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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 2
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := abs(array_y[iii]);
> fi;# end if 3
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 2
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y[iii]) then
array_norms[iii] := abs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sin $eq_no = 1 iii = 1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sin $eq_no = 1 iii = 2
> #emit pre sin 2 $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := -att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sin $eq_no = 1 iii = 3
> #emit pre sin 3 $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := -att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sin $eq_no = 1 iii = 4
> #emit pre sin 4 $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := -att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sin $eq_no = 1 iii = 5
> #emit pre sin 5 $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := -att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,7] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sin $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h^2*factorial_3(0, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h^2*factorial_3(1, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h^2*factorial_3(2, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h^2*factorial_3(3, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h^2*factorial_3(4, 6);
array_y[7] := temporary;
array_y_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y := proc(x) 2.0 - cos(x) end proc
> exact_soln_yp := proc(x)
> sin(x);
> end;
exact_soln_yp := proc(x) sin(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_max_iter,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_iter,
> glob_warned,
> glob_small_float,
> glob_max_hours,
> glob_large_float,
> glob_hmin,
> glob_subiter_method,
> glob_current_iter,
> glob_disp_incr,
> glob_initial_pass,
> years_in_century,
> days_in_year,
> sec_in_min,
> glob_optimal_done,
> djd_debug2,
> glob_display_flag,
> glob_dump,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_optimal_start,
> glob_max_trunc_err,
> glob_h,
> djd_debug,
> glob_percent_done,
> glob_no_eqs,
> glob_relerr,
> glob_hmax,
> glob_clock_start_sec,
> glob_clock_sec,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> hours_in_day,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_dump_analytic,
> glob_smallish_float,
> min_in_hour,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_look_poles,
> glob_hmin_init,
> glob_almost_1,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_reached_optimal_h,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2,
> #END CONST
> array_m1,
> array_tmp1_g,
> array_last_rel_error,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_1st_rel_error,
> array_type_pole,
> array_y_init,
> array_norms,
> array_pole,
> array_y_set_initial,
> array_y_higher,
> array_y_higher_work2,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> ALWAYS := 1;
> DEBUGL := 3;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> glob_log10abserr := 0.0;
> glob_max_iter := 1000;
> glob_not_yet_start_msg := true;
> glob_max_opt_iter := 10;
> glob_iter := 0;
> glob_warned := false;
> glob_small_float := 0.1e-50;
> glob_max_hours := 0.0;
> glob_large_float := 9.0e100;
> glob_hmin := 0.00000000001;
> glob_subiter_method := 3;
> glob_current_iter := 0;
> glob_disp_incr := 0.1;
> glob_initial_pass := true;
> years_in_century := 100.0;
> days_in_year := 365.0;
> sec_in_min := 60.0;
> glob_optimal_done := false;
> djd_debug2 := true;
> glob_display_flag := true;
> glob_dump := false;
> glob_html_log := true;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_optimal_start := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_h := 0.1;
> djd_debug := true;
> glob_percent_done := 0.0;
> glob_no_eqs := 0;
> glob_relerr := 0.1e-10;
> glob_hmax := 1.0;
> glob_clock_start_sec := 0.0;
> glob_clock_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_unchanged_h_cnt := 0;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_not_yet_finished := true;
> hours_in_day := 24.0;
> glob_log10normmin := 0.1;
> glob_normmax := 0.0;
> glob_orig_start_sec := 0.0;
> glob_max_sec := 10000.0;
> glob_dump_analytic := false;
> glob_smallish_float := 0.1e-100;
> min_in_hour := 60.0;
> glob_optimal_expect_sec := 0.1;
> glob_max_minutes := 0.0;
> glob_start := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> glob_almost_1 := 0.9990;
> glob_log10relerr := 0.0;
> MAX_UNCHANGED := 10;
> glob_reached_optimal_h := false;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/h2sinpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 2 ) = sin(x);");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 50;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_yp := proc(x)");
> omniout_str(ALWAYS,"sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 50;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work := Array(1..(3+ 1) ,(1..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_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[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_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_norms[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 <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=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_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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> array_y_init[1 + 1] := exact_soln_yp(x_start);
