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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> 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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
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
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> 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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
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
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> 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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
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
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> 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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
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
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> 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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
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
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> array_y_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cosh $eq_no = 1
> array_tmp1_g[1] := sinh(array_x[1]);
> array_tmp1[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 cosh $eq_no = 1
> array_tmp1_g[2] := att(1,array_tmp1,array_x,1);
> array_tmp1[2] := att(1,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[3] := att(2,array_tmp1,array_x,1);
> array_tmp1[3] := att(2,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[4] := att(3,array_tmp1,array_x,1);
> array_tmp1[4] := att(3,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[5] := att(4,array_tmp1,array_x,1);
> array_tmp1[5] := att(4,array_tmp1_g,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 cosh $eq_no = 1
> array_tmp1_g[kkk] := att(kkk-1,array_tmp1,array_x,1);
> array_tmp1[kkk] := att(kkk-1,array_tmp1_g,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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
array_y_higher_work, glob_last;
array_tmp1_g[1] := sinh(array_x[1]);
array_tmp1[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_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp1[2] := att(1, array_tmp1_g, 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_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp1[3] := att(2, array_tmp1_g, 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_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp1[4] := att(3, array_tmp1_g, 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_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp1[5] := att(4, array_tmp1_g, 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_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, 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 + sinh(x);
> end;
exact_soln_y := proc(x) 1.0 + sinh(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
> ALWAYS,
> DEBUGL,
> glob_iolevel,
> glob_max_terms,
> DEBUGMASSIVE,
> INFO,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_smallish_float,
> glob_small_float,
> glob_hmin,
> glob_html_log,
> glob_warned,
> hours_in_day,
> glob_look_poles,
> glob_large_float,
> glob_max_opt_iter,
> glob_log10relerr,
> glob_current_iter,
> glob_curr_iter_when_opt,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_hmax,
> years_in_century,
> glob_display_flag,
> glob_log10abserr,
> glob_initial_pass,
> min_in_hour,
> glob_normmax,
> glob_optimal_start,
> glob_hmin_init,
> glob_h,
> days_in_year,
> glob_percent_done,
> glob_max_rel_trunc_err,
> glob_max_iter,
> glob_max_hours,
> glob_relerr,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_almost_1,
> djd_debug,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_max_sec,
> glob_warned2,
> glob_disp_incr,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_last_good_h,
> sec_in_min,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_iter,
> glob_start,
> glob_log10_abserr,
> glob_clock_sec,
> djd_debug2,
> glob_dump,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_1,
> #END CONST
> array_m1,
> array_type_pole,
> array_1st_rel_error,
> array_pole,
> array_y,
> array_x,
> array_last_rel_error,
> array_tmp1_g,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_y_init,
> array_norms,
> array_complex_pole,
> array_real_pole,
> array_y_higher,
> array_poles,
> array_y_higher_work2,
> array_y_set_initial,
> array_y_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> ALWAYS := 1;
> DEBUGL := 3;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> INFO := 2;
> MAX_UNCHANGED := 10;
> glob_smallish_float := 0.1e-100;
> glob_small_float := 0.1e-50;
