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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> 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 DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
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
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> 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 DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
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
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> 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 DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
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
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> 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 - 1 - 1;
> while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> if not found then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 3
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 3
> ;
> fi;# end if 2
> ;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
array_complex_pole, array_y_higher_work, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or
abs(array_y_higher[1, m - 1]) < glob_small_float or
abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y_higher[1, m]) or
glob_large_float <= abs(array_y_higher[1, m - 1]) or
glob_large_float <= abs(array_y_higher[1, m - 2]) or
glob_large_float <= abs(array_y_higher[1, m - 3]) or
glob_large_float <= abs(array_y_higher[1, m - 4]) or
glob_large_float <= abs(array_y_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> 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 DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
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
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre sinh $eq_no = 1
> array_tmp1[1] := sinh(array_x[1]);
> array_tmp1_g[1] := cosh(array_x[1]);
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre sinh $eq_no = 1
> array_tmp1[2] := att(1,array_tmp1_g,array_x,1);
> array_tmp1_g[2] := att(1,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sinh $eq_no = 1
> array_tmp1[3] := att(2,array_tmp1_g,array_x,1);
> array_tmp1_g[3] := att(2,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sinh $eq_no = 1
> array_tmp1[4] := att(3,array_tmp1_g,array_x,1);
> array_tmp1_g[4] := att(3,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sinh $eq_no = 1
> array_tmp1[5] := att(4,array_tmp1_g,array_x,1);
> array_tmp1_g[5] := att(4,array_tmp1,array_x,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sinh $eq_no = 1
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1);
> array_tmp1_g[kkk] := att(kkk-1,array_tmp1,array_x,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
array_complex_pole, array_y_higher_work, glob_last;
array_tmp1[1] := sinh(array_x[1]);
array_tmp1_g[1] := cosh(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := att(1, array_tmp1_g, array_x, 1);
array_tmp1_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := att(2, array_tmp1_g, array_x, 1);
array_tmp1_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := att(3, array_tmp1_g, array_x, 1);
array_tmp1_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := att(4, array_tmp1_g, array_x, 1);
array_tmp1_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp1_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp2[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_y_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"| ");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> 1.0 + cosh(x);
> end;
exact_soln_y := proc(x) 1.0 + cosh(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_max_terms,
> INFO,
> ALWAYS,
> glob_iolevel,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_log10_abserr,
> glob_look_poles,
> glob_almost_1,
> years_in_century,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_last_good_h,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_dump,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_large_float,
> days_in_year,
> glob_html_log,
> glob_subiter_method,
> glob_warned,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_dump_analytic,
> glob_smallish_float,
> glob_log10_relerr,
> glob_hmin_init,
> glob_disp_incr,
> glob_clock_sec,
> glob_log10abserr,
> glob_abserr,
> glob_hmin,
> glob_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> djd_debug2,
> glob_log10normmin,
> glob_iter,
> glob_max_trunc_err,
> glob_relerr,
> glob_normmax,
> glob_max_iter,
> centuries_in_millinium,
> sec_in_min,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> min_in_hour,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> djd_debug,
> glob_start,
> glob_orig_start_sec,
> glob_warned2,
> glob_hmax,
> glob_reached_optimal_h,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_pole,
