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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_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 # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> 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 # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
glob_last;
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_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
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> 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 # if number 1
> tmp := abs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_y1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
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
> # Begin Function number 5
> prog_report := proc(x_start,x_end)
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 4 - 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 # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> 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 # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #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 # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> 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 # if number 2
> 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;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #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 - 4 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_y2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_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 # if number 2
> 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 # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #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 # do number 2
> if (abs(array_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> 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 # if number 3
> 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 # if number 4
> 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 # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #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 # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #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 # if number 3
> 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 # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 # if number 3
> 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 # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 # if number 3
> 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 # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 # if number 3
> 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 # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> 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 # if number 3
> 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 # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #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 # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
glob_last;
n := glob_max_terms;
m := n - 5;
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 - 5;
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
> # Begin Function number 7
> get_norms := proc()
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_y2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_y1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_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
> # Begin Function number 8
> atomall := proc()
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> 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 sub $eq_no = 1 i = 1
> array_tmp2[1] := (array_tmp1[1] - (array_const_1D0[1]));
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y2_set_initial[1,5] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (4)) * factorial_3(0,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,3] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,2] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp4[1] := array_y2_higher[4,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp5[1] := (array_m1[1] * (array_tmp4[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if not array_y1_set_initial[2,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[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;# end if 2
> ;
> fi;# end if 1
> ;
> 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 sub $eq_no = 1 i = 2
> array_tmp2[2] := (array_tmp1[2] - (array_const_1D0[2]));
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y2_set_initial[1,6] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (4)) * factorial_3(1,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,4] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,3] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp4[2] := array_y2_higher[4,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp5[2] := ats(2,array_m1,array_tmp4,1);
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if not array_y1_set_initial[2,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[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;# end if 2
> ;
> fi;# end if 1
> ;
> 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 sub $eq_no = 1 i = 3
> array_tmp2[3] := (array_tmp1[3] - (array_const_1D0[3]));
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y2_set_initial[1,7] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (4)) * factorial_3(2,6);
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,5] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,4] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp4[3] := array_y2_higher[4,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp5[3] := ats(3,array_m1,array_tmp4,1);
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if not array_y1_set_initial[2,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[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;# end if 2
> ;
> fi;# end if 1
> ;
> 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 sub $eq_no = 1 i = 4
> array_tmp2[4] := (array_tmp1[4] - (array_const_1D0[4]));
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y2_set_initial[1,8] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (4)) * factorial_3(3,7);
> array_y2[8] := temporary;
> array_y2_higher[1,8] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,7] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,6] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,5] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp4[4] := array_y2_higher[4,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp5[4] := ats(4,array_m1,array_tmp4,1);
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if not array_y1_set_initial[2,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[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;# end if 2
> ;
> fi;# end if 1
> ;
> 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 sub $eq_no = 1 i = 5
> array_tmp2[5] := (array_tmp1[5] - (array_const_1D0[5]));
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y2_set_initial[1,9] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (4)) * factorial_3(4,8);
> array_y2[9] := temporary;
> array_y2_higher[1,9] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,8] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,7] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,6] := temporary
> ;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[5,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp4[5] := array_y2_higher[4,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp5[5] := ats(5,array_m1,array_tmp4,1);
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if not array_y1_set_initial[2,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[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;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit add $eq_no = 1
> array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk];
> #emit sub $eq_no = 1
> array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_1D0[kkk]));
> #emit assign $eq_no = 1
> order_d := 4;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y2_set_initial[1,kkk + order_d] then # if number 2
> temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_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 # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> #emit diff $eq_no = 2
> array_tmp4[kkk] := array_y2_higher[4,kkk];
> #emit mult $eq_no = 2
> array_tmp5[kkk] := ats(kkk,array_m1,array_tmp4,1);
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_y1_set_initial[2,kkk + order_d] then # if number 2
> temporary := array_tmp5[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 # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_y1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
glob_last;
array_tmp1[1] := array_const_0D0[1] + array_y1[1];
array_tmp2[1] := array_tmp1[1] - array_const_1D0[1];
if not array_y2_set_initial[1, 5] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h^4*factorial_3(0, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 3] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 2] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 1] := temporary
end if
end if;
kkk := 2;
array_tmp4[1] := array_y2_higher[4, 1];
array_tmp5[1] := array_m1[1]*array_tmp4[1];
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[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
end if;
kkk := 2;
array_tmp1[2] := array_const_0D0[2] + array_y1[2];
array_tmp2[2] := array_tmp1[2] - array_const_1D0[2];
if not array_y2_set_initial[1, 6] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h^4*factorial_3(1, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 4] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 3] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 2] := temporary
end if
end if;
kkk := 3;
array_tmp4[2] := array_y2_higher[4, 2];
array_tmp5[2] := ats(2, array_m1, array_tmp4, 1);
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[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
end if;
kkk := 3;
array_tmp1[3] := array_const_0D0[3] + array_y1[3];
array_tmp2[3] := array_tmp1[3] - array_const_1D0[3];