> glob_h := 0.00001;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := true;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 2;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[3,iii] := array_y_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 2 ) = sin(x);");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T01:40:51-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"h2sin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 2 ) = sin(x);")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 3
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 3
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 3
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"h2sin diffeq.mxt")
> ;
> logitem_str(html_log_file,"h2sin maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global INFO, ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE,
glob_log10abserr, glob_max_iter, glob_not_yet_start_msg, glob_max_opt_iter,
glob_iter, glob_warned, glob_small_float, glob_max_hours, glob_large_float,
glob_hmin, glob_subiter_method, glob_current_iter, glob_disp_incr,
glob_initial_pass, years_in_century, days_in_year, sec_in_min,
glob_optimal_done, djd_debug2, glob_display_flag, glob_dump, glob_html_log,
glob_curr_iter_when_opt, glob_warned2, glob_optimal_start,
glob_max_trunc_err, glob_h, djd_debug, glob_percent_done, glob_no_eqs,
glob_relerr, glob_hmax, glob_clock_start_sec, glob_clock_sec,
centuries_in_millinium, glob_unchanged_h_cnt, glob_log10_relerr,
glob_log10_abserr, glob_last_good_h, glob_not_yet_finished, hours_in_day,
glob_log10normmin, glob_normmax, glob_orig_start_sec, glob_max_sec,
glob_dump_analytic, glob_smallish_float, min_in_hour,
glob_optimal_expect_sec, glob_max_minutes, glob_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_abserr,
glob_look_poles, glob_hmin_init, glob_almost_1, glob_log10relerr,
MAX_UNCHANGED, glob_reached_optimal_h, array_const_0D0, array_const_2,
array_m1, array_tmp1_g, array_last_rel_error, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_1st_rel_error, array_type_pole, array_y_init,
array_norms, array_pole, array_y_set_initial, array_y_higher,
array_y_higher_work2, array_poles, array_real_pole, array_complex_pole,
array_y_higher_work, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
ALWAYS := 1;
DEBUGL := 3;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
glob_log10abserr := 0.;
glob_max_iter := 1000;
glob_not_yet_start_msg := true;
glob_max_opt_iter := 10;
glob_iter := 0;
glob_warned := false;
glob_small_float := 0.1*10^(-50);
glob_max_hours := 0.;
glob_large_float := 0.90*10^101;
glob_hmin := 0.1*10^(-10);
glob_subiter_method := 3;
glob_current_iter := 0;
glob_disp_incr := 0.1;
glob_initial_pass := true;
years_in_century := 100.0;
days_in_year := 365.0;
sec_in_min := 60.0;
glob_optimal_done := false;
djd_debug2 := true;
glob_display_flag := true;
glob_dump := false;
glob_html_log := true;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_optimal_start := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_h := 0.1;
djd_debug := true;
glob_percent_done := 0.;
glob_no_eqs := 0;
glob_relerr := 0.1*10^(-10);
glob_hmax := 1.0;
glob_clock_start_sec := 0.;
glob_clock_sec := 0.;
centuries_in_millinium := 10.0;
glob_unchanged_h_cnt := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_not_yet_finished := true;
hours_in_day := 24.0;
glob_log10normmin := 0.1;
glob_normmax := 0.;
glob_orig_start_sec := 0.;
glob_max_sec := 10000.0;
glob_dump_analytic := false;
glob_smallish_float := 0.1*10^(-100);
min_in_hour := 60.0;
glob_optimal_expect_sec := 0.1;
glob_max_minutes := 0.;
glob_start := 0;
glob_optimal_clock_start_sec := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_hmin_init := 0.001;
glob_almost_1 := 0.9990;
glob_log10relerr := 0.;
MAX_UNCHANGED := 10;
glob_reached_optimal_h := false;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/h2sinpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 2 ) = sin(x);");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 50;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "2.0 - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_yp := proc(x)");
omniout_str(ALWAYS, "sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 50;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work := Array(1 .. 4, 1 .. 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_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[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_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_norms[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 <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 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_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
array_y_init[2] := exact_soln_yp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := true;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 2 ) = sin(x);");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T01:40:51-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "h2sin");
logitem_str(html_log_file, "diff ( y , x , 2 ) = sin(x);");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"h2sin diffeq.mxt");
logitem_str(html_log_file,
"h2sin maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/h2sinpostode.ode#################
diff ( y , x , 2 ) = sin(x);
!
