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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> 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 INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, 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
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> 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 INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, 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
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_higher[1,m-2]) < glob_small_float ))) do # 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 - 1 - 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 INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or
abs(array_y2_higher[1, m - 1]) < glob_small_float or
abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or
abs(array_y1_higher[1, m - 1]) < glob_small_float or
abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_y2_higher[1, m]) or
glob_large_float <= abs(array_y2_higher[1, m - 1]) or
glob_large_float <= abs(array_y2_higher[1, m - 2]) or
glob_large_float <= abs(array_y2_higher[1, m - 3]) or
glob_large_float <= abs(array_y2_higher[1, m - 4]) or
glob_large_float <= abs(array_y2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_y1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_y1_higher[1, m]) or
glob_large_float <= abs(array_y1_higher[1, m - 1]) or
glob_large_float <= abs(array_y1_higher[1, m - 2]) or
glob_large_float <= abs(array_y1_higher[1, m - 3]) or
glob_large_float <= abs(array_y1_higher[1, m - 4]) or
glob_large_float <= abs(array_y1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> 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 INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, 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
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_y1_higher[2,1];
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y2_set_initial[1,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #emit pre sin $eq_no = 2 iii = 1
> #emit pre sin 1 $eq_no = 2
> array_tmp4[1] := sin(array_x[1]);
> array_tmp4_g[1] := cos(array_x[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_tmp4[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 diff $eq_no = 1 i = 2
> array_tmp1[2] := array_y1_higher[2,2];
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y2_set_initial[1,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #emit pre sin $eq_no = 2 iii = 2
> #emit pre sin 2 $eq_no = 2
> array_tmp4[2] := att(1,array_tmp4_g,array_x,1);
> array_tmp4_g[2] := -att(1,array_tmp4,array_x,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_tmp4[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 diff $eq_no = 1 i = 3
> array_tmp1[3] := array_y1_higher[2,3];
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y2_set_initial[1,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #emit pre sin $eq_no = 2 iii = 3
> #emit pre sin 3 $eq_no = 2
> array_tmp4[3] := att(2,array_tmp4_g,array_x,1);
> array_tmp4_g[3] := -att(2,array_tmp4,array_x,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_tmp4[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 diff $eq_no = 1 i = 4
> array_tmp1[4] := array_y1_higher[2,4];
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y2_set_initial[1,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #emit pre sin $eq_no = 2 iii = 4
> #emit pre sin 4 $eq_no = 2
> array_tmp4[4] := att(3,array_tmp4_g,array_x,1);
> array_tmp4_g[4] := -att(3,array_tmp4,array_x,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_tmp4[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 diff $eq_no = 1 i = 5
> array_tmp1[5] := array_y1_higher[2,5];
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y2_set_initial[1,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #emit pre sin $eq_no = 2 iii = 5
> #emit pre sin 5 $eq_no = 2
> array_tmp4[5] := att(4,array_tmp4_g,array_x,1);
> array_tmp4_g[5] := -att(4,array_tmp4,array_x,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_tmp4[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 diff $eq_no = 1
> array_tmp1[kkk] := array_y1_higher[2,kkk];
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if not array_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 sin $eq_no = 2
> array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_x,1);
> array_tmp4_g[kkk] := -att(kkk-1,array_tmp4,array_x,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_tmp4[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 INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, glob_last;
array_tmp1[1] := array_y1_higher[2, 1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y2_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp2[1]*glob_h*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp4[1] := sin(array_x[1]);
array_tmp4_g[1] := cos(array_x[1]);
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[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_y1_higher[2, 2];
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
if not array_y2_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp2[2]*glob_h*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp4[2] := att(1, array_tmp4_g, array_x, 1);
array_tmp4_g[2] := -att(1, array_tmp4, array_x, 1);
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[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_y1_higher[2, 3];
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
if not array_y2_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp2[3]*glob_h*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp4[3] := att(2, array_tmp4_g, array_x, 1);
array_tmp4_g[3] := -att(2, array_tmp4, array_x, 1);
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[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_y1_higher[2, 4];
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
if not array_y2_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp2[4]*glob_h*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp4[4] := att(3, array_tmp4_g, array_x, 1);
array_tmp4_g[4] := -att(3, array_tmp4, array_x, 1);
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[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_y1_higher[2, 5];
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
if not array_y2_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp2[5]*glob_h*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp4[5] := att(4, array_tmp4_g, array_x, 1);
array_tmp4_g[5] := -att(4, array_tmp4, array_x, 1);
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[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_y1_higher[2, kkk];
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_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] := att(kkk - 1, array_tmp4_g, array_x, 1);
array_tmp4_g[kkk] := -att(kkk - 1, array_tmp4, array_x, 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_tmp4[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)
> 2.0 - cos(x);
> end;
exact_soln_y1 := proc(x) 2.0 - cos(x) end proc
> exact_soln_y2 := proc(x)
> 2.0 - cos(x);
> end;
exact_soln_y2 := proc(x) 2.0 - 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
> INFO,
> ALWAYS,
> DEBUGL,
> glob_max_terms,
> DEBUGMASSIVE,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_log10abserr,
> glob_warned2,
> glob_smallish_float,
> years_in_century,
> days_in_year,
> min_in_hour,
> glob_log10normmin,
> glob_max_hours,
> glob_disp_incr,
> glob_max_minutes,
> glob_start,
> glob_unchanged_h_cnt,
> glob_max_trunc_err,
> glob_look_poles,
> glob_last_good_h,
> glob_display_flag,
> djd_debug,
> glob_max_sec,
> glob_hmax,
> djd_debug2,
> glob_iter,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_relerr,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_not_yet_start_msg,
> glob_dump,
> glob_html_log,
> glob_current_iter,
> glob_warned,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_clock_sec,
> glob_no_eqs,
> glob_max_rel_trunc_err,
> glob_relerr,
> glob_large_float,
> glob_h,
> glob_initial_pass,
> glob_not_yet_finished,
> hours_in_day,
> sec_in_min,
> glob_log10relerr,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_max_iter,
> glob_almost_1,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_small_float,
> glob_optimal_clock_start_sec,
> glob_clock_start_sec,
> centuries_in_millinium,
> glob_subiter_method,
> glob_percent_done,
> glob_log10_abserr,
> glob_max_opt_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_m1,
> array_last_rel_error,
> array_y2,