if not array_y2_set_initial[1, 7] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h^4*factorial_3(2, 6);
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 4] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 3] := temporary
end if
end if;
kkk := 4;
array_tmp4[3] := array_y2_higher[4, 3];
array_tmp5[3] := ats(3, array_m1, array_tmp4, 1);
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[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
end if;
kkk := 4;
array_tmp1[4] := array_const_0D0[4] + array_y1[4];
array_tmp2[4] := array_tmp1[4] - array_const_1D0[4];
if not array_y2_set_initial[1, 8] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h^4*factorial_3(3, 7);
array_y2[8] := temporary;
array_y2_higher[1, 8] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 7] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 5] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 4] := temporary
end if
end if;
kkk := 5;
array_tmp4[4] := array_y2_higher[4, 4];
array_tmp5[4] := ats(4, array_m1, array_tmp4, 1);
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[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
end if;
kkk := 5;
array_tmp1[5] := array_const_0D0[5] + array_y1[5];
array_tmp2[5] := array_tmp1[5] - array_const_1D0[5];
if not array_y2_set_initial[1, 9] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h^4*factorial_3(4, 8);
array_y2[9] := temporary;
array_y2_higher[1, 9] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 8] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 7] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[5, 5] := temporary
end if
end if;
kkk := 6;
array_tmp4[5] := array_y2_higher[4, 5];
array_tmp5[5] := ats(5, array_m1, array_tmp4, 1);
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[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
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk];
array_tmp2[kkk] := array_tmp1[kkk] - array_const_1D0[kkk];
order_d := 4;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp2[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
end if;
array_tmp4[kkk] := array_y2_higher[4, kkk];
array_tmp5[kkk] := ats(kkk, array_m1, array_tmp4, 1);
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := array_tmp5[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
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> 1.0 + sin(x);
> end;
exact_soln_y1 := proc(x) 1.0 + sin(x) end proc
> exact_soln_y2 := proc(x)
> 1.0 + sin(x);
> end;
exact_soln_y2 := proc(x) 1.0 + sin(x) end proc
> exact_soln_y2p := proc(x)
> cos(x);
> end;
exact_soln_y2p := proc(x) cos(x) end proc
> exact_soln_y2pp := proc(x)
> -sin(x);
> end;
exact_soln_y2pp := proc(x) -sin(x) end proc
> exact_soln_y2ppp := proc(x)
> -cos(x);
> end;
exact_soln_y2ppp := proc(x) -cos(x) end proc
>
>
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> glob_iolevel,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> DEBUGL,
> INFO,
> #Top Generate Globals Decl
> glob_h,
> glob_initial_pass,
> djd_debug,
> glob_iter,
> glob_max_rel_trunc_err,
> glob_look_poles,
> sec_in_min,
> glob_smallish_float,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_hmax,
> glob_start,
> centuries_in_millinium,
> years_in_century,
> glob_dump,
> glob_percent_done,
> glob_log10relerr,
> glob_normmax,
> glob_unchanged_h_cnt,
> glob_no_eqs,
> glob_dump_analytic,
> glob_last_good_h,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_max_opt_iter,
> glob_max_minutes,
> glob_hmin_init,
> glob_optimal_done,
> glob_clock_start_sec,
> glob_html_log,
> glob_curr_iter_when_opt,
> glob_orig_start_sec,
> glob_warned2,
> glob_max_iter,
> glob_log10_relerr,
> hours_in_day,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_small_float,
> glob_optimal_start,
> glob_relerr,
> glob_clock_sec,
> glob_almost_1,
> min_in_hour,
> djd_debug2,
> glob_log10abserr,
> MAX_UNCHANGED,
> glob_hmin,
> days_in_year,
> glob_log10normmin,
> glob_warned,
> glob_optimal_clock_start_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> glob_max_trunc_err,
> glob_log10_abserr,
> glob_display_flag,
> glob_subiter_method,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_3,
> array_const_1,
> array_const_1D0,
> array_const_4,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y1_init,
> array_pole,
> array_y2,
> array_y1,
> array_y2_init,
> array_x,
> array_type_pole,
> array_last_rel_error,
> array_1st_rel_error,
> array_norms,
> array_poles,
> array_y1_set_initial,
> array_y2_higher,
> array_y1_higher,
> array_real_pole,
> array_complex_pole,
> array_y2_higher_work,
> array_y1_higher_work2,
> array_y2_higher_work2,
> array_y1_higher_work,
> array_y2_set_initial,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_iolevel := 5;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_terms := 30;
> DEBUGL := 3;
> INFO := 2;
> glob_h := 0.1;
> glob_initial_pass := true;
> djd_debug := true;
> glob_iter := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_look_poles := false;
> sec_in_min := 60.0;
> glob_smallish_float := 0.1e-100;
> glob_max_hours := 0.0;
> glob_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_start := 0;
> centuries_in_millinium := 10.0;
> years_in_century := 100.0;
> glob_dump := false;
> glob_percent_done := 0.0;
> glob_log10relerr := 0.0;
> glob_normmax := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_no_eqs := 0;
> glob_dump_analytic := false;
> glob_last_good_h := 0.1;
> glob_disp_incr := 0.1;
> glob_not_yet_start_msg := true;
> glob_max_opt_iter := 10;
> glob_max_minutes := 0.0;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> glob_clock_start_sec := 0.0;
> glob_html_log := true;
> glob_curr_iter_when_opt := 0;
> glob_orig_start_sec := 0.0;
> glob_warned2 := false;
> glob_max_iter := 1000;
> glob_log10_relerr := 0.1e-10;
> hours_in_day := 24.0;
> glob_optimal_expect_sec := 0.1;
> glob_current_iter := 0;
> glob_max_sec := 10000.0;
> glob_small_float := 0.1e-50;
> glob_optimal_start := 0.0;
> glob_relerr := 0.1e-10;
> glob_clock_sec := 0.0;
> glob_almost_1 := 0.9990;
> min_in_hour := 60.0;
> djd_debug2 := true;
> glob_log10abserr := 0.0;
> MAX_UNCHANGED := 10;
> glob_hmin := 0.00000000001;
> days_in_year := 365.0;
> glob_log10normmin := 0.1;
> glob_warned := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_reached_optimal_h := false;
> glob_not_yet_finished := true;
> glob_max_trunc_err := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_display_flag := true;
> glob_subiter_method := 3;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 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/mtest8postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 4 ) = y1 - 1.0;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.1;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
> omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"1.0 + sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"1.0 + sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"-sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)");
> omniout_str(ALWAYS,"-cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_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_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_y1_init:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y2:= Array(1..(max_terms + 1),[]);
> array_y1:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher := Array(1..(5+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y2_higher_work := Array(1..(5+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(1..(5+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=5 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=5 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=5 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3[1] := 3;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> array_const_4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4[1] := 4;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 5.1;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
> array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);
> glob_h := 0.00001;
> glob_look_poles := true;
> glob_max_iter := 20;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := true;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #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 := 4;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> 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;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_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;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> 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;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_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;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_y2();
> if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_y2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_y1();
> if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_y1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if glob_subiter_method = 1 then # if number 3
> atomall();
> elif glob_subiter_method = 2 then # if number 4
> subiter := 1;
> while subiter <= 5 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 5 + glob_max_terms do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2
> order_diff := 4;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 5;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 5;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 4;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 4;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 4;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 3;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 2;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 2;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 5;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 5;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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 # do number 3
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> 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;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> 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 # do number 3
