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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> 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 glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, 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
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> # emit pre mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_y[1] * (array_y[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 mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_y,array_y,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 mult $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_y,array_y,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 mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_y,array_y,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 mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_y,array_y,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 mult $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_y,array_y,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 glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, glob_last;
array_tmp1[1] := array_y[1]*array_y[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] := ats(2, array_y, array_y, 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] := ats(3, array_y, array_y, 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] := ats(4, array_y, array_y, 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] := ats(5, array_y, array_y, 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] := ats(kkk, array_y, array_y, 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)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 13
> if array_fact_1[nnn] = 0 then # if number 14
> ret := nnn!;
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 14
> ;
> else
> ret := nnn!;
> fi;# end if 13
> ;
> ret;
> # End Function number 17
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := nnn!
end if;
ret
end proc
> # Begin Function number 18
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13
> if array_fact_2[mmm,nnn] = 0 then # if number 14
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 14
> ;
> else
> ret := (mmm!)/(nnn!);
> fi;# end if 13
> ;
> ret;
> # End Function number 18
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := mmm!/nnn!
end if;
ret
end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 1.0/(1.0 - x);
> end;
exact_soln_y := proc(x) 1.0/(1.0 - x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> glob_max_terms,
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> DEBUGL,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_iter,
> glob_smallish_float,
> glob_optimal_start,
> glob_disp_incr,
> glob_reached_optimal_h,
> days_in_year,
> glob_relerr,
> centuries_in_millinium,
> glob_log10_relerr,
> glob_large_float,
> glob_hmin,
> glob_dump,
> glob_log10normmin,
> glob_max_minutes,
> glob_log10relerr,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> MAX_UNCHANGED,
> glob_orig_start_sec,
> glob_small_float,
> glob_abserr,
> glob_hmax,
> min_in_hour,
> glob_look_poles,
> glob_not_yet_finished,
> years_in_century,
> glob_html_log,
> glob_warned2,
> glob_max_hours,
> glob_hmin_init,
> hours_in_day,
> sec_in_min,
> glob_max_opt_iter,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_trunc_err,
> glob_max_rel_trunc_err,
> glob_h,
> glob_optimal_done,
> djd_debug2,
> glob_subiter_method,
> glob_normmax,
> glob_display_flag,
> glob_percent_done,
> glob_log10abserr,
> glob_warned,
> glob_no_eqs,
> glob_max_iter,
> glob_last_good_h,
> glob_initial_pass,
> glob_clock_sec,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_norms,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_fact_1,
> array_last_rel_error,
> array_type_pole,
> array_y_init,
> array_pole,
> array_real_pole,
> array_poles,
> array_y_higher,
> array_y_higher_work,
> array_complex_pole,
> array_y_higher_work2,
> array_fact_2,
> array_y_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> INFO := 2;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> DEBUGL := 3;
> glob_iolevel := 5;
> glob_iter := 0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_start := 0.0;
> glob_disp_incr := 0.1;
> glob_reached_optimal_h := false;
> days_in_year := 365.0;
> glob_relerr := 0.1e-10;
> centuries_in_millinium := 10.0;
> glob_log10_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmin := 0.00000000001;
> glob_dump := false;
> glob_log10normmin := 0.1;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_unchanged_h_cnt := 0;
> glob_almost_1 := 0.9990;
> glob_optimal_expect_sec := 0.1;
> glob_current_iter := 0;
> glob_max_sec := 10000.0;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_not_yet_start_msg := true;
> glob_clock_start_sec := 0.0;
> MAX_UNCHANGED := 10;
> glob_orig_start_sec := 0.0;
> glob_small_float := 0.1e-50;
> glob_abserr := 0.1e-10;
> glob_hmax := 1.0;
> min_in_hour := 60.0;
> glob_look_poles := false;
> glob_not_yet_finished := true;
> years_in_century := 100.0;
> glob_html_log := true;
> glob_warned2 := false;
> glob_max_hours := 0.0;
> glob_hmin_init := 0.001;
> hours_in_day := 24.0;
> sec_in_min := 60.0;
> glob_max_opt_iter := 10;
> glob_start := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_h := 0.1;
> glob_optimal_done := false;
> djd_debug2 := true;
> glob_subiter_method := 3;
> glob_normmax := 0.0;
> glob_display_flag := true;
> glob_percent_done := 0.0;
> glob_log10abserr := 0.0;
> glob_warned := false;
> glob_no_eqs := 0;
> glob_max_iter := 1000;
> glob_last_good_h := 0.1;
> glob_initial_pass := true;
> glob_clock_sec := 0.0;
> djd_debug := true;
> #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/nonlinear1postode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 0.5 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.01;");
> 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,"1.0/(1.0 - x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_m1:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= 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_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_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_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_fact_1[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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_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 <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_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 <=max_terms do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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
> ;
> #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_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
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3
> ;
> iiif := iiif + 1;
> od;# end do number 2
> ;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 0.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.01;
> 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 ) = y * y;");
> 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,"2012-06-18T00:44:30-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"nonlinear1")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 092 | ")
> ;
> logitem_str(html_log_file,"nonlinear1 diffeq.mxt")
> ;
> logitem_str(html_log_file,"nonlinear1 maple results")
> ;
> logitem_str(html_log_file,"Mostly affecting speed of factorials")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter,
tmp;
global glob_max_terms, INFO, ALWAYS, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_iter, glob_smallish_float, glob_optimal_start, glob_disp_incr,
glob_reached_optimal_h, days_in_year, glob_relerr, centuries_in_millinium,
glob_log10_relerr, glob_large_float, glob_hmin, glob_dump,
glob_log10normmin, glob_max_minutes, glob_log10relerr,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_almost_1,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec, glob_log10_abserr,
glob_dump_analytic, glob_not_yet_start_msg, glob_clock_start_sec,
MAX_UNCHANGED, glob_orig_start_sec, glob_small_float, glob_abserr,
glob_hmax, min_in_hour, glob_look_poles, glob_not_yet_finished,
years_in_century, glob_html_log, glob_warned2, glob_max_hours,
glob_hmin_init, hours_in_day, sec_in_min, glob_max_opt_iter, glob_start,
glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_rel_trunc_err,
glob_h, glob_optimal_done, djd_debug2, glob_subiter_method, glob_normmax,
glob_display_flag, glob_percent_done, glob_log10abserr, glob_warned,
glob_no_eqs, glob_max_iter, glob_last_good_h, glob_initial_pass,
glob_clock_sec, djd_debug, array_const_1, array_const_0D0, array_m1,
array_norms, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_1st_rel_error, array_fact_1, array_last_rel_error, array_type_pole,
array_y_init, array_pole, array_real_pole, array_poles, array_y_higher,
array_y_higher_work, array_complex_pole, array_y_higher_work2, array_fact_2,
array_y_set_initial, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
INFO := 2;
ALWAYS := 1;
DEBUGMASSIVE := 4;
DEBUGL := 3;
glob_iolevel := 5;
glob_iter := 0;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_start := 0.;
glob_disp_incr := 0.1;
glob_reached_optimal_h := false;
days_in_year := 365.0;
glob_relerr := 0.1*10^(-10);
centuries_in_millinium := 10.0;
glob_log10_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmin := 0.1*10^(-10);
glob_dump := false;
glob_log10normmin := 0.1;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_curr_iter_when_opt := 0;
glob_unchanged_h_cnt := 0;
glob_almost_1 := 0.9990;
glob_optimal_expect_sec := 0.1;
glob_current_iter := 0;
glob_max_sec := 10000.0;
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_not_yet_start_msg := true;
glob_clock_start_sec := 0.;
MAX_UNCHANGED := 10;
glob_orig_start_sec := 0.;
glob_small_float := 0.1*10^(-50);
glob_abserr := 0.1*10^(-10);
glob_hmax := 1.0;
min_in_hour := 60.0;
glob_look_poles := false;
glob_not_yet_finished := true;
years_in_century := 100.0;
glob_html_log := true;
glob_warned2 := false;
glob_max_hours := 0.;
glob_hmin_init := 0.001;
hours_in_day := 24.0;
sec_in_min := 60.0;
glob_max_opt_iter := 10;
glob_start := 0;
glob_optimal_clock_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_h := 0.1;
glob_optimal_done := false;
djd_debug2 := true;
glob_subiter_method := 3;
glob_normmax := 0.;
glob_display_flag := true;
glob_percent_done := 0.;
glob_log10abserr := 0.;
glob_warned := false;
glob_no_eqs := 0;
glob_max_iter := 1000;
glob_last_good_h := 0.1;
glob_initial_pass := true;
glob_clock_sec := 0.;
djd_debug := true;
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/nonlinear1postode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 0.5 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.01;");
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, "1.0/(1.0 - x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := 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_1st_rel_error := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y_init := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_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_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
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_type_pole[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_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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;
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_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
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.;
x_end := 0.5;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.01;
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 ) = y * y;");
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, "2012-06-18T00:44:30-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"nonlinear1");
logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 092 | ");
logitem_str(html_log_file, "nonlinear1 diffeq.mxt");
logitem_str(html_log_file, "nonlinear1 maple results");
logitem_str(html_log_file, "Mostly affecting speed of factorials");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/nonlinear1postode.ode#################
diff ( y , x , 1 ) = y * y;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 0.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.01;
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)
1.0/(1.0 - 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) = 1.001001001001001001001001001001
y[1] (numeric) = 1.0010010010010010365484123685393
absolute error = 3.55474113675383e-17
relative error = 3.5511863956170761700000000000000e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 1.0020040080160320641282565130261
y[1] (numeric) = 1.0020040080160321355447439290729
absolute error = 7.14164874160468e-17
relative error = 7.1273654441214706399999999999997e-15 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 1.0030090270812437311935807422267
y[1] (numeric) = 1.0030090270812438388036152524857
absolute error = 1.076100345102590e-16
relative error = 1.0728720440672822300000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 1.0040160642570281124497991967871
y[1] (numeric) = 1.0040160642570282565806845368025
absolute error = 1.441308853400154e-16
relative error = 1.4355436179865533840000000000001e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 1.0050251256281407035175879396985
y[1] (numeric) = 1.0050251256281408844994871299519
absolute error = 1.809818991902534e-16
relative error = 1.8007698969430213300000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 1.006036217303822937625754527163
y[1] (numeric) = 1.0060362173038231557917167411861
absolute error = 2.181659622140231e-16
relative error = 2.1685696644073896140000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 1.0070493454179254783484390735146
y[1] (numeric) = 1.0070493454179257340344267820808
absolute error = 2.556859877085662e-16
relative error = 2.5389618579460623660000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 1.0080645161290322580645161290323
y[1] (numeric) = 1.0080645161290325516094325235274
absolute error = 2.935449163944951e-16
relative error = 2.9119655706333913919999999999999e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 1.0090817356205852674066599394551
y[1] (numeric) = 1.0090817356205855991523766375663
absolute error = 3.317457166981112e-16
relative error = 3.2876000524782819920000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.14
NO POLE
x[1] = 0.01
y[1] (analytic) = 1.010101010101010101010101010101
y[1] (numeric) = 1.0101010101010104713014860469996
absolute error = 3.702913850368986e-16
relative error = 3.6658847118652961400000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.011
y[1] (analytic) = 1.0111223458038422649140546006067
y[1] (numeric) = 1.0111223458038426740990007088414
absolute error = 4.091849461082347e-16
relative error = 4.0468391170104411829999999999999e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.012
y[1] (analytic) = 1.0121457489878542510121457489879
y[1] (numeric) = 1.0121457489878546994415989303429
absolute error = 4.484294531813550e-16
relative error = 4.4304829974317873999999999999998e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.013
y[1] (analytic) = 1.0131712259371833839918946301925
y[1] (numeric) = 1.013171225937183872019883022806
absolute error = 4.880279883926135e-16
relative error = 4.8168362454350952450000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.014
y[1] (analytic) = 1.0141987829614604462474645030426
y[1] (numeric) = 1.0141987829614609742311275471202
absolute error = 5.279836630440776e-16
relative error = 5.2059189176146051360000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.015
y[1] (analytic) = 1.0152284263959390862944162436548
y[1] (numeric) = 1.0152284263959396545940341491555
absolute error = 5.682996179055007e-16
relative error = 5.5977512363691818950000000000001e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.016
y[1] (analytic) = 1.016260162601626016260162601626
y[1] (numeric) = 1.0162601626016266252391861213375
absolute error = 6.089790235197115e-16
relative error = 5.9923535914339611600000000000001e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.017
y[1] (analytic) = 1.0172939979654120040691759918616
y[1] (numeric) = 1.0172939979654126540942565033261
absolute error = 6.500250805114645e-16
relative error = 6.3897465414276960350000000000003e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.018
y[1] (analytic) = 1.0183299389002036659877800407332
y[1] (numeric) = 1.0183299389002043574287999405253
absolute error = 6.914410198997921e-16
relative error = 6.7899508154159584220000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.019
y[1] (analytic) = 1.0193679918450560652395514780836
y[1] (numeric) = 1.0193679918450567984696548919875
absolute error = 7.332301034139039e-16
relative error = 7.1929873144903972589999999999999e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.02