> array_y1,
> array_type_pole,
> array_pole,
> array_tmp4_g,
> array_y1_init,
> array_x,
> array_y2_init,
> array_1st_rel_error,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_norms,
> array_y1_set_initial,
> array_y2_higher_work,
> array_poles,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_complex_pole,
> array_y1_higher_work2,
> array_y1_higher_work,
> array_y1_higher,
> array_real_pole,
> array_y2_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> ALWAYS := 1;
> DEBUGL := 3;
> glob_max_terms := 30;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_log10abserr := 0.0;
> glob_warned2 := false;
> glob_smallish_float := 0.1e-100;
> years_in_century := 100.0;
> days_in_year := 365.0;
> min_in_hour := 60.0;
> glob_log10normmin := 0.1;
> glob_max_hours := 0.0;
> glob_disp_incr := 0.1;
> glob_max_minutes := 0.0;
> glob_start := 0;
> glob_unchanged_h_cnt := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_look_poles := false;
> glob_last_good_h := 0.1;
> glob_display_flag := true;
> djd_debug := true;
> glob_max_sec := 10000.0;
> glob_hmax := 1.0;
> djd_debug2 := true;
> glob_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> glob_not_yet_start_msg := true;
> glob_dump := false;
> glob_html_log := true;
> glob_current_iter := 0;
> glob_warned := false;
> glob_optimal_start := 0.0;
> glob_hmin_init := 0.001;
> glob_reached_optimal_h := false;
> glob_clock_sec := 0.0;
> glob_no_eqs := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_h := 0.1;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> hours_in_day := 24.0;
> sec_in_min := 60.0;
> glob_log10relerr := 0.0;
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_max_iter := 1000;
> glob_almost_1 := 0.9990;
> glob_optimal_expect_sec := 0.1;
> glob_normmax := 0.0;
> glob_small_float := 0.1e-50;
> glob_optimal_clock_start_sec := 0.0;
> glob_clock_start_sec := 0.0;
> centuries_in_millinium := 10.0;
> glob_subiter_method := 3;
> glob_percent_done := 0.0;
> glob_log10_abserr := 0.1e-10;
> glob_max_opt_iter := 10;
> #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/mtest5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = sin ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0;");
> 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,"glob_h := 0.00001 ;");
> 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,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"2.0 - cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_m1:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y2:= Array(1..(max_terms + 1),[]);
> array_y1:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_tmp4_g:= Array(1..(max_terms + 1),[]);
> array_y1_init:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y2_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 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_y2_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_type_pole[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_tmp4_g[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_x[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_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_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_norms[term] := 0.0;
> term := term + 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 <=2 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 <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_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 <=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
> ;
> 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 <=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 <=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 <=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 <= 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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_tmp4_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_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_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 := 5.0;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_h := 0.00001 ;
> 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] := false;
> array_y2_set_initial[1,3] := false;
> array_y2_set_initial[1,4] := false;
> 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 := 1;
> #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 <= 2 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 2 + 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 := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #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 := 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 , 1 ) = diff ( y1, x , 1) ;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = sin ( x ) ;");
> 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,"2012-06-13T02:27:00-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest5")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;")
> ;
> 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,"mtest5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest5 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 ) = sin ( x ) ;")
> ;
> 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 INFO, ALWAYS, DEBUGL, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_log10abserr, glob_warned2, glob_smallish_float, years_in_century,
days_in_year, min_in_hour, glob_log10normmin, glob_max_hours,
glob_disp_incr, glob_max_minutes, glob_start, glob_unchanged_h_cnt,
glob_max_trunc_err, glob_look_poles, glob_last_good_h, glob_display_flag,
djd_debug, glob_max_sec, glob_hmax, djd_debug2, glob_iter,
glob_orig_start_sec, glob_abserr, glob_log10_relerr, glob_dump_analytic,
glob_hmin, glob_optimal_done, glob_not_yet_start_msg, glob_dump,
glob_html_log, glob_current_iter, glob_warned, glob_optimal_start,
glob_hmin_init, glob_reached_optimal_h, glob_clock_sec, glob_no_eqs,
glob_max_rel_trunc_err, glob_relerr, glob_large_float, glob_h,
glob_initial_pass, glob_not_yet_finished, hours_in_day, sec_in_min,
glob_log10relerr, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_max_iter,
glob_almost_1, glob_optimal_expect_sec, glob_normmax, glob_small_float,
glob_optimal_clock_start_sec, glob_clock_start_sec, centuries_in_millinium,
glob_subiter_method, glob_percent_done, glob_log10_abserr,
glob_max_opt_iter, array_const_1, array_const_0D0, array_m1,
array_last_rel_error, array_y2, array_y1, array_type_pole, array_pole,
array_tmp4_g, array_y1_init, array_x, array_y2_init, array_1st_rel_error,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_norms,
array_y1_set_initial, array_y2_higher_work, array_poles,
array_y2_higher_work2, array_y2_set_initial, array_complex_pole,
array_y1_higher_work2, array_y1_higher_work, array_y1_higher,
array_real_pole, array_y2_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
ALWAYS := 1;
DEBUGL := 3;
glob_max_terms := 30;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_log10abserr := 0.;
glob_warned2 := false;
glob_smallish_float := 0.1*10^(-100);
years_in_century := 100.0;
days_in_year := 365.0;
min_in_hour := 60.0;
glob_log10normmin := 0.1;
glob_max_hours := 0.;
glob_disp_incr := 0.1;
glob_max_minutes := 0.;
glob_start := 0;
glob_unchanged_h_cnt := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_look_poles := false;
glob_last_good_h := 0.1;
glob_display_flag := true;
djd_debug := true;
glob_max_sec := 10000.0;
glob_hmax := 1.0;
djd_debug2 := true;
glob_iter := 0;
glob_orig_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
glob_not_yet_start_msg := true;
glob_dump := false;
glob_html_log := true;
glob_current_iter := 0;
glob_warned := false;
glob_optimal_start := 0.;
glob_hmin_init := 0.001;
glob_reached_optimal_h := false;
glob_clock_sec := 0.;
glob_no_eqs := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_h := 0.1;
glob_initial_pass := true;
glob_not_yet_finished := true;
hours_in_day := 24.0;
sec_in_min := 60.0;
glob_log10relerr := 0.;
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_max_iter := 1000;
glob_almost_1 := 0.9990;
glob_optimal_expect_sec := 0.1;
glob_normmax := 0.;
glob_small_float := 0.1*10^(-50);
glob_optimal_clock_start_sec := 0.;
glob_clock_start_sec := 0.;
centuries_in_millinium := 10.0;
glob_subiter_method := 3;
glob_percent_done := 0.;
glob_log10_abserr := 0.1*10^(-10);
glob_max_opt_iter := 10;
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/mtest5postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0;");
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, "glob_h := 0.00001 ;");