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 4 ) = y1 - 1.0;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if glob_html_log then # if number 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T03:32:03-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest8")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 4 ) = y1 - 1.0;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 5
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"mtest8 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest8 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> 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 * diff ( y2 , x , 3 ) ;")
> ;
> 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 # if number 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 5
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if glob_html_log then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `subiter` is implicitly declared local to procedure `mainprog`
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,
subiter;
global glob_iolevel, DEBUGMASSIVE, ALWAYS, glob_max_terms, DEBUGL, INFO,
glob_h, glob_initial_pass, djd_debug, glob_iter, glob_max_rel_trunc_err,
glob_look_poles, sec_in_min, glob_smallish_float, glob_max_hours,
glob_abserr, glob_large_float, glob_hmax, glob_start,
centuries_in_millinium, years_in_century, glob_dump, glob_percent_done,
glob_log10relerr, glob_normmax, glob_unchanged_h_cnt, glob_no_eqs,
glob_dump_analytic, glob_last_good_h, glob_disp_incr,
glob_not_yet_start_msg, glob_max_opt_iter, glob_max_minutes, glob_hmin_init,
glob_optimal_done, glob_clock_start_sec, glob_html_log,
glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_max_iter,
glob_log10_relerr, hours_in_day, glob_optimal_expect_sec, glob_current_iter,
glob_max_sec, glob_small_float, glob_optimal_start, glob_relerr,
glob_clock_sec, glob_almost_1, min_in_hour, djd_debug2, glob_log10abserr,
MAX_UNCHANGED, glob_hmin, days_in_year, glob_log10normmin, glob_warned,
glob_optimal_clock_start_sec, glob_reached_optimal_h, glob_not_yet_finished,
glob_max_trunc_err, glob_log10_abserr, glob_display_flag,
glob_subiter_method, array_const_3, array_const_1, array_const_1D0,
array_const_4, array_const_0D0, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_init, array_pole,
array_y2, array_y1, array_y2_init, array_x, array_type_pole,
array_last_rel_error, array_1st_rel_error, array_norms, array_poles,
array_y1_set_initial, array_y2_higher, array_y1_higher, array_real_pole,
array_complex_pole, array_y2_higher_work, array_y1_higher_work2,
array_y2_higher_work2, array_y1_higher_work, array_y2_set_initial,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_iolevel := 5;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_terms := 30;
DEBUGL := 3;
INFO := 2;
glob_h := 0.1;
glob_initial_pass := true;
djd_debug := true;
glob_iter := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_look_poles := false;
sec_in_min := 60.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_hours := 0.;
glob_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_start := 0;
centuries_in_millinium := 10.0;
years_in_century := 100.0;
glob_dump := false;
glob_percent_done := 0.;
glob_log10relerr := 0.;
glob_normmax := 0.;
glob_unchanged_h_cnt := 0;
glob_no_eqs := 0;
glob_dump_analytic := false;
glob_last_good_h := 0.1;
glob_disp_incr := 0.1;
glob_not_yet_start_msg := true;
glob_max_opt_iter := 10;
glob_max_minutes := 0.;
glob_hmin_init := 0.001;
glob_optimal_done := false;
glob_clock_start_sec := 0.;
glob_html_log := true;
glob_curr_iter_when_opt := 0;
glob_orig_start_sec := 0.;
glob_warned2 := false;
glob_max_iter := 1000;
glob_log10_relerr := 0.1*10^(-10);
hours_in_day := 24.0;
glob_optimal_expect_sec := 0.1;
glob_current_iter := 0;
glob_max_sec := 10000.0;
glob_small_float := 0.1*10^(-50);
glob_optimal_start := 0.;
glob_relerr := 0.1*10^(-10);
glob_clock_sec := 0.;
glob_almost_1 := 0.9990;
min_in_hour := 60.0;
djd_debug2 := true;
glob_log10abserr := 0.;
MAX_UNCHANGED := 10;
glob_hmin := 0.1*10^(-10);
days_in_year := 365.0;
glob_log10normmin := 0.1;
glob_warned := false;
glob_optimal_clock_start_sec := 0.;
glob_reached_optimal_h := false;
glob_not_yet_finished := true;
glob_max_trunc_err := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_display_flag := true;
glob_subiter_method := 3;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
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/mtest8postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.1;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
;
omniout_str(ALWAYS,
"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);");
omniout_str(ALWAYS, "glob_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 20;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "1.0 +\tsin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "1.0 +\tsin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "-sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)");
omniout_str(ALWAYS, "-cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_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_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_y1_init := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_y2 := Array(1 .. max_terms + 1, []);
array_y1 := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y2_higher := Array(1 .. 6, 1 .. max_terms + 1, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_y2_higher_work := Array(1 .. 6, 1 .. max_terms + 1, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_higher_work2 := Array(1 .. 6, 1 .. max_terms + 1, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
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_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[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_y1_init[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_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_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 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 <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 5 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 <= 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 <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 5 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_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 5 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_y1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[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_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_const_3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3[term] := 0.; term := term + 1
end do;
array_const_3[1] := 3;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_const_4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4[term] := 0.; term := term + 1
end do;
array_const_4[1] := 4;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
x_start := 0.1;
x_end := 5.1;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
array_y2_init[3] := exact_soln_y2pp(x_start);
array_y2_init[4] := exact_soln_y2ppp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 20;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := true;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
order_diff := 4;
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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 5 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 5 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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 := 4;
ord := 5;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 5;
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)!;
ord := 4;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
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)!;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
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)!;
ord := 3;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 3;
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)!;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 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)!;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_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)!;
ord := 2;
calc_term := 4;
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;
temp_sum := 0.;
ord := 2;
calc_term := 4;
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)!;
ord := 2;
calc_term := 3;
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;
temp_sum := 0.;
ord := 2;
calc_term := 3;
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)!;
ord := 2;
calc_term := 2;
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;
temp_sum := 0.;
ord := 2;
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)!;
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;
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)!;
ord := 1;
calc_term := 5;
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;
temp_sum := 0.;
ord := 1;
calc_term := 5;
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)!;
ord := 1;
calc_term := 4;
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;
temp_sum := 0.;
ord := 1;
calc_term := 4;
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)!;
ord := 1;
calc_term := 3;
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;
temp_sum := 0.;
ord := 1;
calc_term := 3;
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)!;
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;
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)!;
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;
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;
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;
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)!;
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;
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)!;
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;
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_str(INFO, "diff ( y2 , x , 4 ) = y1 - 1.0;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T03:32:03-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest8")
;
logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"mtest8 diffeq.mxt");
logitem_str(html_log_file,
"mtest8 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
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 * diff ( y2 , x , 3 ) ;");
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);
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/mtest8postode.ode#################
diff ( y2 , x , 4 ) = y1 - 1.0;
diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.1;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 20;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
1.0 + sin(x);
end;
exact_soln_y2 := proc(x)
1.0 + sin(x);
end;
exact_soln_y2p := proc(x)
cos(x);
end;
exact_soln_y2pp := proc(x)
-sin(x);
end;
exact_soln_y2ppp := proc(x)
-cos(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.0998334166468281523068141984106
y1[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
h = 0.0001
x[1] = 0.1
y2[1] (analytic) = 1.0998334166468281523068141984106
y2[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.0998334166468281523068141984106
y1[1] (numeric) = 1.0998334166468281523068141984106
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.18
NO POLE
NO POLE
x[1] = 0.1001
y2[1] (analytic) = 1.0999329165640230380377921416845
y2[1] (numeric) = 1.0999329165640230380377921416845
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.0999329165640230380377921416845
y1[1] (numeric) = 1.0999329165641225381214627433772
absolute error = 9.95000836706016927e-14
relative error = 9.0460138224993432887702211551991e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1002
y2[1] (analytic) = 1.1000324154818887589613140090031
y2[1] (numeric) = 1.1000324154818887589613140090045
absolute error = 1.4e-30
relative error = 1.2726897683162410327729518353249e-28 %
h = 0.0001
y1[1] (analytic) = 1.1000324154818887589613140090031
y1[1] (numeric) = 1.1000324154823862580468709308103
absolute error = 4.974990855569218072e-13
relative error = 4.5225856852498613587116343421850e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.37
NO POLE
NO POLE
x[1] = 0.1003
y2[1] (analytic) = 1.1001319133994303258995517487798
y2[1] (numeric) = 1.1001319133994303258995517488002
absolute error = 2.04e-29
relative error = 1.8543230817624023666774426885434e-27 %
h = 0.0001
y1[1] (analytic) = 1.1001319133994303258995517487798
y1[1] (numeric) = 1.1001319134006243199033095627653
absolute error = 1.1939940037578139855e-12
relative error = 1.0853189414970681674906284838449e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.4MB, time=0.58
NO POLE
NO POLE
x[1] = 0.1004
y2[1] (analytic) = 1.1002314103156527596779188409447
y2[1] (numeric) = 1.1002314103156527596779188410728
absolute error = 1.281e-28
relative error = 1.1643005171361953106497222382901e-26 %
h = 0.0001
y1[1] (analytic) = 1.1002314103156527596779188409447
y1[1] (numeric) = 1.1002314103178417415083210454471
absolute error = 2.1889818304022045024e-12
relative error = 1.9895649314121952228589177065676e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.78
NO POLE
NO POLE
x[1] = 0.1005
y2[1] (analytic) = 1.1003309062295610911350200886824
y2[1] (numeric) = 1.1003309062295610911350200892023
absolute error = 5.199e-28
relative error = 4.7249422610649973863407507113785e-26 %
h = 0.0001
y1[1] (analytic) = 1.1003309062295610911350200886824
y1[1] (numeric) = 1.1003309062330435506866692410265
absolute error = 3.4824595516491523441e-12
relative error = 3.1649202362062979273629316159172e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=1.00
NO POLE
NO POLE
x[1] = 0.1006
y2[1] (analytic) = 1.1004304011401603611326013100376
y2[1] (numeric) = 1.1004304011401603611326013116524
absolute error = 1.6148e-27
relative error = 1.4674258347705581655075063918353e-25 %
h = 0.0001
y1[1] (analytic) = 1.1004304011401603611326013100376
y1[1] (numeric) = 1.1004304011452347852802892194142
absolute error = 5.0744241476879093766e-12
relative error = 4.6113085774713949411215396433950e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1007
y2[1] (analytic) = 1.1005298950464556205654989292891
y2[1] (numeric) = 1.1005298950464556205654989334745
absolute error = 4.1854e-27
relative error = 3.8030770620940975847112305765611e-25 %
h = 0.0001
y1[1] (analytic) = 1.1005298950464556205654989292891
y1[1] (numeric) = 1.1005298950534204931582369098929
absolute error = 6.9648725927379806038e-12
relative error = 6.3286537004467098722489559672347e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.20
NO POLE
NO POLE
x[1] = 0.1008
y2[1] (analytic) = 1.1006293879474519303715894679936
y2[1] (numeric) = 1.1006293879474519303715894775101
absolute error = 9.5165e-27
relative error = 8.6464164088396597415659209941650e-25 %
h = 0.0001
y1[1] (analytic) = 1.1006293879474519303715894679936
y1[1] (numeric) = 1.1006293879566057322266386525082
absolute error = 9.1538018550491845146e-12
relative error = 8.3168793740097919964286451967413e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.41
NO POLE
NO POLE
x[1] = 0.1009
y2[1] (analytic) = 1.100728879842154361541738935598
y2[1] (numeric) = 1.1007288798421543615417389551925
absolute error = 1.95945e-26
relative error = 1.7801386298513282567575559361485e-24 %
h = 0.0001
y1[1] (analytic) = 1.100728879842154361541738935598
y1[1] (numeric) = 1.1007288798537955704386406491186
absolute error = 1.16412088969017135206e-11
relative error = 1.0575909390667640782393801187117e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.61
NO POLE
NO POLE
x[1] = 0.101
y2[1] (analytic) = 1.1008283707295679951297521195232
y2[1] (numeric) = 1.1008283707295679951297521568492
absolute error = 3.73260e-26
relative error = 3.3907192976197004443007167945504e-24 %
h = 0.0001
y1[1] (analytic) = 1.1008283707295679951297521195232
y1[1] (numeric) = 1.1008283707439950858043583140049
absolute error = 1.44270906746061944817e-11
relative error = 1.3105667566547834219004257105695e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=34.3MB, alloc=4.4MB, time=1.82
x[1] = 0.1011
y2[1] (analytic) = 1.1009278606086979222623217746172
y2[1] (numeric) = 1.1009278606086979222623218414041
absolute error = 6.67869e-26
relative error = 6.0664192804670990780518423165325e-24 %
h = 0.0001
y1[1] (analytic) = 1.1009278606086979222623217746172
y1[1] (numeric) = 1.1009278606262093664008255239401
absolute error = 1.75114441385037493229e-11
relative error = 1.5906077741389660945062421665063e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1012
y2[1] (analytic) = 1.1010273494785492441489777118801
y2[1] (numeric) = 1.1010273494785492441489778253806
absolute error = 1.135005e-25
relative error = 1.0308599514240429185039002887606e-23 %
h = 0.0001
y1[1] (analytic) = 1.1010273494785492441489777118801
y1[1] (numeric) = 1.1010273494994435103819437676198
absolute error = 2.08942662329660557397e-11
relative error = 1.8977063778535256177651051417170e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=2.03
NO POLE
NO POLE
x[1] = 0.1013
y2[1] (analytic) = 1.1011268373381270720920357863605
y2[1] (numeric) = 1.101126837338127072092035971107
absolute error = 1.847465e-25
relative error = 1.6777949073206469496090767862522e-23 %
h = 0.0001
y1[1] (analytic) = 1.1011268373381270720920357863605
y1[1] (numeric) = 1.1011268373627026259884311943538
absolute error = 2.45755538963954079933e-11
relative error = 2.2318549564920741438229400384498e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=2.24
NO POLE
NO POLE
x[1] = 0.1014
y2[1] (analytic) = 1.101226324186436527496546784124
y2[1] (numeric) = 1.1012263241864365274965470740229
absolute error = 2.898989e-25
relative error = 2.6325097178744921008613354181322e-23 %
h = 0.0001
y1[1] (analytic) = 1.101226324186436527496546784124
y1[1] (numeric) = 1.1012263242149918315577715619194
absolute error = 2.85553040612247777954e-11
relative error = 2.5930459011067368074453203227608e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=2.44
NO POLE
NO POLE
x[1] = 0.1015
y2[1] (analytic) = 1.1013258100224827418802452081946
y2[1] (numeric) = 1.1013258100224827418802456489886
absolute error = 4.407940e-25
relative error = 4.0023941688155071976380199302566e-23 %
h = 0.0001
y1[1] (analytic) = 1.1013258100224827418802452081946
y1[1] (numeric) = 1.1013258100553162555341630834766
absolute error = 3.28335136539178752820e-11
relative error = 2.9812716051072664575321893221544e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1016
y2[1] (analytic) = 1.1014252948452708568834979633685
y2[1] (numeric) = 1.1014252948452708568834986154977
absolute error = 6.521292e-25
relative error = 5.9207755900649771563815915852942e-23 %
h = 0.0001
y1[1] (analytic) = 1.1014252948452708568834979633685
y1[1] (numeric) = 1.1014252948826810364784671734467
absolute error = 3.74101795949692100782e-11
relative error = 3.3965244642601587679618439421856e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=2.65
NO POLE
NO POLE
x[1] = 0.1017
y2[1] (analytic) = 1.101524778653806024279252939803
y2[1] (numeric) = 1.1015247786538060242792538816925
absolute error = 9.418895e-25
relative error = 8.5507790496651443868365739384499e-23 %
h = 0.0001
y1[1] (analytic) = 1.101524778653806024279252939803
y1[1] (numeric) = 1.1015247786960913230781570922533
absolute error = 4.22852987989041524503e-11
relative error = 3.8387968766877677272432241008508e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=2.86
NO POLE
NO POLE
x[1] = 0.1018
y2[1] (analytic) = 1.101624261447093405982987495278
y2[1] (numeric) = 1.1016242614470934059829888270844
absolute error = 1.3318064e-24
relative error = 1.2089479567657119166817662778208e-22 %
h = 0.0001
y1[1] (analytic) = 1.101624261447093405982987495278
y1[1] (numeric) = 1.1016242614945522741572664898276
absolute error = 4.74588681742789945496e-11
relative error = 4.3080812428674215071911733835710e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=3.07
NO POLE
NO POLE
x[1] = 0.1019
y2[1] (analytic) = 1.1017237432241381740626568360333
y2[1] (numeric) = 1.101723743224138174062658683878
absolute error = 1.8478447e-24
relative error = 1.6772305320319021309030924535472e-22 %
h = 0.0001
y1[1] (analytic) = 1.1017237432241381740626568360333
y1[1] (numeric) = 1.1017237432770690586863378477777
absolute error = 5.29308846236810117444e-11