> glob_hmin := 0.00000000001;
> glob_html_log := true;
> glob_warned := false;
> hours_in_day := 24.0;
> glob_look_poles := false;
> glob_large_float := 9.0e100;
> glob_max_opt_iter := 10;
> glob_log10relerr := 0.0;
> glob_current_iter := 0;
> glob_curr_iter_when_opt := 0;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_hmax := 1.0;
> years_in_century := 100.0;
> glob_display_flag := true;
> glob_log10abserr := 0.0;
> glob_initial_pass := true;
> min_in_hour := 60.0;
> glob_normmax := 0.0;
> glob_optimal_start := 0.0;
> glob_hmin_init := 0.001;
> glob_h := 0.1;
> days_in_year := 365.0;
> glob_percent_done := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_iter := 1000;
> glob_max_hours := 0.0;
> glob_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_almost_1 := 0.9990;
> djd_debug := true;
> glob_optimal_expect_sec := 0.1;
> glob_max_minutes := 0.0;
> glob_max_sec := 10000.0;
> glob_warned2 := false;
> glob_disp_incr := 0.1;
> glob_optimal_done := false;
> glob_not_yet_finished := true;
> glob_log10normmin := 0.1;
> glob_orig_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_last_good_h := 0.1;
> sec_in_min := 60.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_reached_optimal_h := false;
> glob_not_yet_start_msg := true;
> glob_clock_start_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_subiter_method := 3;
> glob_iter := 0;
> glob_start := 0;
> glob_log10_abserr := 0.1e-10;
> glob_clock_sec := 0.0;
> djd_debug2 := true;
> glob_dump := false;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/coshpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cosh ( 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 := 0.1;");
> omniout_str(ALWAYS,"x_end := 2.0 ;");
> 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 := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"1.0 + sinh(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_type_pole:= Array(1..(max_terms + 1),[]);
> array_1st_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_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_y_init:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]);
> array_y_higher := Array(1..(2+ 1) ,(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_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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 <=1 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=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_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_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_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_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 := 0.1;
> x_end := 2.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := 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 ) = cosh ( x ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 2
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T01:29:51-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cosh")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cosh ( 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,"cosh diffeq.mxt")
> ;
> logitem_str(html_log_file,"cosh 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 ALWAYS, DEBUGL, glob_iolevel, glob_max_terms, DEBUGMASSIVE, INFO,
MAX_UNCHANGED, glob_smallish_float, glob_small_float, glob_hmin,
glob_html_log, glob_warned, hours_in_day, glob_look_poles, glob_large_float,
glob_max_opt_iter, glob_log10relerr, glob_current_iter,
glob_curr_iter_when_opt, glob_unchanged_h_cnt, glob_no_eqs, glob_hmax,
years_in_century, glob_display_flag, glob_log10abserr, glob_initial_pass,
min_in_hour, glob_normmax, glob_optimal_start, glob_hmin_init, glob_h,
days_in_year, glob_percent_done, glob_max_rel_trunc_err, glob_max_iter,
glob_max_hours, glob_relerr, glob_abserr, glob_log10_relerr,
glob_dump_analytic, glob_almost_1, djd_debug, glob_optimal_expect_sec,
glob_max_minutes, glob_max_sec, glob_warned2, glob_disp_incr,
glob_optimal_done, glob_not_yet_finished, glob_log10normmin,
glob_orig_start_sec, glob_max_trunc_err, glob_last_good_h, sec_in_min,
glob_optimal_clock_start_sec, glob_reached_optimal_h,
glob_not_yet_start_msg, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_iter, glob_start, glob_log10_abserr,
glob_clock_sec, djd_debug2, glob_dump, array_const_0D0, array_const_1,
array_m1, array_type_pole, array_1st_rel_error, array_pole, array_y,
array_x, array_last_rel_error, array_tmp1_g, array_tmp0, array_tmp1,
array_tmp2, array_y_init, array_norms, array_complex_pole, array_real_pole,
array_y_higher, array_poles, array_y_higher_work2, array_y_set_initial,
array_y_higher_work, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
ALWAYS := 1;
DEBUGL := 3;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
