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.962
y[1] (analytic) = 1.42811954301148
y[1] (numeric) = 1.42811954301148
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.963
y[1] (analytic) = 1.428940165784088
y[1] (numeric) = 1.428940165784088
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.964
y[1] (analytic) = 1.429761359616482
y[1] (numeric) = 1.429761359616482
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.965
y[1] (analytic) = 1.430583123687469
y[1] (numeric) = 1.430583123687469
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.966
y[1] (analytic) = 1.431405457175285
y[1] (numeric) = 1.431405457175285
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.967
y[1] (analytic) = 1.432228359257597
y[1] (numeric) = 1.432228359257596
absolute error = 1e-15
relative error = 6.982126792394721e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.968
y[1] (analytic) = 1.433051829111502
y[1] (numeric) = 1.433051829111501
absolute error = 1e-15
relative error = 6.978114675866288e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.969
y[1] (analytic) = 1.43387586591353
y[1] (numeric) = 1.43387586591353
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.97
y[1] (analytic) = 1.434700468839646
y[1] (numeric) = 1.434700468839645
absolute error = 1e-15
relative error = 6.970096000657042e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.971
y[1] (analytic) = 1.435525637065245
y[1] (numeric) = 1.435525637065245
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.972
y[1] (analytic) = 1.436351369765161
y[1] (numeric) = 1.43635136976516
absolute error = 1e-15
relative error = 6.962084772916650e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.973
y[1] (analytic) = 1.437177666113659
y[1] (numeric) = 1.437177666113659
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.974
y[1] (analytic) = 1.438004525284445
y[1] (numeric) = 1.438004525284445
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.975
y[1] (analytic) = 1.438831946450659
y[1] (numeric) = 1.438831946450659
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.976
y[1] (analytic) = 1.439659928784879
y[1] (numeric) = 1.439659928784879
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.977
y[1] (analytic) = 1.440488471459124
y[1] (numeric) = 1.440488471459124
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.978
y[1] (analytic) = 1.44131757364485
y[1] (numeric) = 1.441317573644851
absolute error = 1e-15
relative error = 6.938096213391529e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.979
y[1] (analytic) = 1.442147234512957
y[1] (numeric) = 1.442147234512958
absolute error = 1e-15
relative error = 6.934104757602789e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=144.9MB, alloc=4.4MB, time=9.82
x[1] = 0.98
y[1] (analytic) = 1.442977453233783
y[1] (numeric) = 1.442977453233784
absolute error = 1e-15
relative error = 6.930115212534687e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.981
y[1] (analytic) = 1.443808228977109
y[1] (numeric) = 1.44380822897711
absolute error = 1e-15
relative error = 6.926127583498172e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.982
y[1] (analytic) = 1.444639560912159
y[1] (numeric) = 1.444639560912161
absolute error = 2e-15
relative error = 1.384428375156209e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.983
y[1] (analytic) = 1.445471448207603
y[1] (numeric) = 1.445471448207604
absolute error = 1e-15
relative error = 6.918158094648003e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.984
y[1] (analytic) = 1.446303890031552
y[1] (numeric) = 1.446303890031553
absolute error = 1e-15
relative error = 6.914176245340697e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.985
y[1] (analytic) = 1.447136885551564
y[1] (numeric) = 1.447136885551566
absolute error = 2e-15
relative error = 1.382039266615554e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.986
y[1] (analytic) = 1.447970433934646
y[1] (numeric) = 1.447970433934647
absolute error = 1e-15
relative error = 6.906218363054883e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.987
y[1] (analytic) = 1.448804534347247
y[1] (numeric) = 1.448804534347248
absolute error = 1e-15
relative error = 6.902242340444813e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.988
y[1] (analytic) = 1.449639185955268
y[1] (numeric) = 1.449639185955269
absolute error = 1e-15
relative error = 6.898268270397440e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.989
y[1] (analytic) = 1.450474387924057
y[1] (numeric) = 1.450474387924058
absolute error = 1e-15
relative error = 6.894296158039830e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.99
y[1] (analytic) = 1.451310139418412
y[1] (numeric) = 1.451310139418413
absolute error = 1e-15
relative error = 6.890326008476266e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.991
y[1] (analytic) = 1.452146439602583
y[1] (numeric) = 1.452146439602583
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.992
y[1] (analytic) = 1.452983287640268
y[1] (numeric) = 1.452983287640268
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.993
y[1] (analytic) = 1.45382068269462
y[1] (numeric) = 1.45382068269462
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.994
y[1] (analytic) = 1.454658623928243
y[1] (numeric) = 1.454658623928244
absolute error = 1e-15
relative error = 6.874465139453428e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.995
y[1] (analytic) = 1.455497110503197
y[1] (numeric) = 1.455497110503198
absolute error = 1e-15
relative error = 6.870504879630288e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.996
y[1] (analytic) = 1.456336141580996
y[1] (numeric) = 1.456336141580996
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.997
y[1] (analytic) = 1.457175716322607
y[1] (numeric) = 1.457175716322607
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.998
y[1] (analytic) = 1.458015833888457
y[1] (numeric) = 1.458015833888457
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.999
y[1] (analytic) = 1.458856493438428
y[1] (numeric) = 1.458856493438428
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 1
y[1] (analytic) = 1.45969769413186
y[1] (numeric) = 1.45969769413186
absolute error = 0
relative error = 0 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sin(x);
Iterations = 1000
Total Elapsed Time = 9 Seconds
Elapsed Time(since restart) = 9 Seconds
Expected Time Remaining = 39 Seconds
Optimized Time Remaining = 39 Seconds
Time to Timeout = 14 Minutes 50 Seconds
Percent Done = 20.02 %
> quit
memory used=148.0MB, alloc=4.4MB, time=10.02