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, "2.0 - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "2.0 - cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_y2 := Array(1 .. max_terms + 1, []);
array_y1 := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_tmp4_g := Array(1 .. max_terms + 1, []);
array_y1_init := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y2_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y2_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_y2_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_type_pole[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_tmp4_g[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_x[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_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[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 <= 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 <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[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;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_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[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_tmp4_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_g[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_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_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_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 := 5.0;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_h := 0.00001;
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] := false;
array_y2_set_initial[1, 3] := false;
array_y2_set_initial[1, 4] := false;
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 := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y2_higher[r_order, term_no] := array_y2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y1_higher[r_order, term_no] := array_y1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_y2();
if glob_small_float < abs(array_y2_higher[1, 1]) then
tmp := abs(array_y2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_y1();
if glob_small_float < abs(array_y1_higher[1, 1]) then
tmp := abs(array_y1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_x[1] <= x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + 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 := 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 := 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 , 1 ) = diff ( y1, x , 1) ;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = sin ( x ) ;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-13T02:27:00-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest5")
;
logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;");
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,
"mtest5 diffeq.mxt");
logitem_str(html_log_file,
"mtest5 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 ) = sin ( x ) ;");
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/mtest5postode.ode#################
diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;
diff ( y1 , x , 1 ) = sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_h := 0.00001 ;
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)
2.0 - cos(x);
end;
exact_soln_y2 := proc(x)
2.0 - cos(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y2[1] (analytic) = 1.0049958347219742339044380121961
y2[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.0049958347219742339044380121961
y1[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
h = 0.0001
x[1] = 0.1
y2[1] (analytic) = 1.0049958347219742339044380121961
y2[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 1.0049958347219742339044380121961
y1[1] (numeric) = 1.0049958347219742339044380121961
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.52
NO POLE
NO POLE
x[1] = 0.1001
y2[1] (analytic) = 1.00500582303864310006118068491
y2[1] (numeric) = 1.0050158063803133312502571383936
absolute error = 9.9833416702311890764534836e-06
relative error = 0.00099336157476645022077122473146728 %
h = 0.0001
y1[1] (analytic) = 1.00500582303864310006118068491
y1[1] (numeric) = 1.0050058230386431000611807332781
absolute error = 4.83681e-26
relative error = 4.8127183834376864520341527729514e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.1MB, time=1.18
NO POLE
NO POLE
x[1] = 0.1002
y2[1] (analytic) = 1.0050158213052537275398742184312
y2[1] (numeric) = 1.0050357979385859149343525867125
absolute error = 1.99766333321873944783682813e-05
relative error = 0.0019876934182233023998511670430243 %
h = 0.0001
y1[1] (analytic) = 1.0050158213052537275398742184312
y1[1] (numeric) = 1.005015821305253727539874315167
absolute error = 9.67358e-26
relative error = 9.6253012091257824360361950283837e-24 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=1.78
NO POLE
NO POLE
x[1] = 0.1003
y2[1] (analytic) = 1.0050258295217061336744956568614
y2[1] (numeric) = 1.0050558093965920693741651166307
absolute error = 2.99798748859356996694597693e-05
relative error = 0.0029829954619378473085290392480137 %
h = 0.0001
y1[1] (analytic) = 1.0050258295217061336744956568614
y1[1] (numeric) = 1.0050258295217061336744958019643
absolute error = 1.451029e-25
relative error = 1.4437728438188973666138600203973e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=2.38
NO POLE
NO POLE
x[1] = 0.1004
y2[1] (analytic) = 1.0050358476879002363006043406579
y2[1] (numeric) = 1.0050758407541316799897999459
absolute error = 3.99930662314436891956052421e-05
relative error = 0.0039792676374129665958877951691437 %
h = 0.0001
y1[1] (analytic) = 1.0050358476879002363006043406579
y1[1] (numeric) = 1.0050358476879002363006045341276
absolute error = 1.934697e-25
relative error = 1.9250029782030152765434432154408e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=2.98
NO POLE
NO POLE
x[1] = 0.1005
y2[1] (analytic) = 1.005045875803735853756342728278
y2[1] (numeric) = 1.0050958920110044332060278963436
absolute error = 5.00162072685794496851680656e-05
relative error = 0.0049765098760871443351111054990432 %
h = 0.0001
y1[1] (analytic) = 1.005045875803735853756342728278
y1[1] (numeric) = 1.0050458758037358537563429701139
absolute error = 2.418359e-25
relative error = 2.4062175252110125849240987802809e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.1MB, time=3.59
NO POLE
NO POLE
x[1] = 0.1006
y2[1] (analytic) = 1.0050559138691127048834382127963
y2[1] (numeric) = 1.0051159631670098164542885296064
absolute error = 6.00492978971115708503168101e-05
relative error = 0.0059747221093344785800599641550778 %
h = 0.0001
y1[1] (analytic) = 1.0050559138691127048834382127963
y1[1] (numeric) = 1.0050559138691127048834385029979
absolute error = 2.902016e-25
relative error = 2.8874174659877940502277959895574e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=4.19
NO POLE
NO POLE
x[1] = 0.1007
y2[1] (analytic) = 1.0050659618839304090282059334865
y2[1] (numeric) = 1.0051360542219471181746952728391
absolute error = 7.00923380167091464893393526e-05
relative error = 0.0069739042684646929321153161155742 %
h = 0.0001
y1[1] (analytic) = 1.0050659618839304090282059334865
y1[1] (numeric) = 1.0050659618839304090282062720534
absolute error = 3.385669e-25
relative error = 3.3686037816401471797937681806910e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=4.79
NO POLE
NO POLE
x[1] = 0.1008
y2[1] (analytic) = 1.0050760198480884860425525823578
y2[1] (numeric) = 1.0051561651756154278180425342954
absolute error = 8.01453275269417754899519376e-05
relative error = 0.0079740562847231481172830942425244 %
h = 0.0001
y1[1] (analytic) = 1.0050760198480884860425525823578
y1[1] (numeric) = 1.0050760198480884860425529692894
absolute error = 3.869316e-25
relative error = 3.8497744683877992312337905298146e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=34.3MB, alloc=4.1MB, time=5.41
x[1] = 0.1009
y2[1] (analytic) = 1.0050860877614863562849812056346
y2[1] (numeric) = 1.0051762960278136358478148088223
absolute error = 9.02082663272795628336031877e-05
relative error = 0.0089751780892908535735580498444113 %
h = 0.0001
y1[1] (analytic) = 1.0050860877614863562849812056346
y1[1] (numeric) = 1.0050860877614863562849816409305
absolute error = 4.352959e-25
relative error = 4.3309315022903652540571582180656e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.101
y2[1] (analytic) = 1.005096165624023340621597000171
y2[1] (numeric) = 1.0051964467783404337421977732237
absolute error = 0.0001002811543170931206007730527
relative error = 0.0099772696132844790485427585155033 %
h = 0.0001
y1[1] (analytic) = 1.005096165624023340621597000171