INFO := 2;
MAX_UNCHANGED := 10;
glob_smallish_float := 0.1*10^(-100);
glob_small_float := 0.1*10^(-50);
glob_hmin := 0.1*10^(-10);
glob_html_log := true;
glob_warned := false;
hours_in_day := 24.0;
glob_look_poles := false;
glob_large_float := 0.90*10^101;
glob_max_opt_iter := 10;
glob_log10relerr := 0.;
glob_current_iter := 0;
glob_curr_iter_when_opt := 0;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_hmax := 1.0;
years_in_century := 100.0;
glob_display_flag := true;
glob_log10abserr := 0.;
glob_initial_pass := true;
min_in_hour := 60.0;
glob_normmax := 0.;
glob_optimal_start := 0.;
glob_hmin_init := 0.001;
glob_h := 0.1;
days_in_year := 365.0;
glob_percent_done := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_iter := 1000;
glob_max_hours := 0.;
glob_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_almost_1 := 0.9990;
djd_debug := true;
glob_optimal_expect_sec := 0.1;
glob_max_minutes := 0.;
glob_max_sec := 10000.0;
glob_warned2 := false;
glob_disp_incr := 0.1;
glob_optimal_done := false;
glob_not_yet_finished := true;
glob_log10normmin := 0.1;
glob_orig_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_last_good_h := 0.1;
sec_in_min := 60.0;
glob_optimal_clock_start_sec := 0.;
glob_reached_optimal_h := false;
glob_not_yet_start_msg := true;
glob_clock_start_sec := 0.;
centuries_in_millinium := 10.0;
glob_subiter_method := 3;
glob_iter := 0;
glob_start := 0;
glob_log10_abserr := 0.1*10^(-10);
glob_clock_sec := 0.;
djd_debug2 := true;
glob_dump := false;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/coshpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh ( 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 := 0.1;");
omniout_str(ALWAYS, "x_end := 2.0 ;");
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 := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "1.0 +\t\tsinh(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_type_pole := Array(1 .. max_terms + 1, []);
array_1st_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_last_rel_error := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_y_init := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 2, 1 .. 4, []);
array_real_pole := Array(1 .. 2, 1 .. 4, []);
array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 2, 1 .. 4, []);
array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []);
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_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 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_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_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_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_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 := 0.1;
x_end := 2.0;
array_y_init[1] := exact_soln_y(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 100;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := 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 ) = cosh ( x ) ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T01:29:51-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "cosh");
logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh ( 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,
"cosh diffeq.mxt");
logitem_str(html_log_file,
"cosh 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/coshpostode.ode#################
diff ( y , x , 1 ) = cosh ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 2.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
1.0 + sinh(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y[1] (analytic) = 1.1001667500198440258237293835219
y[1] (numeric) = 1.1001667500198440258237293835219
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1001
y[1] (analytic) = 1.1002672509376508573949694866538
y[1] (numeric) = 1.100267250937650857394969491524
absolute error = 4.8702e-27
relative error = 4.4263791327512491269921828487192e-25 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1002
y[1] (analytic) = 1.1003677528581301991782785884944
y[1] (numeric) = 1.1003677528581301991782785982396
absolute error = 9.7452e-27
relative error = 8.8563118781766437335536548647111e-25 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1003
y[1] (analytic) = 1.100468255782287070379287622881
y[1] (numeric) = 1.1004682557822870703792876375061
absolute error = 1.46251e-26
relative error = 1.3289888120946744035061761876105e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1004
y[1] (analytic) = 1.1005687597111265002404028261919
y[1] (numeric) = 1.1005687597111265002404028457019
absolute error = 1.95100e-26
relative error = 1.7727197712863408592703630286098e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1005