#BEGIN FIRST INPUT BLOCK
Digits := 50;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
array_y_init[1 + 1] := exact_soln_yp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
2.0 - cos(x);
end;
exact_soln_yp := proc(x)
sin(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y[1] (analytic) = 1.0049958347219742339044380121961
y[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1001
y[1] (analytic) = 1.00500582303864310006118068491
y[1] (numeric) = 1.0050058185629718335653003065756
absolute error = 4.4756712664958803783343078885500e-09
relative error = 4.4533784420906664036177363664867e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1002
y[1] (analytic) = 1.0050158213052537275398742184312
y[1] (numeric) = 1.0050158034032985980336186771541
absolute error = 1.7901955129506255541277083085533e-08
relative error = 1.7812610259464651614037120828114e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1003
y[1] (analytic) = 1.0050258295217061336744956568613
y[1] (numeric) = 1.0050257892439495164872211755182
absolute error = 4.0277756617187274481343172773774e-08
relative error = 4.0076339765671039495612297834371e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1004
y[1] (analytic) = 1.0050358476879002363006043406579
y[1] (numeric) = 1.0050357760859195681006943217376
absolute error = 7.1601980668199910018920299878927e-08
relative error = 7.1243210710266027492763204457086e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1005
y[1] (analytic) = 1.005045875803735853756342728278
y[1] (numeric) = 1.0050457639302037220354333126278
absolute error = 1.1187353213172090941565020935444e-07
relative error = 1.1131186627899504740387125942420e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1006
y[1] (analytic) = 1.0050559138691127048834382127963
y[1] (numeric) = 1.0050557527777969374296923301442
absolute error = 1.6109131576745374588265206930829e-07
relative error = 1.6028094909397497039978393467045e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1007
y[1] (analytic) = 1.0050659618839304090282059334865
y[1] (numeric) = 1.0050657426296941633886349500079
absolute error = 2.1925423624563957098347861188931e-07
relative error = 2.1814910121387639623620817604210e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1008
y[1] (analytic) = 1.0050760198480884860425525823578
y[1] (numeric) = 1.0050757334868903389743846506623
absolute error = 2.8636119814706816793169548990368e-07
relative error = 2.8491496413410602660925028135298e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1009
y[1] (analytic) = 1.0050860877614863562849812056346
y[1] (numeric) = 1.0050857253503803931960754226603
absolute error = 3.6241110596308890578297431618585e-07
relative error = 3.6057717878698912260333750880779e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.18
x[1] = 0.101
y[1] (analytic) = 1.005096165624023340621597000171
y[1] (numeric) = 1.0050957182211592449999024785812
absolute error = 4.4740286409562169452158984380309e-07
relative error = 4.4513438554195204618073437689388e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1011
y[1] (analytic) = 1.0051062534355986604271141047886
y[1] (numeric) = 1.0051057121002218032591730635769
absolute error = 5.4133537685716794104121173622873e-07
relative error = 5.3858522420570488566184432820356e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1012
y[1] (analytic) = 1.0051163511961114375858633865286
y[1] (numeric) = 1.0051157069885629667643573666473
absolute error = 6.4420754847082150601988136767629e-07
relative error = 6.4092833402242416514546516429475e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1013
y[1] (analytic) = 1.0051264589054606944928012218079
y[1] (numeric) = 1.0051257028871776242131395327438
absolute error = 7.5601828307027966168906408484491e-07
relative error = 7.5216235367393563781814441663656e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1014
y[1] (analytic) = 1.0051365765635453540545192724681
y[1] (numeric) = 1.0051356997970606542004687758007
absolute error = 8.7676648469985405049666735238545e-07
relative error = 8.7228592127989716310175859992715e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1015
y[1] (analytic) = 1.0051467041702642396902552567095
y[1] (numeric) = 1.0051456977192069252086105927943
absolute error = 1.0064510573144816446639151954574e-06
relative error = 0.00010012976743979816675884180986234 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1016
y[1] (analytic) = 1.0051568417255160753329047148974
y[1] (numeric) = 1.0051556966546112955971980789281
absolute error = 1.1450709047797357066359693438077e-06
