|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
>
> display_alot := proc(iter)
> global
> ALWAYS,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_higher_work,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
#TOP DISPLAY ALOT
> if (iter >= 0) then
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;;
> if glob_iter = 1 then
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;;
> if glob_iter = 1 then
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;;
> 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;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global ALWAYS, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_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_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[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, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[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[2] := relerr
else array_last_rel_error[2] := 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
> adjust_for_pole := proc(h_param)
> global
> ALWAYS,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_higher_work,
> glob_last;
>
> local hnew, sz2, tmp;
#TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_y2_higher[1,1]) > glob_small_float) then
> tmp := abs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then
> glob_normmax := tmp;
> fi;
> fi;;
> if (abs(array_y1_higher[1,1]) > glob_small_float) then
> tmp := abs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then
> glob_normmax := tmp;
> fi;
> fi;;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) 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);
> fi;
> fi;;
> 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];
> fi;;
> hnew := sz2;
> #END block
#BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global ALWAYS, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_higher_work, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(array_y1_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
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_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
> 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;;
> 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;
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, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_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
> check_for_pole := proc()
> global
> ALWAYS,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_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_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_higher[1,m-2]) < glob_small_float ))) do
> m := m - 1;
> od;;
> if (m > 10) then
> rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) 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;
> fi;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;;
#BOTTOM RADII REAL EQ = 1
#IN RADII REAL EQ = 2
#Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
#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_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(array_y1_higher[1,m-2]) < glob_small_float ))) do
> m := m - 1;
> od;;
> if (m > 10) then
> rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;;
#BOTTOM RADII REAL EQ = 2
#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
> if (abs(array_y2_higher[1,n]) > glob_small_float) then
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;;
> n := n - 1;
> od;;
> m := n + cnt;
> if (m <= 10) then
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-5]) >= (glob_large_float)) then
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_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
> 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
> 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 (rcs > 0.0) then
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;
> fi;;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;;
#BOTTOM RADII COMPLEX EQ = 1
#TOP RADII COMPLEX EQ = 2
#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
> if (abs(array_y1_higher[1,n]) > glob_small_float) then
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;;
> n := n - 1;
> od;;
> m := n + cnt;
> if (m <= 10) then
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_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
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then
> 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 (rcs > 0.0) then
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;
> fi;;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;;
#BOTTOM RADII COMPLEX EQ = 2
> 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
> 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");
> fi;;
> fi;;
> 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
> 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");
> fi;;
> fi;;
> 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");
> fi;;
> fi;;
> 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
> 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");
> fi;;
> fi;;
> 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
> 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");
> fi;;
> fi;;
> 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");
> fi;;
> fi;;
#BOTTOM WHICH RADII EQ = 1
> found := false;
#TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;;
> fi;;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;;
> fi;;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then
> omniout_str(ALWAYS,"NO POLE");
> fi;;
> fi;;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;;
> fi;;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;;
> fi;;
> if not found then
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then
> omniout_str(ALWAYS,"NO POLE");
> fi;;
> fi;;
#BOTTOM WHICH RADII EQ = 2
> 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