y1[1] (numeric) = 1.0050961656240233406215974838307
absolute error = 4.836597e-25
relative error = 4.8120738745403068824677547641046e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=6.05
NO POLE
NO POLE
x[1] = 0.1011
y2[1] (analytic) = 1.0051062534355986604271141047886
y2[1] (numeric) = 1.0052166174269943139960913714768
absolute error = 0.0001103639913956535689772666882
relative error = 0.010980330787756366207318180060042 %
h = 0.0001
y1[1] (analytic) = 1.0051062534355986604271141047886
y1[1] (numeric) = 1.0051062534355986604271146368116
absolute error = 5.320230e-25
relative error = 5.2932015712912776856187998661957e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.2MB, time=6.65
NO POLE
NO POLE
x[1] = 0.1012
y2[1] (analytic) = 1.0051163511961114375858633865286
y2[1] (numeric) = 1.0052368079735735701231248897814
absolute error = 0.0001204567774621325372615032528
relative error = 0.011984361543694540250562148165706 %
h = 0.0001
y1[1] (analytic) = 1.0051163511961114375858633865286
y1[1] (numeric) = 1.0051163511961114375858639669144
absolute error = 5.803858e-25
relative error = 5.7743145786985519519206566891596e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.2MB, time=7.30
NO POLE
NO POLE
x[1] = 0.1013
y2[1] (analytic) = 1.0051264589054606944928012218078
y2[1] (numeric) = 1.0052570184178762966576740214219
absolute error = 0.0001305595124156021648727996141
relative error = 0.012989361812022721542912162647019 %
h = 0.0001
y1[1] (analytic) = 1.0051264589054606944928012218078
y1[1] (numeric) = 1.0051264589054606944928018505559
absolute error = 6.287481e-25
relative error = 6.2554128829190262014701862302364e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.2MB, time=7.90
NO POLE
NO POLE
x[1] = 0.1014
y2[1] (analytic) = 1.0051365765635453540545192724681
y2[1] (numeric) = 1.005277248759700389156879921422
absolute error = 0.0001406721961550351023606489539
relative error = 0.013995331523600337251568854147865 %
h = 0.0001
y1[1] (analytic) = 1.0051365765635453540545192724681
y1[1] (numeric) = 1.005136576563545354054519949578
absolute error = 6.771099e-25
relative error = 6.7364964701112206980956116612208e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.2MB, time=8.51
NO POLE
NO POLE
x[1] = 0.1015
y2[1] (analytic) = 1.0051467041702642396902552567095
y2[1] (numeric) = 1.0052974989988435442026702509714
absolute error = 0.0001507948285793045124149942619
relative error = 0.015002270609222532995136488133315 %
h = 0.0001
y1[1] (analytic) = 1.0051467041702642396902552567095
y1[1] (numeric) = 1.0051467041702642396902559821808
absolute error = 7.254713e-25
relative error = 7.2175663213149297238180277784591e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.2MB, time=9.15
NO POLE
NO POLE
x[1] = 0.1016
y2[1] (analytic) = 1.0051568417255160753329047148974
y2[1] (numeric) = 1.005317769135103259403782211605
absolute error = 0.0001609274095871840708774967076
relative error = 0.016010178999620184502696872092922 %
h = 0.0001
y1[1] (analytic) = 1.0051568417255160753329047148974
y1[1] (numeric) = 1.0051568417255160753329054887295
absolute error = 7.738321e-25
relative error = 7.6986204329225941347677617648527e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.2MB, time=9.76
NO POLE
NO POLE
x[1] = 0.1017
y2[1] (analytic) = 1.0051669892291994854300337702324
y2[1] (numeric) = 1.0053380591682768333977875691138
absolute error = 0.0001710699390773479677537988814
relative error = 0.017019056625459909283113027061137 %
h = 0.0001
y1[1] (analytic) = 1.0051669892291994854300337702324
y1[1] (numeric) = 1.0051669892291994854300345924248
absolute error = 8.221924e-25
relative error = 8.1796597859872875173171584801195e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.2MB, time=10.40
NO POLE
NO POLE
x[1] = 0.1018
y2[1] (analytic) = 1.0051771466812129949448928842738
y2[1] (numeric) = 1.0053583690981613658531196671674
absolute error = 0.0001812224169483709082267828936
relative error = 0.018028903417344078304558981387419 %
h = 0.0001
y1[1] (analytic) = 1.0051771466812129949448928842738
y1[1] (numeric) = 1.005177146681212994944893754826
absolute error = 8.705522e-25
relative error = 8.6606843666740402236578150436321e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.2MB, time=11.04
NO POLE
NO POLE
x[1] = 0.1019
y2[1] (analytic) = 1.0051873140814550293574316073064
y2[1] (numeric) = 1.0053786989245537574711024306282
absolute error = 0.0001913848430987281136708233218
relative error = 0.019039719305810827684272041925437 %
h = 0.0001
y1[1] (analytic) = 1.0051873140814550293574316073064
y1[1] (numeric) = 1.005187314081455029357432526218
absolute error = 9.189116e-25
relative error = 9.1416951559889691889727014580308e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.2MB, time=11.67
NO POLE
NO POLE
x[1] = 0.102
y2[1] (analytic) = 1.0051974914298239146653143235401
y2[1] (numeric) = 1.0053990486472507099879813585363
absolute error = 0.0002015572174267953226670349962
relative error = 0.020051504221334070388523894770719 %
h = 0.0001
y1[1] (analytic) = 1.0051974914298239146653143235401
y1[1] (numeric) = 1.0051974914298239146653152908106
absolute error = 9.672705e-25
relative error = 9.6226911452407686345263232488593e-23 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.2MB, time=12.28
NO POLE
NO POLE
x[1] = 0.1021
y2[1] (analytic) = 1.0052076787262178773849369911326
y2[1] (numeric) = 1.0054194182660487261769565067452
absolute error = 0.0002117395398308487920195156126
relative error = 0.021064258094323507942806884767262 %
h = 0.0001
y1[1] (analytic) = 1.0052076787262178773849369911326
y1[1] (numeric) = 1.0052076787262178773849380067615
absolute error = 1.0156289e-24
relative error = 1.0103672320599338412078272912172e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.2MB, time=12.92
NO POLE
NO POLE
x[1] = 0.1022
y2[1] (analytic) = 1.0052178759705350445524448770242
y2[1] (numeric) = 1.0054398077807441098502174601885
absolute error = 0.0002219318102090652977725831643
relative error = 0.02207798085512464215223182020599 %
h = 0.0001
y1[1] (analytic) = 1.0052178759705350445524448770242
y1[1] (numeric) = 1.005217875970535044552445941011
absolute error = 1.0639868e-24
relative error = 1.0584638668236214202370640334355e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.2MB, time=13.53
NO POLE
NO POLE
x[1] = 0.1023
y2[1] (analytic) = 1.0052280831626734437247512865758
y2[1] (numeric) = 1.005460217191132965860980294756
absolute error = 0.0002321340284595221362290081802
relative error = 0.023092672434018786832133645814892 %
h = 0.0001
y1[1] (analytic) = 1.0052280831626734437247512865758
y1[1] (numeric) = 1.0052280831626734437247523989199
absolute error = 1.1123441e-24
relative error = 1.1065589179525461488050416990782e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.2MB, time=14.13
NO POLE
NO POLE
x[1] = 0.1024
y2[1] (analytic) = 1.0052383003025310029805572879987
y2[1] (numeric) = 1.0054806464970112001055265287599
absolute error = 0.0002423461944801971249692407612
relative error = 0.024108332761223079548881324684939 %
h = 0.0001
y1[1] (analytic) = 1.0052383003025310029805572879987
y1[1] (numeric) = 1.0052383003025310029805584486997
absolute error = 1.1607010e-24
relative error = 1.1546525830250218241419461943290e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.2MB, time=14.74
NO POLE
NO POLE
x[1] = 0.1025
y2[1] (analytic) = 1.0052485273900055509213724315671
y2[1] (numeric) = 1.0055010956981745195252440639703
absolute error = 0.0002525683081689686038716324032
relative error = 0.025124961766890493370888266466393 %
h = 0.0001
y1[1] (analytic) = 1.0052485273900055509213724315671
y1[1] (numeric) = 1.0052485273900055509213736406244
absolute error = 1.2090573e-24
relative error = 1.2027446616998851922674805044983e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.2MB, time=15.35
NO POLE
NO POLE
x[1] = 0.1026
y2[1] (analytic) = 1.0052587644249948166725364636016
y2[1] (numeric) = 1.0055215647944184321086701161997
absolute error = 0.0002628003694236154361336525981
relative error = 0.026142559381109848629819636548939 %
h = 0.0001
y1[1] (analytic) = 1.0052587644249948166725364636016
y1[1] (numeric) = 1.0052587644249948166725377210148
absolute error = 1.2574132e-24
relative error = 1.2508353515517338569353106093491e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.2MB, time=15.99
NO POLE
NO POLE
x[1] = 0.1027
y2[1] (analytic) = 1.0052690114073964298842420352155
y2[1] (numeric) = 1.0055420537855382468935361354158
absolute error = 0.0002730423781418170092941002003