> array_y,
> array_x,
> array_type_pole,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y_higher_work2,
> array_real_pole,
> array_y_set_initial,
> array_y_higher,
> array_complex_pole,
> array_y_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> INFO := 2;
> ALWAYS := 1;
> glob_iolevel := 5;
> MAX_UNCHANGED := 10;
> glob_log10_abserr := 0.1e-10;
> glob_look_poles := false;
> glob_almost_1 := 0.9990;
> years_in_century := 100.0;
> glob_log10relerr := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_last_good_h := 0.1;
> glob_optimal_done := false;
> glob_clock_start_sec := 0.0;
> glob_dump := false;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_max_minutes := 0.0;
> glob_large_float := 9.0e100;
> days_in_year := 365.0;
> glob_html_log := true;
> glob_subiter_method := 3;
> glob_warned := false;
> glob_no_eqs := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_dump_analytic := false;
> glob_smallish_float := 0.1e-100;
> glob_log10_relerr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_disp_incr := 0.1;
> glob_clock_sec := 0.0;
> glob_log10abserr := 0.0;
> glob_abserr := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_h := 0.1;
> glob_not_yet_start_msg := true;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> hours_in_day := 24.0;
> djd_debug2 := true;
> glob_log10normmin := 0.1;
> glob_iter := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_normmax := 0.0;
> glob_max_iter := 1000;
> centuries_in_millinium := 10.0;
> sec_in_min := 60.0;
> glob_current_iter := 0;
> glob_max_sec := 10000.0;
> glob_small_float := 0.1e-50;
> min_in_hour := 60.0;
> glob_percent_done := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_unchanged_h_cnt := 0;
> glob_optimal_start := 0.0;
> djd_debug := true;
> glob_start := 0;
> glob_orig_start_sec := 0.0;
> glob_warned2 := false;
> glob_hmax := 1.0;
> glob_reached_optimal_h := false;
> glob_display_flag := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sinhpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.0;");
> omniout_str(ALWAYS,"x_end := 10.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> 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,"1.0 + cosh(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_m1:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> 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_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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[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_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_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_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.0;
> x_end := 10.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #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] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> if glob_html_log then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y();
> if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := abs(array_y_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 3
> glob_log10normmin := log10norm;
> fi;# end if 3
> fi;# end if 2
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> if (glob_look_poles) then # if number 2
> #left paren 0004C
> check_for_pole();
> fi;# end if 2
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 2
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 2
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 2
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sinh ( 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,"2012-06-13T04:13:12-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sinh")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh ( 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,"sinh diffeq.mxt")
> ;
> logitem_str(html_log_file,"sinh maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 2
> ;
> if glob_html_log then # if number 2
> fclose(html_log_file);
> fi;# end if 2
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, DEBUGMASSIVE, glob_max_terms, INFO, ALWAYS, glob_iolevel,
MAX_UNCHANGED, glob_log10_abserr, glob_look_poles, glob_almost_1,
years_in_century, glob_log10relerr, glob_optimal_clock_start_sec,
glob_max_hours, glob_last_good_h, glob_optimal_done, glob_clock_start_sec,
glob_dump, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_large_float, days_in_year, glob_html_log, glob_subiter_method,
glob_warned, glob_no_eqs, glob_max_rel_trunc_err, glob_dump_analytic,
glob_smallish_float, glob_log10_relerr, glob_hmin_init, glob_disp_incr,
glob_clock_sec, glob_log10abserr, glob_abserr, glob_hmin, glob_h,
glob_not_yet_start_msg, glob_initial_pass, glob_not_yet_finished,
hours_in_day, djd_debug2, glob_log10normmin, glob_iter, glob_max_trunc_err,
glob_relerr, glob_normmax, glob_max_iter, centuries_in_millinium,