y[1] (analytic) = 1.0204081632653061224489795918367
y[1] (numeric) = 1.0204081632653068978446034045113
absolute error = 7.753956238126746e-16
relative error = 7.5988771133642110800000000000003e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.021
y[1] (analytic) = 1.0214504596527068437180796731359
y[1] (numeric) = 1.0214504596527076616589848809025
absolute error = 8.179409052077666e-16
relative error = 8.0076414619840350139999999999996e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.022
y[1] (analytic) = 1.0224948875255623721881390593047
y[1] (numeric) = 1.0224948875255632330574424497371
absolute error = 8.608693033904324e-16
relative error = 8.4193017871584288720000000000000e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.023
y[1] (analytic) = 1.0235414534288638689866939611054
y[1] (numeric) = 1.0235414534288647731709001231455
absolute error = 9.041842061620401e-16
relative error = 8.8338796942031317770000000000002e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.024
y[1] (analytic) = 1.0245901639344262295081967213115
y[1] (numeric) = 1.0245901639344271773972303896829
absolute error = 9.478890336683714e-16
relative error = 9.2513969686033048639999999999998e-14 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.29
NO POLE
x[1] = 0.025
y[1] (analytic) = 1.025641025641025641025641025641
y[1] (numeric) = 1.0256410256410266330128797633778
absolute error = 9.919872387377368e-16
relative error = 9.6718755776929338000000000000002e-14 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.026
y[1] (analytic) = 1.0266940451745379876796714579055
y[1] (numeric) = 1.0266940451745390241619786808612
absolute error = 1.0364823072229557e-15
relative error = 1.0095337672351588518000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.027
y[1] (analytic) = 1.0277492291880781089414182939363
y[1] (numeric) = 1.0277492291880791903191766411863
absolute error = 1.0813777583472500e-15
relative error = 1.0521805588718742500000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.028
y[1] (analytic) = 1.0288065843621399176954732510288
y[1] (numeric) = 1.0288065843621410443726183051293
absolute error = 1.1266771450541005e-15
relative error = 1.0951301849925856860000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.029
y[1] (analytic) = 1.029866117404737384140061791967
y[1] (numeric) = 1.0298661174047385565241161530801
absolute error = 1.1723840543611131e-15
relative error = 1.1383849167846408201000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.03
y[1] (analytic) = 1.0309278350515463917525773195876
y[1] (numeric) = 1.0309278350515476102546850375356
absolute error = 1.2185021077179480e-15
relative error = 1.1819470444864095600000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.031
y[1] (analytic) = 1.0319917440660474716202270381837
y[1] (numeric) = 1.0319917440660487366551884065443
absolute error = 1.2650349613683606e-15
relative error = 1.2258188775659414214000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.032
y[1] (analytic) = 1.0330578512396694214876033057851
y[1] (numeric) = 1.033057851239670733473910022191
absolute error = 1.3119863067164059e-15
relative error = 1.2700027449014809112000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.033
y[1] (analytic) = 1.0341261633919338159255429162358
y[1] (numeric) = 1.0341261633919351752854136130943
absolute error = 1.3593598706968585e-15
relative error = 1.3145009949638621695000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.034
y[1] (analytic) = 1.0351966873706004140786749482402
y[1] (numeric) = 1.0351966873706018212380910981422
absolute error = 1.4071594161499020e-15
relative error = 1.3593159960008053320000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.035
y[1] (analytic) = 1.0362694300518134715025906735751
y[1] (numeric) = 1.0362694300518149268913328737149
absolute error = 1.4553887422001398e-15
relative error = 1.4044501362231349070000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.036
y[1] (analytic) = 1.037344398340248962655601659751
y[1] (numeric) = 1.0373443983402504667072862997332
absolute error = 1.5040516846399822e-15
relative error = 1.4499058239929428408000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.037
y[1] (analytic) = 1.0384215991692627206645898234683
y[1] (numeric) = 1.0384215991692642738167061409341
absolute error = 1.5531521163174658e-15
relative error = 1.4956854880137195654000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.038
y[1] (analytic) = 1.039501039501039501039501039501
y[1] (numeric) = 1.0395010395010411037334485680602
absolute error = 1.6026939475285592e-15
relative error = 1.5417915775224739504000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.039
y[1] (analytic) = 1.0405827263267429760665972944849
y[1] (numeric) = 1.0405827263267446287477237084976
absolute error = 1.6526811264140127e-15
relative error = 1.5882265624838662047000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.04
y[1] (analytic) = 1.0416666666666666666666666666667
y[1] (numeric) = 1.0416666666666683697843060274757
absolute error = 1.7031176393608090e-15
relative error = 1.6349929337863766399999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=0.44
NO POLE
x[1] = 0.041
y[1] (analytic) = 1.0427528675703858185610010427529
y[1] (numeric) = 1.042752867570387572568512451026
absolute error = 1.7540075114082731e-15
relative error = 1.6820932034405339028999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.042
y[1] (analytic) = 1.0438413361169102296450939457202
y[1] (numeric) = 1.0438413361169120349999006046197
absolute error = 1.8053548066588995e-15
relative error = 1.7295299047792257210000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.043
y[1] (analytic) = 1.0449320794148380355276907001045
y[1] (numeric) = 1.044932079414839892691319394062
absolute error = 1.8571636286939575e-15
relative error = 1.7773055926601173275000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.044
y[1] (analytic) = 1.0460251046025104602510460251046
y[1] (numeric) = 1.0460251046025123696891670190394
absolute error = 1.9094381209939348e-15
relative error = 1.8254228436702016688000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.045
y[1] (analytic) = 1.0471204188481675392670157068063
y[1] (numeric) = 1.0471204188481695014494830706858
absolute error = 1.9621824673638795e-15
relative error = 1.8738842563325049225000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.046
y[1] (analytic) = 1.0482180293501048218029350104822
y[1] (numeric) = 1.0482180293501068372038273741866
absolute error = 2.0154008923637044e-15
relative error = 1.9226924513149739976000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.047
y[1] (analytic) = 1.0493179433368310598111227701994
y[1] (numeric) = 1.049317943336833128908784513715
absolute error = 2.0690976617435156e-15
relative error = 1.9718500716415703667999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.048
y[1] (analytic) = 1.0504201680672268907563025210084
y[1] (numeric) = 1.0504201680672290140333854050379
absolute error = 2.1232770828840295e-15
relative error = 2.0213597829055960840000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.049
y[1] (analytic) = 1.0515247108307045215562565720294
y[1] (numeric) = 1.0515247108307066994997618141721
absolute error = 2.1779435052421427e-15
relative error = 2.0712242734852777077000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.05
y[1] (analytic) = 1.0526315789473684210526315789474
y[1] (numeric) = 1.0526315789473706541539523806685
absolute error = 2.2331013208017211e-15
relative error = 2.1214462547616350449999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.051
y[1] (analytic) = 1.0537407797681770284510010537408
y[1] (numeric) = 1.0537407797681793172059655834151
absolute error = 2.2887549645296743e-15
relative error = 2.1720284613386609107000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.052
y[1] (analytic) = 1.0548523206751054852320675105485
y[1] (numeric) = 1.0548523206751078301409823479306
absolute error = 2.3449089148373821e-15
relative error = 2.2229736512658382308000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.053
y[1] (analytic) = 1.0559662090813093980992608236536
y[1] (numeric) = 1.0559662090813117996669548711967
absolute error = 2.4015676940475431e-15
relative error = 2.2742846062630233157000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.054
y[1] (analytic) = 1.0570824524312896405919661733615
y[1] (numeric) = 1.0570824524312920993278350398749
absolute error = 2.4587358688665134e-15
relative error = 2.3259641319477216764000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.055
y[1] (analytic) = 1.0582010582010582010582010582011
y[1] (numeric) = 1.0582010582010607174762519204074
absolute error = 2.5164180508622063e-15
relative error = 2.3780150580647849534999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.056
y[1] (analytic) = 1.0593220338983050847457627118644
y[1] (numeric) = 1.0593220338983076593646596594884
absolute error = 2.5746188969476240e-15
relative error = 2.4304402387185570560000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.0MB, time=0.60
NO POLE
x[1] = 0.057
y[1] (analytic) = 1.0604453870625662778366914103924
y[1] (numeric) = 1.0604453870625689111798012804859
absolute error = 2.6333431098700935e-15
relative error = 2.4832425526074981704999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.058
y[1] (analytic) = 1.0615711252653927813163481953291
y[1] (numeric) = 1.0615711252653954739117869016101
absolute error = 2.6925954387062810e-15
relative error = 2.5364249032613167020000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.059
y[1] (analytic) = 1.0626992561105207226354941551541
y[1] (numeric) = 1.0626992561105234750161735182114
absolute error = 2.7523806793630573e-15
relative error = 2.5899902192806369193000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.06
y[1] (analytic) = 1.0638297872340425531914893617021
y[1] (numeric) = 1.0638297872340453658951644459934
absolute error = 2.8127036750842913e-15
relative error = 2.6439414545792338220000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.061
y[1] (analytic) = 1.0649627263045793397231096911608
y[1] (numeric) = 1.0649627263045822132924266548072
absolute error = 2.8735693169636464e-15
relative error = 2.6982815886288639696000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.062
y[1] (analytic) = 1.0660980810234541577825159914712
y[1] (numeric) = 1.0660980810234570927650604549301
absolute error = 2.9349825444634589e-15
relative error = 2.7530136267067244482000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.063
y[1] (analytic) = 1.0672358591248665955176093916756
y[1] (numeric) = 1.067235859124869592465955331451
absolute error = 2.9969483459397754e-15
relative error = 2.8081406001455695497999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.064
y[1] (analytic) = 1.0683760683760683760683760683761
y[1] (numeric) = 1.0683760683760714355401352420059
absolute error = 3.0594717591736298e-15
relative error = 2.8636655665865174927999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.065
y[1] (analytic) = 1.069518716577540106951871657754
y[1] (numeric) = 1.0695187165775432295097435663942
absolute error = 3.1225578719086402e-15
relative error = 2.9195916102345785870000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.066
y[1] (analytic) = 1.0706638115631691648822269807281
y[1] (numeric) = 1.0706638115631723510940493757356
absolute error = 3.1862118223950075e-15
relative error = 2.9759218421169370049999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.067
y[1] (analytic) = 1.0718113612004287245444801714898
y[1] (numeric) = 1.0718113612004319749832801114897
absolute error = 3.2504387999399999e-15
relative error = 3.0326594003440199067000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.068
y[1] (analytic) = 1.0729613733905579399141630901288
y[1] (numeric) = 1.0729613733905612551582085551335
absolute error = 3.3152440454650047e-15
relative error = 3.0898074503733843803999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.069
y[1] (analytic) = 1.0741138560687432867883995703545
y[1] (numeric) = 1.074113856068746667421251639591
absolute error = 3.3806328520692365e-15
relative error = 3.1473691852764591814999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.07
y[1] (analytic) = 1.0752688172043010752688172043011
y[1] (numeric) = 1.0752688172043045218793828044863
absolute error = 3.4466105656001852e-15
relative error = 3.2053478260081722359999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.071
y[1] (analytic) = 1.0764262648008611410118406889128
y[1] (numeric) = 1.0764262648008646541944259198058
absolute error = 3.5131825852308930e-15
relative error = 3.2637466216794995970000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.072
y[1] (analytic) = 1.0775862068965517241379310344828
y[1] (numeric) = 1.0775862068965553044922950786324
absolute error = 3.5803543640441496e-15
relative error = 3.3225688498329708287999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.0MB, time=0.76
NO POLE
x[1] = 0.073
y[1] (analytic) = 1.0787486515641855447680690399137
y[1] (numeric) = 1.0787486515641891928994786636094
absolute error = 3.6481314096236957e-15
relative error = 3.3818178167211659139000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.074
y[1] (analytic) = 1.0799136069114470842332613390929
y[1] (numeric) = 1.0799136069114508007525459916181
absolute error = 3.7165192846525252e-15
relative error = 3.4414968575882383351999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.075
y[1] (analytic) = 1.0810810810810810810810810810811
y[1] (numeric) = 1.0810810810810848666046885994623
absolute error = 3.7855236075183812e-15
relative error = 3.5016093369545026099999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.076
y[1] (analytic) = 1.0822510822510822510822510822511
y[1] (numeric) = 1.0822510822510861062323040087889
absolute error = 3.8551500529265378e-15
relative error = 3.5621586489041209271999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.077
y[1] (analytic) = 1.0834236186348862405200433369447
y[1] (numeric) = 1.0834236186348901659243958569094
absolute error = 3.9254043525199647e-15
relative error = 3.6231482173759274181000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.078
y[1] (analytic) = 1.0845986984815618221258134490239
y[1] (numeric) = 1.0845986984815658184181089559942
absolute error = 3.9962922955069703e-15
relative error = 3.6845814964574266165999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.079
y[1] (analytic) = 1.0857763300760043431053203040174
y[1] (numeric) = 1.0857763300760084109250496004405
absolute error = 4.0678197292964231e-15
relative error = 3.7464619706820056750999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.08
y[1] (analytic) = 1.0869565217391304347826086956522
y[1] (numeric) = 1.086956521739134574775168836301
absolute error = 4.1399925601406488e-15
relative error = 3.8087931553293968959999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.081
y[1] (analytic) = 1.0881392818280739934711643090316
y[1] (numeric) = 1.0881392818280782062879180951382
absolute error = 4.2128167537861066e-15
relative error = 3.8715785967294319653999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.082
y[1] (analytic) = 1.0893246187363834422657952069717
y[1] (numeric) = 1.0893246187363877285641313389168
absolute error = 4.2862983361319451e-15
relative error = 3.9348218725691256017999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.083
y[1] (analytic) = 1.0905125408942202835332606324973
y[1] (numeric) = 1.0905125408942246439766545290405
absolute error = 4.3604433938965432e-15
relative error = 3.9985265922031301143999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.084
y[1] (analytic) = 1.0917030567685589519650655021834
y[1] (numeric) = 1.0917030567685633872231407943244
absolute error = 4.4352580752921410e-15
relative error = 4.0626963969676011560000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.085
y[1] (analytic) = 1.0928961748633879781420765027322
y[1] (numeric) = 1.0928961748633924888906672103991
absolute error = 4.5107485907076669e-15
relative error = 4.1273349604975152135000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.086
y[1] (analytic) = 1.0940919037199124726477024070022
y[1] (numeric) = 1.0940919037199170595689158068729
absolute error = 4.5869212133998707e-15
relative error = 4.1924459890474818198000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.087
y[1] (analytic) = 1.0952902519167579408543263964951
y[1] (numeric) = 1.0952902519167626046366065893671
absolute error = 4.6637822801928720e-15
relative error = 4.2580332218160921359999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.088
y[1] (analytic) = 1.0964912280701754385964912280702
y[1] (numeric) = 1.0964912280701801799346834143053
absolute error = 4.7413381921862351e-15
relative error = 4.3241004312738464111999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=0.92
NO POLE
x[1] = 0.089
y[1] (analytic) = 1.0976948408342480790340285400659
y[1] (numeric) = 1.0976948408342528986294440117507