relative error = 0.027161125533905824691992877623219 %
h = 0.0001
y1[1] (analytic) = 1.0052690114073964298842420352155
y1[1] (numeric) = 1.0052690114073964298842433409841
absolute error = 1.3057686e-24
relative error = 1.2989245517196419127858984468072e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.2MB, time=16.61
NO POLE
NO POLE
x[1] = 0.1028
y2[1] (analytic) = 1.0052792683371079207325584058118
y2[1] (numeric) = 1.0055625626713290739688147153626
absolute error = 0.0002832943342211532362563095508
relative error = 0.028180660155238971739967772553084 %
h = 0.0001
y1[1] (analytic) = 1.0052792683371079207325584058118
y1[1] (numeric) = 1.0052792683371079207325597599353
absolute error = 1.3541235e-24
relative error = 1.3470122608217475917877160719193e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.2MB, time=17.23
NO POLE
NO POLE
x[1] = 0.1029
y2[1] (analytic) = 1.0052895352140267199204561413216
y2[1] (numeric) = 1.0055830914515858244767684926688
absolute error = 0.0002935562375591045563123513472
relative error = 0.029201163175005722564322374185628 %
h = 0.0001
y1[1] (analytic) = 1.0052895352140267199204561413216
y1[1] (numeric) = 1.0052895352140267199204575437994
absolute error = 1.4024778e-24
relative error = 1.3950983780025240889330168206187e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.2MB, time=17.87
NO POLE
NO POLE
x[1] = 0.103
y2[1] (analytic) = 1.0052998120380501586788328071734
y2[1] (numeric) = 1.0056036401261032106150010354236
absolute error = 0.0003038280880530519361682282502
relative error = 0.03022263452303840436561112503259 %
h = 0.0001
y1[1] (analytic) = 1.0052998120380501586788328071734
y1[1] (numeric) = 1.0052998120380501586788342580051
absolute error = 1.4508317e-24
relative error = 1.4431831008291152988008737400215e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.2MB, time=18.48
NO POLE
NO POLE
x[1] = 0.1031
y2[1] (analytic) = 1.0053100988090754687675396559837
y2[1] (numeric) = 1.005624208694675745638509721199
absolute error = 0.0003141098856002768709700652153
relative error = 0.03124507412910525056650148664717 %
h = 0.0001
y1[1] (analytic) = 1.0053100988090754687675396559837
y1[1] (numeric) = 1.0053100988090754687675411551688
absolute error = 1.4991851e-24
relative error = 1.4912663284453082219570667171403e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.2MB, time=19.09
NO POLE
NO POLE
x[1] = 0.1032
y2[1] (analytic) = 1.0053203955269997824764093099572
y2[1] (numeric) = 1.0056447971570977438617406044979
absolute error = 0.0003244016300979613853312945407
relative error = 0.032268481922910412634085395830497 %
h = 0.0001
y1[1] (analytic) = 1.0053203955269997824764093099572
y1[1] (numeric) = 1.0053203955269997824764108574952
absolute error = 1.5475380e-24
relative error = 1.5393480594699005459885051172232e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1033
y2[1] (analytic) = 1.005330702191720132626284437988
y2[1] (numeric) = 1.0056654055131633206606452736081
absolute error = 0.0003347033214431880343608356201
relative error = 0.033292857834093971912361861656263 %
h = 0.0001
y1[1] (analytic) = 1.005330702191720132626284437988
y1[1] (numeric) = 1.0053307021917201326262860338784
absolute error = 1.5958904e-24
relative error = 1.5874282925218551986717239163730e-22 %
h = 0.0001
memory used=122.0MB, alloc=4.2MB, time=19.72
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1034
y2[1] (analytic) = 1.0053410188031334525700474274499
y2[1] (numeric) = 1.0056860337626663924747396968411
absolute error = 0.0003450149595329399046922693912
relative error = 0.034318201792231951464887014596017 %
h = 0.0001
y1[1] (analytic) = 1.0053410188031334525700474274499
y1[1] (numeric) = 1.0053410188031334525700490716922
absolute error = 1.6442423e-24
relative error = 1.6355070262203004984017462772698e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.2MB, time=20.38
NO POLE
NO POLE
x[1] = 0.1035
y2[1] (analytic) = 1.0053513453611365761936510506671
y2[1] (numeric) = 1.005706681905400676809165058135
absolute error = 0.0003553365442641006155140074679
relative error = 0.03534451372683632792758791583583 %
h = 0.0001
y1[1] (analytic) = 1.0053513453611365761936510506671
y1[1] (numeric) = 1.0053513453611365761936527432607
absolute error = 1.6925936e-24
relative error = 1.6835841597168163940000537388593e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.2MB, time=21.05
NO POLE
NO POLE
x[1] = 0.1036
y2[1] (analytic) = 1.0053616818656262379171501260534
y2[1] (numeric) = 1.0057273499411596922367505820017
absolute error = 0.0003656680755334543196004559483
relative error = 0.036371793567355043371736432371609 %
h = 0.0001
y1[1] (analytic) = 1.0053616818656262379171501260534
y1[1] (numeric) = 1.0053616818656262379171518669979
absolute error = 1.7409445e-24
relative error = 1.7316598905673129226577246409324e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.2MB, time=21.71
NO POLE
NO POLE
x[1] = 0.1037
y2[1] (analytic) = 1.0053720283164990726957341739114
y2[1] (numeric) = 1.0057480378697367584000783477965
absolute error = 0.0003760095532376857043441738851
relative error = 0.037400041243172017177079480013657 %
h = 0.0001
y1[1] (analytic) = 1.0053720283164990726957341739114
y1[1] (numeric) = 1.0053720283164990726957359632062
absolute error = 1.7892948e-24
relative error = 1.7797340184570122469264710583752e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.2MB, time=22.39
NO POLE
NO POLE
x[1] = 0.1038
y2[1] (analytic) = 1.0053823847136516160207610668791
y2[1] (numeric) = 1.005768745690924996013550093291
absolute error = 0.0003863609772733799927890264119
relative error = 0.038429256683607157915121934209843 %
h = 0.0001
y1[1] (analytic) = 1.0053823847136516160207610668791
y1[1] (numeric) = 1.0053823847136516160207629045237
absolute error = 1.8376446e-24
relative error = 1.8278066414734225505775443940977e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.2MB, time=23.02
NO POLE
NO POLE
x[1] = 0.1039
y2[1] (analytic) = 1.0053927510569803039207916750157
y2[1] (numeric) = 1.0057894734045173268654560075269
absolute error = 0.0003967223475370229446643325112
relative error = 0.039459439817916375242558504924905 %
h = 0.0001
y1[1] (analytic) = 1.0053927510569803039207916750157
y1[1] (numeric) = 1.0053927510569803039207935610097
absolute error = 1.8859940e-24
relative error = 1.8758778577001217204419285359615e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.2MB, time=23.68
NO POLE
NO POLE
x[1] = 0.104
y2[1] (analytic) = 1.0054031273463814729626255055154
y2[1] (numeric) = 1.0058102210103064738200455129318
absolute error = 0.0004070936639250008574200074164
relative error = 0.040490590575291591804850869555984 %
h = 0.0001
y1[1] (analytic) = 1.0054031273463814729626255055154
y1[1] (numeric) = 1.0054031273463814729626274398582
absolute error = 1.9343428e-24
relative error = 1.9239474668289750033143347914607e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.2MB, time=24.33
NO POLE
NO POLE
x[1] = 0.1041
y2[1] (analytic) = 1.005413513581751360252337337038
y2[1] (numeric) = 1.0058309885080849608196000366746
absolute error = 0.0004174749263336005672626996366
relative error = 0.041522708884860755149946354614275 %
h = 0.0001
y1[1] (analytic) = 1.005413513581751360252337337038
y1[1] (numeric) = 1.0054135135817513602523393197293
absolute error = 1.9826913e-24
relative error = 1.9720157658680455250328525555774e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.2MB, time=25.01
NO POLE
NO POLE
x[1] = 0.1042
y2[1] (analytic) = 1.005423909762986103436314848648
y2[1] (numeric) = 1.0058517758976451128865077712411
absolute error = 0.0004278661346590094501929225931
relative error = 0.042555794675687849652134454012123 %
h = 0.0001
y1[1] (analytic) = 1.005423909762986103436314848648
y1[1] (numeric) = 1.0054239097629861034363168796871
absolute error = 2.0310391e-24
relative error = 2.0200823555894822418514107060752e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.2MB, time=25.70
NO POLE
NO POLE
x[1] = 0.1043
y2[1] (analytic) = 1.0054343158899817407022972433492
y2[1] (numeric) = 1.0058725831787790561253404242086
absolute error = 0.0004382672887973154230431808594
relative error = 0.043589847876772908446037469185112 %
h = 0.0001
y1[1] (analytic) = 1.0054343158899817407022972433492
y1[1] (numeric) = 1.0054343158899817407022993227356
absolute error = 2.0793864e-24
relative error = 2.0681474335390935479160455397712e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.2MB, time=26.36
NO POLE
NO POLE
x[1] = 0.1044
y2[1] (analytic) = 1.0054447319626342107804148662065