sec_in_min, glob_current_iter, glob_max_sec, glob_small_float, min_in_hour,
glob_percent_done, glob_curr_iter_when_opt, glob_unchanged_h_cnt,
glob_optimal_start, djd_debug, glob_start, glob_orig_start_sec,
glob_warned2, glob_hmax, glob_reached_optimal_h, glob_display_flag,
array_const_0D0, array_const_1, array_m1, array_last_rel_error, array_pole,
array_y, array_x, array_type_pole, array_tmp0, array_tmp1_g, array_tmp1,
array_tmp2, array_y_init, array_1st_rel_error, array_norms, array_poles,
array_y_higher_work2, array_real_pole, array_y_set_initial, array_y_higher,
array_complex_pole, array_y_higher_work, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
INFO := 2;
ALWAYS := 1;
glob_iolevel := 5;
MAX_UNCHANGED := 10;
glob_log10_abserr := 0.1*10^(-10);
glob_look_poles := false;
glob_almost_1 := 0.9990;
years_in_century := 100.0;
glob_log10relerr := 0.;
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_last_good_h := 0.1;
glob_optimal_done := false;
glob_clock_start_sec := 0.;
glob_dump := false;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_max_minutes := 0.;
glob_large_float := 0.90*10^101;
days_in_year := 365.0;
glob_html_log := true;
glob_subiter_method := 3;
glob_warned := false;
glob_no_eqs := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_dump_analytic := false;
glob_smallish_float := 0.1*10^(-100);
glob_log10_relerr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_disp_incr := 0.1;
glob_clock_sec := 0.;
glob_log10abserr := 0.;
glob_abserr := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_h := 0.1;
glob_not_yet_start_msg := true;
glob_initial_pass := true;
glob_not_yet_finished := true;
hours_in_day := 24.0;
djd_debug2 := true;
glob_log10normmin := 0.1;
glob_iter := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_normmax := 0.;
glob_max_iter := 1000;
centuries_in_millinium := 10.0;
sec_in_min := 60.0;
glob_current_iter := 0;
glob_max_sec := 10000.0;
glob_small_float := 0.1*10^(-50);
min_in_hour := 60.0;
glob_percent_done := 0.;
glob_curr_iter_when_opt := 0;
glob_unchanged_h_cnt := 0;
glob_optimal_start := 0.;
djd_debug := true;
glob_start := 0;
glob_orig_start_sec := 0.;
glob_warned2 := false;
glob_hmax := 1.0;
glob_reached_optimal_h := false;
glob_display_flag := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sinhpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.0;");
omniout_str(ALWAYS, "x_end := 10.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
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, "1.0 + \t cosh(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_m1[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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[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_norms[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_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_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
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_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.;
x_end := 10.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
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] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y();
if glob_small_float < abs(array_y_higher[1, 1]) then
tmp := abs(array_y_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
if glob_look_poles then check_for_pole() end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = sinh ( 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, "2012-06-13T04:13:12-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sinh");
logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh ( 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,
"sinh diffeq.mxt");
logitem_str(html_log_file,
"sinh 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/sinhpostode.ode#################
diff ( y , x , 1 ) = sinh ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.0;
x_end := 10.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#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)
1.0 + cosh(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0
y[1] (analytic) = 2
y[1] (numeric) = 2
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0001
y[1] (analytic) = 2.0000000050000000041666666680556
y[1] (numeric) = 2.0000000050000000041666667166667
absolute error = 4.86111e-26
relative error = 2.4305549939236125101273124856529e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0002
y[1] (analytic) = 2.0000000200000000666666667555556
y[1] (numeric) = 2.0000000200000000666666668527778
absolute error = 9.72222e-26
relative error = 4.8611099513889003240739981635806e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0003
y[1] (analytic) = 2.0000000450000003375000010125
y[1] (numeric) = 2.0000000450000003375000011583334
absolute error = 1.458334e-25