absolute error = 4.8195954154716848e-15
relative error = 4.3906514234947048527999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.09
y[1] (analytic) = 1.0989010989010989010989010989011
y[1] (numeric) = 1.098901098901103799659382957478
absolute error = 4.8985604818585769e-15
relative error = 4.4576900384913049790000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.091
y[1] (analytic) = 1.10011001100110011001100110011
y[1] (numeric) = 1.1001100110011050882509907083499
absolute error = 4.9782399896082399e-15
relative error = 4.5252201505538900691000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.092
y[1] (analytic) = 1.1013215859030837004405286343612
y[1] (numeric) = 1.1013215859030887590811328116685
absolute error = 5.0586406041773073e-15
relative error = 4.5932456685929950284000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.093
y[1] (analytic) = 1.1025358324145534729878721058434
y[1] (numeric) = 1.1025358324145586127569310760022
absolute error = 5.1397690589701588e-15
relative error = 4.6617705364859340316000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.094
y[1] (analytic) = 1.1037527593818984547461368653422
y[1] (numeric) = 1.1037527593819036763782929659352
absolute error = 5.2216321561005930e-15
relative error = 4.7307987334271372579999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.095
y[1] (analytic) = 1.1049723756906077348066298342541
y[1] (numeric) = 1.1049723756906130390433969971093
absolute error = 5.3042367671628552e-15
relative error = 4.8003342742823839560000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.096
y[1] (analytic) = 1.1061946902654867256637168141593
y[1] (numeric) = 1.1061946902654921132535508263027
absolute error = 5.3875898340121434e-15
relative error = 4.8703812099469776336000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.097
y[1] (analytic) = 1.1074197120708748615725359911406
y[1] (numeric) = 1.1074197120708803332709055458641
absolute error = 5.4716983695547235e-15
relative error = 4.9409436277079153205000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.098
y[1] (analytic) = 1.1086474501108647450110864745011
y[1] (numeric) = 1.1086474501108703015805450222787
absolute error = 5.5565694585477776e-15
relative error = 5.0120256516100953952000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.099
y[1] (analytic) = 1.1098779134295227524972253052164
y[1] (numeric) = 1.1098779134295283947074837143366
absolute error = 5.6422102584091202e-15
relative error = 5.0836314428266173002000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1
y[1] (analytic) = 1.1111111111111111111111111111111
y[1] (numeric) = 1.1111111111111168397391111480237
absolute error = 5.7286280000369126e-15
relative error = 5.1557652000332213400000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.112347052280311457174638487208
y[1] (numeric) = 1.1123470522803172730046271267188
absolute error = 5.8158299886395108e-15
relative error = 5.2284311597869202092000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.113585746102449888641425389755
y[1] (numeric) = 1.113585746102455792465029965338
absolute error = 5.9038236045755830e-15
relative error = 5.3016335969088735340000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.1148272017837235228539576365663
y[1] (numeric) = 1.1148272017837295154702618412022
absolute error = 5.9926163042046359e-15
relative error = 5.3753768248715584023000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.1160714285714285714285714285714
y[1] (numeric) = 1.1160714285714346536441921766604
absolute error = 6.0822156207480890e-15
relative error = 5.4496651961902877440000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=1.07
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.1173184357541899441340782122905
y[1] (numeric) = 1.1173184357541961167632433733318
absolute error = 6.1726291651610413e-15
relative error = 5.5245031028191319635000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.1185682326621923937360178970917
y[1] (numeric) = 1.1185682326621986576006449119647
absolute error = 6.2638646270148730e-15
relative error = 5.5998949765512964620000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.1198208286674132138857782754759
y[1] (numeric) = 1.1198208286674195698155536663062
absolute error = 6.3559297753908303e-15
relative error = 5.6758452894240114579000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.1210762331838565022421524663677
y[1] (numeric) = 1.1210762331838629510746122511097
absolute error = 6.4488324597847420e-15
relative error = 5.7523585541279898640000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.1223344556677890011223344556678
y[1] (numeric) = 1.1223344556677955437029454786863
absolute error = 6.5425806110230185e-15
relative error = 5.8294393244215094834999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.1235955056179775280898876404494
y[1] (numeric) = 1.1235955056179841652721298305363
absolute error = 6.6371822421900869e-15
relative error = 5.9070921955491773410000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.111
y[1] (analytic) = 1.1248593925759280089988751406074
y[1] (numeric) = 1.124859392575934741644324708025
absolute error = 6.7326454495674176e-15
relative error = 5.9853218046654342464000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.112
y[1] (analytic) = 1.1261261261261261261261261261261
y[1] (numeric) = 1.126126126126132955104539710427
absolute error = 6.8289784135843009e-15
relative error = 6.0641328312628591992000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.113
y[1] (analytic) = 1.1273957158962795941375422773393
y[1] (numeric) = 1.1273957158962865203269420578715
absolute error = 6.9261893997805322e-15
relative error = 6.1435299976053320614000000000003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.114
y[1] (analytic) = 1.1286681715575620767494356659142
y[1] (numeric) = 1.1286681715575691010361954470847
absolute error = 7.0242867597811705e-15
relative error = 6.2235180691661170630000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.115
y[1] (analytic) = 1.1299435028248587570621468926554
y[1] (numeric) = 1.1299435028248658803410791761884
absolute error = 7.1232789322835330e-15
relative error = 6.3041018550709267049999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.116
y[1] (analytic) = 1.1312217194570135746606334841629
y[1] (numeric) = 1.1312217194570207978350775407583
absolute error = 7.2231744440565954e-15
relative error = 6.3852862085460303336000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.117
y[1] (analytic) = 1.1325028312570781426953567383918
y[1] (numeric) = 1.132502831257085466677267691357
absolute error = 7.3239819109529652e-15
relative error = 6.4670760273714682716000000000003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.118
y[1] (analytic) = 1.1337868480725623582766439909297
y[1] (numeric) = 1.1337868480725697839866829245328
absolute error = 7.4257100389336031e-15
relative error = 6.5494762543394379342000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.119
y[1] (analytic) = 1.1350737797956867196367763904654
y[1] (numeric) = 1.1350737797956942480044014959309
absolute error = 7.5283676251054655e-15
relative error = 6.6324918777179151054999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.12
y[1] (analytic) = 1.1363636363636363636363636363636
y[1] (numeric) = 1.1363636363636439955999224086102
absolute error = 7.6319635587722466e-15
relative error = 6.7161279317195770080000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=30.5MB, alloc=4.1MB, time=1.23
x[1] = 0.121
y[1] (analytic) = 1.1376564277588168373151308304892
y[1] (numeric) = 1.1376564277588245738219533288887
absolute error = 7.7365068224983995e-15
relative error = 6.8003894969760931605000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.122
y[1] (analytic) = 1.1389521640091116173120728929385
y[1] (numeric) = 1.1389521640091194593185660795594
absolute error = 7.8420064931866209e-15
relative error = 6.8852817010178531502000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.123
y[1] (analytic) = 1.1402508551881413911060433295325
y[1] (numeric) = 1.1402508551881493395777864985151
absolute error = 7.9484717431689826e-15
relative error = 6.9708097187591977402000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.124
y[1] (analytic) = 1.1415525114155251141552511415525
y[1] (numeric) = 1.1415525114155331700670924534524
absolute error = 8.0559118413118999e-15
relative error = 7.0569787729892243124000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.125
y[1] (analytic) = 1.1428571428571428571428571428571
y[1] (numeric) = 1.1428571428571510214790112779852
absolute error = 8.1643361541351281e-15
relative error = 7.1437941348682370875000000000003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.126
y[1] (analytic) = 1.1441647597254004576659038901602
y[1] (numeric) = 1.1441647597254087314200508351401
absolute error = 8.2737541469449799e-15
relative error = 7.2312611244299124325999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.127
y[1] (analytic) = 1.145475372279495990836197021764
y[1] (numeric) = 1.1454753722795043750115820037263
absolute error = 8.3841753849819623e-15
relative error = 7.3193851110892530879000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.128
y[1] (analytic) = 1.146788990825688073394495412844
y[1] (numeric) = 1.1467889908256965690040299958754
absolute error = 8.4956095345830314e-15
relative error = 7.4081715141564033808000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.129
y[1] (analytic) = 1.1481056257175660160734787600459
y[1] (numeric) = 1.1481056257175746241398431187152
absolute error = 8.6080663643586693e-15
relative error = 7.4976258033564009603000000000002e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.13
y[1] (analytic) = 1.1494252873563218390804597701149
y[1] (numeric) = 1.1494252873563305606362061551033
absolute error = 8.7215557463849884e-15
relative error = 7.5877534993549399080000000000003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.131
y[1] (analytic) = 1.1507479861910241657077100115075
y[1] (numeric) = 1.1507479861910330017953674225796
absolute error = 8.8360876574110721e-15
relative error = 7.6785601742902216548999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.132
y[1] (analytic) = 1.1520737327188940092165898617512
y[1] (numeric) = 1.1520737327189029608887699435163
absolute error = 8.9516721800817651e-15
relative error = 7.7700514523109721067999999999997e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.133
y[1] (analytic) = 1.1534025374855824682814302191465
y[1] (numeric) = 1.1534025374855915366009343952736
absolute error = 9.0683195041761271e-15
relative error = 7.8622330101207021956999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.134
y[1] (analytic) = 1.1547344110854503464203233256351
y[1] (numeric) = 1.1547344110854595324602511874051
absolute error = 9.1860399278617700e-15
relative error = 7.9551105775282928200000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.135
y[1] (analytic) = 1.1560693641618497109826589595376
y[1] (numeric) = 1.156069364161859015826517924838
absolute error = 9.3048438589653004e-15
relative error = 8.0486899380049848459999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.136
y[1] (analytic) = 1.1574074074074074074074074074074
y[1] (numeric) = 1.1574074074074168321492236664996
absolute error = 9.4247418162590922e-15
relative error = 8.1429769292478556608000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.137
y[1] (analytic) = 1.158748551564310544611819235226
y[1] (numeric) = 1.1587485515643200903562499998443
absolute error = 9.5457444307646183e-15
relative error = 8.2379774437498655928999999999997e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.1MB, time=1.39
NO POLE
x[1] = 0.138
y[1] (analytic) = 1.1600928074245939675174013921114
y[1] (numeric) = 1.1600928074246036353798484646857
absolute error = 9.6678624470725743e-15
relative error = 8.3336974293765590465999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.139
y[1] (analytic) = 1.1614401858304297328687572590012
y[1] (numeric) = 1.1614401858304395239754819390297
absolute error = 9.7911067246800285e-15
relative error = 8.4301428899495045384999999999997e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.14
y[1] (analytic) = 1.1627906976744186046511627906977
y[1] (numeric) = 1.1627906976744285201394021355375
absolute error = 9.9154882393448398e-15
relative error = 8.5273198858365622279999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.141
y[1] (analytic) = 1.1641443538998835855646100116414
y[1] (numeric) = 1.1641443538998936265826944692256
absolute error = 1.00410180844575842e-14
relative error = 8.6252345345490648278000000000003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.142
y[1] (analytic) = 1.1655011655011655011655011655012
y[1] (numeric) = 1.1655011655011756688729735967392
absolute error = 1.01677074724312380e-14
relative error = 8.7238930113460022039999999999997e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.143
y[1] (analytic) = 1.1668611435239206534422403733956
y[1] (numeric) = 1.1668611435239309490099764822641
absolute error = 1.02955677361088685e-14
relative error = 8.8233015498453003044999999999997e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.144
y[1] (analytic) = 1.1682242990654205607476635514019
y[1] (numeric) = 1.1682242990654309853579937409866
absolute error = 1.04246103301895847e-14
relative error = 8.9234664426422845031999999999998e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.145
y[1] (analytic) = 1.1695906432748538011695906432749
y[1] (numeric) = 1.1695906432748643560164233162834
absolute error = 1.05548468326730085e-14
relative error = 9.0243940419354222674999999999996e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.146
y[1] (analytic) = 1.1709601873536299765807962529274
y[1] (numeric) = 1.1709601873536406628697425754544
absolute error = 1.06862889463225270e-14
relative error = 9.1260907601594380580000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.147
y[1] (analytic) = 1.1723329425556858147713950762016
y[1] (numeric) = 1.1723329425556966337198952237942
absolute error = 1.08189485001475926e-14
relative error = 9.2285630706258964878000000000003e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.148
y[1] (analytic) = 1.1737089201877934272300469483568
y[1] (numeric) = 1.173708920187804380067497853698
absolute error = 1.09528374509053412e-14
relative error = 9.3318175081713507024000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.149
y[1] (analytic) = 1.1750881316098707403055229142186
y[1] (numeric) = 1.1750881316098818282734075360218
absolute error = 1.10879678846218032e-14
relative error = 9.4358606698131545231999999999997e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.15
y[1] (analytic) = 1.1764705882352941176470588235294
y[1] (numeric) = 1.1764705882353053419990769565147
absolute error = 1.12243520181329853e-14
relative error = 9.5406992154130375050000000000001e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.151
y[1] (analytic) = 1.1778563015312131919905771495878
y[1] (numeric) = 1.177856301531224553992777795694
absolute error = 1.13620022006461062e-14
relative error = 9.6463398683485441637999999999996e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.152
y[1] (analytic) = 1.1792452830188679245283018867925
y[1] (numeric) = 1.1792452830188794254592172080673
absolute error = 1.15009309153212748e-14
relative error = 9.7527894161924410303999999999996e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.153
y[1] (analytic) = 1.180637544273907910271546635183
y[1] (numeric) = 1.1806375442739195514223275090831
absolute error = 1.16411507808739001e-14
relative error = 9.8600547114001933847000000000000e-13 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=1.56
NO POLE
x[1] = 0.154
y[1] (analytic) = 1.1820330969267139479905437352246
y[1] (numeric) = 1.1820330969267257306650969333562
absolute error = 1.17826745531981316e-14
relative error = 9.9681426720056193335999999999999e-13 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.155
y[1] (analytic) = 1.183431952662721893491124260355
y[1] (numeric) = 1.1834319526627338190062512719851
absolute error = 1.19255151270116301e-14
relative error = 1.0077060282324827434500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.156
y[1] (analytic) = 1.1848341232227488151658767772512
y[1] (numeric) = 1.1848341232227608848514142992248
absolute error = 1.20696855375219736e-14
relative error = 1.0186814593668545718400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.157
y[1] (analytic) = 1.1862396204033214709371293001186
y[1] (numeric) = 1.1862396204033336861360914151285
absolute error = 1.22151989621150099e-14
relative error = 1.0297412725062953345700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.158
y[1] (analytic) = 1.1876484560570071258907363420428
y[1] (numeric) = 1.1876484560570194879594584075129
absolute error = 1.23620687220654701e-14
relative error = 1.0408861863979125824200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.159