relative error = 0.00011391962500240601897117772653927 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1017
y[1] (analytic) = 1.0051669892291994854300337702324
y[1] (numeric) = 1.0051656966042686135932833440449
absolute error = 1.2926249308718367504261874728657e-06
relative error = 0.00012859802845923850081038071613977 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1018
y[1] (analytic) = 1.0051771466812129949448928842737
y[1] (numeric) = 1.0051756975691737172813890303648
absolute error = 1.4491120392776635038539089284112e-06
relative error = 0.00014416484139757728535860662428607 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1019
y[1] (analytic) = 1.0051873140814550293574316073064
y[1] (numeric) = 1.005185699550321434593559931648
absolute error = 1.6145311335947638716756583124389e-06
relative error = 0.00016061992734857882047444821962379 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.0051974914298239146653143235401
y[1] (numeric) = 1.0051957025487065832994147138828
absolute error = 1.7888811173313658996096572989052e-06
relative error = 0.00017796314978729266670366360455694 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1021
y[1] (analytic) = 1.0052076787262178773849369911326
y[1] (numeric) = 1.0052057065653239709961977375976
absolute error = 1.9721608939063887392535350391154e-06
relative error = 0.00019619437213267984353805176001723 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1022
y[1] (analytic) = 1.0052178759705350445524448770242
y[1] (numeric) = 1.0052157116011683950988309818967
absolute error = 2.1643693666494536138951275075712e-06
relative error = 0.00021531345774763118401736992788155 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1023
y[1] (analytic) = 1.0052280831626734437247512865758
y[1] (numeric) = 1.0052257176572346428299660703197
absolute error = 2.3655054388008947852162561301728e-06
relative error = 0.00023532026993898569766918533378661 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1024
y[1] (analytic) = 1.0052383003025310029805572879987
y[1] (numeric) = 1.0052357247345174912100363986227
absolute error = 2.5755680135117705208893760277368e-06
relative error = 0.00025621467195754894178155155456401 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=0.39
NO POLE
x[1] = 0.1025
y[1] (analytic) = 1.0052485273900055509213724315671
y[1] (numeric) = 1.0052457328340117070473093645829
absolute error = 2.7945559938438740630669841988633e-06
relative error = 0.00027799652699811140100339763833276 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1026
y[1] (analytic) = 1.0052587644249948166725364636016
y[1] (numeric) = 1.0052557419567120469279386999236
absolute error = 3.0224682827697445977636779572602e-06
relative error = 0.0003006656981994668752675158914409 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1027
y[1] (analytic) = 1.0052690114073964298842420352155
y[1] (numeric) = 1.0052657521036132572060169044616
absolute error = 3.2593037831726782251307539297006e-06
relative error = 0.00032422204864443087603103205494373 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1028
y[1] (analytic) = 1.0052792683371079207325584058118
y[1] (numeric) = 1.0052757632757100739936277825739
absolute error = 3.5050613978467389306232379118717e-06
relative error = 0.00034866544135985903082823940414455 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1029
y[1] (analytic) = 1.0052895352140267199204561413216
y[1] (numeric) = 1.0052857754739972231508990820857
absolute error = 3.7597400294967695570592358704407e-06
relative error = 0.00037399573931666549613067611790527 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.0052998120380501586788328071734
y[1] (numeric) = 1.005295788699469420276055235677
absolute error = 4.0233385807384027775714963707485e-06
relative error = 0.00040021280542984137850932307995991 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1031
y[1] (analytic) = 1.0053100988090754687675396559837
y[1] (numeric) = 1.005305802953121370695470204909
absolute error = 4.2958559540980720694510747006115e-06
relative error = 0.00042731650255847316409379709233424 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1032
y[1] (analytic) = 1.0053203955269997824764093099572
y[1] (numeric) = 1.0053158182359477694537204269683
absolute error = 4.5772910520130226888829889517986e-06
relative error = 0.00045530669350576115632341230119118 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1033
y[1] (analytic) = 1.005330702191720132626284437988
y[1] (numeric) = 1.0053258345489433013036378642297
absolute error = 4.8676427768313226465737583118248e-06