y[1] (analytic) = 1.100669264645653528050856029779
y[1] (numeric) = 1.1006692646456535280508560541786
absolute error = 2.43996e-26
relative error = 2.2167967057620293337756275830067e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1006
y[1] (analytic) = 1.100769770586873203156755052868
y[1] (numeric) = 1.1007697705868732031567550821622
absolute error = 2.92942e-26
relative error = 2.6612467731905333681420895800343e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1007
y[1] (analytic) = 1.1008702775357905849711341960284
y[1] (numeric) = 1.1008702775357905849711342302221
absolute error = 3.41937e-26
relative error = 3.1060607864297910136807891608987e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1008
y[1] (analytic) = 1.1009707854934107429840048353119
y[1] (numeric) = 1.10097078549341074298400487441
absolute error = 3.90981e-26
relative error = 3.5512386445820001498616378168450e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1009
y[1] (analytic) = 1.1010712944607387567724061171611
y[1] (numeric) = 1.1010712944607387567724061611684
absolute error = 4.40073e-26
relative error = 3.9967711647185423966413724246238e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.101
y[1] (analytic) = 1.1011718044387797160104557541879
y[1] (numeric) = 1.1011718044387797160104558031093
absolute error = 4.89214e-26
relative error = 4.4426673297300006881870183663177e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1011
y[1] (analytic) = 1.1012723154285387204794009219234
y[1] (numeric) = 1.1012723154285387204794009757639
absolute error = 5.38405e-26
relative error = 4.8889361192239737461866826414455e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1012
y[1] (analytic) = 1.1013728274310208800776692566388
y[1] (numeric) = 1.1013728274310208800776693154032
absolute error = 5.87644e-26
relative error = 5.3355592707938331471073008559397e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1013
y[1] (analytic) = 1.1014733404472313148309199543376
y[1] (numeric) = 1.1014733404472313148309200180308
absolute error = 6.36932e-26
relative error = 5.7825457649423130427059465104714e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1014
y[1] (analytic) = 1.1015738544781751549020949710211
y[1] (numeric) = 1.101573854478175154902095039648
absolute error = 6.86269e-26
relative error = 6.2298955009702134359115822292001e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.20
NO POLE
x[1] = 0.1015
y[1] (analytic) = 1.1016743695248575406014703243258
y[1] (numeric) = 1.1016743695248575406014703978913
absolute error = 7.35655e-26
relative error = 6.6776083782114448825051753220549e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1016
y[1] (analytic) = 1.1017748855882836223967074966348
y[1] (numeric) = 1.1017748855882836223967075751437
absolute error = 7.85089e-26
relative error = 7.1256752197687660757414846248061e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1017
y[1] (analytic) = 1.1018754026694585609229049397626
y[1] (numeric) = 1.1018754026694585609229050232198
absolute error = 8.34572e-26
relative error = 7.5741050029624407247070842378579e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1018
y[1] (analytic) = 1.1019759207693875269926496813146
y[1] (numeric) = 1.101975920769387526992649769725
absolute error = 8.84104e-26
relative error = 8.0228976272251780558635285222974e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1019
y[1] (analytic) = 1.1020764398890757016060690328212
y[1] (numeric) = 1.1020764398890757016060691261898
absolute error = 9.33686e-26
relative error = 8.4720620658034913990168319839645e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.102
y[1] (analytic) = 1.1021769600295282759608823997477
y[1] (numeric) = 1.1021769600295282759608824980793
absolute error = 9.83316e-26
relative error = 8.9215800698070853537816903010816e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1021
y[1] (analytic) = 1.1022774811917504514624531934796
y[1] (numeric) = 1.1022774811917504514624532967791
absolute error = 1.032995e-25
relative error = 9.3714606133761868954687623178519e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1022
y[1] (analytic) = 1.1023780033767474397338408453848
y[1] (numeric) = 1.102378003376747439733840953657
absolute error = 1.082722e-25
relative error = 9.8216945247769985972247154129901e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1023
y[1] (analytic) = 1.1024785265855244626258529230522
y[1] (numeric) = 1.1024785265855244626258530363021
absolute error = 1.132499e-25
relative error = 1.0272299847031503225973262984741e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1024
y[1] (analytic) = 1.102579050819086752227097348809
y[1] (numeric) = 1.1025790508190867522270974670414
absolute error = 1.182324e-25