relative error = 7.2916698359374274609385936230329e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0004
y[1] (analytic) = 2.0000000800000010666666723555556
y[1] (numeric) = 2.0000000800000010666666725500001
absolute error = 1.944445e-25
relative error = 9.7222246111110103703730982715425e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0005
y[1] (analytic) = 2.0000001250000026041666883680557
y[1] (numeric) = 2.0000001250000026041666886111113
absolute error = 2.430556e-25
relative error = 1.2152779240451281647863462471499e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0006
y[1] (analytic) = 2.0000001800000054000000648000004
y[1] (numeric) = 2.0000001800000054000000650916672
absolute error = 2.916668e-25
relative error = 1.4583338687499478750031983748352e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0007
y[1] (analytic) = 2.000000245000010004166830068057
y[1] (numeric) = 2.0000002450000100041668304083349
absolute error = 3.402779e-25
relative error = 1.7013892915798032709829413767609e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0008
y[1] (analytic) = 2.0000003200000170666670307555597
y[1] (numeric) = 2.0000003200000170666670311444488
absolute error = 3.888891e-25
relative error = 1.9444451888887531852001912084940e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0009
y[1] (analytic) = 2.0000004050000273375007381125107
y[1] (numeric) = 2.0000004050000273375007385500109
absolute error = 4.375002e-25
relative error = 2.1875005570311073008017253579385e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.001
y[1] (analytic) = 2.0000005000000416666680555555804
y[1] (numeric) = 2.0000005000000416666680560416917
absolute error = 4.861113e-25
relative error = 2.4305558923609762731731529669728e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0011
y[1] (analytic) = 2.0000006050000610041691271681087
y[1] (numeric) = 2.0000006050000610041691277028312
absolute error = 5.347225e-25
relative error = 2.6736116912323818514745937718439e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0012
y[1] (analytic) = 2.0000007200000864000041472001066
y[1] (numeric) = 2.0000007200000864000041477834403
absolute error = 5.833337e-25
relative error = 2.9166674499995920001069919773287e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0013
y[1] (analytic) = 2.0000008450001190041733705682579
y[1] (numeric) = 2.0000008450001190041733712002027
absolute error = 6.319448e-25
relative error = 3.1597226650169860202314911545071e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0014
y[1] (analytic) = 2.0000009800001600666771243559216
y[1] (numeric) = 2.0000009800001600666771250364776
absolute error = 6.805560e-25
relative error = 3.4027783326383446715007628765712e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.21
NO POLE
x[1] = 0.0015
y[1] (analytic) = 2.0000011250002109375158203131356
y[1] (numeric) = 2.0000011250002109375158210423028
absolute error = 7.291672e-25
relative error = 3.6458339492180190432861174462544e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0016
y[1] (analytic) = 2.0000012800002730666899683566208
y[1] (numeric) = 2.0000012800002730666899691343991
absolute error = 7.777783e-25
relative error = 3.8888890111105019262538080673650e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0017
y[1] (analytic) = 2.0000014450003480042001910697857
y[1] (numeric) = 2.0000014450003480042001918961752
absolute error = 8.263895e-25
relative error = 4.1319445146693691843577336056172e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0018
y[1] (analytic) = 2.0000016200004374000472392027331
y[1] (numeric) = 2.0000016200004374000472400777339
absolute error = 8.750008e-25
relative error = 4.3750004562486736258712456926139e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0019
y[1] (analytic) = 2.0000018050005430042320081722677
y[1] (numeric) = 2.0000018050005430042320090958797
absolute error = 9.236120e-25
relative error = 4.6180558322033576245394756305916e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.002
y[1] (analytic) = 2.0000020000006666667555555619048
y[1] (numeric) = 2.0000020000006666667555565341279
absolute error = 9.722231e-25
relative error = 4.8611106388877407418302462123460e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0021
y[1] (analytic) = 2.0000022050008103376191196218807
y[1] (numeric) = 2.000002205000810337619120642715
absolute error = 1.0208343e-24
relative error = 5.1041658726550573489888532766385e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0022
y[1] (analytic) = 2.0000024200009760668241387691656
y[1] (numeric) = 2.0000024200009760668241398386112
absolute error = 1.0694456e-24
relative error = 5.3472215298593392474312024802970e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0023
y[1] (analytic) = 2.0000026450011660043722720874779