y2[1] (numeric) = 1.0058934103512787177249319571981
absolute error = 0.0004486783886445069445170909916
relative error = 0.044624868417052025370731552894447 %
h = 0.0001
y1[1] (analytic) = 1.0054447319626342107804148662065
y1[1] (numeric) = 1.0054447319626342107804169939398
absolute error = 2.1277333e-24
relative error = 2.1162110977961480808916284930599e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.2MB, time=27.01
NO POLE
NO POLE
x[1] = 0.1045
y2[1] (analytic) = 1.0054551579808393529442298170443
y2[1] (numeric) = 1.0059142574149358259604593139845
absolute error = 0.0004590994340964730162294969402
relative error = 0.045660856225397366923994436068092 %
h = 0.0001
y1[1] (analytic) = 1.0054551579808393529442298170443
y1[1] (numeric) = 1.0054551579808393529442319931239
absolute error = 2.1760796e-24
relative error = 2.1642731480636244087201030105707e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.2MB, time=27.68
NO POLE
NO POLE
x[1] = 0.1046
y2[1] (analytic) = 1.0054655939444929070117775577094
y2[1] (numeric) = 1.005935124369541910195525137743
absolute error = 0.0004695304250490031837475800336
relative error = 0.046697811230617184226676114076557 %
h = 0.0001
y1[1] (analytic) = 1.0054655939444929070117775577094
y1[1] (numeric) = 1.0054655939444929070117797821348
absolute error = 2.2244254e-24
relative error = 2.2123336824221557713800629343517e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.2MB, time=28.34
NO POLE
NO POLE
x[1] = 0.1047
y2[1] (analytic) = 1.0054760398534905133466095138901
y2[1] (numeric) = 1.0059560112148883008842424774112
absolute error = 0.0004799713613977875376329635211
relative error = 0.047735733361455824997188765699378 %
h = 0.0001
y1[1] (analytic) = 1.0054760398534905133466095138901
y1[1] (numeric) = 1.0054760398534905133466117866608
absolute error = 2.2727707e-24
relative error = 2.2603926994930371230305959495516e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.2MB, time=29.01
NO POLE
NO POLE
x[1] = 0.1048
y2[1] (analytic) = 1.0054864957077277128588366714797
y2[1] (numeric) = 1.0059769179507661295733214831464
absolute error = 0.0004904222430384167144848116667
relative error = 0.048774622546593745536112175497317 %
h = 0.0001
y1[1] (analytic) = 1.0054864957077277128588366714797
y1[1] (numeric) = 1.0054864957077277128588389925952
absolute error = 2.3211155e-24
relative error = 2.3084501978977309100440081085363e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.2MB, time=29.70
NO POLE
NO POLE
x[1] = 0.1049
y2[1] (analytic) = 1.0054969615070999470061741674745
y2[1] (numeric) = 1.0059978445769663289041580908568
absolute error = 0.0005008830698663818979839233823
relative error = 0.049814478714647522720910927149292 %
h = 0.0001
y1[1] (analytic) = 1.0054969615070999470061741674745
y1[1] (numeric) = 1.0054969615070999470061765369343
absolute error = 2.3694598e-24
relative error = 2.3565061762578672208437568914643e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.2MB, time=30.38
NO POLE
NO POLE
x[1] = 0.105
y2[1] (analytic) = 1.0055074372515025577949868753959
y2[1] (numeric) = 1.0060187910932796326149246957856
absolute error = 0.0005113538417770748199378203897
relative error = 0.050855301794169866010759632507108 %
h = 0.0001
y1[1] (analytic) = 1.0055074372515025577949868753959
y1[1] (numeric) = 1.0055074372515025577949892931995
absolute error = 2.4178036e-24
relative error = 2.4045606331952439357027479901654e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.3MB, time=31.05
NO POLE
NO POLE
x[1] = 0.1051
y2[1] (analytic) = 1.0055179229408307877813359852258
y2[1] (numeric) = 1.0060397574994965755426628151277
absolute error = 0.0005218345586657877613268299019
relative error = 0.051897091713649629461472458346761 %
h = 0.0001
y1[1] (analytic) = 1.0055179229408307877813359852258
y1[1] (numeric) = 1.0055179229408307877813384513727
absolute error = 2.4661469e-24
relative error = 2.4526135673318268765019631262460e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.3MB, time=31.70
NO POLE
NO POLE
x[1] = 0.1052
y2[1] (analytic) = 1.0055284185749797800720265778451
y2[1] (numeric) = 1.0060607437954074936253777396574
absolute error = 0.0005323252204277135533511618123
relative error = 0.052939848401511823750533209724283 %
h = 0.0001
y1[1] (analytic) = 1.0055284185749797800720265778451
y1[1] (numeric) = 1.0055284185749797800720290923347
absolute error = 2.5144896e-24
relative error = 2.5006648778395522765881421595194e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.3MB, time=32.35
NO POLE
NO POLE
x[1] = 0.1053
y2[1] (analytic) = 1.0055389241538445783256561939646
y2[1] (numeric) = 1.0060817499808025239041351743468
absolute error = 0.0005428258269579455784789803822
relative error = 0.05398357178611762821222222614313 %
h = 0.0001
y1[1] (analytic) = 1.0055389241538445783256561939646
y1[1] (numeric) = 1.0055389241538445783256587567965
absolute error = 2.5628319e-24
relative error = 2.5487147622421566767021346289422e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.3MB, time=32.98
NO POLE
NO POLE
x[1] = 0.1054
y2[1] (analytic) = 1.0055494396773201267536643975387
y2[1] (numeric) = 1.0061027760554716045251598679533
absolute error = 0.0005533363781514777714954704146
relative error = 0.055028261795764402882836343623256 %
h = 0.0001
y1[1] (analytic) = 1.0055494396773201267536643975387
y1[1] (numeric) = 1.0055494396773201267536670087124
absolute error = 2.6111737e-24
relative error = 2.5967631197108748768425191599945e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.3MB, time=33.60
NO POLE
NO POLE
x[1] = 0.1055
y2[1] (analytic) = 1.0055599651453012701213833336496
y2[1] (numeric) = 1.0061238220192044747419362315554
absolute error = 0.0005638568739032046205528979058
relative error = 0.056073918358685700555998173233956 %
h = 0.0001
y1[1] (analytic) = 1.0055599651453012701213833336496
y1[1] (numeric) = 1.0055599651453012701213859931645
absolute error = 2.6595149e-24
relative error = 2.6448098494212682479354129041646e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=205.9MB, alloc=4.3MB, time=34.25
x[1] = 0.1056
y2[1] (analytic) = 1.0055705005576827537490892808531
y2[1] (numeric) = 1.0061448878717906749173109460164
absolute error = 0.0005743873141079211682216651633
relative error = 0.057120541403051278848050943479644 %
h = 0.0001
y1[1] (analytic) = 1.0055705005576827537490892808531
y1[1] (numeric) = 1.0055705005576827537490919887087
absolute error = 2.7078556e-24
relative error = 2.6928550494453061029318200137719e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.1057
y2[1] (analytic) = 1.0055810459143592235130551979753
y2[1] (numeric) = 1.0061659736130195465255975583541
absolute error = 0.0005849276986603230125423603788
relative error = 0.058168130856967112273535151085055 %
h = 0.0001
y1[1] (analytic) = 1.0055810459143592235130551979753
y1[1] (numeric) = 1.0055810459143592235130579541712
absolute error = 2.7561959e-24
relative error = 2.7408988178509608692772689486619e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.3MB, time=34.91
NO POLE
NO POLE
x[1] = 0.1058
y2[1] (analytic) = 1.005591601215225225846604265349
y2[1] (numeric) = 1.0061870792426802321546830669958
absolute error = 0.0005954780274550063080788016468
relative error = 0.059216686648475404330743262024834 %
h = 0.0001
y1[1] (analytic) = 1.005591601215225225846604265349
y1[1] (numeric) = 1.0055916012152252258466070698846
absolute error = 2.8045356e-24
relative error = 2.7889409543703513422869142393034e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.3MB, time=35.56
NO POLE
NO POLE
x[1] = 0.1059
y2[1] (analytic) = 1.005602166460175207741164420479
y2[1] (numeric) = 1.0062082047605616755081364958977
absolute error = 0.0006060383003864677669720754187
relative error = 0.060266208705554599597348701713883 %
h = 0.0001
y1[1] (analytic) = 1.005602166460175207741164420479
y1[1] (numeric) = 1.0056021664601752077411672733539
absolute error = 2.8528749e-24
relative error = 2.8369816565157352463926562076170e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.3MB, time=36.25
NO POLE
NO POLE
x[1] = 0.106
y2[1] (analytic) = 1.0056127416491035167473238881278
y2[1] (numeric) = 1.0062293501664526214073194575076
absolute error = 0.0006166085173491046599955693798
relative error = 0.061316696956119395836105370159174 %
h = 0.0001
y1[1] (analytic) = 1.0056127416491035167473238881278
y1[1] (numeric) = 1.0056127416491035167473267893413
absolute error = 2.9012135e-24
relative error = 2.8850206245818866038962970388680e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.3MB, time=36.91