relative error = 0.00048418324101903792198498045798436 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1034
y[1] (analytic) = 1.0053410188031334525700474274499
y[1] (numeric) = 1.0053358518931026406963631567361
absolute error = 5.1669100308118736842707138097859e-06
relative error = 0.00051394600778978674553221846371212 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1035
y[1] (analytic) = 1.0053513453611365761936510506671
y[1] (numeric) = 1.0053458702694204517713988776953
absolute error = 5.4750917161244222521729717510437e-06
relative error = 0.00054459485645366009168162947132327 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1036
y[1] (analytic) = 1.0053616818656262379171501260534
y[1] (numeric) = 1.0053558896788913883466628920934
absolute error = 5.7921867348495704872339600666485e-06
relative error = 0.00057612964959049807627972165093295 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1037
y[1] (analytic) = 1.0053720283164990726957341739114
y[1] (numeric) = 1.0053659101225100939085418185236
absolute error = 6.1181939889787871923553877944769e-06
relative error = 0.00060855024972434694543642655446494 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1038
y[1] (analytic) = 1.0053823847136516160207610668791
y[1] (numeric) = 1.0053759316012712016019445943312
absolute error = 6.4531123804144188164725479001437e-06
relative error = 0.00064185651932347756291957685064496 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1039
y[1] (analytic) = 1.0053927510569803039207916750157
y[1] (numeric) = 1.005385954116169334220356144172
absolute error = 6.7969408109697004355308436368350e-06
relative error = 0.00067604832080040390580530103792939 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.1MB, time=0.60
x[1] = 0.104
y[1] (analytic) = 1.0054031273463814729626255055154
y[1] (numeric) = 1.0053959776681991041958911520867
absolute error = 7.1496781823687667343534286342979e-06
relative error = 0.00071112551651190156837919058196679 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1041
y[1] (analytic) = 1.005413513581751360252337337038
y[1] (numeric) = 1.0054060022583551135893479371872
absolute error = 7.5113233962466629893998508983101e-06
relative error = 0.00074708796875902627428309276555474 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1042
y[1] (analytic) = 1.005423909762986103436314848648
y[1] (numeric) = 1.0054160278876319540802624330572
absolute error = 7.8818753541493560524155908930431e-06
relative error = 0.00078393553978713239690238038277511 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1043
y[1] (analytic) = 1.0054343158899817407022972433492
y[1] (numeric) = 1.0054260545570242069569622709653
absolute error = 8.2613329575337453349723838698237e-06
relative error = 0.00082166809178589148798854725506554 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1044
y[1] (analytic) = 1.0054447319626342107804148662065
y[1] (numeric) = 1.0054360822675264431066209669899
absolute error = 8.6496951077676737938992165968910e-06
relative error = 0.00086028548688931081451197639541542 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1045
y[1] (analytic) = 1.0054551579808393529442298170443
y[1] (numeric) = 1.0054461110201332230053122131556
absolute error = 9.0469607061299389176038886358384e-06
relative error = 0.00089978758717575190373972549766268 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1046
y[1] (analytic) = 1.0054655939444929070117775577094
y[1] (numeric) = 1.0054561408158390967080642726811
absolute error = 9.4531286538103037132850283015257e-06
relative error = 0.00094017425466794909653317228101181 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1047
y[1] (analytic) = 1.0054760398534905133466095138901
y[1] (numeric) = 1.0054661716556386038389144794367
absolute error = 9.8681978519095076950344534333407e-06
relative error = 0.00098144535133302810886036007539728 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1048
y[1] (analytic) = 1.0054864957077277128588366714797
y[1] (numeric) = 1.0054762035405262735809638417126
absolute error = 1.0292167201439277872829767096787e-05
relative error = 0.0010236007390825246015178818911785 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1049
y[1] (analytic) = 1.0054969615070999470061741674745
y[1] (numeric) = 1.0054862364714966246664317503962
absolute error = 1.0725035603322339742417078325474e-05
relative error = 0.0010666402797724027580571390768745 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.0055074372515025577949868753959
y[1] (numeric) = 1.0054962704495441653667107916579
absolute error = 1.1166801958392428276083738004675e-05