y[1] (analytic) = 1.1890606420927467300832342449465
y[1] (numeric) = 1.1890606420927592403915185151102
absolute error = 1.25103082842701637e-14
relative error = 1.0521169267071207671700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.16
y[1] (analytic) = 1.1904761904761904761904761904762
y[1] (numeric) = 1.1904761904762031361217391945551
absolute error = 1.26599312630040789e-14
relative error = 1.0634342260923426276000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.161
y[1] (analytic) = 1.1918951132300357568533969010727
y[1] (numeric) = 1.1918951132300485678048186007932
absolute error = 1.28109514216997205e-14
relative error = 1.0748388242806065499500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.162
y[1] (analytic) = 1.1933174224343675417661097852029
y[1] (numeric) = 1.1933174224343805051487845352208
absolute error = 1.29633826747500179e-14
relative error = 1.0863314681440515000200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.163
y[1] (analytic) = 1.1947431302270011947431302270012
y[1] (numeric) = 1.1947431302270143119822195621467
absolute error = 1.31172390893351455e-14
relative error = 1.0979129117773516783500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.164
y[1] (analytic) = 1.1961722488038277511961722488038
y[1] (numeric) = 1.1961722488038410237310595224044
absolute error = 1.32725348872736006e-14
relative error = 1.1095839165760730101600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.165
y[1] (analytic) = 1.1976047904191616766467065868263
y[1] (numeric) = 1.1976047904191751059311534847161
absolute error = 1.34292844468978898e-14
relative error = 1.1213452513159737983000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.166
y[1] (analytic) = 1.1990407673860911270983213429257
y[1] (numeric) = 1.199040767386104714600626298107
absolute error = 1.35875023049551813e-14
relative error = 1.1331976922332621204200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.167
y[1] (analytic) = 1.2004801920768307322929171668667
y[1] (numeric) = 1.2004801920768444794960757001514
absolute error = 1.37472031585332847e-14
relative error = 1.1451420231058226155100000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.168
y[1] (analytic) = 1.2019230769230769230769230769231
y[1] (numeric) = 1.2019230769230908314787900892485
absolute error = 1.39084018670123254e-14
relative error = 1.1571790353354254732800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.169
y[1] (analytic) = 1.2033694344163658243080625752106
y[1] (numeric) = 1.2033694344163798954215166177015
absolute error = 1.40711134540424909e-14
relative error = 1.1693095280309309937900000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=1.72
NO POLE
x[1] = 0.17
y[1] (analytic) = 1.2048192771084337349397590361446
y[1] (numeric) = 1.204819277108447970292868584368
absolute error = 1.42353531095482234e-14
relative error = 1.1815343080925025422000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.171
y[1] (analytic) = 1.2062726176115802171290711700844
y[1] (numeric) = 1.2062726176115946182652629293339
absolute error = 1.44011361917592495e-14
relative error = 1.1938541902968417835500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.172
y[1] (analytic) = 1.2077294685990338164251207729469
y[1] (numeric) = 1.2077294685990483849033500417814
absolute error = 1.45684782292688345e-14
relative error = 1.2062699973834594966000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.173
y[1] (analytic) = 1.2091898428053204353083434099154
y[1] (numeric) = 1.2091898428053351727032665295785
absolute error = 1.47373949231196631e-14
relative error = 1.2187825601419961383700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.174
y[1] (analytic) = 1.2106537530266343825665859564165
y[1] (numeric) = 1.2106537530266492904687348741637
absolute error = 1.49079021489177472e-14
relative error = 1.2313927175006059187200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.175
y[1] (analytic) = 1.2121212121212121212121212121212
y[1] (numeric) = 1.2121212121212272012280801868951
absolute error = 1.50800159589747739e-14
relative error = 1.2441013166154188467500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.176
y[1] (analytic) = 1.2135922330097087378640776699029
y[1] (numeric) = 1.2135922330097239916166621492127
absolute error = 1.52537525844793098e-14
relative error = 1.2569092129610951275200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.177
y[1] (analytic) = 1.2150668286755771567436208991495
y[1] (numeric) = 1.2150668286755925858720585964353
absolute error = 1.54291284376972858e-14
relative error = 1.2698172704224866213400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.178
y[1] (analytic) = 1.216545012165450121654501216545
y[1] (numeric) = 1.2165450121654657278146154187382
absolute error = 1.56061601142021932e-14
relative error = 1.2828263613874202810400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.179
y[1] (analytic) = 1.2180267965895249695493300852619
y[1] (numeric) = 1.218026796589540754413725220689
absolute error = 1.57848643951354271e-14
relative error = 1.2959373668406185649100000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.18
y[1] (analytic) = 1.2195121951219512195121951219512
y[1] (numeric) = 1.219512195121967184770444619175
absolute error = 1.59652582494972238e-14
relative error = 1.3091511764587723516000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.181
y[1] (analytic) = 1.2210012210012210012210012210012
y[1] (numeric) = 1.2210012210012371485798376896429
absolute error = 1.61473588364686417e-14
relative error = 1.3224686887067817552300000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.182
y[1] (analytic) = 1.2224938875305623471882640586797
y[1] (numeric) = 1.222493887530578678371771823725
absolute error = 1.63311835077650453e-14
relative error = 1.3358908109351807055400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.183
y[1] (analytic) = 1.2239902080783353733170134638923
y[1] (numeric) = 1.2239902080783518900668234854509
absolute error = 1.65167498100215586e-14
relative error = 1.3494184594787613376200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.184
y[1] (analytic) = 1.2254901960784313725490196078431
y[1] (numeric) = 1.2254901960784480766245068188038
absolute error = 1.67040754872109607e-14
relative error = 1.3630525597564143931200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.185
y[1] (analytic) = 1.2269938650306748466257668711656
y[1] (numeric) = 1.2269938650306917398042499656705
absolute error = 1.68931784830945049e-14
relative error = 1.3767940463722021493500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=1.87
NO POLE
x[1] = 0.186
y[1] (analytic) = 1.2285012285012285012285012285012
y[1] (numeric) = 1.2285012285012455853054449346523
absolute error = 1.70840769437061511e-14
relative error = 1.3906438632176806995400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.187
y[1] (analytic) = 1.2300123001230012300123001230012
y[1] (numeric) = 1.2300123001230185068015199937085
absolute error = 1.72767892198707073e-14
relative error = 1.4046029635754885034900000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.188
y[1] (analytic) = 1.2315270935960591133004926108374
y[1] (numeric) = 1.2315270935960765846343623672218
absolute error = 1.74713338697563844e-14
relative error = 1.4186723102242184132800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.189
y[1] (analytic) = 1.2330456226880394574599260172626
y[1] (numeric) = 1.2330456226880571251895874795418
absolute error = 1.76677296614622792e-14
relative error = 1.4328528755445908431200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.19
y[1] (analytic) = 1.2345679012345679012345679012346
y[1] (numeric) = 1.2345679012345857672301435425391
absolute error = 1.78659955756413045e-14
relative error = 1.4471456416269456645000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.191
y[1] (analytic) = 1.23609394313967861557478368356
y[1] (numeric) = 1.2360939431396966817255918426575
absolute error = 1.80661508081590975e-14
relative error = 1.4615516003800709877499999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.192
y[1] (analytic) = 1.2376237623762376237623762376238
y[1] (numeric) = 1.2376237623762558919771490270676
absolute error = 1.82682147727894438e-14
relative error = 1.4760717536413870590400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.193
y[1] (analytic) = 1.2391573729863692688971499380421
y[1] (numeric) = 1.2391573729863877411042538848063
absolute error = 1.84722071039467642e-14
relative error = 1.4907071132885038709400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.194
y[1] (analytic) = 1.2406947890818858560794044665012
y[1] (numeric) = 1.2406947890819045342270639227214
absolute error = 1.86781476594562202e-14
relative error = 1.5054587013521713481200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.195
y[1] (analytic) = 1.2422360248447204968944099378882
y[1] (numeric) = 1.242236024844739382950933299891
absolute error = 1.88860565233620028e-14
relative error = 1.5203275501306412254000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.196
y[1] (analytic) = 1.2437810945273631840796019900498
y[1] (numeric) = 1.2437810945273822800336107644285
absolute error = 1.90959540087743787e-14
relative error = 1.5353147023054600474799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.197
y[1] (analytic) = 1.24533001245330012453300124533
y[1] (numeric) = 1.245330012453319432393662001407
absolute error = 1.93078606607560770e-14
relative error = 1.5504212110587129831000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.198
y[1] (analytic) = 1.2468827930174563591022443890274
y[1] (numeric) = 1.2468827930174758808995036376367
absolute error = 1.95217972592486093e-14
relative error = 1.5656481401917384658600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.199
y[1] (analytic) = 1.2484394506866416978776529338327
y[1] (numeric) = 1.2484394506866614356624749729593
absolute error = 1.97377848220391266e-14
relative error = 1.5809965642453340406600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.2
y[1] (analytic) = 1.25
y[1] (numeric) = 1.2500000000000199558446077684241
absolute error = 1.99558446077684241e-14
relative error = 1.5964675686214739280000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.201
y[1] (analytic) = 1.2515644555694618272841051314143
y[1] (numeric) = 1.2515644555694820032822241121314
absolute error = 2.01759981189807171e-14
relative error = 1.6120622497065592962900000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=2.03
NO POLE
x[1] = 0.202
y[1] (analytic) = 1.2531328320802005012531328320802
y[1] (numeric) = 1.2531328320802208995202380479007
absolute error = 2.03982671052158205e-14
relative error = 1.6277817149962224759000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.203
y[1] (analytic) = 1.2547051442910915934755332496863
y[1] (numeric) = 1.2547051442911122161490993940609
absolute error = 2.06226735661443746e-14
relative error = 1.6436270832217066556200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.204
y[1] (analytic) = 1.2562814070351758793969849246231
y[1] (numeric) = 1.2562814070351967286367396713946
absolute error = 2.08492397547467715e-14
relative error = 1.6595994844778430114000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.205
y[1] (analytic) = 1.2578616352201257861635220125786
y[1] (numeric) = 1.2578616352201468641517025490243
absolute error = 2.10779881805364457e-14
relative error = 1.6757000603526474331500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.206
y[1] (analytic) = 1.2594458438287153652392947103275
y[1] (numeric) = 1.2594458438287366741809075385317
absolute error = 2.13089416128282042e-14
relative error = 1.6919299640585594134799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.207
y[1] (analytic) = 1.2610340479192938209331651954603
y[1] (numeric) = 1.2610340479193153630562492477442
absolute error = 2.15421230840522839e-14
relative error = 1.7082903605653461132700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.208
y[1] (analytic) = 1.2626262626262626262626262626263
y[1] (numeric) = 1.2626262626262844038185193774574
absolute error = 2.17775558931148311e-14
relative error = 1.7247824267346946231199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.209
y[1] (analytic) = 1.2642225031605562579013906447535
y[1] (numeric) = 1.2642225031605782731649994502697
absolute error = 2.20152636088055162e-14
relative error = 1.7414073514565163314200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.21
y[1] (analytic) = 1.2658227848101265822784810126582
y[1] (numeric) = 1.2658227848101488375485542656598
absolute error = 2.22552700732530016e-14
relative error = 1.7581663357869871264000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.211
y[1] (analytic) = 1.2674271229404309252217997465146
y[1] (numeric) = 1.2674271229404534228212051755114
absolute error = 2.24975994054289968e-14
relative error = 1.7750605930883478475200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.212
y[1] (analytic) = 1.2690355329949238578680203045685
y[1] (numeric) = 1.2690355329949466001440250062156
absolute error = 2.27422760047016471e-14
relative error = 1.7920913491704897914800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.213
y[1] (analytic) = 1.2706480304955527318932655654384
y[1] (numeric) = 1.2706480304955757212178200044491
absolute error = 2.29893245544390107e-14
relative error = 1.8092598424343501420900000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.214
y[1] (analytic) = 1.2722646310432569974554707379135
y[1] (numeric) = 1.2722646310432802362254964013114
absolute error = 2.32387700256633979e-14
relative error = 1.8265673240171430749400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.215
y[1] (analytic) = 1.2738853503184713375796178343949
y[1] (numeric) = 1.2738853503184948282172985917467
absolute error = 2.34906376807573518e-14
relative error = 1.8440150579394521163000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.216
y[1] (analytic) = 1.2755102040816326530612244897959
y[1] (numeric) = 1.2755102040816563980143017118654
absolute error = 2.37449530772220695e-14
relative error = 1.8616043212542102488000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.217
y[1] (analytic) = 1.2771392081736909323116219667944
y[1] (numeric) = 1.2771392081737149340536934558659
absolute error = 2.40017420714890715e-14
relative error = 1.8793364041975942984500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=53.4MB, alloc=4.1MB, time=2.19
x[1] = 0.218
y[1] (analytic) = 1.278772378516624040920716112532
y[1] (numeric) = 1.2787723785166483019515388984749
absolute error = 2.42610308227859429e-14
relative error = 1.8972126103418607347800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.219
y[1] (analytic) = 1.2804097311139564660691421254802
y[1] (numeric) = 1.2804097311139809889149391824626
absolute error = 2.45228457970569824e-14
relative error = 1.9152342567501503254399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.22
y[1] (analytic) = 1.2820512820512820512820512820513
y[1] (numeric) = 1.2820512820513068384958222216624
absolute error = 2.47872137709396111e-14
relative error = 1.9334026741332896658000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.221
y[1] (analytic) = 1.2836970474967907573812580231065
y[1] (numeric) = 1.2836970474968158115430938205113
absolute error = 2.50541618357974048e-14
relative error = 1.9517192070086178339200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.222
y[1] (analytic) = 1.2853470437017994858611825192802
y[1] (numeric) = 1.2853470437018248095785843299102
absolute error = 2.53237174018106300e-14
relative error = 1.9701852138608670140000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.223
y[1] (analytic) = 1.2870012870012870012870012870013
y[1] (numeric) = 1.2870012870013125971952034121796
absolute error = 2.55959082021251783e-14
relative error = 1.9888020673051263539100000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.224
y[1] (analytic) = 1.2886597938144329896907216494845
y[1] (numeric) = 1.2886597938144588604530187102922
absolute error = 2.58707622970608077e-14
relative error = 2.0075711542519186775200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.225
y[1] (analytic) = 1.2903225806451612903225806451613
y[1] (numeric) = 1.2903225806451874386306590247777
absolute error = 2.61483080783796164e-14
relative error = 2.0264938760744202710000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.226
y[1] (analytic) = 1.2919896640826873385012919896641
y[1] (numeric) = 1.2919896640827137670755656053536
absolute error = 2.64285742736156895e-14
relative error = 2.0455716487778543673000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.227
y[1] (analytic) = 1.2936610608020698576972833117723
y[1] (numeric) = 1.2936610608020965692872337786468
absolute error = 2.67115899504668745e-14
relative error = 2.0648059031710893988500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.228
y[1] (analytic) = 1.2953367875647668393782383419689
y[1] (numeric) = 1.2953367875647938367627595916272