NO POLE
NO POLE
x[1] = 0.1061
y2[1] (analytic) = 1.005623326781904400975887704808
y2[1] (numeric) = 1.0062505154601416157934987045494
absolute error = 0.0006271886782372148176109997414
relative error = 0.062368151328020756110613915486248 %
h = 0.0001
y1[1] (analytic) = 1.005623326781904400975887704808
y1[1] (numeric) = 1.0056233267819044009758906543597
absolute error = 2.9495517e-24
relative error = 2.9330581555211746548923765245987e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.3MB, time=37.58
NO POLE
NO POLE
x[1] = 0.1062
y2[1] (analytic) = 1.0056339218584720090989352376741
y2[1] (numeric) = 1.0062717006414170057299606706086
absolute error = 0.0006377787829449966310254329345
relative error = 0.063420571749045920911150995823191 %
h = 0.0001
y1[1] (analytic) = 1.0056339218584720090989352376741
y1[1] (numeric) = 1.0056339218584720090989382355634
absolute error = 2.9978893e-24
relative error = 2.9810940490747568989152202688354e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.3MB, time=38.25
NO POLE
NO POLE
x[1] = 0.1063
y2[1] (analytic) = 1.0056445268787003903508786978002
y2[1] (numeric) = 1.0062929057100669394041279994979
absolute error = 0.0006483788313665490532493016977
relative error = 0.064473958146918420290557757270473 %
h = 0.0001
y1[1] (analytic) = 1.0056445268787003903508786978002
y1[1] (numeric) = 1.0056445268787003903508817440266
absolute error = 3.0462264e-24
relative error = 3.0291284033084904293407306229443e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.3MB, time=38.94
NO POLE
NO POLE
x[1] = 0.1064
y2[1] (analytic) = 1.0056551418424834945295226478354
y2[1] (numeric) = 1.0063141306658793661296780633809
absolute error = 0.0006589888233958716001554155455
relative error = 0.065528310449298086010183752188799 %
h = 0.0001
y1[1] (analytic) = 1.0056551418424834945295226478354
y1[1] (numeric) = 1.0056551418424834945295257423985
absolute error = 3.0945631e-24
relative error = 3.0771613162842095797786145938714e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.3MB, time=39.62
NO POLE
NO POLE
x[1] = 0.1065
y2[1] (analytic) = 1.0056657667497151719971245040248
y2[1] (numeric) = 1.0063353755086420363486634696338
absolute error = 0.000669608758926864351538965609
relative error = 0.066583628583781063695882519756475 %
h = 0.0001
y1[1] (analytic) = 1.0056657667497151719971245040248
y1[1] (numeric) = 1.0056657667497151719971276469241
absolute error = 3.1428993e-24
relative error = 3.1251926871864858000961604586420e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.3MB, time=40.29
NO POLE
NO POLE
x[1] = 0.1066
y2[1] (analytic) = 1.0056764016002891736814560325861
y2[1] (numeric) = 1.0063566402381425016336345564231
absolute error = 0.000680238637853327952178523837
relative error = 0.06763991247789982500405504749416 %
h = 0.0001
y1[1] (analytic) = 1.0056764016002891736814560325861
y1[1] (numeric) = 1.0056764016002891736814592238209
absolute error = 3.1912348e-24
relative error = 3.1732223157686972493248873392804e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.3MB, time=40.95
NO POLE
NO POLE
x[1] = 0.1067
y2[1] (analytic) = 1.0056870463940991510768658404304
y2[1] (numeric) = 1.0063779248541681146897638769782
absolute error = 0.0006908784600689636128980365478
relative error = 0.068697162059123179797737329829774 %
h = 0.0001
y1[1] (analytic) = 1.0056870463940991510768658404304
y1[1] (numeric) = 1.0056870463940991510768690800004
absolute error = 3.2395700e-24
relative error = 3.2212505983998802285107300755262e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.3MB, time=41.63
NO POLE
NO POLE
x[1] = 0.1068
y2[1] (analytic) = 1.005697701131038656245342860219
y2[1] (numeric) = 1.0063992293565060293569726725379
absolute error = 0.0007015282254673731116298123189
relative error = 0.069755377254856288332728236615874 %
h = 0.0001
y1[1] (analytic) = 1.005697701131038656245342860219
y1[1] (numeric) = 1.0056977011310386562453461481235
absolute error = 3.2879045e-24
relative error = 3.2692771359647349111416115989128e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.3MB, time=42.31
NO POLE
NO POLE
x[1] = 0.1069
y2[1] (analytic) = 1.0057083658110011418175808297414
y2[1] (numeric) = 1.0064205537449432006120593339496
absolute error = 0.0007121879339420587944785042082
relative error = 0.070814557992440673453753902298473 %
h = 0.0001
y1[1] (analytic) = 1.0057083658110011418175808297414
y1[1] (numeric) = 1.0057083658110011418175841659799
absolute error = 3.3362385e-24
relative error = 3.3173021259594118898404793650151e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.3MB, time=42.98
NO POLE
NO POLE
x[1] = 0.107
y2[1] (analytic) = 1.0057190404338799609940437656082
y2[1] (numeric) = 1.0064418980192663845708298518993
absolute error = 0.0007228575853864235767860862911
relative error = 0.071874704199154232800664842672675 %
h = 0.0001
y1[1] (analytic) = 1.0057190404338799609940437656082
y1[1] (numeric) = 1.0057190404338799609940471501803
absolute error = 3.3845721e-24
relative error = 3.3653256664404530226578606905771e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.3MB, time=43.65
NO POLE
NO POLE
x[1] = 0.1071
y2[1] (analytic) = 1.0057297249995683675460324312455
y2[1] (numeric) = 1.006463262179262138490230255752
absolute error = 0.0007335371796937709441978245065
relative error = 0.072935815802211251024662004169717 %
h = 0.0001
y1[1] (analytic) = 1.0057297249995683675460324312455
y1[1] (numeric) = 1.0057297249995683675460358641506
absolute error = 3.4329051e-24
relative error = 3.4133475571694704674084732503249e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.3MB, time=44.33
NO POLE
NO POLE
x[1] = 0.1072
y2[1] (analytic) = 1.0057404195079595158167517991808
y2[1] (numeric) = 1.0064846462247168207704810409802
absolute error = 0.0007442267167573049537292417994
relative error = 0.073997892728762412014547947248261 %
h = 0.0001
y1[1] (analytic) = 1.0057404195079595158167517991808
y1[1] (numeric) = 1.0057404195079595158167552804183
absolute error = 3.4812375e-24
relative error = 3.4613677967751689711959246908875e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.3MB, time=45.01
NO POLE
NO POLE
x[1] = 0.1073
y2[1] (analytic) = 1.00575112395894646072237950761
y2[1] (numeric) = 1.0065060501554165909572135851601
absolute error = 0.0007549261964701302348340775501
relative error = 0.075060934905894811132999362848909 %
h = 0.0001
y1[1] (analytic) = 1.00575112395894646072237950761
y1[1] (numeric) = 1.0057511239589464607223830371795
absolute error = 3.5295695e-24
relative error = 3.5093865827427827362935019589606e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.3MB, time=45.68
NO POLE
NO POLE
x[1] = 0.1074
y2[1] (analytic) = 1.0057618383524221577531353112351
y2[1] (numeric) = 1.0065274739711474097436085525136
absolute error = 0.0007656356187252519904732412785
relative error = 0.076124942260631967462857117880994 %
h = 0.0001
y1[1] (analytic) = 1.0057618383524221577531353112351
y1[1] (numeric) = 1.005761838352422157753138889136
absolute error = 3.5779009e-24
relative error = 3.5574037148407813290056373947457e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.3MB, time=46.36
NO POLE
NO POLE
x[1] = 0.1075
y2[1] (analytic) = 1.0057725626882794629743515263608
y2[1] (numeric) = 1.0065489176716950389725362869743
absolute error = 0.0007763549834155759981847606135
relative error = 0.077189914719933836063430023021088 %
h = 0.0001
y1[1] (analytic) = 1.0057725626882794629743515263608
y1[1] (numeric) = 1.0057725626882794629743551525926
absolute error = 3.6262318e-24
relative error = 3.6054192911244519976351224170153e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.3MB, time=47.01
NO POLE
NO POLE
x[1] = 0.1076
y2[1] (analytic) = 1.0057832969664111330275444702404
y2[1] (numeric) = 1.0065703812568450416386991937575
absolute error = 0.0007870842904339086111547235171
relative error = 0.078255852210696820236808513225789 %
h = 0.0001
y1[1] (analytic) = 1.0057832969664111330275444702404
y1[1] (numeric) = 1.0057832969664111330275481448026
absolute error = 3.6745622e-24
relative error = 3.6534333102200191791907616853759e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.3MB, time=47.68
NO POLE
NO POLE
x[1] = 0.1077
y2[1] (analytic) = 1.0057940411867098251314868946597
y2[1] (numeric) = 1.0065918647263827818907761094111
absolute error = 0.0007978235396729567592892147514
relative error = 0.079322754659753783804184428387132 %
h = 0.0001
y1[1] (analytic) = 1.0057940411867098251314868946597
y1[1] (numeric) = 1.0057940411867098251314906175518