relative error = 1.0723258338000092741318966945418e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1025
y[1] (analytic) = 1.102679576078439550874034720614
y[1] (numeric) = 1.1026795760784395508740348438339
absolute error = 1.232199e-25
relative error = 1.1174588037462181428069821630091e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1026
y[1] (analytic) = 1.1027801023645881111610307354315
y[1] (numeric) = 1.1027801023645881111610308636438
absolute error = 1.282123e-25
relative error = 1.1626279774642865851358336765840e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1027
y[1] (analytic) = 1.1028806296785376959504087151832
y[1] (numeric) = 1.1028806296785376959504088483926
absolute error = 1.332094e-25
relative error = 1.2078315314942763180253664854864e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1028
y[1] (analytic) = 1.1029811580212935783825022353791
y[1] (numeric) = 1.1029811580212935783825023735907
absolute error = 1.382116e-25
relative error = 1.2530730828434673859510018122592e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1029
y[1] (analytic) = 1.1030816873938610418857078565303
y[1] (numeric) = 1.1030816873938610418857079997488
absolute error = 1.432185e-25
relative error = 1.2983489947908372013254349108055e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.103
y[1] (analytic) = 1.1031822177972453801865379584404
y[1] (numeric) = 1.1031822177972453801865381066708
absolute error = 1.482304e-25
relative error = 1.3436619772205516762137999302273e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1031
y[1] (analytic) = 1.1032827492324518973196736774795
y[1] (numeric) = 1.1032827492324518973196738307267
absolute error = 1.532472e-25
relative error = 1.3890111134848549429030661813101e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1032
y[1] (analytic) = 1.1033832817004859076380179469394
y[1] (numeric) = 1.1033832817004859076380181052082
absolute error = 1.582688e-25
relative error = 1.4343954872696917139421591274428e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1033
y[1] (analytic) = 1.1034838152023527358227486405706
y[1] (numeric) = 1.103483815202352735822748803866
absolute error = 1.632954e-25
relative error = 1.4798169012570021260474068104849e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1034
y[1] (analytic) = 1.1035843497390577168933718194031
y[1] (numeric) = 1.1035843497390577168933719877299
absolute error = 1.683268e-25
relative error = 1.5252735329184473828773056220225e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1035
y[1] (analytic) = 1.1036848853116061962177750819492
y[1] (numeric) = 1.1036848853116061962177752553123
absolute error = 1.733631e-25
relative error = 1.5707662785565279303357046568819e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1036
y[1] (analytic) = 1.1037854219210035295222810178911
y[1] (numeric) = 1.1037854219210035295222811962954
absolute error = 1.784043e-25
relative error = 1.6162951281736366421915379357261e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.0MB, time=0.44
NO POLE
x[1] = 0.1037
y[1] (analytic) = 1.1038859595682550829017007653524
y[1] (numeric) = 1.1038859595682550829017009488028
absolute error = 1.834504e-25
relative error = 1.6618600717754392300792199822670e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1038
y[1] (analytic) = 1.1039864982543662328293876718548
y[1] (numeric) = 1.1039864982543662328293878603562
absolute error = 1.885014e-25
relative error = 1.7074610993708725162780989025213e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1039
y[1] (analytic) = 1.1040870379803423661672910590597
y[1] (numeric) = 1.1040870379803423661672912526169
absolute error = 1.935572e-25
relative error = 1.7530972952464475402192586037672e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.104
y[1] (analytic) = 1.1041875787471888801760100913961
y[1] (numeric) = 1.1041875787471888801760102900141
absolute error = 1.986180e-25
relative error = 1.7987704609514985085151576862498e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1041
y[1] (analytic) = 1.1042881205559111825248477486752
y[1] (numeric) = 1.1042881205559111825248479523589
absolute error = 2.036837e-25
relative error = 1.8444796806965858869883589332728e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1042
y[1] (analytic) = 1.1043886634075146913018649027918
y[1] (numeric) = 1.104388663407514691301865111546
absolute error = 2.087542e-25
relative error = 1.8902240390253860603467690275149e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1043
y[1] (analytic) = 1.104489207303004835023934498613
y[1] (numeric) = 1.1044892073030048350239347124426
absolute error = 2.138296e-25
relative error = 1.9360044316063482335101825700047e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1044