relative error = 0.0011105638352030738709098085312302 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1051
y[1] (analytic) = 1.0055179229408307877813359852258
y[1] (numeric) = 1.0055063054756633934824216642459
absolute error = 1.1617465167394298914320979988739e-05
relative error = 0.0011553712671194149357073503008497 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1052
y[1] (analytic) = 1.0055284185749797800720265778451
y[1] (numeric) = 1.0055163415508487963334682014875
absolute error = 1.2077024130983738558376357535715e-05
relative error = 0.0012010624372107872537893852619393 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1053
y[1] (analytic) = 1.0055389241538445783256561939646
y[1] (numeric) = 1.0055263786760948507490924980995
absolute error = 1.2545477749727576563695865133675e-05
relative error = 0.0012476372071110550428957704543738 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1054
y[1] (analytic) = 1.0055494396773201267536643975387
y[1] (numeric) = 1.005536416852396023057930141903
absolute error = 1.3022824924103695734255635784313e-05
relative error = 0.0012950954383986040560371975083328 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1055
y[1] (analytic) = 1.0055599651453012701213833336496
y[1] (numeric) = 1.0055464560807467690780655505458
absolute error = 1.3509064554501043317783103800498e-05
relative error = 0.0013434369925963602085391374781534 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.81
NO POLE
x[1] = 0.1056
y[1] (analytic) = 1.0055705005576827537490892808531
y[1] (numeric) = 1.0055564963621415341070874133299
absolute error = 1.4004195541219642001867523165573e-05
relative error = 0.0013926617311718082132539532748094 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1057
y[1] (analytic) = 1.0055810459143592235130551979753
y[1] (numeric) = 1.0055665376975747529121442382438
absolute error = 1.4508216784470600910959731493298e-05
relative error = 0.0014427695155370102239359987675603 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1058
y[1] (analytic) = 1.005591601215225225846604265349
y[1] (numeric) = 1.0055765800880408497200000042993
absolute error = 1.5021127184376126604261049618433e-05
relative error = 0.0014937602070486244867745215068088 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1059
y[1] (analytic) = 1.005602166460175207741164420479
y[1] (numeric) = 1.0055866235345342382070899192722
absolute error = 1.5542925640969534074501206839078e-05
relative error = 0.0015456336670079240000791839040751 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.0056127416491035167473238881278
y[1] (numeric) = 1.005596668038049321489576282946
absolute error = 1.6073611054195257747605181822984e-05
relative error = 0.0015983897566608151821130155912288 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1061
y[1] (analytic) = 1.005623326781904400975887704808
y[1] (numeric) = 1.0056067135995804921134044559588
absolute error = 1.6613182323908862483248849181177e-05
relative error = 0.0016520283371978565470676075697263 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1062
y[1] (analytic) = 1.0056339218584720090989352376741
y[1] (numeric) = 1.0056167602201221320443589343524
absolute error = 1.7161638349877054576303321703325e-05
relative error = 0.0017065492697542773891753566515764 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1063
y[1] (analytic) = 1.0056445268787003903508786978002
y[1] (numeric) = 1.0056268079006686126581195299219
absolute error = 1.7718978031777692759167878240420e-05
relative error = 0.0017619524154099964749535665871031 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1064
y[1] (analytic) = 1.0056551418424834945295226478354
y[1] (numeric) = 1.0056368566422142947303176564682
absolute error = 1.8285200269199799204991367211430e-05
relative error = 0.0018182376351896407435752101702938 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1065
y[1] (analytic) = 1.0056657667497151719971245040249
y[1] (numeric) = 1.0056469064457535284265927220492
absolute error = 1.8860303961643570531781975701724e-05
relative error = 0.0018754047900625640153611545106135 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1066
y[1] (analytic) = 1.0056764016002891736814560325861
y[1] (numeric) = 1.0056569573122806532926486273319
absolute error = 1.9444288008520388807405254112154e-05
relative error = 0.0019334537409428657083886495606305 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1067
y[1] (analytic) = 1.0056870463940991510768658404304
y[1] (numeric) = 1.0056670092427899982443103701441
absolute error = 2.0037151309152832555470286308830e-05
relative error = 0.0019923843486894095632108778916377 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1068