relative error = 4.8043699656305387101220906280288e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=61.0MB, alloc=4.4MB, time=3.27
x[1] = 0.102
y2[1] (analytic) = 1.1018232239839455107486422960806
y2[1] (numeric) = 1.1018232239839455107486448168008
absolute error = 2.5207202e-24
relative error = 2.2877718903815091568842156062779e-22 %
h = 0.0001
y1[1] (analytic) = 1.1018232239839455107486422960806
y1[1] (numeric) = 1.1018232240426468557923708201226
absolute error = 5.87013450437285240420e-11
relative error = 5.3276554501617449945487435328030e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1021
y2[1] (analytic) = 1.1019227037255206084436995148916
y2[1] (numeric) = 1.1019227037255206084437029013381
absolute error = 3.3864465e-24
relative error = 3.0732160146539048548574804935938e-22 %
h = 0.0001
y1[1] (analytic) = 1.1019227037255206084436995148916
y1[1] (numeric) = 1.1019227037902908547687704724917
absolute error = 6.47702463250709576001e-11
relative error = 5.8779301039979900791351970822378e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=3.48
NO POLE
NO POLE
x[1] = 0.1022
y2[1] (analytic) = 1.1020221824478686697329065133617
y2[1] (numeric) = 1.1020221824478686697329110002743
absolute error = 4.4869126e-24
relative error = 4.0715265731161941438273795124900e-22 %
h = 0.0001
y1[1] (analytic) = 1.1020221824478686697329065133617
y1[1] (numeric) = 1.10202218251900625508529541969
absolute error = 7.11375853523889063283e-11
relative error = 6.4551863370276651247909146832501e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.5MB, time=3.70
NO POLE
NO POLE
x[1] = 0.1023
y2[1] (analytic) = 1.1021216601499949073936116679517
y2[1] (numeric) = 1.102121660149994907393617538441
absolute error = 5.8704893e-24
relative error = 5.3265347304770753860088683786306e-22 %
h = 0.0001
y1[1] (analytic) = 1.1021216601499949073936116679517
y1[1] (numeric) = 1.1021216602277982663980058615294
absolute error = 7.78033590043941935777e-11
relative error = 7.0594165614897204945381627518617e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.5MB, time=3.91
NO POLE
NO POLE
x[1] = 0.1024
y2[1] (analytic) = 1.1022211368309045444053815829051
y2[1] (numeric) = 1.1022211368309045444053891755714
absolute error = 7.5926663e-24
relative error = 6.8885145151819171657881464561988e-22 %
h = 0.0001
y1[1] (analytic) = 1.1022211368309045444053815829051
y1[1] (numeric) = 1.1022211369156721085592115168272
absolute error = 8.47675641538299339221e-11
relative error = 7.6906131919727838912860736424198e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1025
y2[1] (analytic) = 1.102320612489602813959948860445
y2[1] (numeric) = 1.1023206124896028139599585771634
absolute error = 9.7167184e-24
relative error = 8.8147842741094065788421720542393e-22 %
h = 0.0001
y1[1] (analytic) = 1.102320612489602813959948860445
y1[1] (numeric) = 1.1023206125816330116274194554716
absolute error = 9.20301976674705950266e-11
relative error = 8.3487686454142788729460667711390e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.5MB, time=4.11
NO POLE
NO POLE
x[1] = 0.1026
y2[1] (analytic) = 1.1024200871250949594711597688478
y2[1] (numeric) = 1.1024200871250949594711720832502
absolute error = 1.23144024e-23
relative error = 1.1170335649555927689332415162079e-21 %
h = 0.0001
y1[1] (analytic) = 1.1024200871250949594711597688478
y1[1] (numeric) = 1.1024200872246862158772818284554
absolute error = 9.95912564061220596076e-11
relative error = 9.0338753410995437450675215633836e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.5MB, time=4.32
NO POLE
NO POLE
x[1] = 0.1027
y2[1] (analytic) = 1.102519560736386234584921808297
y2[1] (numeric) = 1.1025195607363862345849372749798
absolute error = 1.54666828e-23
relative error = 1.4028488337811997000760816399814e-21 %
h = 0.0001
y1[1] (analytic) = 1.102519560736386234584921808297
y1[1] (numeric) = 1.1025195608438369718095434957776
absolute error = 1.074507372246216874806e-10
relative error = 9.7459257006609508304831041933828e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.5MB, time=4.53
NO POLE
NO POLE
x[1] = 0.1028
y2[1] (analytic) = 1.1026190333224819031891511744154
y2[1] (numeric) = 1.1026190333224819031891704389039
absolute error = 1.92644885e-23
relative error = 1.7471572608311518248174716117714e-21 %
h = 0.0001
y1[1] (analytic) = 1.1026190333224819031891511744154
y1[1] (numeric) = 1.1026190334380905401609895521145
absolute error = 1.156086369718383776991e-10
relative error = 1.0484912148077026116079269040747e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=87.7MB, alloc=4.5MB, time=4.74
x[1] = 0.1029
y2[1] (analytic) = 1.102718504882387239423720119378
y2[1] (numeric) = 1.1027185048823872394237439288761
absolute error = 2.38094981e-23
relative error = 2.1591637389398350650449237701550e-21 %
h = 0.0001
y1[1] (analytic) = 1.102718504882387239423720119378
y1[1] (numeric) = 1.10271850500645219191439275016
absolute error = 1.240649524906726307820e-10
relative error = 1.1250827109671569276272298758398e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.103
y2[1] (analytic) = 1.1028179754151075276904042105046
y2[1] (numeric) = 1.102817975415107527690433425461
absolute error = 2.92149564e-23
relative error = 2.6491186262178315660044586430199e-21 %
h = 0.0001
y1[1] (analytic) = 1.1028179754151075276904042105046
y1[1] (numeric) = 1.1028179755479272083084608215356
absolute error = 1.328196806180566110310e-10
relative error = 1.2043663014112774073142292226916e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.5MB, time=4.94
NO POLE
NO POLE
x[1] = 0.1031
y2[1] (analytic) = 1.1029174449196480626628294862341
y2[1] (numeric) = 1.1029174449196480626628650927535
absolute error = 3.56065194e-23
relative error = 3.2283938896799367458760854526067e-21 %
h = 0.0001
y1[1] (analytic) = 1.1029174449196480626628294862341
y1[1] (numeric) = 1.1029174450615208808477836951712
absolute error = 1.418728181849542089371e-10
relative error = 1.2863412292412349132959907064457e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.5MB, time=5.15
NO POLE
NO POLE
x[1] = 0.1032
y2[1] (analytic) = 1.1030169133950141492964195093798
y2[1] (numeric) = 1.10301691339501414929646263251
absolute error = 4.31231302e-23
relative error = 3.9095620090964712966782556299873e-21 %
h = 0.0001
y1[1] (analytic) = 1.1030169133950141492964195093798
y1[1] (numeric) = 1.1030169135462385113127806130571
absolute error = 1.512243620163611036773e-10
relative error = 1.3710067377924639099022143329945e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.5MB, time=5.36
NO POLE
NO POLE
x[1] = 0.1033
y2[1] (analytic) = 1.103116380840211102838342317567
y2[1] (numeric) = 1.103116380840211102838394235491
absolute error = 5.19179240e-23
relative error = 4.7064774761531193737487332164444e-21 %
h = 0.0001
y1[1] (analytic) = 1.103116380840211102838342317567
y1[1] (numeric) = 1.103116381001085411769647143267
absolute error = 1.608743089313048257000e-10
relative error = 1.4583620706345746160477787342816e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1034
y2[1] (analytic) = 1.1032158472542442488374572707527
y2[1] (numeric) = 1.1032158472542442488375194299164
absolute error = 6.21591637e-23
relative error = 5.6343610232490579098479865745046e-21 %
h = 0.0001
y1[1] (analytic) = 1.1032158472542442488374572707527
y1[1] (numeric) = 1.1032158474250669045803020901534
absolute error = 1.708226557428448194007e-10
relative error = 1.5484064715712651957104329414243e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.5MB, time=5.56
NO POLE
NO POLE
x[1] = 0.1035
y2[1] (analytic) = 1.1033153126361189231542617957292
y2[1] (numeric) = 1.1033153126361189231543358269334
absolute error = 7.40312042e-23
relative error = 6.7098864080042009637703187944274e-21 %
h = 0.0001
y1[1] (analytic) = 1.1033153126361189231542617957292
y1[1] (numeric) = 1.1033153128171883224123343016158
absolute error = 1.810693992580725058866e-10
relative error = 1.6411391846402339859726256900810e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.5MB, time=5.77
NO POLE
NO POLE
x[1] = 0.1036
y2[1] (analytic) = 1.1034147769848404719708380275103
y2[1] (numeric) = 1.1034147769848404719709257629984
absolute error = 8.77354881e-23
relative error = 7.9512699965595417256046762126644e-21 %
h = 0.0001
y1[1] (analytic) = 1.1034147769848404719708380275103
y1[1] (numeric) = 1.1034147771764550082489493733416
absolute error = 1.916145362781113458313e-10
relative error = 1.7365594541130917626200447637920e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.5MB, time=5.97
NO POLE
NO POLE
x[1] = 0.1037
y2[1] (analytic) = 1.1035142402994142518007993475029
y2[1] (numeric) = 1.1035142402994142518009028390722
absolute error = 1.034915693e-22
relative error = 9.3783628267379535683344023061879e-21 %
h = 0.0001
y1[1] (analytic) = 1.1035142402994142518007993475029
y1[1] (numeric) = 1.1035142405018723153989162499209
absolute error = 2.024580635981169024180e-10
relative error = 1.8346665244952740432640675426129e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=114.4MB, alloc=4.5MB, time=6.18
x[1] = 0.1038
y2[1] (analytic) = 1.1036137025788456294992368183617
y2[1] (numeric) = 1.1036137025788456294993583565305
absolute error = 1.215381688e-22
relative error = 1.1012745539131880383165353760052e-20 %
h = 0.0001
y1[1] (analytic) = 1.1036137025788456294992368183617
y1[1] (numeric) = 1.1036137027924456075065137227357
absolute error = 2.135999780072769043740e-10
relative error = 1.9354596405259534279952133868520e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1039
y2[1] (analytic) = 1.1037131638221399822726655154307
y2[1] (numeric) = 1.1037131638221399822728076496887
absolute error = 1.421342580e-22
relative error = 1.2877825748475398555555652378097e-20 %
h = 0.0001
y1[1] (analytic) = 1.1037131638221399822726655154307
y1[1] (numeric) = 1.1037131640471802585614768245235
absolute error = 2.250402762888113090928e-10
relative error = 2.0389380471779519775157880552008e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.5MB, time=6.41
NO POLE
NO POLE
x[1] = 0.104
y2[1] (analytic) = 1.1038126240283026976889707546695
y2[1] (numeric) = 1.1038126240283026976891363148427
absolute error = 1.655601732e-22
relative error = 1.4998938188965203922855442289756e-20 %