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;;
#BOTTOM WHICH RADIUS EQ = 1
#TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;;
#BOTTOM WHICH RADIUS EQ = 2
#BOTTOM CHECK FOR POLE
> display_pole();
> 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, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_higher_work, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or
abs(array_y2_higher[1, m - 1]) < glob_small_float or
abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_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;
m := n - 2;
while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or
abs(array_y1_higher[1, m - 1]) < glob_small_float or
abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_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[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 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_y2_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_y2_higher[1, m]) or
glob_large_float <= abs(array_y2_higher[1, m - 1]) or
glob_large_float <= abs(array_y2_higher[1, m - 2]) or
glob_large_float <= abs(array_y2_higher[1, m - 3]) or
glob_large_float <= abs(array_y2_higher[1, m - 4]) or
glob_large_float <= abs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_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;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y1_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[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_y1_higher[1, m]) or
glob_large_float <= abs(array_y1_higher[1, m - 1]) or
glob_large_float <= abs(array_y1_higher[1, m - 2]) or
glob_large_float <= abs(array_y1_higher[1, m - 3]) or
glob_large_float <= abs(array_y1_higher[1, m - 4]) or
glob_large_float <= abs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_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[2, 1] := glob_large_float;
array_complex_pole[2, 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[2, 1] := rad_c;
array_complex_pole[2, 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;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 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[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 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[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 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;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> get_norms := proc()
> global
> ALWAYS,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_higher_work,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then
> set_z(array_norms,glob_max_terms+1);
#TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do
> if (abs(array_y2[iii]) > array_norms[iii]) then
> array_norms[iii] := abs(array_y2[iii]);
> fi;;
> iii := iii + 1;
> od;
> ;
> iii := 1;
> while (iii <= glob_max_terms) do
> if (abs(array_y1[iii]) > array_norms[iii]) then
> array_norms[iii] := abs(array_y1[iii]);
> fi;;
> iii := iii + 1;
> od;
#GET NORMS
> ;
> fi;;
> end;
get_norms := proc()
local iii;
global ALWAYS, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_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_y2[iii]) then
array_norms[iii] := abs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_y1[iii]) then
array_norms[iii] := abs(array_y1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> atomall := proc()
> global
> ALWAYS,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_higher_work,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
#TOP ATOMALL
#END OUTFILE1
#BEGIN ATOMHDR1
#emit pre add $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D0[1] + array_y1[1];
#emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then
> temporary := array_tmp1[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,1] := temporary
> ;
> fi;;
> kkk := 2;
# emit pre mult $eq_no = 2 i = 1
> array_tmp3[1] := (array_m1[1] * (array_y2[1]));
#emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then
> temporary := array_tmp3[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,1] := temporary
> ;
> fi;;
> kkk := 2;
#END ATOMHDR1
#BEGIN ATOMHDR2
#emit pre add $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D0[2] + array_y1[2];
#emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then
> temporary := array_tmp1[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary
> ;
> fi;;
> kkk := 3;
# emit pre mult $eq_no = 2 i = 2
> array_tmp3[2] := ats(2,array_m1,array_y2,1);
#emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then
> temporary := array_tmp3[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary
> ;
> fi;;
> kkk := 3;
#END ATOMHDR2
#BEGIN ATOMHDR3
#emit pre add $eq_no = 1 i = 3
> array_tmp1[3] := array_const_0D0[3] + array_y1[3];
#emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then
> temporary := array_tmp1[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> fi;;
> kkk := 4;
# emit pre mult $eq_no = 2 i = 3
> array_tmp3[3] := ats(3,array_m1,array_y2,1);
#emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then
> temporary := array_tmp3[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,3] := temporary
> ;
> fi;;
> kkk := 4;
#END ATOMHDR3
#BEGIN ATOMHDR4
#emit pre add $eq_no = 1 i = 4
> array_tmp1[4] := array_const_0D0[4] + array_y1[4];
#emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then
> temporary := array_tmp1[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> fi;;
> kkk := 5;
# emit pre mult $eq_no = 2 i = 4
> array_tmp3[4] := ats(4,array_m1,array_y2,1);
#emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then
> temporary := array_tmp3[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,4] := temporary
> ;
> fi;;
> kkk := 5;
#END ATOMHDR4
#BEGIN ATOMHDR5
#emit pre add $eq_no = 1 i = 5
> array_tmp1[5] := array_const_0D0[5] + array_y1[5];
#emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then
> temporary := array_tmp1[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> fi;;