y[1] (analytic) = 1.1045897522433870526467958391554
y[1] (numeric) = 1.1045897522433870526467960580654
absolute error = 2.189100e-25
relative error = 1.9818217537814439586397959251662e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1045
y[1] (analytic) = 1.1046902982296667935751089751513
y[1] (numeric) = 1.1046902982296667935751091991464
absolute error = 2.239951e-25
relative error = 2.0276732796419569708637981108269e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1046
y[1] (analytic) = 1.1047908452628495176725091991029
y[1] (numeric) = 1.1047908452628495176725094281881
absolute error = 2.290852e-25
relative error = 2.0735617151633486818992719789466e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1047
y[1] (analytic) = 1.1048913933439406952716616439278
y[1] (numeric) = 1.1048913933439406952716618781079
absolute error = 2.341801e-25
relative error = 2.1194852400040578223012546403258e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1048
y[1] (analytic) = 1.1049919424739458071843159862935
y[1] (numeric) = 1.1049919424739458071843162255734
absolute error = 2.392799e-25
relative error = 2.1654447494366402721832813565213e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1049
y[1] (analytic) = 1.1050924926538703447113612547435
y[1] (numeric) = 1.1050924926538703447113614991282
absolute error = 2.443847e-25
relative error = 2.2114411384074485418914930667561e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.105
y[1] (analytic) = 1.1051930438847198096528807427147
y[1] (numeric) = 1.105193043884719809652880992209
absolute error = 2.494943e-25
relative error = 2.2574725870788613735989591442822e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1051
y[1] (analytic) = 1.1052935961674997143182070265462
y[1] (numeric) = 1.105293596167499714318207281155
absolute error = 2.546088e-25
relative error = 2.3035399904860732674262390242060e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1052
y[1] (analytic) = 1.1053941495032155815359770885814
y[1] (numeric) = 1.1053941495032155815359773483096
absolute error = 2.597282e-25
relative error = 2.3496433386835512017191091636684e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1053
y[1] (analytic) = 1.1054947038928729446641875454627
y[1] (numeric) = 1.1054947038928729446641878103151
absolute error = 2.648524e-25
relative error = 2.3957817171566052482747700553608e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1054
y[1] (analytic) = 1.1055952593374773476002499817194
y[1] (numeric) = 1.105595259337477347600250251701
absolute error = 2.699816e-25
relative error = 2.4419569251932680853977086605555e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1055
y[1] (analytic) = 1.105695815838034344791046388751
y[1] (numeric) = 1.1056958158380343447910466638666
absolute error = 2.751156e-25
relative error = 2.4881671437951770468797510095000e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1056
y[1] (analytic) = 1.1057963733955495012429847093035
y[1] (numeric) = 1.1057963733955495012429849895581
absolute error = 2.802546e-25
relative error = 2.5344141719277584738025027296941e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1057
y[1] (analytic) = 1.1058969320110283925320544875428
y[1] (numeric) = 1.1058969320110283925320547729411
absolute error = 2.853983e-25
relative error = 2.5806952866847623005909718471496e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1058
y[1] (analytic) = 1.1059974916854766048138826248219
y[1] (numeric) = 1.105997491685476604813882915369
absolute error = 2.905471e-25
relative error = 2.6270140952781268987259718934310e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.1MB, time=0.68
x[1] = 0.1059
y[1] (analytic) = 1.1060980524198997348337892412466
y[1] (numeric) = 1.1060980524198997348337895369473
absolute error = 2.957007e-25
relative error = 2.6733678750547637147012479402225e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.106
y[1] (analytic) = 1.1061986142153033899368436431364
y[1] (numeric) = 1.1061986142153033899368439439956
absolute error = 3.008592e-25
relative error = 2.7197575203384109339201505772732e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1061
y[1] (analytic) = 1.1062991770726931880779203964839
y[1] (numeric) = 1.1062991770726931880779207025064
absolute error = 3.060225e-25
relative error = 2.7661821172980203736420884507487e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1062
y[1] (analytic) = 1.1063997409930747578317555065116
y[1] (numeric) = 1.1063997409930747578317558177024
absolute error = 3.111908e-25
relative error = 2.8126434639317926567741827685358e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1063
y[1] (analytic) = 1.106500305977453738403002703428
y[1] (numeric) = 1.106500305977453738403003019792