h = 0.0001
y1[1] (analytic) = 1.1038126240283026976889707546695
y1[1] (numeric) = 1.1038126242650816529089431205162
absolute error = 2.367789552199723658467e-10
relative error = 2.1451009896576536287597372576594e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.5MB, time=6.64
NO POLE
NO POLE
x[1] = 0.1041
y2[1] (analytic) = 1.103912083196339173687354216966
y2[1] (numeric) = 1.1039120831963391736875463357261
absolute error = 1.921187601e-22
relative error = 1.7403447523078721019858147939421e-20 %
h = 0.0001
y1[1] (analytic) = 1.103912083196339173687354216966
y1[1] (numeric) = 1.1039120834451551852593988960551
absolute error = 2.488160115720446790891e-10
relative error = 2.2539477134049166479742003019393e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.5MB, time=6.85
NO POLE
NO POLE
x[1] = 0.1042
y2[1] (analytic) = 1.1040115413252548185882799687365
y2[1] (numeric) = 1.1040115413252548185885021052833
absolute error = 2.221365468e-22
relative error = 2.0120853676343583973149372645620e-20 %
h = 0.0001
y1[1] (analytic) = 1.1040115413252548185882799687365
y1[1] (numeric) = 1.1040115415864062606986252405822
absolute error = 2.611514421103452718457e-10
relative error = 2.3654774640929861212372699783552e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1043
y2[1] (analytic) = 1.1041109984140550511034203787124
y2[1] (numeric) = 1.1041109984140550511036763436607
absolute error = 2.559649483e-22
relative error = 2.3182899968179651416668427897635e-20 %
h = 0.0001
y1[1] (analytic) = 1.1041109984140550511034203787124
y1[1] (numeric) = 1.104110998687840294697644027908
absolute error = 2.737852435942236491956e-10
relative error = 2.4796894876284064824027827127760e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.5MB, time=7.06
NO POLE
NO POLE
x[1] = 0.1044
y2[1] (analytic) = 1.1042104544617453003456019308154
y2[1] (numeric) = 1.1042104544617453003458959123149
absolute error = 2.939814995e-22
relative error = 2.6623683765365473657664712927605e-20 %
h = 0.0001
y1[1] (analytic) = 1.1042104544617453003456019308154
y1[1] (numeric) = 1.1042104547484627131226637926571
absolute error = 2.867174127770618618417e-10
relative error = 2.5965830301509340784484764440782e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.5MB, time=7.27
NO POLE
NO POLE
x[1] = 0.1045
y2[1] (analytic) = 1.1043099094673310058387509330207
y2[1] (numeric) = 1.1043099094673310058390875241398
absolute error = 3.365911191e-22
relative error = 3.0479769873871392099507117317212e-20 %
h = 0.0001
y1[1] (analytic) = 1.1043099094673310058387509330207
y1[1] (numeric) = 1.1043099097672789522450255027917
absolute error = 2.999479464062745697710e-10
relative error = 2.7161573380334497722147340550824e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.5MB, time=7.48
NO POLE
NO POLE
x[1] = 0.1046
y2[1] (analytic) = 1.1044093634298176175278391221099
y2[1] (numeric) = 1.104409363429817617528223349512
absolute error = 3.842274021e-22
relative error = 3.4790306459079262047776716243949e-20 %
h = 0.0001
y1[1] (analytic) = 1.1044093634298176175278391221099
y1[1] (numeric) = 1.1044093637432944587511482281136
absolute error = 3.134768412233091060037e-10
relative error = 2.8384116578818715825057433628662e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.5MB, time=7.69
NO POLE
NO POLE
x[1] = 0.1047
y2[1] (analytic) = 1.1045088163482105957888291642125
y2[1] (numeric) = 1.1045088163482105957892665181561
absolute error = 4.373539436e-22
relative error = 3.9597143737250038380604703722220e-20 %
h = 0.0001
y1[1] (analytic) = 1.1045088163482105957888291642125
y1[1] (numeric) = 1.1045088166755146897524747046453
absolute error = 3.273040939636455404328e-10
relative error = 2.9633452365350673615502724149016e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1048
y2[1] (analytic) = 1.1046082682215154114386200510382
y2[1] (numeric) = 1.1046082682215154114391165167295
absolute error = 4.964656913e-22
relative error = 4.4944955201117505809339197791633e-20 %
h = 0.0001
y1[1] (analytic) = 1.1046082682215154114386200510382
y1[1] (numeric) = 1.1046082685629451127954167947905
absolute error = 3.414297013567967437523e-10
relative error = 3.0909573210647675097866669322521e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.5MB, time=7.89
NO POLE
NO POLE
x[1] = 0.1049
y2[1] (analytic) = 1.1047077190487375457449923916998
y2[1] (numeric) = 1.1047077190487375457455544820279
absolute error = 5.620903281e-22
relative error = 5.0881361504744013937767229185864e-20 %
h = 0.0001
y1[1] (analytic) = 1.1047077190487375457449923916998
y1[1] (numeric) = 1.104707719404591205871300843175
absolute error = 3.558536601263084514752e-10
relative error = 3.2212471587754777279647607715000e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.5MB, time=8.11
NO POLE
NO POLE
x[1] = 0.105
y2[1] (analytic) = 1.1048071688288824904365536000268
y2[1] (numeric) = 1.1048071688288824904371883897118
absolute error = 6.347896850e-22
relative error = 5.7457057024067797757749168382422e-20 %
h = 0.0001
y1[1] (analytic) = 1.1048071688288824904365536000268
y1[1] (numeric) = 1.1048071691994584574263129280681
absolute error = 3.705759669897593280413e-10
relative error = 3.3542139972043918065465307378547e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.5MB, time=8.32
NO POLE
NO POLE
x[1] = 0.1051
y2[1] (analytic) = 1.1049066175609557477126829772711
y2[1] (numeric) = 1.1049066175609557477133981384545
absolute error = 7.151611834e-22
relative error = 6.4725939010003786126513722163957e-20 %
h = 0.0001
y1[1] (analytic) = 1.1049066175609557477126829772711
y1[1] (numeric) = 1.1049066179465523663714440082854
absolute error = 3.855966186587610310143e-10
relative error = 3.4898570841213044523828117189536e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1052
y2[1] (analytic) = 1.1050060652439628302534766901051
y2[1] (numeric) = 1.1050060652439628302542805294122
absolute error = 8.038393071e-22
relative error = 7.2745239359616424836873059867355e-20 %
h = 0.0001
y1[1] (analytic) = 1.1050060652439628302534766901051
y1[1] (numeric) = 1.1050060656448784420924349654732
absolute error = 4.009156118389582753681e-10
relative error = 3.6281756675285241526470211570032e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.5MB, time=8.52
NO POLE
NO POLE
x[1] = 0.1053
y2[1] (analytic) = 1.1051055118769092612296926438124
y2[1] (numeric) = 1.105105511876909261230594140917
absolute error = 9.014971046e-22
relative error = 8.1575659058011474418494573083695e-20 %
h = 0.0001
y1[1] (analytic) = 1.1051055118769092612296926438124
y1[1] (numeric) = 1.1051055122934422044597215416755
absolute error = 4.165329432300288978631e-10
relative error = 3.7691689956607860760149964393884e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.5MB, time=8.73
NO POLE
NO POLE
x[1] = 0.1054
y2[1] (analytic) = 1.1052049574588005743126952505717
y2[1] (numeric) = 1.1052049574588005743137040982927
absolute error = 1.0088477210e-21
relative error = 9.1281505225930680455874675355306e-20 %
h = 0.0001
y1[1] (analytic) = 1.1052049574588005743126952505717
y1[1] (numeric) = 1.1052049578912491838383791720836
absolute error = 4.324486095256839215119e-10
relative error = 3.9128363169851650110673861290434e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.5MB, time=8.94
NO POLE
NO POLE
x[1] = 0.1055
y2[1] (analytic) = 1.1053044019886423136844000927352
y2[1] (numeric) = 1.1053044019886423136855267386948
absolute error = 1.1266459596e-21
relative error = 1.0193083078045833965826632209473e-19 %
h = 0.0001
y1[1] (analytic) = 1.1053044019886423136844000927352
y1[1] (numeric) = 1.1053044024373049210980677128692
absolute error = 4.486626074136676201340e-10
relative error = 4.0591768802009883418928592029978e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.5MB, time=9.15
NO POLE
NO POLE
x[1] = 0.1056
y2[1] (analytic) = 1.1054038454654400340472184810008
y2[1] (numeric) = 1.1054038454654400340484741708744
absolute error = 1.2556898736e-21
relative error = 1.1359557674338293159541744534187e-19 %
h = 0.0001
y1[1] (analytic) = 1.1054038454654400340472184810008
y1[1] (numeric) = 1.1054038459306149676229760640018
absolute error = 4.651749335757575830010e-10
relative error = 4.2081899342397490608875972351004e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1057
y2[1] (analytic) = 1.1055032878881993006340019073801
y2[1] (numeric) = 1.1055032878881993006353987297674
absolute error = 1.3968223873e-21
relative error = 1.2635171714127566696345220530105e-19 %
h = 0.0001
y1[1] (analytic) = 1.1055032878881993006340019073801
y1[1] (numeric) = 1.1055032883701848853217666869502
absolute error = 4.819855846877647795701e-10
relative error = 4.3598747282650188187130656419965e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.5MB, time=9.36
NO POLE
NO POLE
x[1] = 0.1058
y2[1] (analytic) = 1.1056027292559256892179863928614
y2[1] (numeric) = 1.1056027292559256892195373258089
absolute error = 1.5509329475e-21
relative error = 1.4027940655897105351058265357332e-19 %
h = 0.0001
y1[1] (analytic) = 1.1056027292559256892179863928614
y1[1] (numeric) = 1.1056027297550202466375200171692
absolute error = 4.990945574195336243078e-10
relative error = 4.5142305116723610114111681431220e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.5MB, time=9.57
NO POLE
NO POLE
x[1] = 0.1059
y2[1] (analytic) = 1.1057021695676247861227367296688
y2[1] (numeric) = 1.1057021695676247861244556888735
absolute error = 1.7189592047e-21
relative error = 1.5546313030860598222142619237739e-19 %
h = 0.0001
y1[1] (analytic) = 1.1057021695676247861227367296688
y1[1] (numeric) = 1.1057021700841266345576787712725
absolute error = 5.165018484349420416037e-10
relative error = 4.6712565340892439046577980198198e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.5MB, time=9.77
NO POLE
NO POLE
x[1] = 0.106
y2[1] (analytic) = 1.1058016088223021882320906180187
y2[1] (numeric) = 1.1058016088223021882339925067424
absolute error = 1.9018887237e-21
relative error = 1.7199185717640113929527234397506e-19 %
h = 0.0001
y1[1] (analytic) = 1.1058016088223021882320906180187
y1[1] (numeric) = 1.1058016093565096426239921487908
absolute error = 5.342074543919015307721e-10
relative error = 4.8309520453749537951159151941182e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1061