> kkk := 6;
# emit pre mult $eq_no = 2 i = 5
> array_tmp3[5] := ats(5,array_m1,array_y2,1);
#emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then
> temporary := array_tmp3[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,5] := temporary
> ;
> fi;;
> kkk := 6;
#END ATOMHDR5
#BEGIN OUTFILE3
#Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do
#END OUTFILE3
#BEGIN OUTFILE4
#emit add $eq_no = 1
> array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk];
#emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then
> temporary := array_tmp1[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do
> temporary := temporary / glob_h * convfp(adj2);
> array_y2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;
> fi;;
#emit mult $eq_no = 2
> array_tmp3[kkk] := ats(kkk,array_m1,array_y2,1);
#emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then
> temporary := array_tmp3[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y1[kkk + order_d] := temporary;
> array_y1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do
> temporary := temporary / glob_h * convfp(adj2);
> array_y1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;
> fi;;
> kkk := kkk + 1;
> od;;
#BOTTOM ATOMALL
#END OUTFILE4
#BEGIN OUTFILE5
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global ALWAYS, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_higher_work, glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y1[1];
if 1 <= glob_max_terms then
temporary := array_tmp1[1]*glob_h*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp3[1] := array_m1[1]*array_y2[1];
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*glob_h*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_const_0D0[2] + array_y1[2];
if 2 <= glob_max_terms then
temporary := array_tmp1[2]*glob_h*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp3[2] := ats(2, array_m1, array_y2, 1);
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*glob_h*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_const_0D0[3] + array_y1[3];
if 3 <= glob_max_terms then
temporary := array_tmp1[3]*glob_h*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp3[3] := ats(3, array_m1, array_y2, 1);
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*glob_h*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_const_0D0[4] + array_y1[4];
if 4 <= glob_max_terms then
temporary := array_tmp1[4]*glob_h*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp3[4] := ats(4, array_m1, array_y2, 1);
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*glob_h*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_const_0D0[5] + array_y1[5];
if 5 <= glob_max_terms then
temporary := array_tmp1[5]*glob_h*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary
end if;
kkk := 6;
array_tmp3[5] := ats(5, array_m1, array_y2, 1);
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*glob_h*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp1[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_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_y2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp3[kkk] := ats(kkk, array_m1, array_y2, 1);
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp3[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_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_y1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
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;
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;
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;
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;
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;
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;
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;
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;
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;
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
> 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
> 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
> 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
> 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
> 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
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;
> else
> fprintf(fd,"Unknown");
> fi;
> fprintf(fd," | ");
> 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
> 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
> 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
> 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
> 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
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;
> else
> printf(" Unknown\n");
> fi;
> 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
>
> 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
> 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;
> od;
> fi;;
> ret_ats
> 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
>
> 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
> 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);
> fi;;
> iii_att := iii_att + 1;
> od;;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;;
> ret_att;
> 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
> 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
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;
> 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
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> 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");
> fi;
> fprintf(file," | ");
> 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
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> 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
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;;
> if (glob_max_iter < 2) then
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;;
> if (errflag) then
>
> quit;