absolute error = 3.163640e-25
relative error = 2.8591406463329644419952206914192e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1064
y[1] (analytic) = 1.1066008720268357796362898344824
y[1] (numeric) = 1.1066008720268357796362901560245
absolute error = 3.215421e-25
relative error = 2.9056736545947923147039786628234e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1065
y[1] (analytic) = 1.1067014391422265420262753624195
y[1] (numeric) = 1.1067014391422265420262756891445
absolute error = 3.267250e-25
relative error = 2.9522415752276914582824188086255e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1066
y[1] (analytic) = 1.1068020073246316967277049704342
y[1] (numeric) = 1.1068020073246316967277053023471
absolute error = 3.319129e-25
relative error = 2.9988462055856025097136509752619e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1067
y[1] (analytic) = 1.106902576575056925565468273728
y[1] (numeric) = 1.1069025765750569255654686108336
absolute error = 3.371056e-25
relative error = 3.0454857286813942151409064751039e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1068
y[1] (analytic) = 1.1070031468945079210446556377655
y[1] (numeric) = 1.1070031468945079210446559800687
absolute error = 3.423032e-25
relative error = 3.0921610382072369089527054715195e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1069
y[1] (analytic) = 1.1071037182839903863606151033344
y[1] (numeric) = 1.1071037182839903863606154508401
absolute error = 3.475057e-25
relative error = 3.1388721242724527573949503047488e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.107
y[1] (analytic) = 1.1072042907445100354090094185068
y[1] (numeric) = 1.1072042907445100354090097712199
absolute error = 3.527131e-25
relative error = 3.1856189769895803986108788807458e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1071
y[1] (analytic) = 1.1073048642770725927958731776047
y[1] (numeric) = 1.1073048642770725927958735355301
absolute error = 3.579254e-25
relative error = 3.2324015864743732503626494862256e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1072
y[1] (analytic) = 1.1074054388826837938476700672684
y[1] (numeric) = 1.1074054388826837938476704304109
absolute error = 3.631425e-25
relative error = 3.2792190398341591826837953974169e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1073
y[1] (analytic) = 1.1075060145623493846213502197295
y[1] (numeric) = 1.107506014562349384621350588094
absolute error = 3.683645e-25
relative error = 3.3260722303667646973581924650326e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1074
y[1] (analytic) = 1.1076065913170751219144076733889
y[1] (numeric) = 1.1076065913170751219144080469804
absolute error = 3.735915e-25
relative error = 3.3729620510451780495518734340454e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1075
y[1] (analytic) = 1.1077071691478667732749379408003
y[1] (numeric) = 1.1077071691478667732749383196236
absolute error = 3.788233e-25
relative error = 3.4198866862206905070076569357449e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1076
y[1] (analytic) = 1.1078077480557301170116956841592
y[1] (numeric) = 1.1078077480557301170116960682192
absolute error = 3.840600e-25
relative error = 3.4668470289546956746999618154599e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1077
y[1] (analytic) = 1.1079083280416709422041524983988
y[1] (numeric) = 1.1079083280416709422041528877005
absolute error = 3.893017e-25
relative error = 3.5138439719839120217616495354514e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1078
y[1] (analytic) = 1.1080089091066950487125548019937
y[1] (numeric) = 1.1080089091066950487125551965419
absolute error = 3.945482e-25
relative error = 3.5608757001610644934913267350664e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1079
y[1] (analytic) = 1.10810949125180824718798183557
y[1] (numeric) = 1.1081094912518082471879822353695
absolute error = 3.997995e-25
relative error = 3.6079422038733268079978148732465e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.108
y[1] (analytic) = 1.1082100744780163590824037684248
y[1] (numeric) = 1.1082100744780163590824041734806
absolute error = 4.050558e-25
relative error = 3.6550452782229703533831296112383e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1081
y[1] (analytic) = 1.1083106587863252166587399130543
y[1] (numeric) = 1.1083106587863252166587403233713
absolute error = 4.103170e-25
relative error = 3.7021840108379426552147548031901e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.93
NO POLE
x[1] = 0.1082
y[1] (analytic) = 1.1084112441777406630009170477914
y[1] (numeric) = 1.1084112441777406630009174633745
absolute error = 4.155831e-25
relative error = 3.7493583918692064022413644009816e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1083