absolute error = 2.69973845212496583e-14
relative error = 2.0841980850404736207600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.229
y[1] (analytic) = 1.2970168612191958495460440985733
y[1] (numeric) = 1.2970168612192231355337915167087
absolute error = 2.72859877474181354e-14
relative error = 2.1037496553259382393400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.23
y[1] (analytic) = 1.2987012987012987012987012987013
y[1] (numeric) = 1.2987012987013262787284454467736
absolute error = 2.75774297441480723e-14
relative error = 2.1234620902994015671000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.231
y[1] (analytic) = 1.3003901170351105331599479843953
y[1] (numeric) = 1.3003901170351384049009329714866
absolute error = 2.78717409849870913e-14
relative error = 2.1433368817455073209700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.232
y[1] (analytic) = 1.3020833333333333333333333333333
y[1] (numeric) = 1.302083333333361502285639905348
absolute error = 2.81689523065720147e-14
relative error = 2.1633755371447307289600000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.233
y[1] (analytic) = 1.3037809647979139504563233376793
y[1] (numeric) = 1.3037809647979424195512367521059
absolute error = 2.84690949134144266e-14
relative error = 2.1835795798588865202199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.234
y[1] (analytic) = 1.3054830287206266318537859007833
y[1] (numeric) = 1.3054830287206554040541686563131
absolute error = 2.87722003827555298e-14
relative error = 2.2039505493190735826800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.1MB, time=2.35
NO POLE
x[1] = 0.235
y[1] (analytic) = 1.307189542483660130718954248366
y[1] (numeric) = 1.3071895424836892090196237397566
absolute error = 2.90783006694913906e-14
relative error = 2.2244900012160913809000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.236
y[1] (analytic) = 1.3089005235602094240837696335079
y[1] (numeric) = 1.3089005235602388115118808031948
absolute error = 2.93874281111696869e-14
relative error = 2.2451995076933640791599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.237
y[1] (analytic) = 1.3106159895150720838794233289646
y[1] (numeric) = 1.3106159895151017834948563880556
absolute error = 2.96996154330590910e-14
relative error = 2.2660806575424086433000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.238
y[1] (analytic) = 1.3123359580052493438320209973753
y[1] (numeric) = 1.3123359580052793587277742898136
absolute error = 3.00148957532924383e-14
relative error = 2.2871350564008837984600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.239
y[1] (analytic) = 1.3140604467805519053876478318003
y[1] (numeric) = 1.314060446780582238690235916656
absolute error = 3.03333025880848557e-14
relative error = 2.3083643269532575187699999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.24
y[1] (analytic) = 1.3157894736842105263157894736842
y[1] (numeric) = 1.3157894736842411811856465017237
absolute error = 3.06548698570280395e-14
relative error = 2.3297701091341310020000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.241
y[1] (analytic) = 1.3175230566534914361001317523057
y[1] (numeric) = 1.3175230566535224157320202142019
absolute error = 3.09796318884618962e-14
relative error = 2.3513540603342579215799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.242
y[1] (analytic) = 1.3192612137203166226912928759894
y[1] (numeric) = 1.3192612137203479303147178007693
absolute error = 3.13076234249247799e-14
relative error = 2.3731178556092983164200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.243
y[1] (analytic) = 1.321003963011889035667107001321
y[1] (numeric) = 1.3210039630119206745467356849008
absolute error = 3.16388796286835798e-14
relative error = 2.3950631878913469908600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.244
y[1] (analytic) = 1.3227513227513227513227513227513
y[1] (numeric) = 1.3227513227513547247588386676871
absolute error = 3.19734360873449358e-14
relative error = 2.4171917682032771464800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.245
y[1] (analytic) = 1.3245033112582781456953642384106
y[1] (numeric) = 1.3245033112583104570241837872894
absolute error = 3.23113288195488788e-14
relative error = 2.4395053258759403494000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.246
y[1] (analytic) = 1.3262599469496021220159151193634
y[1] (numeric) = 1.3262599469496347746101958655821
absolute error = 3.26525942807462187e-14
relative error = 2.4620056087682648899800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.247
y[1] (analytic) = 1.3280212483399734395750332005312
y[1] (numeric) = 1.3280212483400064368444022615537
absolute error = 3.29972693690610225e-14
relative error = 2.4846943834902949942500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.248
y[1] (analytic) = 1.3297872340425531914893617021277
y[1] (numeric) = 1.3297872340425865368807929416783
absolute error = 3.33453914312395506e-14
relative error = 2.5075734356292142051199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.249
y[1] (analytic) = 1.3315579227696404793608521970706
y[1] (numeric) = 1.3315579227696741763591208841135
absolute error = 3.36969982686870429e-14
relative error = 2.5306445699783969217899999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.25
y[1] (analytic) = 1.3333333333333333333333333333333
y[1] (numeric) = 1.3333333333333673854614769271024
absolute error = 3.40521281435937691e-14
relative error = 2.5539096107695326825000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.1MB, time=2.51
NO POLE
x[1] = 0.251
y[1] (analytic) = 1.3351134846461949265687583444593
y[1] (numeric) = 1.3351134846462293373885434962432
absolute error = 3.44108197851517839e-14
relative error = 2.5773704019078686141100000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.252
y[1] (analytic) = 1.3368983957219251336898395721925
y[1] (numeric) = 1.3368983957219599068022354360461
absolute error = 3.47731123958638536e-14
relative error = 2.6010288072106162492800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.253
y[1] (analytic) = 1.3386880856760374832663989290495
y[1] (numeric) = 1.3386880856760726223120568750919
absolute error = 3.51390456579460424e-14
relative error = 2.6248867106485693672800000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.254
y[1] (analytic) = 1.3404825737265415549597855227882
y[1] (numeric) = 1.3404825737265770636195253482669
absolute error = 3.55086597398254787e-14
relative error = 2.6489460165909807110200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.255
y[1] (analytic) = 1.3422818791946308724832214765101
y[1] (numeric) = 1.3422818791946667544785242113533
absolute error = 3.58819953027348432e-14
relative error = 2.6732086500537458183999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.256
y[1] (analytic) = 1.3440860215053763440860215053763
y[1] (numeric) = 1.3440860215054126031795289105268
absolute error = 3.62590935074051505e-14
relative error = 2.6976765569509431972000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.257
y[1] (analytic) = 1.3458950201884253028263795423957
y[1] (numeric) = 1.3458950201884619428224004008179
absolute error = 3.66399960208584222e-14
relative error = 2.7223517043497807694600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.258
y[1] (analytic) = 1.3477088948787061994609164420485
y[1] (numeric) = 1.3477088948787432242059397439288
absolute error = 3.70247450233018803e-14
relative error = 2.7472360807289995182600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.259
y[1] (analytic) = 1.3495276653171390013495276653171
y[1] (numeric) = 1.3495276653171764147327427906305
absolute error = 3.74133832151253134e-14
relative error = 2.7723316962407857229400000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.26
y[1] (analytic) = 1.3513513513513513513513513513514
y[1] (numeric) = 1.3513513513513891573051753546544
absolute error = 3.78059538240033030e-14
relative error = 2.7976405829762444219999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.261
y[1] (analytic) = 1.3531799729364005412719891745602
y[1] (numeric) = 1.3531799729364387437726012785844
absolute error = 3.82025006121040242e-14
relative error = 2.8231647952344873883800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.262
y[1] (analytic) = 1.3550135501355013550135501355014
y[1] (numeric) = 1.3550135501355399580814335418653
absolute error = 3.86030678834063639e-14
relative error = 2.8489064097953896558199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.263
y[1] (analytic) = 1.3568521031207598371777476255088
y[1] (numeric) = 1.3568521031207988448782387526448
absolute error = 3.90077004911271360e-14
relative error = 2.8748675261960699232000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.264
y[1] (analytic) = 1.3586956521739130434782608695652
y[1] (numeric) = 1.3586956521739524599221061297626
absolute error = 3.94164438452601974e-14
relative error = 2.9010502670111505286400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.265
y[1] (analytic) = 1.3605442176870748299319727891156
y[1] (numeric) = 1.3605442176871146592758930184233
absolute error = 3.98293439202293077e-14
relative error = 2.9274567781368541159500000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.266
y[1] (analytic) = 1.3623978201634877384196185286104
y[1] (numeric) = 1.3623978201635279848668811852135
absolute error = 4.02464472626566031e-14
relative error = 2.9540892290789946675399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.1MB, time=2.67
NO POLE
x[1] = 0.267
y[1] (analytic) = 1.3642564802182810368349249658936
y[1] (numeric) = 1.364256480218321704635924214486
absolute error = 4.06678009992485924e-14
relative error = 2.9809498132449218229200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.268
y[1] (analytic) = 1.3661202185792349726775956284153
y[1] (numeric) = 1.3661202185792760661304404300277
absolute error = 4.10934528448016124e-14
relative error = 3.0080407482394780276800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.269
y[1] (analytic) = 1.3679890560875512995896032831737
y[1] (numeric) = 1.3679890560875928230407136118946
absolute error = 4.15234511103287209e-14
relative error = 3.0353642761650294977900000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.27
y[1] (analytic) = 1.369863013698630136986301369863
y[1] (numeric) = 1.3698630136986720948310126798977
absolute error = 4.19578447113100347e-14
relative error = 3.0629226639256325331000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.271
y[1] (analytic) = 1.3717421124828532235939643347051
y[1] (numeric) = 1.3717421124828956202771404032657
absolute error = 4.23966831760685606e-14
relative error = 3.0907182035353980677399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.272
y[1] (analytic) = 1.3736263736263736263736263736264
y[1] (numeric) = 1.3736263736264164663902806472278
absolute error = 4.28400166542736014e-14
relative error = 3.1187532124311181819199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.273
y[1] (analytic) = 1.3755158184319119669876203576341
y[1] (numeric) = 1.3755158184319552548835459314921
absolute error = 4.32878959255738580e-14
relative error = 3.1470300337892194766000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.274
y[1] (analytic) = 1.3774104683195592286501377410468
y[1] (numeric) = 1.377410468319602969022546103433
absolute error = 4.37403724083623862e-14
relative error = 3.1755510368471092381200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.275
y[1] (analytic) = 1.3793103448275862068965517241379
y[1] (numeric) = 1.3793103448276304043947203997438
absolute error = 4.41974981686756059e-14
relative error = 3.2043186172289814277500000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.276
y[1] (analytic) = 1.3812154696132596685082872928177
y[1] (numeric) = 1.3812154696133043278342165214179
absolute error = 4.46593259292286002e-14
relative error = 3.2333351972761506544800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.277
y[1] (analytic) = 1.3831258644536652835408022130014
y[1] (numeric) = 1.3831258644537104094498808019838
absolute error = 4.51259090785889824e-14
relative error = 3.2626032263819834275200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.278
y[1] (analytic) = 1.3850415512465373961218836565097
y[1] (numeric) = 1.3850415512465829934235641481591
absolute error = 4.55973016804916494e-14
relative error = 3.2921251813314970866800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.279
y[1] (analytic) = 1.3869625520110957004160887656033
y[1] (numeric) = 1.3869625520111417739745720623874
absolute error = 4.60735584832967841e-14
relative error = 3.3219035666456981336100000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.28
y[1] (analytic) = 1.3888888888888888888888888888889
y[1] (numeric) = 1.3888888888889354436238184823985
absolute error = 4.65547349295935096e-14
relative error = 3.3519409149307326912000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.281
y[1] (analytic) = 1.3908205841446453407510431154381
y[1] (numeric) = 1.3908205841446923816382090670828
absolute error = 4.70408871659516447e-14
relative error = 3.3822397872319232539300000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.282
y[1] (analytic) = 1.3927576601671309192200557103064
y[1] (numeric) = 1.3927576601671784512921085343575
absolute error = 4.75320720528240511e-14
relative error = 3.4128027733927668689800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.1MB, time=2.83
NO POLE
x[1] = 0.283
y[1] (analytic) = 1.3947001394700139470013947001395
y[1] (numeric) = 1.3947001394700619753485693022523
absolute error = 4.80283471746021128e-14
relative error = 3.4436324924189714877599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.284
y[1] (analytic) = 1.3966480446927374301675977653631
y[1] (numeric) = 1.3966480446927859599384475922934
absolute error = 4.85297708498269303e-14
relative error = 3.4747315928476082094800000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.285
y[1] (analytic) = 1.3986013986013986013986013986014
y[1] (numeric) = 1.3986013986014476378007429574633
absolute error = 4.90364021415588619e-14
relative error = 3.5061027531214586258500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.286
y[1] (analytic) = 1.4005602240896358543417366946779
y[1] (numeric) = 1.4005602240896854026426046027706
absolute error = 4.95483008679080927e-14
relative error = 3.5377486819686378187799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.287
y[1] (analytic) = 1.4025245441795231416549789621318
y[1] (numeric) = 1.4025245441795732071825916910912
absolute error = 5.00655276127289594e-14
relative error = 3.5696721187875748052200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.288
y[1] (analytic) = 1.4044943820224719101123595505618
y[1] (numeric) = 1.4044943820225224982560960313722
absolute error = 5.05881437364808104e-14
relative error = 3.6018758340374337004800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.289
y[1] (analytic) = 1.4064697609001406469760900140647
y[1] (numeric) = 1.4064697609001917631874772722972
absolute error = 5.11162113872582325e-14
relative error = 3.6343626296340603307500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.29
y[1] (analytic) = 1.4084507042253521126760563380282
y[1] (numeric) = 1.4084507042254037624695683315538
absolute error = 5.16497935119935256e-14
relative error = 3.6671353393515403175999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.291
y[1] (analytic) = 1.4104372355430183356840620592384
y[1] (numeric) = 1.4104372355430705246379298936008
absolute error = 5.21889538678343624e-14
relative error = 3.7001968292294562941599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.292
y[1] (analytic) = 1.4124293785310734463276836158192
y[1] (numeric) = 1.4124293785311261800847173154407
absolute error = 5.27337570336996215e-14
relative error = 3.7335499979859332022000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.293
y[1] (analytic) = 1.4144271570014144271570014144272
y[1] (numeric) = 1.4144271570014677114254234308683
absolute error = 5.32842684220164411e-14
relative error = 3.7671977774365623857699999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.294
y[1] (analytic) = 1.416430594900849858356940509915
y[1] (numeric) = 1.4164305949009036989112311515095
absolute error = 5.38405542906415945e-14
relative error = 3.8011431329192965717000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.295
y[1] (analytic) = 1.4184397163120567375886524822695
y[1] (numeric) = 1.418439716312111140270407452615
absolute error = 5.44026817549703455e-14
relative error = 3.8353890637254093577500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.296
y[1] (analytic) = 1.4204545454545454545454545454545
y[1] (numeric) = 1.4204545454546004252642547814589
absolute error = 5.49707188002360044e-14
relative error = 3.8699386035366147097600000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.297
y[1] (analytic) = 1.4224751066856330014224751066856
y[1] (numeric) = 1.4224751066856885461567691101455