y[1] (analytic) = 1.005697701131038656245342860219
y[1] (numeric) = 1.0056770622382758815575807563238
absolute error = 2.0638892762774687762103895214715e-05
relative error = 0.0020521964741058423756823616146715 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1069
y[1] (analytic) = 1.0057083658110011418175808297414
y[1] (numeric) = 1.0056871162997326108586972169676
absolute error = 2.1249511268530958883612773775310e-05
relative error = 0.0021128899779406127378850202519198 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.0057190404338799609940437656082
y[1] (numeric) = 1.005697171428154483114188732177
absolute error = 2.1869005725477879855033431221788e-05
relative error = 0.0021744647208869897871496712734773 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.03
NO POLE
x[1] = 0.1071
y[1] (analytic) = 1.0057297249995683675460324312455
y[1] (numeric) = 1.005707227624535784620932861401
absolute error = 2.2497375032582925099569844546105e-05
relative error = 0.0022369205635830819631677629267556 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1072
y[1] (analytic) = 1.0057404195079595158167517991808
y[1] (numeric) = 1.0057172848898707909962128804757
absolute error = 2.3134618088724820538918705093684e-05
relative error = 0.0023002573666118557731881269005763 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1073
y[1] (analytic) = 1.00575112395894646072237950761
y[1] (numeric) = 1.0057273432251537671677750254598
absolute error = 2.3780733792693554604482150170440e-05
relative error = 0.0023644749905011545652935362830797 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1074
y[1] (analytic) = 1.0057618383524221577531353112351
y[1] (numeric) = 1.0057374026313789673638858433655
absolute error = 2.4435721043190389249467869552008e-05
relative error = 0.0024295732957237173097518521920659 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1075
y[1] (analytic) = 1.0057725626882794629743515263608
y[1] (numeric) = 1.005747463109540635103389649884
absolute error = 2.5099578738827870961876476774177e-05
relative error = 0.0024955521426971973884365403782479 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1076
y[1] (analytic) = 1.0057832969664111330275444702404
y[1] (numeric) = 1.0057575246606330031857660942053
absolute error = 2.5772305778129841778376035074651e-05
relative error = 0.0025624113917841813923113370261414 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1077
y[1] (analytic) = 1.0057940411867098251314868946597
y[1] (numeric) = 1.0057675872856502936811878310318
absolute error = 2.6453901059531450299063627847410e-05
relative error = 0.0026301509032922079269738409039468 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1078
y[1] (analytic) = 1.0058047953490680970832814137484
y[1] (numeric) = 1.0057776509855867179205782998849
absolute error = 2.7144363481379162703113863462020e-05
relative error = 0.0026987705374737864262528069427847 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1079
y[1] (analytic) = 1.0058155594533784072594349260082
y[1] (numeric) = 1.0057877157614364764856696118039
absolute error = 2.7843691941930773765314204291450e-05
relative error = 0.0027682701545264159738539142570468 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.0058263334995331146169340305467
y[1] (numeric) = 1.0057977816141937591990605435369
absolute error = 2.8551885339355417873487009783009e-05
relative error = 0.0028386496145926041330487795513993 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1081
y[1] (analytic) = 1.0058371174874244786943214375069
y[1] (numeric) = 1.0058078485448527451142746393235
absolute error = 2.9268942571733580046798183398198e-05
relative error = 0.0029099087777598857844019847961426 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1082
y[1] (analytic) = 1.0058479114169446596127733726807
y[1] (numeric) = 1.0058179165544076025058184203674
absolute error = 2.9994862537057106954952313238390e-05
relative error = 0.0029820475040608419715308859911812 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1083
y[1] (analytic) = 1.0058587152879857180771779762961
y[1] (numeric) = 1.0058279856438524888592397021
absolute error = 3.0729644133229217938274196164380e-05
relative error = 0.003055065653473118754892967779798 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1084
y[1] (analytic) = 1.0058695291004396153772146959678
y[1] (numeric) = 1.0058380558141815508611860193326
absolute error = 3.1473286258064516028676635209001e-05
relative error = 0.0031289630859194460735955066167485 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1085