> fi;
> 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
>
> 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
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;
> fi;;
> sec_left;
> 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
>
> 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
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;;
> rrr
> 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
>
> factorial_1 := proc(nnn)
> nnn!;
>
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> convfp := proc(mmm)
> (mmm);
>
> end;
convfp := proc(mmm) mmm end proc
> convfloat := proc(mmm)
> (mmm);
>
> 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
> exact_soln_y1 := proc(x)
> cos(x);
> end;
exact_soln_y1 := proc(x) cos(x) end proc
> exact_soln_y2 := proc(x)
> -sin(x);
> end;
exact_soln_y2 := proc(x) -sin(x) end proc
>
#END USER DEF BLOCK
#END OUTFILE5
> 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,
> glob_max_terms,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_start,
> glob_no_eqs,
> glob_max_iter,
> glob_log10normmin,
> glob_iter,
> glob_current_iter,
> hours_in_day,
> sec_in_min,
> glob_log10abserr,
> glob_orig_start_sec,
> glob_max_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_hmin,
> glob_optimal_done,
> glob_initial_pass,
> glob_clock_sec,
> min_in_hour,
> glob_small_float,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_dump_analytic,
> centuries_in_millinium,
> glob_dump,
> glob_normmax,
> glob_max_order,
> glob_curr_iter_when_opt,
> glob_max_sec,
> glob_warned2,
> glob_abserr,
> glob_hmax,
> glob_reached_optimal_h,
> years_in_century,
> djd_debug2,
> glob_display_flag,
> glob_max_hours,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_smallish_float,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_look_poles,
> glob_hmin_init,
> glob_not_yet_finished,
> days_in_year,
> glob_unchanged_h_cnt,
> glob_last_good_h,
> glob_almost_1,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_max_minutes,
> glob_log10relerr,
> glob_warned,
> glob_h,
> glob_html_log,
> glob_optimal_start,
> glob_clock_start_sec,
> djd_debug,
> glob_percent_done,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_0D0,
> array_const_1,
#END CONST
> array_x,
> array_last_rel_error,
> array_pole,
> array_y1_init,
> array_y2_init,
> array_norms,
> array_m1,
> array_type_pole,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_1st_rel_error,
> array_complex_pole,
> array_poles,
> array_y1_higher_work2,
> array_real_pole,
> array_y2_higher_work2,
> array_y2_higher_work,
> array_y2_higher,
> array_y1_higher,
> array_y1_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> ALWAYS := 1;
> glob_max_terms := 30;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> MAX_UNCHANGED := 10;
> glob_start := 0;
> glob_no_eqs := 0;
> glob_max_iter := 1000;
> glob_log10normmin := 0.1;
> glob_iter := 0;
> glob_current_iter := 0;
> hours_in_day := 24.0;
> sec_in_min := 60.0;
> glob_log10abserr := 0.0;
> glob_orig_start_sec := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> glob_initial_pass := true;
> glob_clock_sec := 0.0;
> min_in_hour := 60.0;
> glob_small_float := 0.1e-50;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> centuries_in_millinium := 10.0;
> glob_dump := false;
> glob_normmax := 0.0;
> glob_max_order := 30;
> glob_curr_iter_when_opt := 0;
> glob_max_sec := 10000.0;
> glob_warned2 := false;
> glob_abserr := 0.1e-10;
> glob_hmax := 1.0;
> glob_reached_optimal_h := false;
> years_in_century := 100.0;
> djd_debug2 := true;
> glob_display_flag := true;
> glob_max_hours := 0.0;
> glob_disp_incr := 0.1;
> glob_not_yet_start_msg := true;
> glob_smallish_float := 0.1e-100;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_look_poles := false;
> glob_hmin_init := 0.001;
> glob_not_yet_finished := true;
> days_in_year := 365.0;
> glob_unchanged_h_cnt := 0;
> glob_last_good_h := 0.1;
> glob_almost_1 := 0.9990;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_warned := false;
> glob_h := 0.1;
> glob_html_log := true;
> glob_optimal_start := 0.0;
> glob_clock_start_sec := 0.0;
> djd_debug := true;
> glob_percent_done := 0.0;
#Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 1;
> glob_no_eqs := 2;
> 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/mtest3.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 ;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 0.5;");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"array_y1_init[1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS," cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"-sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> 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
> 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_x:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y1_init:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_y2:= Array(1..(max_terms + 1),[]);
> array_y1:= 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_tmp3:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y2_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do
> array_x[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_pole[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_norms[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_m1[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_y2[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_y1[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;;
> term := 1;
> while term <= max_terms do
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= 3 do
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= 3 do
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= max_terms do
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= 3 do
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= max_terms do
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= max_terms do