absolute error = 5.55447342940034599e-14
relative error = 3.9047948208684432309700000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.298
y[1] (analytic) = 1.4245014245014245014245014245014
y[1] (numeric) = 1.4245014245014806262225002845296
absolute error = 5.61247979988600282e-14
relative error = 3.9399608195199739796400000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=72.4MB, alloc=4.1MB, time=2.99
x[1] = 0.299
y[1] (analytic) = 1.4265335235378031383737517831669
y[1] (numeric) = 1.4265335235378598493543370901865
absolute error = 5.67109805853070196e-14
relative error = 3.9754397390300220739600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.3
y[1] (analytic) = 1.4285714285714285714285714285714
y[1] (numeric) = 1.4285714285714858747822162840588
absolute error = 5.73033536448554874e-14
relative error = 4.0112347551398841180000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.301
y[1] (analytic) = 1.4306151645207439198855507868383
y[1] (numeric) = 1.4306151645208018218752541165287
absolute error = 5.79019897033296904e-14
relative error = 4.0473490802627453589600000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.302
y[1] (analytic) = 1.4326647564469914040114613180516
y[1] (numeric) = 1.4326647564470499109736956999149
absolute error = 5.85069622343818633e-14
relative error = 4.0837859639598540583399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.303
y[1] (analytic) = 1.4347202295552367288378766140603
y[1] (numeric) = 1.4347202295552958471835498360207
absolute error = 5.91183456732219604e-14
relative error = 4.1205486934235706398799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.304
y[1] (analytic) = 1.4367816091954022988505747126437
y[1] (numeric) = 1.4367816091954620350660052787468
absolute error = 5.97362154305661031e-14
relative error = 4.1576405939674007757599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.305
y[1] (analytic) = 1.4388489208633093525179856115108
y[1] (numeric) = 1.4388489208633697131658924190467
absolute error = 6.03606479068075359e-14
relative error = 4.1950650295231237450500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.306
y[1] (analytic) = 1.440922190201729106628242074928
y[1] (numeric) = 1.4409221902017900983487484888919
absolute error = 6.09917205064139639e-14
relative error = 4.2328254031451290946599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.307
y[1] (analytic) = 1.4430014430014430014430014430014
y[1] (numeric) = 1.4430014430015046309546539982218
absolute error = 6.16295116525552204e-14
relative error = 4.2709251575220767737200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.308
y[1] (analytic) = 1.445086705202312138728323699422
y[1] (numeric) = 1.4450867052023744128291256647075
absolute error = 6.22741008019652855e-14
relative error = 4.3093677754959977565999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.309
y[1] (analytic) = 1.4471780028943560057887120115774
y[1] (numeric) = 1.4471780028944189313571720543339
absolute error = 6.29255684600427565e-14
relative error = 4.3481567805889544741500000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.31
y[1] (analytic) = 1.4492753623188405797101449275362
y[1] (numeric) = 1.4492753623189041637063411214793
absolute error = 6.35839961961939431e-14
relative error = 4.3872957375373820739000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.311
y[1] (analytic) = 1.4513788098693759071117561683599
y[1] (numeric) = 1.4513788098694401565784155912058
absolute error = 6.42494666594228459e-14
relative error = 4.4267882528342340825100000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.312
y[1] (analytic) = 1.4534883720930232558139534883721
y[1] (numeric) = 1.4534883720930881778775476607245
absolute error = 6.49220635941723524e-14
relative error = 4.4666379752790578451200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.313
y[1] (analytic) = 1.4556040756914119359534206695779
y[1] (numeric) = 1.4556040756914775378252770906491
absolute error = 6.56018718564210712e-14
relative error = 4.5068485965361275914399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.314
y[1] (analytic) = 1.4577259475218658892128279883382
y[1] (numeric) = 1.4577259475219321781902580286438
absolute error = 6.62889774300403056e-14
relative error = 4.5474238517007649641600000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.315
y[1] (analytic) = 1.459854014598540145985401459854
y[1] (numeric) = 1.4598540145986071294528448756125
absolute error = 6.69834674434157585e-14
relative error = 4.5883675198739794572500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.1MB, time=3.15
NO POLE
x[1] = 0.316
y[1] (analytic) = 1.4619883040935672514619883040936
y[1] (numeric) = 1.4619883040936349368921746427372
absolute error = 6.76854301863386436e-14
relative error = 4.6296834247455632222399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.317
y[1] (analytic) = 1.4641288433382137628111273792094
y[1] (numeric) = 1.4641288433382821577662545501802
absolute error = 6.83949551271709708e-14
relative error = 4.6713754351857773056399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.318
y[1] (analytic) = 1.4662756598240469208211143695015
y[1] (numeric) = 1.4662756598241160329540446593652
absolute error = 6.91121329302898637e-14
relative error = 4.7134474658457687043399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.319
y[1] (analytic) = 1.4684287812041116005873715124816
y[1] (numeric) = 1.4684287812041814376428453283422
absolute error = 6.98370554738158606e-14
relative error = 4.7559034777668601068600000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.32
y[1] (analytic) = 1.4705882352941176470588235294118
y[1] (numeric) = 1.4705882352941882168746911596577
absolute error = 7.05698158676302459e-14
relative error = 4.7987474789988567211999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.321
y[1] (analytic) = 1.4727540500736377025036818851252
y[1] (numeric) = 1.4727540500737090130121535716821
absolute error = 7.13105084716865569e-14
relative error = 4.8419835252275172135099999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.322
y[1] (analytic) = 1.4749262536873156342182890855457
y[1] (numeric) = 1.4749262536873876934472037070533
absolute error = 7.20592289146215076e-14
relative error = 4.8856157204113382152800000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.323
y[1] (analytic) = 1.477104874446085672082717872969
y[1] (numeric) = 1.4771048744461584881568305436448
absolute error = 7.28160741126706758e-14
relative error = 4.9296482174278047516599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.324
y[1] (analytic) = 1.4792899408284023668639053254438
y[1] (numeric) = 1.4792899408284759480061942198456
absolute error = 7.35811422888944018e-14
relative error = 4.9740852187292615616800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.325
y[1] (analytic) = 1.4814814814814814814814814814815
y[1] (numeric) = 1.4814814814815558360144742009327
absolute error = 7.43545329927194512e-14
relative error = 5.0189309770085629559999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.326
y[1] (analytic) = 1.4836795252225519287833827893175
y[1] (numeric) = 1.4836795252226270651305025914225
absolute error = 7.51363471198021050e-14
relative error = 5.0641897958746618770000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.327
y[1] (analytic) = 1.4858841010401188707280832095097
y[1] (numeric) = 1.4858841010401947974150154279573
absolute error = 7.59266869322184476e-14
relative error = 5.1098660305383015234799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.328
y[1] (analytic) = 1.4880952380952380952380952380952
y[1] (numeric) = 1.4880952380953148208941742258336
absolute error = 7.67256560789877384e-14
relative error = 5.1559640885079760204800000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.329
y[1] (analytic) = 1.4903129657228017883755588673621
y[1] (numeric) = 1.4903129657228793217351758022259
absolute error = 7.75333596169348638e-14
relative error = 5.2024884302963293609800000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.33
y[1] (analytic) = 1.4925373134328358208955223880597
y[1] (numeric) = 1.4925373134329141707995542860477
absolute error = 7.83499040318979880e-14
relative error = 5.2494435701371651960000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.331
y[1] (analytic) = 1.4947683109118086696562032884903
y[1] (numeric) = 1.4947683109118878450534635761277
absolute error = 7.91753972602876374e-14
relative error = 5.2968340767132429420599999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.1MB, time=3.31
NO POLE
x[1] = 0.332
y[1] (analytic) = 1.4970059880239520958083832335329
y[1] (numeric) = 1.4970059880240321057570942371087
absolute error = 8.00099487110035758e-14
relative error = 5.3446645738950388634400000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.333
y[1] (analytic) = 1.4992503748125937031484257871064
y[1] (numeric) = 1.4992503748126745568177135030607
absolute error = 8.08536692877159543e-14
relative error = 5.3929397414906541518100000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.334
y[1] (analytic) = 1.5015015015015015015015015015015
y[1] (numeric) = 1.5015015015015832081729130188475
absolute error = 8.17066714115173460e-14
relative error = 5.4416643160070552436000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.335
y[1] (analytic) = 1.5037593984962406015037593984962
y[1] (numeric) = 1.503759398496323170572803350901
absolute error = 8.25690690439524048e-14
relative error = 5.4908430914228349192000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.336
y[1] (analytic) = 1.5060240963855421686746987951807
y[1] (numeric) = 1.5060240963856256096524092272025
absolute error = 8.34409777104320218e-14
relative error = 5.5404809199726862475200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.337
y[1] (analytic) = 1.5082956259426847662141779788839
y[1] (numeric) = 1.5082956259427690887287020178722
absolute error = 8.43225145240389883e-14
relative error = 5.5905827129437849242899999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.338
y[1] (analytic) = 1.5105740181268882175226586102719
y[1] (numeric) = 1.5105740181269734313208683425844
absolute error = 8.52137982097323125e-14
relative error = 5.6411534414842790875000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.339
y[1] (analytic) = 1.5128593040847201210287443267776
y[1] (numeric) = 1.5128593040848062359778732842555
absolute error = 8.61149491289574779e-14
relative error = 5.6921981374240892891900000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.34
y[1] (analytic) = 1.5151515151515151515151515151515
y[1] (numeric) = 1.5151515151516021776044561852299
absolute error = 8.70260893046700784e-14
relative error = 5.7437218941082251744000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.341
y[1] (analytic) = 1.517450682852807283763277693475
y[1] (numeric) = 1.5174506828528952311057244738845
absolute error = 8.79473424467804095e-14
relative error = 5.7957298672428289860499999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.342
y[1] (analytic) = 1.5197568389057750759878419452888
y[1] (numeric) = 1.5197568389058639548218199720373
absolute error = 8.88788339780267485e-14
relative error = 5.8482272757541600512999999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.343
y[1] (analytic) = 1.52207001522070015220700152207
y[1] (numeric) = 1.522070015220789972898061807278
absolute error = 8.98206910602852080e-14
relative error = 5.9012194026607381656000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.344
y[1] (analytic) = 1.524390243902439024390243902439
y[1] (numeric) = 1.5243902439025297974328652266465
absolute error = 9.07730426213242075e-14
relative error = 5.9547115959588680120000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.345
y[1] (analytic) = 1.5267175572519083969465648854962
y[1] (numeric) = 1.5267175572520001329659468972621
absolute error = 9.17360193820117659e-14
relative error = 6.0087092695217706664499999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.346
y[1] (analytic) = 1.5290519877675840978593272171254
y[1] (numeric) = 1.5290519877676768076132112011087
absolute error = 9.27097538839839833e-14
relative error = 6.0632179040125525078199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.347
y[1] (analytic) = 1.531393568147013782542113323124
y[1] (numeric) = 1.5313935681471074769226311063714
absolute error = 9.36943805177832474e-14
relative error = 6.1182430478112460552200000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.1MB, time=3.47
NO POLE
x[1] = 0.348
y[1] (analytic) = 1.5337423312883435582822085889571
y[1] (numeric) = 1.5337423312884382483177600638286
absolute error = 9.46900355514748715e-14
relative error = 6.1737903179561616217999999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.349
y[1] (analytic) = 1.5360983102918586789554531490015
y[1] (numeric) = 1.5360983102919543758126129000495
absolute error = 9.56968571597510480e-14
relative error = 6.2298654010997932248000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.35
y[1] (analytic) = 1.5384615384615384615384615384615
y[1] (numeric) = 1.5384615384616351765239150696363
absolute error = 9.67149854535311748e-14
relative error = 6.2864740544795263620000000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.351
y[1] (analytic) = 1.5408320493066255778120184899846
y[1] (numeric) = 1.5408320493067233223745285577869
absolute error = 9.77445625100678023e-14
relative error = 6.3436221069034003692700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.352
y[1] (analytic) = 1.5432098765432098765432098765432
y[1] (numeric) = 1.543209876543308662275613444172
absolute error = 9.87857324035676288e-14
relative error = 6.4013154597511823462400000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.353
y[1] (analytic) = 1.5455950540958268933539412673879
y[1] (numeric) = 1.5455950540959267319951776045539
absolute error = 9.98386412363371660e-14
relative error = 6.4595600879910146402000000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.354
y[1] (analytic) = 1.5479876160990712074303405572755
y[1] (numeric) = 1.5479876160991721108675110201672
absolute error = 1.009034371704628917e-13
relative error = 6.5183620412119028038200000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.355
y[1] (analytic) = 1.5503875968992248062015503875969
y[1] (numeric) = 1.5503875968993267864720104235009
absolute error = 1.019802704600359040e-13
relative error = 6.5777274446723158080000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.356
y[1] (analytic) = 1.5527950310559006211180124223602
y[1] (numeric) = 1.5527950310560036904114963536567
absolute error = 1.030692934839312965e-13
relative error = 6.6376625003651754946000000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.357
y[1] (analytic) = 1.5552099533437013996889580093313
y[1] (numeric) = 1.5552099533438055703497371620118
absolute error = 1.041706607791526805e-13
relative error = 6.6981734880995173561499999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.358
y[1] (analytic) = 1.5576323987538940809968847352025
y[1] (numeric) = 1.5576323987539993655259594876986
absolute error = 1.052845290747524961e-13
relative error = 6.7592667665991102496200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.359
y[1] (analytic) = 1.56006240249609984399375975039
y[1] (numeric) = 1.5600624024962062550510860893551
absolute error = 1.064110573263389651e-13
relative error = 6.8209487746183276629100000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.36
y[1] (analytic) = 1.5625
y[1] (numeric) = 1.5625000000001075504067511807682
absolute error = 1.075504067511807682e-13
relative error = 6.8832260320755691648000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.361
y[1] (analytic) = 1.5649452269170579029733959311424
y[1] (numeric) = 1.5649452269171666057142598518932
absolute error = 1.087027408639207508e-13
relative error = 6.9461051412045359761200000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.362
y[1] (analytic) = 1.5673981191222570532915360501567
y[1] (numeric) = 1.5673981191223669215170489603508
absolute error = 1.098682255129101941e-13
relative error = 7.0095927877236703835800000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.363
y[1] (analytic) = 1.5698587127158555729984301412873
y[1] (numeric) = 1.5698587127159666200273473167155
absolute error = 1.110470289171754282e-13
relative error = 7.0736957420240747763399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.1MB, time=3.63
NO POLE
x[1] = 0.364
y[1] (analytic) = 1.5723270440251572327044025157233
y[1] (numeric) = 1.5723270440252694720261065445266
absolute error = 1.122393217040288033e-13
relative error = 7.1384208603762318898799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.365
y[1] (analytic) = 1.5748031496062992125984251968504
y[1] (numeric) = 1.5748031496064126578753725331339
absolute error = 1.134452769473362835e-13
relative error = 7.2037750861558540022500000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.366
y[1] (analytic) = 1.5772870662460567823343848580442
y[1] (numeric) = 1.5772870662461714474045913122265