y[1] (numeric) = 2.0000026450011660043722732055347
absolute error = 1.1180568e-24
relative error = 5.5902766068559282895519348766549e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0024
y[1] (analytic) = 2.0000028800013824002654208273004
y[1] (numeric) = 2.0000028800013824002654219939684
absolute error = 1.1666680e-24
relative error = 5.8333315999984640026357734165731e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0025
y[1] (analytic) = 2.0000031250016276045057509058998
y[1] (numeric) = 2.000003125001627604505752121179
absolute error = 1.2152792e-24
relative error = 6.0763865056411399586911817841351e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0026
y[1] (analytic) = 2.000003380001904067095716407348
y[1] (numeric) = 2.0000033800019040670957176712385
absolute error = 1.2638905e-24
relative error = 6.3194418201373076473335671810573e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0027
y[1] (analytic) = 2.000003645002214338038084082547
y[1] (numeric) = 2.0000036450022143380380853950488
absolute error = 1.3125018e-24
relative error = 6.5624970398418790947652817573486e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0028
y[1] (analytic) = 2.0000039200025610673359588492565
y[1] (numeric) = 2.0000039200025610673359602103695
absolute error = 1.3611130e-24
relative error = 6.8055516611100294863109821382207e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0029
y[1] (analytic) = 2.0000042050029470049928102921246
y[1] (numeric) = 2.000004205002947004992811701849
absolute error = 1.4097244e-24
relative error = 7.0486071802930172936547990923475e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.003
y[1] (analytic) = 2.0000045000033750010125001627232
y[1] (numeric) = 2.0000045000033750010125016210589
absolute error = 1.4583357e-24
relative error = 7.2916620937479843835605327369329e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0031
y[1] (analytic) = 2.0000048050038480053993108795861
y[1] (numeric) = 2.0000048050038480053993123865331
absolute error = 1.5069470e-24
relative error = 7.5347168978281561522022835010547e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0032
y[1] (analytic) = 2.0000051200043690681579750282519
y[1] (numeric) = 2.0000051200043690681579765838103
absolute error = 1.5555584e-24
relative error = 7.7777720888864616424714248928153e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0033
y[1] (analytic) = 2.0000054450049413392937058613117
y[1] (numeric) = 2.0000054450049413392937074654814
absolute error = 1.6041697e-24
relative error = 8.0208266632795924083300347607595e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0034
y[1] (analytic) = 2.0000057800055680688122287984608
y[1] (numeric) = 2.0000057800055680688122304512419
absolute error = 1.6527811e-24
relative error = 8.2638816173591189013955908711659e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0035
y[1] (analytic) = 2.0000061250062526067198139265565
y[1] (numeric) = 2.0000061250062526067198156279489
absolute error = 1.7013924e-24
relative error = 8.5069359474820655737390539164372e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0036
y[1] (analytic) = 2.0000064800069984030233094996801
y[1] (numeric) = 2.000006480006998403023311249684
absolute error = 1.7500039e-24
relative error = 8.7499911499980560240394432316116e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=0.44
NO POLE
x[1] = 0.0037
y[1] (analytic) = 2.0000068450078090077301764392063
y[1] (numeric) = 2.0000068450078090077301782378216
absolute error = 1.7986153e-24
relative error = 8.9930457212659055856605352728415e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0038
y[1] (analytic) = 2.0000072200086880708485238338772
y[1] (numeric) = 2.0000072200086880708485256811039
absolute error = 1.8472267e-24
relative error = 9.2361001576383089794377723401778e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0039
y[1] (analytic) = 2.0000076050096393423871454398835
y[1] (numeric) = 2.0000076050096393423871473357216
absolute error = 1.8958381e-24
relative error = 9.4791544554694966695704611231455e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.004
y[1] (analytic) = 2.0000080000106666723555571809527
y[1] (numeric) = 2.0000080000106666723555591254023
absolute error = 1.9444496e-24
relative error = 9.7222091111117037436048048990935e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0041
y[1] (analytic) = 2.0000084050117740107640356484441
y[1] (numeric) = 2.0000084050117740107640376415053
absolute error = 1.9930612e-24
relative error = 9.9652641209188662749514010291107e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0042
y[1] (analytic) = 2.0000088200129654076236576014519
y[1] (numeric) = 2.0000088200129654076236596431246
absolute error = 2.0416727e-24
relative error = 1.0208318481249320185367225168762e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0043