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= max_terms do
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= max_terms do
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
> ord := 1;
> while ord <=2 do
> term := 1;
> while term <= max_terms do
> array_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;;
> ord := ord + 1;
> od;;
#BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_x[term] := 0.0;
> term := term + 1;
> od;;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_m1[term] := 0.0;
> term := term + 1;
> od;;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;;
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_y1[term] := 0.0;
> term := term + 1;
> od;;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_y2[term] := 0.0;
> term := term + 1;
> od;;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;;
> array_const_0D0[1] := 0.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do
> array_const_1[term] := 0.0;
> term := term + 1;
> od;;
> array_const_1[1] := 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do
> array_m1[term] := 0.0;
> term := term + 1;
> od;;
> array_m1[1] := -1.0;
#END ARRAYS DEFINED AND INITIALIZATED
#TOP SECOND INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 0.5;
> glob_h := 0.00001;
> array_y1_init[1] := exact_soln_y1(x_start);
> array_y2_init[1] := exact_soln_y2(x_start);
> glob_max_iter := 20;
#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
> if glob_html_log then
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;;
#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_y2
> term_no := 1;
> while (term_no <= order_diff) do
> array_y2[term_no] := array_y2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;;
> 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_y2_higher[r_order,term_no] := array_y2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;;
> r_order := r_order + 1;
> od;
> ;
> order_diff := 1;
#Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do
> array_y1[term_no] := array_y1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;;
> 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_y1_higher[r_order,term_no] := array_y1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;;
> r_order := r_order + 1;
> od;
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y2();
> if (abs(array_y2_higher[1,1]) > glob_small_float) then
> tmp := abs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then
> glob_log10normmin := log10norm;
> fi;
> fi;;
> display_alot(current_iter)
> ;
> start_array_y1();
> if (abs(array_y1_higher[1,1]) > glob_small_float) then
> tmp := abs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then
> glob_log10normmin := log10norm;
> fi;
> fi;;
> 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 #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;
> sub_iter := 1;
> while sub_iter <= 2 do
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;;
> if (glob_look_poles) then #left paren 0004C
> check_for_pole();
> fi;;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> order_diff := 1;
#Jump Series array_y2
#START PART 1 SUM AND ADJUST
#START SUM AND ADJUST EQ =1
#sum_and_adjust array_y2
> order_diff := 1;
#BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 1;
> ord := 2;
> calc_term := 1;
#adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;;
#AFTER ADJUST SUBSERIES EQ =1
#BEFORE SUM SUBSERIES EQ =1
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
#sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;;
> array_y2_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
> order_diff := 1;
> ord := 1;
> calc_term := 2;
#adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;;
#AFTER ADJUST SUBSERIES EQ =1
#BEFORE SUM SUBSERIES EQ =1
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
#sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;;
> array_y2_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
> order_diff := 1;
> ord := 1;
> calc_term := 1;
#adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;;
#AFTER ADJUST SUBSERIES EQ =1
#BEFORE SUM SUBSERIES EQ =1
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
#sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;;
> array_y2_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
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;;
> term_no := term_no - 1;
> od;;
#END PART 2 HEVE MOVED TERMS to REGULAR Array
> order_diff := 1;
#Jump Series array_y1
#START PART 1 SUM AND ADJUST
#START SUM AND ADJUST EQ =2
#sum_and_adjust array_y1
> order_diff := 1;
#BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
#adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;;
#AFTER ADJUST SUBSERIES EQ =2
#BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
#sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
#AFTER SUM SUBSERIES EQ =2
#BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
#adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;;
#AFTER ADJUST SUBSERIES EQ =2
#BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
#sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
#AFTER SUM SUBSERIES EQ =2
#BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
#adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;;
#AFTER ADJUST SUBSERIES EQ =2
#BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
#sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
#AFTER SUM SUBSERIES EQ =2
#END SUM AND ADJUST EQ =2
#END PART 1
#START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;;
> term_no := term_no - 1;
> od;;
#END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;;
> glob_clock_sec := elapsed_time_seconds();
> 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,"2012-05-26T17:34:48-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest3")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 ;")
> ;
> 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;
> fi;;