absolute error = 1.146650702064541823e-13
relative error = 7.2697654510891951578199999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.367
y[1] (analytic) = 1.5797788309636650868878357030016
y[1] (numeric) = 1.5797788309637809857674015508182
absolute error = 1.158988795658478166e-13
relative error = 7.3363990765181667907799999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.368
y[1] (analytic) = 1.5822784810126582278481012658228
y[1] (numeric) = 1.5822784810127753747337766709425
absolute error = 1.171468856754051197e-13
relative error = 7.4036831746856035650399999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.369
y[1] (analytic) = 1.5847860538827258320126782884311
y[1] (numeric) = 1.5847860538828442412844697469577
absolute error = 1.184092717914585266e-13
relative error = 7.4716250500410330284599999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.37
y[1] (analytic) = 1.5873015873015873015873015873016
y[1] (numeric) = 1.5873015873017069878111201160222
absolute error = 1.196862238185287206e-13
relative error = 7.5402321005673093977999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.371
y[1] (analytic) = 1.5898251192368839427662957074722
y[1] (numeric) = 1.5898251192370049206966475115833
absolute error = 1.209779303518041111e-13
relative error = 7.6095118191284785881899999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.372
y[1] (analytic) = 1.5923566878980891719745222929936
y[1] (numeric) = 1.5923566878982114565572426631991
absolute error = 1.222845827203702055e-13
relative error = 7.6794717948392489054000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.373
y[1] (analytic) = 1.5948963317384370015948963317384
y[1] (numeric) = 1.5948963317385606079699275350679
absolute error = 1.236063750312033295e-13
relative error = 7.7501197144564487596500000000002e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.374
y[1] (analytic) = 1.5974440894568690095846645367412
y[1] (numeric) = 1.5974440894569939530888784801977
absolute error = 1.249435042139434565e-13
relative error = 7.8214633637928603769000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.375
y[1] (analytic) = 1.6
y[1] (numeric) = 1.600000000000126296170066461212
absolute error = 1.262961700664612120e-13
relative error = 7.8935106291538257500000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.376
y[1] (analytic) = 1.6025641025641025641025641025641
y[1] (numeric) = 1.6025641025642302286778653370023
absolute error = 1.276645753012344382e-13
relative error = 7.9662694987970289436800000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.377
y[1] (analytic) = 1.6051364365971107544141252006421
y[1] (numeric) = 1.6051364365972398033397177506674
absolute error = 1.290489255925500253e-13
relative error = 8.0397480644158665761899999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.378
y[1] (analytic) = 1.6077170418006430868167202572347
y[1] (numeric) = 1.6077170418007735362463448042829
absolute error = 1.304494296245470482e-13
relative error = 8.1139545226468263980400000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.379
y[1] (analytic) = 1.6103059581320450885668276972625
y[1] (numeric) = 1.610305958132176954865967814845
absolute error = 1.318662991401175825e-13
relative error = 8.1888971766013018732499999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=91.5MB, alloc=4.2MB, time=3.79
x[1] = 0.38
y[1] (analytic) = 1.6129032258064516129032258064516
y[1] (numeric) = 1.6129032258065849126522164883759
absolute error = 1.332997489906819243e-13
relative error = 8.2645844374222793066000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.381
y[1] (analytic) = 1.6155088852988691437802907915994
y[1] (numeric) = 1.6155088852990038937774776468853
absolute error = 1.347499971868552859e-13
relative error = 8.3410248258663421972099999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.382
y[1] (analytic) = 1.6181229773462783171521035598706
y[1] (numeric) = 1.6181229773464145344170535832778
absolute error = 1.362172649500234072e-13
relative error = 8.4182269739114465649599999999997e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.383
y[1] (analytic) = 1.6207455429497568881685575364668
y[1] (numeric) = 1.6207455429498945899453223813548
absolute error = 1.377017767648448880e-13
relative error = 8.4961996263909295895999999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.384
y[1] (analytic) = 1.6233766233766233766233766233766
y[1] (numeric) = 1.6233766233767625803838093218038
absolute error = 1.392037604326984272e-13
relative error = 8.5749516426542231155200000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.385
y[1] (analytic) = 1.6260162601626016260162601626016
y[1] (numeric) = 1.6260162601627423494633862561432
absolute error = 1.407234471260935416e-13
relative error = 8.6544919982547528084000000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.386
y[1] (analytic) = 1.6286644951140065146579804560261
y[1] (numeric) = 1.6286644951141487757294245197588
absolute error = 1.422610714440637327e-13
relative error = 8.7348297866655131877799999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.387
y[1] (analytic) = 1.6313213703099510603588907014682
y[1] (numeric) = 1.6313213703100948772303592629436
absolute error = 1.438168714685614754e-13
relative error = 8.8159742210228184420199999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.388
y[1] (analytic) = 1.6339869281045751633986928104575
y[1] (numeric) = 1.6339869281047205544875146852734
absolute error = 1.453910888218748159e-13
relative error = 8.8979346358987387330800000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.389
y[1] (analytic) = 1.6366612111292962356792144026187
y[1] (numeric) = 1.6366612111294432196479394884112
absolute error = 1.469839687250857925e-13
relative error = 8.9807204891027419217499999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.39
y[1] (analytic) = 1.6393442622950819672131147540984
y[1] (numeric) = 1.6393442622952305629731723454224
absolute error = 1.485957600575913240e-13
relative error = 9.0643413635130707639999999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.391
y[1] (analytic) = 1.6420361247947454844006568144499
y[1] (numeric) = 1.6420361247948957111160745221055
absolute error = 1.502267154177076556e-13
relative error = 9.1488069689383962260400000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.392
y[1] (analytic) = 1.6447368421052631578947368421053
y[1] (numeric) = 1.644736842105415034985921222012
absolute error = 1.518770911843799067e-13
relative error = 9.2341271440102983273599999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.393
y[1] (analytic) = 1.6474464579901153212520593080725
y[1] (numeric) = 1.6474464579902688683996393268024
absolute error = 1.535471475800187299e-13
relative error = 9.3203118581071369049299999999999e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.394
y[1] (analytic) = 1.650165016501650165016501650165
y[1] (numeric) = 1.6501650165018054021652361367284
absolute error = 1.552371487344865634e-13
relative error = 9.4073712133098857420400000000001e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.395
y[1] (analytic) = 1.6528925619834710743801652892562
y[1] (numeric) = 1.6528925619836280217429155457058
absolute error = 1.569473627502564496e-13
relative error = 9.4953154463905152008000000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.396
y[1] (analytic) = 1.6556291390728476821192052980132
y[1] (numeric) = 1.6556291390730063601809740649009
absolute error = 1.586780617687668877e-13
relative error = 9.5841549308335200170800000000003e-12 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.2MB, time=3.94
NO POLE
x[1] = 0.397
y[1] (analytic) = 1.658374792703150912106135986733
y[1] (numeric) = 1.6583747927033113416281739834309
absolute error = 1.604295220379966979e-13
relative error = 9.6739001788912008833700000000000e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.398
y[1] (analytic) = 1.661129568106312292358803986711
y[1] (numeric) = 1.66112956810647449438278527111
absolute error = 1.622020239812843990e-13
relative error = 9.7645618436733208197999999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.399
y[1] (analytic) = 1.6638935108153078202995008319468
y[1] (numeric) = 1.6638935108154718161517682490774
absolute error = 1.639958522674171306e-13
relative error = 9.8561507212717695490599999999997e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.4
y[1] (analytic) = 1.6666666666666666666666666666667
y[1] (numeric) = 1.6666666666668324779625486813681
absolute error = 1.658112958820147014e-13
relative error = 9.9486777529208820839999999999998e-12 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.401
y[1] (analytic) = 1.669449081803005008347245409015
y[1] (numeric) = 1.6694490818031726569954456439171
absolute error = 1.676486482002349021e-13
relative error = 1.0042154027194070635790000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.402
y[1] (analytic) = 1.6722408026755852842809364548495
y[1] (numeric) = 1.6722408026757547924879972816433
absolute error = 1.695082070608267938e-13
relative error = 1.0136590782237442269240000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.403
y[1] (analytic) = 1.6750418760469011725293132328308
y[1] (numeric) = 1.675041876047072562804154792101
absolute error = 1.713902748415592702e-13
relative error = 1.0231999408041088430940000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.404
y[1] (analytic) = 1.6778523489932885906040268456376
y[1] (numeric) = 1.6778523489934618857625628984268
absolute error = 1.732951585360527892e-13
relative error = 1.0328391448748746236320000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.405
y[1] (analytic) = 1.6806722689075630252100840336134
y[1] (numeric) = 1.6806722689077382483799160763995
absolute error = 1.752231698320427861e-13
relative error = 1.0425778605006545772950000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.406
y[1] (analytic) = 1.6835016835016835016835016835017
y[1] (numeric) = 1.6835016835018606763086927874074
absolute error = 1.771746251911039057e-13
relative error = 1.0524172736351571998580000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.407
y[1] (analytic) = 1.6863406408094435075885328836425
y[1] (numeric) = 1.6863406408096226574344627484821
absolute error = 1.791498459298648396e-13
relative error = 1.0623585863640984988280000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.408
y[1] (analytic) = 1.6891891891891891891891891891892
y[1] (numeric) = 1.6891891891893703383474919333947
absolute error = 1.811491583027442055e-13
relative error = 1.0724030171522456965600000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.409
y[1] (analytic) = 1.692047377326565143824027072758
y[1] (numeric) = 1.6920473773267483167176133113473
absolute error = 1.831728935862385893e-13
relative error = 1.0825518010946700627630000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.41
y[1] (analytic) = 1.694915254237288135593220338983
y[1] (numeric) = 1.694915254237473356981385133536
absolute error = 1.852213881647945530e-13
relative error = 1.0928061901722878627000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.411
y[1] (analytic) = 1.697792869269949066213921901528
y[1] (numeric) = 1.6977928692701363611975401986523
absolute error = 1.872949836182971243e-13
relative error = 1.1031674535117700621270000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.412
y[1] (analytic) = 1.7006802721088435374149659863946
y[1] (numeric) = 1.7006802721090329314417771943997
absolute error = 1.893940268112080051e-13
relative error = 1.1136368776499030699880000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.2MB, time=4.11
NO POLE
x[1] = 0.413
y[1] (analytic) = 1.7035775127768313458262350936968
y[1] (numeric) = 1.7035775127770228646962184811746
absolute error = 1.915188699833874778e-13
relative error = 1.1242157668024844946860000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.414
y[1] (analytic) = 1.7064846416382252559726962457338
y[1] (numeric) = 1.7064846416384189258435388804824
absolute error = 1.936698708426347486e-13
relative error = 1.1349054431378396267960000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.415
y[1] (analytic) = 1.7094017094017094017094017094017
y[1] (numeric) = 1.7094017094019052491020606916462
absolute error = 1.958473926589822445e-13
relative error = 1.1457072470550461303250000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.416
y[1] (analytic) = 1.7123287671232876712328767123288
y[1] (numeric) = 1.7123287671234857230372374925047
absolute error = 1.980518043607801759e-13
relative error = 1.1566225374669562272560000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.417
y[1] (analytic) = 1.7152658662092624356775300171527
y[1] (numeric) = 1.7152658662094627191581626256463
absolute error = 2.002834806326084936e-13
relative error = 1.1676526920881075176880000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.418
y[1] (analytic) = 1.718213058419243986254295532646
y[1] (numeric) = 1.71821305841944652905631058685
absolute error = 2.025428020150542040e-13
relative error = 1.1787991077276154672800000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.419
y[1] (analytic) = 1.7211703958691910499139414802065
y[1] (numeric) = 1.7211703958693958800689478730683
absolute error = 2.048301550063928618e-13
relative error = 1.1900632005871425270580000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.42
y[1] (analytic) = 1.7241379310344827586206896551724
y[1] (numeric) = 1.7241379310346899045528558691098
absolute error = 2.071459321662139374e-13
relative error = 1.2014464065640408369200000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.421
y[1] (analytic) = 1.7271157167530224525043177892919
y[1] (numeric) = 1.7271157167532319430365388199429
absolute error = 2.094905322210306510e-13
relative error = 1.2129501815597674692900000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.422
y[1] (analytic) = 1.7301038062283737024221453287197
y[1] (numeric) = 1.7301038062285855667823172445085
absolute error = 2.118643601719157888e-13
relative error = 1.2245760017936732592640000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.423
y[1] (analytic) = 1.7331022530329289428076256499133
y[1] (numeric) = 1.7331022530331432106350298558695
absolute error = 2.142678274042059562e-13
relative error = 1.2363253641222683672740000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.424
y[1] (analytic) = 1.7361111111111111111111111111111
y[1] (numeric) = 1.736111111111327812462910428801
absolute error = 2.167013517993176899e-13
relative error = 1.2481997863640698938240000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.425
y[1] (analytic) = 1.7391304347826086956521739130435
y[1] (numeric) = 1.7391304347828278610100226328829
absolute error = 2.191653578487198394e-13
relative error = 1.2602008076301390765500000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.426
y[1] (analytic) = 1.7421602787456445993031358885017
y[1] (numeric) = 1.742160278745866259579905996142
absolute error = 2.216602767701076403e-13
relative error = 1.2723299886604178553220000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.427
y[1] (analytic) = 1.7452006980802792321116928446771
y[1] (numeric) = 1.7452006980805034186583186696192
absolute error = 2.241865466258249421e-13
relative error = 1.2845889121659769182330000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.428
y[1] (analytic) = 1.7482517482517482517482517482517
y[1] (numeric) = 1.7482517482519749963606953303682
absolute error = 2.267446124435821165e-13
relative error = 1.2969791831772897063800000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.2MB, time=4.26
NO POLE
x[1] = 0.429
y[1] (analytic) = 1.7513134851138353765323992994746
y[1] (numeric) = 1.7513134851140647114587388177357
absolute error = 2.293349263395182611e-13
relative error = 1.3095024293986492708810000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.43
y[1] (analytic) = 1.7543859649122807017543859649123
y[1] (numeric) = 1.754385964912512659702029622344
absolute error = 2.319579476436574317e-13
relative error = 1.3221603015688473606900000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.431
y[1] (analytic) = 1.7574692442882249560632688927944
y[1] (numeric) = 1.757469244288459570206296702575
absolute error = 2.346141430278097806e-13
relative error = 1.3349544738282376516140000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.432
y[1] (analytic) = 1.7605633802816901408450704225352
y[1] (numeric) = 1.7605633802819274448317063921875
absolute error = 2.373039866359696523e-13
relative error = 1.3478866440923076250640000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.433
y[1] (analytic) = 1.7636684303350970017636684303351
y[1] (numeric) = 1.763668430335337029723885694224
absolute error = 2.400279602172638889e-13
relative error = 1.3609585344318862500630000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.434
y[1] (analytic) = 1.7667844522968197879858657243816
y[1] (numeric) = 1.7667844522970625745391272292134