y2[1] (analytic) = 1.1059010470189635030001026972731
y2[1] (numeric) = 1.1059010470189635030022034579974
absolute error = 2.1007607243e-21
relative error = 1.8995919480886223289681454504362e-19 %
h = 0.0001
y1[1] (analytic) = 1.1059010470189635030001026972731
y1[1] (numeric) = 1.1059010475711748749424599284175
absolute error = 5.522113719423572311444e-10
relative error = 4.9933162956205082088972276791341e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.5MB, time=9.98
NO POLE
NO POLE
x[1] = 0.1062
y2[1] (analytic) = 1.1060004841566143484609884713902
y2[1] (numeric) = 1.1060004841566143484633051392427
absolute error = 2.3166678525e-21
relative error = 2.0946354777290947635717187407442e-19 %
h = 0.0001
y1[1] (analytic) = 1.1060004841566143484609884713902
y1[1] (numeric) = 1.1060004847271279461932764586416
absolute error = 5.705135977322879872514e-10
relative error = 5.1583485351485691371062840830937e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=10.19
NO POLE
NO POLE
x[1] = 0.1063
y2[1] (analytic) = 1.1060999202342603532390681285749
y2[1] (numeric) = 1.1060999202342603532416188865546
absolute error = 2.5507579797e-21
relative error = 2.3060827806223656839364676569941e-19 %
h = 0.0001
y1[1] (analytic) = 1.1060999202342603532390681285749
y1[1] (numeric) = 1.106099920823374481640774542668
absolute error = 5.891141284017064140931e-10
relative error = 5.3260480145133563084272383786478e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=10.40
NO POLE
NO POLE
x[1] = 0.1064
y2[1] (analytic) = 1.1061993552509071565587102550263
y2[1] (numeric) = 1.1061993552509071565615144910606
absolute error = 2.8042360343e-21
relative error = 2.5350186844612160075419985790483e-19 %
h = 0.0001
y1[1] (analytic) = 1.1061993552509071565587102550263
y1[1] (numeric) = 1.1061993558589201171433692175269
absolute error = 6.080129605846589625006e-10
relative error = 5.4964139845005604987768533148670e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=10.61
NO POLE
NO POLE
x[1] = 0.1065
y2[1] (analytic) = 1.1062987892055604082542754426865
y2[1] (numeric) = 1.1062987892055604082573538085472
absolute error = 3.0783658607e-21
relative error = 2.7825808820694745765298464374471e-19 %
h = 0.0001
y1[1] (analytic) = 1.1062987892055604082542754426865
y1[1] (numeric) = 1.1062987898327704991635014272717
absolute error = 6.272100909092259845852e-10
relative error = 5.6694456961272568779614168429462e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1066
y2[1] (analytic) = 1.1063982220972257687800597908883
y2[1] (numeric) = 1.1063982220972257687834342629981
absolute error = 3.3744721098e-21
relative error = 3.0499616163550424949075950450043e-19 %
h = 0.0001
y1[1] (analytic) = 1.1063982220972257687800597908883
y1[1] (numeric) = 1.1063982227439312847775815901668
absolute error = 6.467055159975217992785e-10
relative error = 5.8451424006418183933539211300655e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=10.81
NO POLE
NO POLE
x[1] = 0.1067
y2[1] (analytic) = 1.1064976539249089092202383018042
y2[1] (numeric) = 1.1064976539249089092239322439624
absolute error = 3.6939421582e-21
relative error = 3.3384093902929185989819499900417e-19 %
h = 0.0001
y1[1] (analytic) = 1.1064976539249089092202383018042
y1[1] (numeric) = 1.1064976545914081416859330597652
absolute error = 6.664992324656947579610e-10
relative error = 6.0235033495238291905509024385198e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=11.02
NO POLE
NO POLE
x[1] = 0.1068
y2[1] (analytic) = 1.1065970846876155112988081695962
y2[1] (numeric) = 1.1065970846876155113028463976544
absolute error = 4.0382280582e-21
relative error = 3.6492307038202283603210218443323e-19 %
h = 0.0001
y1[1] (analytic) = 1.1065970846876155112988081695962
y1[1] (numeric) = 1.1065970853742067482227354797772
absolute error = 6.865912369239273101810e-10
relative error = 6.2045277944839980710072240634992e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.5MB, time=11.23
NO POLE
NO POLE
x[1] = 0.1069
y2[1] (analytic) = 1.1066965143843512673895319631674
y2[1] (numeric) = 1.1066965143843512673939408116845
absolute error = 4.4088485171e-21
relative error = 3.9837918162709822779835759915299e-19 %
h = 0.0001
y1[1] (analytic) = 1.1066965143843512673895319631674
y1[1] (numeric) = 1.1066965150913327933659680326301
absolute error = 7.069815259764360694627e-10
relative error = 6.3882149874640719866208785128249e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=209.8MB, alloc=4.5MB, time=11.44
x[1] = 0.107
y2[1] (analytic) = 1.1067959430141218805258807024165
y2[1] (numeric) = 1.1067959430141218805306880933226
absolute error = 4.8073909061e-21
relative error = 4.3435205346055928955899600185838e-19 %
h = 0.0001
y1[1] (analytic) = 1.1067959430141218805258807024165
y1[1] (numeric) = 1.1067959437417919767473525816199
absolute error = 7.276700962214718792034e-10
relative error = 6.5745641806367495712489371399595e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1071
y2[1] (analytic) = 1.1068953705759330644109768278945
y2[1] (numeric) = 1.1068953705759330644162123411941
absolute error = 5.2355132996e-21
relative error = 4.7299080281417109685536615606587e-19 %
h = 0.0001
y1[1] (analytic) = 1.1068953705759330644109768278945
y1[1] (numeric) = 1.1068953713245900086622967065551
absolute error = 7.486569442513198786606e-10
relative error = 6.7635746264055947091439167256004e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=11.65
NO POLE
NO POLE
x[1] = 0.1072
y2[1] (analytic) = 1.1069947970687905434275370637652
y2[1] (numeric) = 1.1069947970687905434332320103092
absolute error = 5.6949465440e-21
relative error = 5.1445106689567451647324258116553e-19 %
h = 0.0001
y1[1] (analytic) = 1.1069947970687905434275370637652
y1[1] (numeric) = 1.1069947978387326100798366327939
absolute error = 7.699420666522995690287e-10
relative error = 6.9552455774049501402899002758655e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.5MB, time=11.86
NO POLE
NO POLE
x[1] = 0.1073
y2[1] (analytic) = 1.1070942224917000526478151739699
y2[1] (numeric) = 1.1070942224917000526540026703262
absolute error = 6.1874963563e-21
relative error = 5.5889518982169451313427788130799e-19 %
h = 0.0001
y1[1] (analytic) = 1.1070942224917000526478151739699
y1[1] (numeric) = 1.1070942232832255126525800535747
absolute error = 7.915254600047648796048e-10
relative error = 7.1495762864998511026159544973233e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.5MB, time=12.06
NO POLE
NO POLE
x[1] = 0.1074
y2[1] (analytic) = 1.1071936468436673378435446114965
y2[1] (numeric) = 1.1071936468436673378502596569492
absolute error = 6.7150454527e-21
relative error = 6.0649241185974270074882659886241e-19 %
h = 0.0001
y1[1] (analytic) = 1.1071936468436673378435446114965
y1[1] (numeric) = 1.1071936476570744587266488455404
absolute error = 8.134071208831042340439e-10
relative error = 7.3465660067859390110716248975449e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1075
y2[1] (analytic) = 1.1072930701236981554958810606538
y2[1] (numeric) = 1.1072930701236981555031606163608
absolute error = 7.2795557070e-21
relative error = 6.5741906125961618700851423216030e-19 %
h = 0.0001
y1[1] (analytic) = 1.1072930701236981554958810606538
y1[1] (numeric) = 1.1072930709592852013516216773583
absolute error = 8.355870458557406167045e-10
relative error = 7.5462139915893751735556189973793e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.5MB, time=12.27
NO POLE
NO POLE
x[1] = 0.1076
y2[1] (analytic) = 1.1073924923307982728053448722518
y2[1] (numeric) = 1.1073924923307982728132279425904
absolute error = 7.8830703386e-21
relative error = 7.1185874865450898818601915237033e-19 %
h = 0.0001
y1[1] (analytic) = 1.1073924923307982728053448722518
y1[1] (numeric) = 1.1073924931888635042904765113342
absolute error = 8.580652314851316390824e-10
relative error = 7.7485194944667545436598947007284e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.5MB, time=12.48
NO POLE
NO POLE
x[1] = 0.1077
y2[1] (analytic) = 1.1074919134639734677017633915879
y2[1] (numeric) = 1.1074919134639734677102911077186
absolute error = 8.5277161307e-21
relative error = 7.7000256408440179752582157814606e-19 %
h = 0.0001
y1[1] (analytic) = 1.1074919134639734677017633915879
y1[1] (numeric) = 1.1074919143448151420295329979231
absolute error = 8.808416743277696063352e-10
relative error = 7.9534817692050195102338331230273e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.5MB, time=12.69
NO POLE
NO POLE
x[1] = 0.1078
y2[1] (analytic) = 1.107591333522229528854213179141
y2[1] (numeric) = 1.1075913335222295288634288848187
absolute error = 9.2157056777e-21
relative error = 8.3204927654980060982827201421564e-19 %
h = 0.0001
y1[1] (analytic) = 1.107591333522229528854213179141
y1[1] (numeric) = 1.1075913344261458997883947630358
absolute error = 9.039163709341815838948e-10
relative error = 8.1611000698213737237262199848009e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=236.5MB, alloc=4.5MB, time=12.89
x[1] = 0.1079
y2[1] (analytic) = 1.1076907525045722556809621238716
y2[1] (numeric) = 1.1076907525045722556909114635352
absolute error = 9.9493396636e-21
relative error = 8.9820553625673892644885874364761e-19 %
h = 0.0001
y1[1] (analytic) = 1.1076907525045722556809621238716
y1[1] (numeric) = 1.107690753431861573529891588043
absolute error = 9.272893178489294641714e-10
relative error = 8.3713736505631959593187592253089e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.108
y2[1] (analytic) = 1.1077901704100074583594114490316
y2[1] (numeric) = 1.1077901704100074583701424582001
absolute error = 1.07310091685e-20
relative error = 9.6868607928957474201304579793484e-19 %
h = 0.0001
y1[1] (analytic) = 1.1077901704100074583594114490316
y1[1] (numeric) = 1.1077901713609679699700214823764
absolute error = 9.509605116106100333448e-10
relative error = 8.5843017659079540167953217846150e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.5MB, time=13.10
NO POLE
NO POLE
x[1] = 0.1081
y2[1] (analytic) = 1.1078895872375409578360376103814
y2[1] (numeric) = 1.1078895872375409578476008083882
absolute error = 1.15631980068e-20
relative error = 1.0437139350350038014798718965931e-18 %