y[1] (analytic) = 1.1085118306532685520239278476534
y[1] (numeric) = 1.1085118306532685520239282685074
absolute error = 4.208540e-25
relative error = 3.7965675093605648218467219100045e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1084
y[1] (analytic) = 1.1086124182139147484838894235
y[1] (numeric) = 1.1086124182139147484838898496298
absolute error = 4.261298e-25
relative error = 3.8438122557434241802741143093940e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1085
y[1] (analytic) = 1.1087130068606851279881019696032
y[1] (numeric) = 1.1087130068606851279881024010137
absolute error = 4.314105e-25
relative error = 3.8910926211782839402603792620614e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1086
y[1] (analytic) = 1.1088135965945855770051075197284
y[1] (numeric) = 1.1088135965945855770051079564245
absolute error = 4.366961e-25
relative error = 3.9384085958288331202670768535089e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1087
y[1] (analytic) = 1.1089141874166219928747488118284
y[1] (numeric) = 1.1089141874166219928747492538151
absolute error = 4.419867e-25
relative error = 3.9857610716449822814005291497500e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1088
y[1] (analytic) = 1.1090147793278002838182282614504
y[1] (numeric) = 1.1090147793278002838182287087324
absolute error = 4.472820e-25
relative error = 4.0331473334476935400832161146910e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1089
y[1] (analytic) = 1.1091153723291263689481670439558
y[1] (numeric) = 1.1091153723291263689481674965381
absolute error = 4.525823e-25
relative error = 4.0805700767593155199706881399266e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.109
y[1] (analytic) = 1.1092159664216061782786642856553
y[1] (numeric) = 1.1092159664216061782786647435428
absolute error = 4.578875e-25
relative error = 4.1280283899732450539551218000480e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1091
y[1] (analytic) = 1.1093165616062456527353563639582
y[1] (numeric) = 1.1093165616062456527353568271558
absolute error = 4.631976e-25
relative error = 4.1755222632690938254129388168571e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1092
y[1] (analytic) = 1.1094171578840507441654763166371
y[1] (numeric) = 1.1094171578840507441654767851496
absolute error = 4.685125e-25
relative error = 4.2230507854554558781440451106337e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1093
y[1] (analytic) = 1.1095177552560274153479133603084
y[1] (numeric) = 1.1095177552560274153479138341408
absolute error = 4.738324e-25
relative error = 4.2706157495484200590363930849754e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1094
y[1] (analytic) = 1.10961835372318164000327251823
y[1] (numeric) = 1.1096183537231816400032729973871
absolute error = 4.791571e-25
relative error = 4.3182153430704349086329764490028e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1095
y[1] (analytic) = 1.1097189532865194028039343575153
y[1] (numeric) = 1.109718953286519402803934842002
absolute error = 4.844867e-25
relative error = 4.3658504575879755512841184213122e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1096
y[1] (analytic) = 1.1098195539470466993841148358658
y[1] (numeric) = 1.1098195539470466993841153256869
absolute error = 4.898211e-25
relative error = 4.4135201822491140401955051625976e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1097
y[1] (analytic) = 1.1099201557057695363499252579211
y[1] (numeric) = 1.1099201557057695363499257530817
absolute error = 4.951606e-25
relative error = 4.4612272103946087366691043940702e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1098
y[1] (analytic) = 1.1100207585636939312894323413291
y[1] (numeric) = 1.110020758563693931289432841834
absolute error = 5.005049e-25
relative error = 4.5089688290841148708248451995413e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.1099
y[1] (analytic) = 1.1101213625218259127827183926345
y[1] (numeric) = 1.1101213625218259127827188984886
absolute error = 5.058541e-25
relative error = 4.5567459295699706533376424174892e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
x[1] = 0.11
y[1] (analytic) = 1.1102219675811715204119415930882
y[1] (numeric) = 1.1102219675811715204119421042964
absolute error = 5.112082e-25
relative error = 4.6045585020603017257105687853892e-23 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y , x , 1 ) = cosh ( x ) ;
Iterations = 100
Total Elapsed Time = 1 Seconds
Elapsed Time(since restart) = 1 Seconds
Expected Time Remaining = 3 Minutes 22 Seconds
Optimized Time Remaining = 3 Minutes 21 Seconds
Time to Timeout = 14 Minutes 58 Seconds
Percent Done = 0.5316 %
> quit
memory used=18.4MB, alloc=4.1MB, time=1.12