y[1] (analytic) = 2.0000092450142450129463404669153
y[1] (numeric) = 2.0000092450142450129463425571996
absolute error = 2.0902843e-24
relative error = 1.0451373188452996402835853602136e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0044
y[1] (analytic) = 2.0000096800156170767448838397388
y[1] (numeric) = 2.0000096800156170767448859786346
absolute error = 2.1388958e-24
relative error = 1.0694427238888655933439131994221e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0045
y[1] (analytic) = 2.0000101250170859490330119829189
y[1] (numeric) = 2.0000101250170859490330141704264
absolute error = 2.1875075e-24
relative error = 1.0937482128903283796023822176357e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0046
y[1] (analytic) = 2.0000105800186560798254173276828
y[1] (numeric) = 2.0000105800186560798254195638018
absolute error = 2.2361190e-24
relative error = 1.1180535854861035300423646740925e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0047
y[1] (analytic) = 2.0000110450203320191378049736341
y[1] (numeric) = 2.0000110450203320191378072583647
absolute error = 2.2847306e-24
relative error = 1.1423589913108572533540303847373e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0048
y[1] (analytic) = 2.0000115200221184169869381889106
y[1] (numeric) = 2.0000115200221184169869405222529
absolute error = 2.3333423e-24
relative error = 1.1666644299999808149372218939682e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0049
y[1] (analytic) = 2.000012005024020023390684910352
y[1] (numeric) = 2.000012005024020023390687292306
absolute error = 2.3819540e-24
relative error = 1.1909698511891646751974549960800e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.005
y[1] (analytic) = 2.0000125000260416883680652436783
y[1] (numeric) = 2.0000125000260416883680676742439
absolute error = 2.4305656e-24
relative error = 1.2152752045141478774970685458729e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0051
y[1] (analytic) = 2.00001300502818836193929996368
y[1] (numeric) = 2.0000130050281883619393024428573
absolute error = 2.4791773e-24
relative error = 1.2395805896097451894754802610307e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0052
y[1] (analytic) = 2.0000135200304650941258600144208
y[1] (numeric) = 2.0000135200304650941258625422098
absolute error = 2.5277890e-24
relative error = 1.2638859561116844827042493958109e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0053
y[1] (analytic) = 2.0000140450328770349505170094518
y[1] (numeric) = 2.0000140450328770349505195858526
absolute error = 2.5764008e-24
relative error = 1.2881913536550430013819874619402e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0054
y[1] (analytic) = 2.0000145800354294344373947320399
y[1] (numeric) = 2.0000145800354294344373973570524
absolute error = 2.6250125e-24
relative error = 1.3124966818759386168375724051543e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0055
y[1] (analytic) = 2.0000151250381276426120216354082
y[1] (numeric) = 2.0000151250381276426120243090326
absolute error = 2.6736244e-24
relative error = 1.3368020904087067279823163310345e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0056
y[1] (analytic) = 2.0000156800409771095013843429924
y[1] (numeric) = 2.0000156800409771095013870652286
absolute error = 2.7222362e-24
relative error = 1.3611074288898703793378420305655e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0057
y[1] (analytic) = 2.0000162450439833851339821487097
y[1] (numeric) = 2.0000162450439833851339849195578
absolute error = 2.7708481e-24
relative error = 1.3854127969540891681017425363009e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0058
y[1] (analytic) = 2.0000168200471521195398825172444
y[1] (numeric) = 2.0000168200471521195398853367045
absolute error = 2.8194601e-24
relative error = 1.4097181942367508685190964551810e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.1MB, time=0.69
x[1] = 0.0059
y[1] (analytic) = 2.0000174050504890627507775843488
y[1] (numeric) = 2.0000174050504890627507804524208
absolute error = 2.8680720e-24
relative error = 1.4340235203741126925311634708229e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.006
y[1] (analytic) = 2.0000180000540000648000416571595
y[1] (numeric) = 2.0000180000540000648000445738435
absolute error = 2.9166840e-24
relative error = 1.4583288750007500663744964527962e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0061
y[1] (analytic) = 2.0000186050576910757227897145318
y[1] (numeric) = 2.0000186050576910757227926798278
absolute error = 2.9652960e-24
relative error = 1.4826342077525150010548783469237e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0062
y[1] (analytic) = 2.0000192200615681455559369073906
y[1] (numeric) = 2.0000192200615681455559399212986
absolute error = 3.0139080e-24