h = 0.0001
y1[1] (analytic) = 1.1078895872375409578360376103814
y1[1] (numeric) = 1.1078895882124709065878926486283
absolute error = 9.749299487518550382469e-10
relative error = 8.7998836705631186571642814345729e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.5MB, time=13.31
NO POLE
NO POLE
x[1] = 0.1082
y2[1] (analytic) = 1.1079890029861785858363340867174
y2[1] (numeric) = 1.107989002986178585848782571811
absolute error = 1.24484850936e-20
relative error = 1.1235206360396779534030535323011e-18 %
h = 0.0001
y1[1] (analytic) = 1.1079890029861785858363340867174
y1[1] (numeric) = 1.10798900398537621163566534005
absolute error = 9.991976257993312533326e-10
relative error = 9.0181186194660775759908040685487e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.5MB, time=13.52
NO POLE
NO POLE
x[1] = 0.1083
y2[1] (analytic) = 1.1080884176549261848747530626082
y2[1] (numeric) = 1.1080884176549261848881426094505
absolute error = 1.33895468423e-20
relative error = 1.2083464305706412615802518900321e-18 %
h = 0.0001
y1[1] (analytic) = 1.1080884176549261848747530626082
y1[1] (numeric) = 1.1080884186786897241484936103493
absolute error = 1.0237635392737405477411e-09
relative error = 9.2390058677840494134393025636054e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1084
y2[1] (analytic) = 1.1081878312427896082646470032422
y2[1] (numeric) = 1.1081878312427896082790361628331
absolute error = 1.43891595909e-20
relative error = 1.2984404976512976528256861318913e-18 %
h = 0.0001
y1[1] (analytic) = 1.1081878312427896082646470032422
y1[1] (numeric) = 1.1081878322914172939544669556877
absolute error = 1.0486276856898199524455e-09
relative error = 9.4625446709139978009892687424593e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.5MB, time=13.72
NO POLE
NO POLE
x[1] = 0.1085
y2[1] (analytic) = 1.1082872437487747201282101212859
y2[1] (numeric) = 1.1082872437487747201436603233444
absolute error = 1.54502020585e-20
relative error = 1.3940611647067043264298683575551e-18 %
h = 0.0001
y1[1] (analytic) = 1.1082872437487747201282101212859
y1[1] (numeric) = 1.1082872448225647816845518487787
absolute error = 1.0737900615563417274928e-09
relative error = 9.6887342844825454448256135814270e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.5MB, time=13.93
NO POLE
NO POLE
x[1] = 0.1086
y2[1] (analytic) = 1.1083866551718873954064197356531
y2[1] (numeric) = 1.1083866551718873954229953934854
absolute error = 1.65756578323e-20
relative error = 1.4954761278436237609631645482182e-18 %
h = 0.0001
y1[1] (analytic) = 1.1083866551718873954064197356531
y1[1] (numeric) = 1.1083866562711380587825331649864
absolute error = 1.0992506633761134293333e-09
relative error = 9.9175739643458882458766743285497e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.5MB, time=14.14
NO POLE
NO POLE
x[1] = 0.1087
y2[1] (analytic) = 1.1084860655111335198689775220874
y2[1] (numeric) = 1.1084860655111335198867461399707
absolute error = 1.77686178833e-20
relative error = 1.6029626746013014118607312888524e-18 %
h = 0.0001
y1[1] (analytic) = 1.1084860655111335198689775220874
y1[1] (numeric) = 1.1084860666361430075149555003264
absolute error = 1.1250094876459779782390e-09
relative error = 1.0149062966589709456478476153064e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=263.2MB, alloc=4.5MB, time=14.36
x[1] = 0.1088
y2[1] (analytic) = 1.1085854747655189901242506554567
y2[1] (numeric) = 1.1085854747655189901432829385692
absolute error = 1.90322831125e-20
relative error = 1.7168079093337921032595718354278e-18 %
h = 0.0001
y1[1] (analytic) = 1.1085854747655189901242506554567
y1[1] (numeric) = 1.1085854759165855209810643812684
absolute error = 1.1510665308568137258117e-09
relative error = 1.0383200547529093873653770776773e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1089
y2[1] (analytic) = 1.1086848829340497136292128436612
y2[1] (numeric) = 1.108684882934049713649582810588
absolute error = 2.03699669268e-20
relative error = 1.8373089811500307553651957836440e-18 %
h = 0.0001
y1[1] (analytic) = 1.1086848829340497136292128436612
y1[1] (numeric) = 1.1086848841114715031227473662421
absolute error = 1.1774217894935345225809e-09
relative error = 1.0619985963708442068988967869697e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.5MB, time=14.58
NO POLE
NO POLE
x[1] = 0.109
y2[1] (analytic) = 1.1087842900157316086993852530554
y2[1] (numeric) = 1.1087842900157316087211703509003
absolute error = 2.17850978449e-20
relative error = 1.9647733144371038617748464488771e-18 %
h = 0.0001
y1[1] (analytic) = 1.1087842900157316086993852530554
y1[1] (numeric) = 1.1087842912198068687344750387459
absolute error = 1.2040752600350897856905e-09
relative error = 1.0859418471901384655082163245606e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.5MB, time=14.81
NO POLE
NO POLE
x[1] = 0.1091
y2[1] (analytic) = 1.1088836960095706045187773252847
y2[1] (numeric) = 1.1088836960095706045420585474172
absolute error = 2.32812221325e-20
relative error = 2.0995188419019791733726011797442e-18 %
h = 0.0001
y1[1] (analytic) = 1.1088836960095706045187773252847
y1[1] (numeric) = 1.1088836972405975434732418919603
absolute error = 1.2310269389544645666756e-09
relative error = 1.1101497329110696588556225611361e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.5MB, time=15.02
NO POLE
NO POLE
x[1] = 0.1092
y2[1] (analytic) = 1.1089831009145726411498274854369
y2[1] (numeric) = 1.1089831009145726411746894919047
absolute error = 2.48620064678e-20
relative error = 2.2418742402202911432969226737613e-18 %
h = 0.0001
y1[1] (analytic) = 1.1089831009145726411498274854369
y1[1] (numeric) = 1.1089831021728494638685071047653
absolute error = 1.2582768227186796193284e-09
relative error = 1.1346221792568211509610165156367e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1093
y2[1] (analytic) = 1.1090825047297436695433437414095
y2[1] (numeric) = 1.1090825047297436695698749820463
absolute error = 2.65312406368e-20
relative error = 2.3921791682454693159233240860635e-18 %
h = 0.0001
y1[1] (analytic) = 1.1090825047297436695433437414095
y1[1] (numeric) = 1.1090825060155685773321352090634
absolute error = 1.2858249077887914676539e-09
relative error = 1.1593591119734736118097351378887e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.5MB, time=15.22
NO POLE
NO POLE
x[1] = 0.1094
y2[1] (analytic) = 1.1091819074540896515484441743935
y2[1] (numeric) = 1.1091819074540896515767370146515
absolute error = 2.82928402580e-20
relative error = 2.5507845077405460705057513464211e-18 %
h = 0.0001
y1[1] (analytic) = 1.1091819074540896515484441743935
y1[1] (numeric) = 1.1091819087677608421683366483078
absolute error = 1.3136711906198924739143e-09
relative error = 1.1843604568299964586102924493953e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.5MB, time=15.46
NO POLE
NO POLE
x[1] = 0.1095
y2[1] (analytic) = 1.1092813090866165599224973203738
y2[1] (numeric) = 1.1092813090866165599526481699113
absolute error = 3.01508495375e-20
relative error = 2.7180526067212150543117389110909e-18 %
h = 0.0001
y1[1] (analytic) = 1.1092813090866165599224973203738
y1[1] (numeric) = 1.1092813104284322275836082271379
absolute error = 1.3418156676611109067641e-09
relative error = 1.2096261396182393007020707546085e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.5MB, time=15.68
NO POLE
NO POLE
x[1] = 0.1096
y2[1] (analytic) = 1.1093807096263303783410624425475
y2[1] (numeric) = 1.1093807096263303783731718866007
absolute error = 3.21094440532e-20
relative error = 2.8943575252913253570285248053919e-18 %
h = 0.0001
y1[1] (analytic) = 1.1093807096263303783410624425475
y1[1] (numeric) = 1.1093807109965887136966734520206
absolute error = 1.3702583353556110094731e-09
relative error = 1.2351560861529233881086655679805e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=289.9MB, alloc=4.5MB, time=15.90
x[1] = 0.1097
y2[1] (analytic) = 1.1094801090722371014078296945594
y2[1] (numeric) = 1.1094801090722371014420026281293
absolute error = 3.41729335699e-20
relative error = 3.0800852841314918670483613727185e-18 %
h = 0.0001
y1[1] (analytic) = 1.1094801090722371014078296945594
y1[1] (numeric) = 1.1094801104712362915484227628001
absolute error = 1.3989991901405930682407e-09
relative error = 1.2609502222716330637381788779200e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1098
y2[1] (analytic) = 1.1095795074233427346645601744576
y2[1] (numeric) = 1.1095795074233427347009059393406
absolute error = 3.63457648830e-20
relative error = 3.2756341154318778310066078654218e-18 %
h = 0.0001
y1[1] (analytic) = 1.1095795074233427346645601744576
y1[1] (numeric) = 1.1095795088513809631118536550555
absolute error = 1.4280382284472934805979e-09
relative error = 1.2870084738348072192254454385395e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.5MB, time=16.13
NO POLE
NO POLE
x[1] = 0.1099
y2[1] (analytic) = 1.1096789046786532946010258692669
y2[1] (numeric) = 1.1096789046786532946396583939598
absolute error = 3.86325246929e-20
relative error = 3.4814147164568665466889430953209e-18 %
h = 0.0001
y1[1] (analytic) = 1.1096789046786532946010258692669
y1[1] (numeric) = 1.109678906136028741302010693167
absolute error = 1.4573754467009848239001e-09
relative error = 1.3133307667257307544172178506616e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.5MB, time=16.36
NO POLE
NO POLE
x[1] = 0.11
y2[1] (analytic) = 1.1097783008371748086649494900834
y2[1] (numeric) = 1.1097783008371748087059874325921
absolute error = 4.10379425087e-20
relative error = 3.6978505056138263926147755452642e-18 %
h = 0.0001
y1[1] (analytic) = 1.1097783008371748086649494900834
y1[1] (numeric) = 1.1097783023241856499859254139916
absolute error = 1.4870108413209759239082e-09
relative error = 1.3399170268505260404962890998952e-07 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y2 , x , 4 ) = y1 - 1.0;
diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;
Iterations = 100
Total Elapsed Time = 16 Seconds
Elapsed Time(since restart) = 16 Seconds
Expected Time Remaining = 2 Hours 15 Minutes 0 Seconds
Optimized Time Remaining = 2 Hours 14 Minutes 53 Seconds
Time to Timeout = 14 Minutes 43 Seconds
Percent Done = 0.202 %
> quit
memory used=299.1MB, alloc=4.5MB, time=16.44