> 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
> fi;;
> log_revs(html_log_file," 067 | ")
> ;
> logitem_str(html_log_file,"Testing Systems of Equations")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 ;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 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;
> fi;;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;;
> if glob_html_log then
> fclose(html_log_file);
> fi;
> ;
> ;;
#END OUTFILEMAIN
> 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, glob_max_terms, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel,
MAX_UNCHANGED, glob_start, glob_no_eqs, glob_max_iter, glob_log10normmin,
glob_iter, glob_current_iter, hours_in_day, sec_in_min, glob_log10abserr,
glob_orig_start_sec, glob_max_trunc_err, glob_relerr, glob_large_float,
glob_hmin, glob_optimal_done, glob_initial_pass, glob_clock_sec,
min_in_hour, glob_small_float, glob_log10_relerr, glob_log10_abserr,
glob_dump_analytic, centuries_in_millinium, glob_dump, glob_normmax,
glob_max_order, glob_curr_iter_when_opt, glob_max_sec, glob_warned2,
glob_abserr, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug2, glob_display_flag, glob_max_hours, glob_disp_incr,
glob_not_yet_start_msg, glob_smallish_float, glob_optimal_clock_start_sec,
glob_max_rel_trunc_err, glob_look_poles, glob_hmin_init,
glob_not_yet_finished, days_in_year, glob_unchanged_h_cnt, glob_last_good_h,
glob_almost_1, glob_max_opt_iter, glob_optimal_expect_sec, glob_max_minutes,
glob_log10relerr, glob_warned, glob_h, glob_html_log, glob_optimal_start,
glob_clock_start_sec, djd_debug, glob_percent_done, array_const_0D0,
array_const_1, array_x, array_last_rel_error, array_pole, array_y1_init,
array_y2_init, array_norms, array_m1, array_type_pole, array_y2, array_y1,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_1st_rel_error,
array_complex_pole, array_poles, array_y1_higher_work2, array_real_pole,
array_y2_higher_work2, array_y2_higher_work, array_y2_higher,
array_y1_higher, array_y1_higher_work, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
ALWAYS := 1;
glob_max_terms := 30;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
MAX_UNCHANGED := 10;
glob_start := 0;
glob_no_eqs := 0;
glob_max_iter := 1000;
glob_log10normmin := 0.1;
glob_iter := 0;
glob_current_iter := 0;
hours_in_day := 24.0;
sec_in_min := 60.0;
glob_log10abserr := 0.;
glob_orig_start_sec := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
glob_initial_pass := true;
glob_clock_sec := 0.;
min_in_hour := 60.0;
glob_small_float := 0.1*10^(-50);
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
centuries_in_millinium := 10.0;
glob_dump := false;
glob_normmax := 0.;
glob_max_order := 30;
glob_curr_iter_when_opt := 0;
glob_max_sec := 10000.0;
glob_warned2 := false;
glob_abserr := 0.1*10^(-10);
glob_hmax := 1.0;
glob_reached_optimal_h := false;
years_in_century := 100.0;
djd_debug2 := true;
glob_display_flag := true;
glob_max_hours := 0.;
glob_disp_incr := 0.1;
glob_not_yet_start_msg := true;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_clock_start_sec := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_look_poles := false;
glob_hmin_init := 0.001;
glob_not_yet_finished := true;
days_in_year := 365.0;
glob_unchanged_h_cnt := 0;
glob_last_good_h := 0.1;
glob_almost_1 := 0.9990;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_warned := false;
glob_h := 0.1;
glob_html_log := true;
glob_optimal_start := 0.;
glob_clock_start_sec := 0.;
djd_debug := true;
glob_percent_done := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 1;
glob_no_eqs := 2;
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/mtest3.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 ;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 0.5;");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "array_y1_init[1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_max_iter := 20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, " cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "-sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
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_x := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y1_init := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_y2 := Array(1 .. max_terms + 1, []);
array_y1 := 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_tmp3 := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_y2_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[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_tmp3[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;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_y1_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 <= 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_y2_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_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[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_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[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 := 0.5;
glob_h := 0.00001;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_max_iter := 20;
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();
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_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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_y2();
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_y1();
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(array_y1_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;
sub_iter := 1;
while sub_iter <= 2 do atomall(); sub_iter := sub_iter + 1 end do;
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;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_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_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, "2012-05-26T17:34:48-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest3");
logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 ;");
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, " 067 | ");
logitem_str(html_log_file, "Testing Systems of Equations");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 ;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 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;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/mtest3.ode#################
diff ( y2 , x , 1 ) = y1 ;
diff ( y1 , x , 1 ) = m1 * y2 ;
!
Digits := 32;
max_terms := 30;
!
x_start := 0.1;
x_end := 0.5;
glob_h := 0.00001;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_max_iter := 20;
!
exact_soln_y1 := proc(x)
cos(x);
end;
exact_soln_y2 := proc(x)
-sin(x);
end;
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y2[1] (analytic) = -0.099833416646828152306814198410622
y2[1] (numeric) = -0.099833416646828152306814198410622
absolute error = 0
relative error = 0 %
h = 1e-05
y1[1] (analytic) = 0.99500416527802576609556198780387
y1[1] (numeric) = 0.99500416527802576609556198780387
absolute error = 0
relative error = 0 %
h = 1e-05
x[1] = 0.1
y2[1] (analytic) = -0.099833416646828152306814198410622
y2[1] (numeric) = -0.099833416646828152306814198410622
absolute error = 0
relative error = 0 %
h = 1e-05
y1[1] (analytic) = 0.99500416527802576609556198780387
y1[1] (numeric) = 0.99500416527802576609556198780387
absolute error = 0
relative error = 0 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10001
y2[1] (analytic) = -0.099843366683489095898147798163638
y2[1] (numeric) = -0.099823466600183867050880977940792
absolute error = 1.9900083305228847266820222846e-05
relative error = 0.019931302365147193585750625285358 %
h = 1e-05
y1[1] (analytic) = 0.99500316689410910618945499081414
y1[1] (numeric) = 0.99500516356244200947469557832173
absolute error = 1.99666833290328524058750759e-06
relative error = 0.00020066954551872054653900807584692 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10002
y2[1] (analytic) = -0.099853316710165702821215691132408
y2[1] (numeric) = -0.09981351654355723513501255698804
absolute error = 3.9800166608467686203134144368e-05
relative error = 0.039858632561992581332335121541088 %
h = 1e-05
y1[1] (analytic) = 0.9950021684106921295947662525112
y1[1] (numeric) = 0.99500616174735773649841413886175
absolute error = 3.99333666560690364788635055e-06
relative error = 0.00040133949376064414103426426867695 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10003
y2[1] (analytic) = -0.099863266726856978073350224916315
y2[1] (numeric) = -0.09980356647694925156487159045224
absolute error = 5.9700249907726508478634464075e-05
relative error = 0.059781991781839910564405446059843 %
h = 1e-05
y1[1] (analytic) = 0.99500116982777493615983746972246
y1[1] (numeric) = 0.99500715983277284734822609755338
absolute error = 5.99000499791118838862783092e-06
relative error = 0.00060200984476711723144024664005643 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10004
y2[1] (analytic) = -0.099873216733561926652882280281826
y2[1] (numeric) = -0.099793616400360911347118868398683
absolute error = 7.9600333201015305763411883143e-05
relative error = 0.079701381215516598714424011005918 %
h = 1e-05
y1[1] (analytic) = 0.99500017114535762574296036095926
y1[1] (numeric) = 0.99500815781868724221558994414338
absolute error = 7.98667332961647262958318412e-06
relative error = 0.0008026805985794865927906116911582 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10005
y2[1] (analytic) = -0.099883166730279553559141370662659
y2[1] (numeric) = -0.099783666313793209489413216557414
absolute error = 9.9500416486344069728154105245e-05
relative error = 0.09961680205337397136858987159515 %
h = 1e-05
y1[1] (analytic) = 0.99499917236344029821237665643104
y1[1] (numeric) = 0.99500915570510082130191423997667
absolute error = 9.98334166052308953758354563e-06
relative error = 0.0010033517552390993272327514572615 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10006
y2[1] (analytic) = -0.099893116717008863792455741659854
y2[1] (numeric) = -0.099773716217247141000411396822465
absolute error = 0.000119400499761722792044344837389
relative error = 0.1195282554852875001700230040274 %
h = 1e-05
y1[1] (analytic) = 0.99499817348202305344627808805855
y1[1] (numeric) = 0.99501015349201348481855762797619
absolute error = 1.198000999043137227953991764e-05
relative error = 0.0012040233147873028640623511666768 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10007
y2[1] (analytic) = -0.099903066693748862354152470541733
y2[1] (numeric) = -0.099763766110723700889768007750989
absolute error = 0.000139300583025161464384462790744
relative error = 0.1394357427006570405793065225942 %
h = 1e-05
y1[1] (analytic) = 0.99499717450110599133280637948601
y1[1] (numeric) = 0.99501115117942513298682884262176
absolute error = 1.397667831914165402246313575e-05
relative error = 0.0014046952772654449597579474721973 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10008
y2[1] (analytic) = -0.099913016660498554246557565743775
y2[1] (numeric) = -0.099753815994223884168135385062295
absolute error = 0.00015920066627467007842218068148
relative error = 0.1593392648884070694924866056145 %
h = 1e-05
y1[1] (analytic) = 0.99499617542068921177005323609226
y1[1] (numeric) = 0.99501214876733566603798671992796
absolute error = 1.597334664645426793348383570e-05
relative error = 0.0016053676427148736980154872531312 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10009
y2[1] (analytic) = -0.099922966617256944472996066368378
y2[1] (numeric) = -0.099743865867748685847163502136782
absolute error = 0.000179100749508258625832564231596
relative error = 0.17923882323698692271662982005535 %
h = 1e-05
y1[1] (analytic) = 0.99499517624077281466606033500102
y1[1] (numeric) = 0.995013146255744984213240207421
absolute error = 1.797001497216954717987241998e-05