relative error = 1.5069395182648397390878458173683e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0063
y[1] (analytic) = 2.0000198450656374243382590590996
y[1] (numeric) = 2.0000198450656374243382621216197
absolute error = 3.0625201e-24
relative error = 1.5312448561726611425746220928505e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0064
y[1] (analytic) = 2.0000204800699051621104541658494
y[1] (numeric) = 2.0000204800699051621104572769816
absolute error = 3.1111322e-24
relative error = 1.5555501711118773209349733754571e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0065
y[1] (analytic) = 2.0000211250743777089152048970641
y[1] (numeric) = 2.0000211250743777089152080568084
absolute error = 3.1597443e-24
relative error = 1.5798554627179220270815239778880e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0066
y[1] (analytic) = 2.0000217800790615147972420958285
y[1] (numeric) = 2.0000217800790615147972453041849
absolute error = 3.2083564e-24
relative error = 1.6041607306262297916867883516884e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0067
y[1] (analytic) = 2.0000224450839631298034092793353
y[1] (numeric) = 2.0000224450839631298034125363039
absolute error = 3.2569686e-24
relative error = 1.6284660244716748145328153532590e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0068
y[1] (analytic) = 2.0000231200890892039827281393538
y[1] (numeric) = 2.0000231200890892039827314449346
absolute error = 3.3055808e-24
relative error = 1.6527712938902205895808927547587e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0069
y[1] (analytic) = 2.0000238050944464873864650427198
y[1] (numeric) = 2.0000238050944464873864683969128
absolute error = 3.3541930e-24
relative error = 1.6770765385173033037268219205756e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.007
y[1] (analytic) = 2.0000245001000418300681985318487
y[1] (numeric) = 2.000024500100041830068201934654
absolute error = 3.4028053e-24
relative error = 1.7013818079877474752355110567799e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0071
y[1] (analytic) = 2.0000252051058821820838878252711
y[1] (numeric) = 2.0000252051058821820838912766887
absolute error = 3.4514176e-24
relative error = 1.7256870519375682014702103802582e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0072
y[1] (analytic) = 2.0000259201119745934919423181925
y[1] (numeric) = 2.0000259201119745934919458182225
absolute error = 3.5000300e-24
relative error = 1.7499923200015554405183932773533e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0073
y[1] (analytic) = 2.0000266451183262143532920830777
y[1] (numeric) = 2.0000266451183262143532956317201
absolute error = 3.5486424e-24
relative error = 1.7742975618157597527277267355169e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0074
y[1] (analytic) = 2.0000273801249442947314593702598
y[1] (numeric) = 2.0000273801249442947314629675145
absolute error = 3.5972547e-24
relative error = 1.7986027270163045721758410530808e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0075
y[1] (analytic) = 2.0000281251318361846926311085754
y[1] (numeric) = 2.0000281251318361846926347544426
absolute error = 3.6458672e-24
relative error = 1.8229079652365762450552550933923e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0076
y[1] (analytic) = 2.0000288801390093343057324060272
y[1] (numeric) = 2.0000288801390093343057361005069
absolute error = 3.6944797e-24
relative error = 1.8472131761133469863033707783984e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0077
y[1] (analytic) = 2.0000296451464712936425010504726
y[1] (numeric) = 2.0000296451464712936425047935648
absolute error = 3.7430922e-24
relative error = 1.8715183592820576841201101034124e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0078
y[1] (analytic) = 2.0000304201542297127775630103415
y[1] (numeric) = 2.0000304201542297127775668020462
absolute error = 3.7917047e-24
relative error = 1.8958235143781501502864680449773e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0079
y[1] (analytic) = 2.0000312051622923417885089353824
y[1] (numeric) = 2.0000312051622923417885127756997
absolute error = 3.8403173e-24
relative error = 1.9201286910362870154300500698197e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.008
y[1] (analytic) = 2.0000320001706670307559716574388
y[1] (numeric) = 2.0000320001706670307559755463687
absolute error = 3.8889299e-24
relative error = 1.9444338388926523426698951136213e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0081
y[1] (analytic) = 2.0000328051793617297637046912549
y[1] (numeric) = 2.0000328051793617297637086287975
absolute error = 3.9375426e-24
relative error = 1.9687390075818699214520316259955e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.94
NO POLE
x[1] = 0.0082
y[1] (analytic) = 2.000033620188384488898661735314
y[1] (numeric) = 2.0000336201883844888986657214693