y[1] (analytic) = 1.0058803528541982133884346737992
y[1] (numeric) = 1.0058481270663889243894631593991
absolute error = 3.2225787809288998971514400073115e-05
relative error = 0.0032037396612676566152223031409095 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=22.8MB, alloc=4.2MB, time=1.24
x[1] = 0.1086
y[1] (analytic) = 1.005891186549153274573342127626
y[1] (numeric) = 1.0058581994014687345030938033855
absolute error = 3.2987147684540070248324240486448e-05
relative error = 0.0032793952393307046936722423508173 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1087
y[1] (analytic) = 1.0059020301851964619824767263904
y[1] (numeric) = 1.0058682728204150954323762755482
absolute error = 3.3757364781366550100450842205871e-05
relative error = 0.0033559296798666851350044381319233 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1088
y[1] (analytic) = 1.0059128837622193392554969596347
y[1] (numeric) = 1.0058783473242221105689434010193
absolute error = 3.4536437997228686553558615414856e-05
relative error = 0.0034333428425788521712847166372833 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1089
y[1] (analytic) = 1.0059237472801133706222645011039
y[1] (numeric) = 1.0058884229138838724558214718986
absolute error = 3.5324366229498166443029205279005e-05
relative error = 0.0035116345871156383424281909786657 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.0059346207387699209039295664461
y[1] (numeric) = 1.0058984995903944627774893218317
absolute error = 3.6121148375458126440244614403660e-05
relative error = 0.0035908047730706734060326776427387 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1091
y[1] (analytic) = 1.005945504138080255514017265
y[1] (numeric) = 1.005908577354747952349937509173
absolute error = 3.6926783332303164079755826930777e-05
relative error = 0.0036708532599828032551977030070533 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1092
y[1] (analytic) = 1.0059563974779355404595149456589
y[1] (numeric) = 1.0059186562079384011107276088349
absolute error = 3.7741269997139348787336824003372e-05
relative error = 0.0037517799073361088443238462929946 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1093
y[1] (analytic) = 1.0059673007582268423419605368001
y[1] (numeric) = 1.0059287361509598581090516129198
absolute error = 3.8564607266984232908923880316999e-05
relative error = 0.0038335845745599251228871632577237 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1094
y[1] (analytic) = 1.0059782139788451283585318802682
y[1] (numeric) = 1.0059388171848063614957914402367
absolute error = 3.9396794038766862740440031468867e-05
relative error = 0.0039162671210288599771834328943778 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1095
y[1] (analytic) = 1.0059891371396812663031370594024
y[1] (numeric) = 1.0059488993104719385135785548006
absolute error = 4.0237829209327789558504601806347e-05
relative error = 0.0039998274060628131800369673794346 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1096
y[1] (analytic) = 1.0060000702406260245675057210971
y[1] (numeric) = 1.0059589825289506054868536934146
absolute error = 4.1087711675419080652027682467791e-05
relative error = 0.0040842652889269953484687234781864 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1097
y[1] (analytic) = 1.0060110132815700721422813918831
y[1] (numeric) = 1.0059690668412363678119267024338
absolute error = 4.1946440333704330354689449299691e-05
relative error = 0.0041695806288319469093184515937036 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1098
y[1] (analytic) = 1.0060219662624039786181147880204
y[1] (numeric) = 1.0059791522483232199470364838101
absolute error = 4.2814014080758671078304210325414e-05
relative error = 0.0042557732849335570728156166215013 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1099
y[1] (analytic) = 1.006032929183018214186758119591
y[1] (numeric) = 1.0059892387512051454024110505185
absolute error = 4.3690431813068784347069072431845e-05
relative error = 0.0043428431163330828140938227513525 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.0060439020433031496421603885802
y[1] (numeric) = 1.0059993263508761167303276914632
absolute error = 4.4575692427032911832697116931477e-05
relative error = 0.0044307899820771678626434723393273 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 2 ) = sin(x);
Iterations = 100
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Expected Time Remaining = 11 Minutes 15 Seconds
Optimized Time Remaining = 11 Minutes 12 Seconds
Time to Timeout = 14 Minutes 58 Seconds
Percent Done = 0.2061 %
> quit
memory used=26.5MB, alloc=4.2MB, time=1.43