relative error = 0.0018060404111769374897828869729002 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.1001
y2[1] (analytic) = -0.099932916564023038037792141684529
y2[1] (numeric) = -0.099733915731299100939499870514776
absolute error = 0.000199000832723937098292271169753
relative error = 0.19913441893437103230303745506546 %
h = 1e-05
y1[1] (analytic) = 0.99499417696135689993881931509004
y1[1] (numeric) = 0.99501414364465298776374837411459
absolute error = 1.996668329608782492905902455e-05
relative error = 0.0020067135826929850732945926153828 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.18
x[1] = 0.10011
y2[1] (analytic) = -0.09994286650079583994626919062737
y2[1] (numeric) = -0.099723965584876124458789440395262
absolute error = 0.000218900915919715487479750232108
relative error = 0.21902605316805916373821639502748 %
h = 1e-05
y1[1] (analytic) = 0.99499317758244156751627176699931
y1[1] (numeric) = 0.99501514093405957695062042048484
absolute error = 2.196335161800943434865348553e-05
relative error = 0.0022073871573043655141061401859946 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10012
y2[1] (analytic) = -0.099952816427574355204749941297668
y2[1] (numeric) = -0.099714015428480751419674501134523
absolute error = 0.000238800999093603785075440163145
relative error = 0.2389137271250766529927059832063 %
h = 1e-05
y1[1] (analytic) = 0.99499217810402691733630922313827
y1[1] (numeric) = 0.99501613812396465204491568844413
absolute error = 2.396001993773470860646530586e-05
relative error = 0.0024080611350524282051287167775681 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10013
y2[1] (analytic) = -0.099962766344357588820556550461181
y2[1] (numeric) = -0.099704065262113976837794581744674
absolute error = 0.000258701082243611982761968716507
relative error = 0.2587974419919746434278602476207 %
h = 1e-05
y1[1] (analytic) = 0.99499117852611304934677314769202
y1[1] (numeric) = 0.99501713521436811332764367131403
absolute error = 2.595668825506398087052362201e-05
relative error = 0.0026087355159785228666637222091345 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10014
y2[1] (analytic) = -0.099972716251144545802010703047924
y2[1] (numeric) = -0.099694115085776795729786351392097
absolute error = 0.000278601165367750072224351655827
relative error = 0.27867719895483032256068478137379 %
h = 1e-05
y1[1] (analytic) = 0.99499017884870006350545492662652
y1[1] (numeric) = 0.99501813220526986108976402379718
absolute error = 2.795335656979758430909717066e-05
relative error = 0.0028094103001239995464373312296292 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10015
y2[1] (analytic) = -0.099982666147934231158433711651342
y2[1] (numeric) = -0.099684164899470203113283519895779
absolute error = 0.000298501248464028045150191755563
relative error = 0.2985529991992471586868274903697 %
h = 1e-05
y1[1] (analytic) = 0.99498917907178805978009585769285
y1[1] (numeric) = 0.99501912909666979563218657194819
absolute error = 2.995002488173585209071425534e-05
relative error = 0.0030100854875302086196350562855796 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10016
y2[1] (analytic) = -0.099992616034725649900146616027373
y2[1] (numeric) = -0.099674214703195194006916738225548
absolute error = 0.000318401331530455893229877801825
relative error = 0.3184248439103551373618223420835 %
h = 1e-05
y1[1] (analytic) = 0.99498817919537713814838714043039
y1[1] (numeric) = 0.99502012588856781726577132314356
absolute error = 3.194669319067911738418271317e-05
relative error = 0.0032107610782385007889363108669072 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10017
y2[1] (analytic) = -0.10000256591151780703847028259342
y2[1] (numeric) = -0.099664264496952763430313499000212
absolute error = 0.000338301414565043608156783593208
relative error = 0.33829273427281099774068516990492 %
h = 1e-05
y1[1] (analytic) = 0.99498717921946739859796986616909
y1[1] (numeric) = 0.99502112258096382631132847605059
absolute error = 3.394336149642771335860988150e-05
relative error = 0.0034114370722902270845489734108054 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10018
y2[1] (analytic) = -0.10001251577830970758572550392721
y2[1] (numeric) = -0.099654314280743906404098036985591
absolute error = 0.000358201497565801181627466941619
relative error = 0.35815667147079846877596050844945 %
h = 1e-05
y1[1] (analytic) = 0.99498617914405894112643500803067
y1[1] (numeric) = 0.9950221191738577230996184305953
absolute error = 3.594002979878197318342256463e-05
relative error = 0.0036121134697267388642439517818477 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.10019
y2[1] (analytic) = -0.10002246563510035655523309826558
y2[1] (numeric) = -0.099644364054569617949891229592461
absolute error = 0.000378101580530738605341868673119
relative error = 0.3780166566880285052743183562327 %
h = 1e-05
y1[1] (analytic) = 0.99498517896915186574132341092889
y1[1] (numeric) = 0.99502311566724940797135179792936
absolute error = 3.793669809754223002838700047e-05
relative error = 0.0038127902705893878133897483143163 %
h = 1e-05
TOP MAIN SOLVE Loop
x[1] = 0.1002
y2[1] (analytic) = -0.10003241548188875896131400900311
y2[1] (numeric) = -0.099634413818430893090310497374387
absolute error = 0.000398001663457865871003511628723
relative error = 0.39787269110773952381179968306757 %
h = 1e-05
y1[1] (analytic) = 0.99498417869474627246012578156879
y1[1] (numeric) = 0.995024112061138781277189410396
absolute error = 3.993336639250881706362882721e-05
relative error = 0.0040134674749195259449870254238502 %
h = 1e-05
Finished!
Maximum Iterations Reached before Solution Completed!
Iterations = 20
Total Elapsed Time = 0 Seconds
Elapsed Time(since restart) = 0 Seconds
Expected Time Remaining = 8 Minutes 26 Seconds
Optimized Time Remaining = 8 Minutes 9 Seconds
Time to Timeout = 14 Minutes 59 Seconds
Percent Done = 0.0525 %
> quit
memory used=6.2MB, alloc=3.0MB, time=0.31