absolute error = 2.427865532615048318e-13
relative error = 1.3741718914601173479880000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.435
y[1] (analytic) = 1.7699115044247787610619469026549
y[1] (numeric) = 1.7699115044250243413250843064219
absolute error = 2.455802631374037670e-13
relative error = 1.3875284867263312835500000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.436
y[1] (analytic) = 1.7730496453900709219858156028369
y[1] (numeric) = 1.7730496453903193315810491046957
absolute error = 2.484095952335018588e-13
relative error = 1.4010301171169504836320000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.437
y[1] (analytic) = 1.7761989342806394316163410301954
y[1] (numeric) = 1.7761989342808907066794429071358
absolute error = 2.512750631018769404e-13
relative error = 1.4146786052635671744520000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.438
y[1] (analytic) = 1.7793594306049822064056939501779
y[1] (numeric) = 1.7793594306052363835942986360725
absolute error = 2.541771886046858946e-13
relative error = 1.4284757999583347276520000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.439
y[1] (analytic) = 1.78253119429590017825311942959
y[1] (numeric) = 1.7825311942961572947551830333383
absolute error = 2.571165020636037483e-13
relative error = 1.4424235765768170279630000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.44
y[1] (analytic) = 1.7857142857142857142857142857143
y[1] (numeric) = 1.7857142857145458078281265077512
absolute error = 2.600935424122220369e-13
relative error = 1.4565238375084434066400000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.441
y[1] (analytic) = 1.7889087656529516994633273703041
y[1] (numeric) = 1.7889087656532148083206788407634
absolute error = 2.631088573514704593e-13
relative error = 1.4707785125947198674870000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.442
y[1] (analytic) = 1.7921146953405017921146953405018
y[1] (numeric) = 1.7921146953407679551182034678494
absolute error = 2.661630035081273476e-13
relative error = 1.4851895595753505996080000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.443
y[1] (analytic) = 1.7953321364452423698384201077199
y[1] (numeric) = 1.7953321364455116263850165937369
absolute error = 2.692565465964860170e-13
relative error = 1.4997589645424271146900000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.444
y[1] (analytic) = 1.7985611510791366906474820143885
y[1] (numeric) = 1.7985611510794090807090652600284
absolute error = 2.723900615832456399e-13
relative error = 1.5144887424028457578440000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
memory used=106.8MB, alloc=4.2MB, time=4.43
x[1] = 0.445
y[1] (analytic) = 1.8018018018018018018018018018018
y[1] (numeric) = 1.8018018018020773659346574987123
absolute error = 2.755641328556969105e-13
relative error = 1.5293809373491178532750000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.446
y[1] (analytic) = 1.8050541516245487364620938628159
y[1] (numeric) = 1.8050541516248275158164871372412
absolute error = 2.787793543932744253e-13
relative error = 1.5444376233387403161620000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.447
y[1] (analytic) = 1.8083182640144665461121157323689
y[1] (numeric) = 1.8083182640147485824420582817806
absolute error = 2.820363299425494117e-13
relative error = 1.5596609045822982467010000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.448
y[1] (analytic) = 1.8115942028985507246376811594203
y[1] (numeric) = 1.8115942028988360603108768976008
absolute error = 2.853356731957381805e-13
relative error = 1.5750529160404747563600000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.449
y[1] (analytic) = 1.814882032667876588021778584392
y[1] (numeric) = 1.8148820326681652660297513878665
absolute error = 2.886780079728034745e-13
relative error = 1.5906158239301471444950000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.45
y[1] (analytic) = 1.8181818181818181818181818181818
y[1] (numeric) = 1.818181818182110245786589045901
absolute error = 2.920639684072277192e-13
relative error = 1.6063518262397524556000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.451
y[1] (analytic) = 1.8214936247723132969034608378871
y[1] (numeric) = 1.8214936247726087911025963769578
absolute error = 2.954941991355390707e-13
relative error = 1.6222631532541094981430000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.452
y[1] (analytic) = 1.8248175182481751824817518248175
y[1] (numeric) = 1.8248175182484741518372424979052
absolute error = 2.989693554906730877e-13
relative error = 1.6383520680888885205960000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.453
y[1] (analytic) = 1.8281535648994515539305301645338
y[1] (numeric) = 1.8281535648997540440342294193707
absolute error = 3.024901036992548369e-13
relative error = 1.6546208672349239578430000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.454
y[1] (analytic) = 1.8315018315018315018315018315018
y[1] (numeric) = 1.8315018315021375589525847197823
absolute error = 3.060571210828882805e-13
relative error = 1.6710718811125700115300000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.455
y[1] (analytic) = 1.8348623853211009174311926605505
y[1] (numeric) = 1.8348623853214105885274562024277
absolute error = 3.096710962635418772e-13
relative error = 1.6877074746363032307400000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.456
y[1] (analytic) = 1.8382352941176470588235294117647
y[1] (numeric) = 1.8382352941179603915529025332385
absolute error = 3.133327293731214738e-13
relative error = 1.7045300477897808174720000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.457
y[1] (analytic) = 1.8416206261510128913443830570902
y[1] (numeric) = 1.8416206261513299340766503808479
absolute error = 3.170427322673237577e-13
relative error = 1.7215420362115680043110000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.458
y[1] (analytic) = 1.8450184501845018450184501845018
y[1] (numeric) = 1.8450184501848226468471940503029
absolute error = 3.208018287438658011e-13
relative error = 1.7387459117917526419620000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.459
y[1] (analytic) = 1.8484288354898336414048059149723
y[1] (numeric) = 1.8484288354901582521595711035077
absolute error = 3.246107547651885354e-13
relative error = 1.7561441832796699765140000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.46
y[1] (analytic) = 1.8518518518518518518518518518519
y[1] (numeric) = 1.8518518518521803221105375862234
absolute error = 3.284702586857343715e-13
relative error = 1.7737393969029656061000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.461
y[1] (analytic) = 1.8552875695732838589981447124304
y[1] (numeric) = 1.8552875695736162400996286140466
absolute error = 3.323811014839016162e-13
relative error = 1.7915341369982297113180000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.2MB, time=4.59
NO POLE
x[1] = 0.462
y[1] (analytic) = 1.8587360594795539033457249070632
y[1] (numeric) = 1.8587360594798902474027236878994
absolute error = 3.363440569987808362e-13
relative error = 1.8095310266534408987560000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.463
y[1] (analytic) = 1.8621973929236499068901303538175
y[1] (numeric) = 1.8621973929239902668023021347034
absolute error = 3.403599121717808859e-13
relative error = 1.8277327283624633572830000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.464
y[1] (analytic) = 1.8656716417910447761194029850746
y[1] (numeric) = 1.8656716417913892055866962400222
absolute error = 3.444294672932549476e-13
relative error = 1.8461419446918465191360000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.465
y[1] (analytic) = 1.869158878504672897196261682243
y[1] (numeric) = 1.8691588785050214507325159218798
absolute error = 3.485535362542396368e-13
relative error = 1.8647614189601820568800000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.466
y[1] (analytic) = 1.8726591760299625468164794007491
y[1] (numeric) = 1.8726591760303152797632828237476
absolute error = 3.527329468034229985e-13
relative error = 1.8835939359302788119900000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.467
y[1] (analytic) = 1.8761726078799249530956848030019
y[1] (numeric) = 1.8761726078802819216364942630692
absolute error = 3.569685408094600673e-13
relative error = 1.9026423225144221587090000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.468
y[1] (analytic) = 1.8796992481203007518796992481203
y[1] (numeric) = 1.8796992481206620130542280057086
absolute error = 3.612611745287575883e-13
relative error = 1.9219094484929903697560000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.469
y[1] (analytic) = 1.8832391713747645951035781544256
y[1] (numeric) = 1.8832391713751302068224570069206
absolute error = 3.656117188788524950e-13
relative error = 1.9413982272467067484500000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.47
y[1] (analytic) = 1.8867924528301886792452830188679
y[1] (numeric) = 1.8867924528305587003050005306898
absolute error = 3.700210597175118219e-13
relative error = 1.9611116165028126560700000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.471
y[1] (analytic) = 1.8903591682419659735349716446125
y[1] (numeric) = 1.8903591682423404636330993295041
absolute error = 3.744900981276848916e-13
relative error = 1.9810526190954530765640000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.472
y[1] (analytic) = 1.8939393939393939393939393939394
y[1] (numeric) = 1.8939393939397729591446478358035
absolute error = 3.790197507084418641e-13
relative error = 2.0012242837405730424480000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.473
y[1] (analytic) = 1.8975332068311195445920303605313
y[1] (numeric) = 1.8975332068315031555419023965992
absolute error = 3.836109498720360679e-13
relative error = 2.0216297058256300778330000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.474
y[1] (analytic) = 1.9011406844106463878326996197719
y[1] (numeric) = 1.9011406844110346524768468507319
absolute error = 3.882646441472309600e-13
relative error = 2.0422720282144348496000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.475
y[1] (analytic) = 1.9047619047619047619047619047619
y[1] (numeric) = 1.9047619047622977437032509408359
absolute error = 3.929817984890360740e-13
relative error = 2.0631544420674393885000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.476
y[1] (analytic) = 1.9083969465648854961832061068702
y[1] (numeric) = 1.9083969465652832595778011067963
absolute error = 3.977633945949999261e-13
relative error = 2.0842801876777996127640000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.477
y[1] (analytic) = 1.9120458891013384321223709369025
y[1] (numeric) = 1.912045889101741042553599148462
absolute error = 4.026104312282115595e-13
relative error = 2.1056525553235464561850000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.2MB, time=4.75
NO POLE
x[1] = 0.478
y[1] (analytic) = 1.9157088122605363984674329501916
y[1] (numeric) = 1.915708812260943922391980116403
absolute error = 4.075239245471662114e-13
relative error = 2.1272748861362076235080000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.479
y[1] (analytic) = 1.9193857965451055662188099808061
y[1] (numeric) = 1.9193857965455180711272526353073
absolute error = 4.125049084426545012e-13
relative error = 2.1491505729862299512520000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.48
y[1] (analytic) = 1.9230769230769230769230769230769
y[1] (numeric) = 1.9230769230773406313579587616301
absolute error = 4.175544348818385532e-13
relative error = 2.1712830613855604766400000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.481
y[1] (analytic) = 1.9267822736030828516377649325626
y[1] (numeric) = 1.9267822736035055252120246151592
absolute error = 4.226735742596825966e-13
relative error = 2.1936758504077526763540000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.482
y[1] (analytic) = 1.9305019305019305019305019305019
y[1] (numeric) = 1.9305019305023583653462598403218
absolute error = 4.278634157579098199e-13
relative error = 2.2163324936259728670820000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.483
y[1] (analytic) = 1.9342359767891682785299806576402
y[1] (numeric) = 1.9342359767896014035976923192571
absolute error = 4.331250677116616169e-13
relative error = 2.2392566000692905593730000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.484
y[1] (analytic) = 1.9379844961240310077519379844961
y[1] (numeric) = 1.9379844961244694674099220243261
absolute error = 4.384596579840398300e-13
relative error = 2.2624518351976455228000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.485
y[1] (analytic) = 1.9417475728155339805825242718447
y[1] (numeric) = 1.9417475728159778489168729890408
absolute error = 4.438683343487171961e-13
relative error = 2.2859219218958935599150000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.486
y[1] (analytic) = 1.9455252918287937743190661478599
y[1] (numeric) = 1.9455252918292431265839469537825
absolute error = 4.493522648808059226e-13
relative error = 2.3096706414873424421640000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.487
y[1] (analytic) = 1.9493177387914230019493177387914
y[1] (numeric) = 1.9493177387918779145876739179612
absolute error = 4.549126383561791698e-13
relative error = 2.3337018347671991410740000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.488
y[1] (analytic) = 1.953125
y[1] (numeric) = 1.9531250000004605506646594452094
absolute error = 4.605506646594452094e-13
relative error = 2.3580194030563594721280000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.489
y[1] (analytic) = 1.9569471624266144814090019569472
y[1] (numeric) = 1.9569471624270807489842027360911
absolute error = 4.662675752007791439e-13
relative error = 2.3826273092759814253290000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.49
y[1] (analytic) = 1.960784313725490196078431372549
y[1] (numeric) = 1.9607843137259622607017731948937
absolute error = 4.720646233418223447e-13
relative error = 2.4075295790432939579700000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.491
y[1] (analytic) = 1.9646365422396856581532416502947
y[1] (numeric) = 1.9646365422401636012380725154686
absolute error = 4.779430848308651739e-13
relative error = 2.4327303017891037351510000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.492
y[1] (analytic) = 1.968503937007874015748031496063
y[1] (numeric) = 1.9685039370083579200062790301829
absolute error = 4.839042582475341199e-13
relative error = 2.4582336318974733290920000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.493
y[1] (analytic) = 1.972386587771203155818540433925
y[1] (numeric) = 1.9723865877716931052839976441158
absolute error = 4.899494654572101908e-13
relative error = 2.4840437898680556673560000000001e-11 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.2MB, time=4.91
NO POLE
x[1] = 0.494
y[1] (analytic) = 1.9762845849802371541501976284585
y[1] (numeric) = 1.9762845849807332342022730397469
absolute error = 4.960800520754112884e-13
relative error = 2.5101650635015811193040000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.495
y[1] (analytic) = 1.980198019801980198019801980198
y[1] (numeric) = 1.9801980198024824954077443575242
absolute error = 5.022973879423773262e-13
relative error = 2.5366018091090054973100000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.496
y[1] (analytic) = 1.984126984126984126984126984127
y[1] (numeric) = 1.9841269841274927298517350871889
absolute error = 5.086028676081030619e-13
relative error = 2.5633584527448394319760000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.497
y[1] (analytic) = 1.9880715705765407554671968190855
y[1] (numeric) = 1.988071570577055753378024889089
absolute error = 5.149979108280700035e-13
relative error = 2.5904394914651921176050000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.498
y[1] (analytic) = 1.9920318725099601593625498007968
y[1] (numeric) = 1.9920318725104816433256197361038
absolute error = 5.214839630699353070e-13
relative error = 2.6178494946110752411400000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.499
y[1] (analytic) = 1.9960079840319361277445109780439
y[1] (numeric) = 1.9960079840324641902405424203802
absolute error = 5.280624960314423363e-13
relative error = 2.6455931051175261048630000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.5
y[1] (analytic) = 2
y[1] (numeric) = 2.0000000000005347350081698244918
absolute error = 5.347350081698244918e-13
relative error = 2.6736750408491224590000000000000e-11 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.501
y[1] (analytic) = 2.0040080160320641282565130260521
y[1] (numeric) = 2.0040080160326056312817560071046
absolute error = 5.415030252429810525e-13
relative error = 2.7021000959624754519750000000000e-11 %
h = 0.001
Finished!
diff ( y , x , 1 ) = y * y;
Iterations = 501
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Time to Timeout = 14 Minutes 55 Seconds
Percent Done = 100.4 %
> quit
memory used=120.0MB, alloc=4.2MB, time=4.98