absolute error = 3.9861553e-24
relative error = 1.9930441467401639963751633460241e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0083
y[1] (analytic) = 2.0000344451977434582510771727074
y[1] (numeric) = 2.0000344451977434582510812074755
absolute error = 4.0347681e-24
relative error = 2.0173493060021185643783902729933e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0084
y[1] (analytic) = 2.0000352802074468879145475720373
y[1] (numeric) = 2.0000352802074468879145516554182
absolute error = 4.0833809e-24
relative error = 2.0416544350039991000866176958959e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0085
y[1] (analytic) = 2.0000361252175031279861141883526
y[1] (numeric) = 2.0000361252175031279861183203464
absolute error = 4.1319938e-24
relative error = 2.0659595833803488566097199047353e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0086
y[1] (analytic) = 2.0000369802279206285663464641195
y[1] (numeric) = 2.0000369802279206285663506447262
absolute error = 4.1806067e-24
relative error = 2.0902647007674755871419091760246e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0087
y[1] (analytic) = 2.0000378452387079397594265302271
y[1] (numeric) = 2.0000378452387079397594307594467
absolute error = 4.2292196e-24
relative error = 2.1145697868008269627094205290514e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0088
y[1] (analytic) = 2.0000387202498737116732347070294
y[1] (numeric) = 2.0000387202498737116732389848619
absolute error = 4.2778325e-24
relative error = 2.1388748411158516994340399459394e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0089
y[1] (analytic) = 2.0000396052614266944194360054242
y[1] (numeric) = 2.0000396052614266944194403318697
absolute error = 4.3264455e-24
relative error = 2.1631799133470094587547776587868e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.009
y[1] (analytic) = 2.0000405002733757381135676279698
y[1] (numeric) = 2.0000405002733757381135720030283
absolute error = 4.3750585e-24
relative error = 2.1874849531306964465597436507516e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0091
y[1] (analytic) = 2.0000414052857297928751274700404
y[1] (numeric) = 2.000041405285729792875131893712
absolute error = 4.4236716e-24
relative error = 2.2117900101013287265072751072625e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0092
y[1] (analytic) = 2.0000423202984979088276636210213
y[1] (numeric) = 2.000042320298497908827668093306
absolute error = 4.4722847e-24
relative error = 2.2360950338953479286589870956639e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0093
y[1] (analytic) = 2.0000432453116892360988648655442
y[1] (numeric) = 2.0000432453116892360988693864421
absolute error = 4.5208979e-24
relative error = 2.2604000741471255675830474009762e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0094
y[1] (analytic) = 2.0000441803253130248206521847644
y[1] (numeric) = 2.0000441803253130248206567542755
absolute error = 4.5695111e-24
relative error = 2.2847050804931497460429408259276e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0095
y[1] (analytic) = 2.0000451253393786251292712576799
y[1] (numeric) = 2.0000451253393786251292758758043
absolute error = 4.6181244e-24
relative error = 2.3090101025677464782105656695730e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0096
y[1] (analytic) = 2.0000460803538954871653859624943
y[1] (numeric) = 2.0000460803538954871653906292319
absolute error = 4.6667376e-24
relative error = 2.3333150400086033703812630518767e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0097
y[1] (analytic) = 2.0000470453688731610741728780228
y[1] (numeric) = 2.0000470453688731610741775933738
absolute error = 4.7153510e-24
relative error = 2.3576200424477201446681389582815e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0098
y[1] (analytic) = 2.0000480203843212970054167851449
y[1] (numeric) = 2.0000480203843212970054215491093
absolute error = 4.7639644e-24
relative error = 2.3819250095228091028387179816341e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.0099
y[1] (analytic) = 2.0000490054002496451136071683018
y[1] (numeric) = 2.0000490054002496451136119808796
absolute error = 4.8125778e-24
relative error = 2.4062299408693275093553598718580e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.01
y[1] (analytic) = 2.0000500004166680555580357170414
y[1] (numeric) = 2.0000500004166680555580405782327
absolute error = 4.8611913e-24
relative error = 2.4305348861214838404208842561571e-22 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = sinh ( x ) ;
Iterations = 100
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Expected Time Remaining = 18 Minutes 8 Seconds
Optimized Time Remaining = 18 Minutes 2 Seconds
Time to Timeout = 14 Minutes 58 Seconds
Percent Done = 0.101 %
> quit
memory used=18.5MB, alloc=4.1MB, time=1.15