absolute error = 3.7228921e-24
relative error = 3.7014457707538791308158699851220e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.3MB, time=48.37
NO POLE
NO POLE
x[1] = 0.1078
y2[1] (analytic) = 1.0058047953490680970832814137484
y2[1] (numeric) = 1.0066133680800934250335686603271
absolute error = 0.0008085727310253279502872465787
relative error = 0.080390621993874063392173078924598 %
h = 0.0001
y1[1] (analytic) = 1.0058047953490680970832814137484
y1[1] (numeric) = 1.0058047953490680970832851849698
absolute error = 3.7712214e-24
relative error = 3.7494565719297294952149096319252e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.3MB, time=49.05
NO POLE
NO POLE
x[1] = 0.1079
y2[1] (analytic) = 1.0058155594533784072594349260082
y2[1] (numeric) = 1.0066348913177619375301496096918
absolute error = 0.0008193318643835302707146836836
relative error = 0.081459454139763480729133778147125 %
h = 0.0001
y1[1] (analytic) = 1.0058155594533784072594349260082
y1[1] (numeric) = 1.0058155594533784072594387455584
absolute error = 3.8195502e-24
relative error = 3.7974658117993092196978751651724e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
x[1] = 0.108
y2[1] (analytic) = 1.0058263334995331146169340305467
y2[1] (numeric) = 1.0066564344391730870040131928531
absolute error = 0.0008301009396399723870791623064
relative error = 0.082529251024064354951485020428877 %
h = 0.0001
y1[1] (analytic) = 1.0058263334995331146169340305467
y1[1] (numeric) = 1.0058263334995331146169378984252
absolute error = 3.8678785e-24
relative error = 3.8454734889895337934726849230498e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.3MB, time=49.71
NO POLE
NO POLE
x[1] = 0.1081
y2[1] (analytic) = 1.0058371174874244786943214375069
y2[1] (numeric) = 1.0066779974441114422412274410842
absolute error = 0.0008408799566869635469060035773
relative error = 0.083600012573355514920010481434804 %
h = 0.0001
y1[1] (analytic) = 1.0058371174874244786943214375069
y1[1] (numeric) = 1.0058371174874244786943253537132
absolute error = 3.9162063e-24
relative error = 3.8934796021274911200418880516526e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.3MB, time=50.38
NO POLE
NO POLE
x[1] = 0.1082
y2[1] (analytic) = 1.0058479114169446596127733726807
y2[1] (numeric) = 1.0066995803323613731925884937207
absolute error = 0.00085166891541671357981512104
relative error = 0.08467173871415231154615201371703 %
h = 0.0001
y1[1] (analytic) = 1.0058479114169446596127733726807
y1[1] (numeric) = 1.0058479114169446596127773372142
absolute error = 3.9645335e-24
relative error = 3.9414840504218328830706231963024e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.3MB, time=51.05
NO POLE
NO POLE
x[1] = 0.1083
y2[1] (analytic) = 1.0058587152879857180771779762961
y2[1] (numeric) = 1.0067211831037070509757768986509
absolute error = 0.0008624678157213328985989223548
relative error = 0.08574442937290663012828580832834 %
h = 0.0001
y1[1] (analytic) = 1.0058587152879857180771779762961
y1[1] (numeric) = 1.0058587152879857180771819891564
absolute error = 4.0128603e-24
relative error = 3.9894870313382776750315843983461e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.3MB, time=51.73
NO POLE
NO POLE
x[1] = 0.1084
y2[1] (analytic) = 1.0058695291004396153772146959678
y2[1] (numeric) = 1.0067428057579324478775159011375
absolute error = 0.0008732766574928325003012051697
relative error = 0.086818084476006902697977890118142 %
h = 0.0001
y1[1] (analytic) = 1.0058695291004396153772146959678
y1[1] (numeric) = 1.0058695291004396153772187571543
absolute error = 4.0611865e-24
relative error = 4.0374883446682837367981651429046e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.3MB, time=52.41
NO POLE
NO POLE
x[1] = 0.1085
y2[1] (analytic) = 1.0058803528541982133884346737992
y2[1] (numeric) = 1.0067644482948213373557317209483
absolute error = 0.0008840954406231239672970471491
relative error = 0.087892703949778120376215111665762 %
h = 0.0001
y1[1] (analytic) = 1.0058803528541982133884346737992
y1[1] (numeric) = 1.0058803528541982133884387833114
absolute error = 4.1095122e-24
relative error = 4.0854880884582417750806596107500e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.3MB, time=53.09
NO POLE
NO POLE
x[1] = 0.1086
y2[1] (analytic) = 1.005891186549153274573342127626
y2[1] (numeric) = 1.0067861107141572940417158177751
absolute error = 0.0008949241650040194683736901491
relative error = 0.088968287720481845739607807928072 %
h = 0.0001
y1[1] (analytic) = 1.005891186549153274573342127626
y1[1] (numeric) = 1.0058911865491532745733462854633
absolute error = 4.1578373e-24
relative error = 4.1334861619217752433681840041726e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.3MB, time=53.77
NO POLE
NO POLE
x[1] = 0.1087
y2[1] (analytic) = 1.0059020301851964619824767263904
y2[1] (numeric) = 1.0068077930157236937422891449191
absolute error = 0.0009057628305272317598124185287
relative error = 0.090044835714316225196560270892142 %
h = 0.0001
y1[1] (analytic) = 1.0059020301851964619824767263904
y1[1] (numeric) = 1.0059020301851964619824809325523
absolute error = 4.2061619e-24
relative error = 4.1814826631034875284546045052404e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.3MB, time=54.45
NO POLE
NO POLE
x[1] = 0.1088
y2[1] (analytic) = 1.0059128837622193392554969596347
y2[1] (numeric) = 1.0068294951993037134419683912209
absolute error = 0.0009166114370843741864714315862
relative error = 0.091122347857416001373405200709408 %
h = 0.0001
y1[1] (analytic) = 1.0059128837622193392554969596347
y1[1] (numeric) = 1.0059128837622193392555012141207
absolute error = 4.2544860e-24
relative error = 4.2294775906316833457562816227405e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.3MB, time=55.11
NO POLE
NO POLE
x[1] = 0.1089
y2[1] (analytic) = 1.0059237472801133706222645011039
y2[1] (numeric) = 1.0068512172646803313051342112135
absolute error = 0.0009274699845669606828697101096
relative error = 0.092200824075852525510498286925634 %
h = 0.0001
y1[1] (analytic) = 1.0059237472801133706222645011039
y1[1] (numeric) = 1.0059237472801133706222688039135
absolute error = 4.3028096e-24
relative error = 4.2774709431348410113432812690942e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.3MB, time=55.79
NO POLE
NO POLE
x[1] = 0.109
y2[1] (analytic) = 1.0059346207387699209039295664461
y2[1] (numeric) = 1.0068729592116363266782014434767
absolute error = 0.0009383384728664057742718770306
relative error = 0.093280264295633769868269070690092 %
h = 0.0001
y1[1] (analytic) = 1.0059346207387699209039295664461
y1[1] (numeric) = 1.0059346207387699209039339175787
absolute error = 4.3511326e-24
relative error = 4.3254626198315734699280202758346e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.3MB, time=56.46
NO POLE
NO POLE
x[1] = 0.1091
y2[1] (analytic) = 1.005945504138080255514017265
y2[1] (numeric) = 1.006894721039954280091791317171
absolute error = 0.000949216901874024577774052171
relative error = 0.094360668442704340143224235939252 %
h = 0.0001
y1[1] (analytic) = 1.005945504138080255514017265
y1[1] (numeric) = 1.0059455041380802555140216644551
absolute error = 4.3994551e-24
relative error = 4.3734527187628968528246891125008e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.3MB, time=57.14
NO POLE
NO POLE
x[1] = 0.1092
y2[1] (analytic) = 1.0059563974779355404595149456589
y2[1] (numeric) = 1.0069165027494165732629056467298
absolute error = 0.0009601052714810328033907010709
relative error = 0.095442036442945487893899474803192 %
h = 0.0001
y1[1] (analytic) = 1.0059563974779355404595149456589
y1[1] (numeric) = 1.0059563974779355404595193934361
absolute error = 4.4477772e-24
relative error = 4.4214413379657011560604666450074e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.3MB, time=57.83
NO POLE
NO POLE
x[1] = 0.1093
y2[1] (analytic) = 1.0059673007582268423419605368001
y2[1] (numeric) = 1.0069383043398053890971030146874
absolute error = 0.0009710035815785467551424778873
relative error = 0.096524368222175122976756069598711 %
h = 0.0001
y1[1] (analytic) = 1.0059673007582268423419605368001
y1[1] (numeric) = 1.0059673007582268423419650328988
absolute error = 4.4960987e-24
relative error = 4.4694282772523117901199284522462e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.3MB, time=58.51
NO POLE
NO POLE
x[1] = 0.1094
y2[1] (analytic) = 1.0059782139788451283585318802682
y2[1] (numeric) = 1.0069601258109027116906769426216
absolute error = 0.0009819118320575833321450623534
relative error = 0.097607663706147825992018331139314 %
h = 0.0001
y1[1] (analytic) = 1.0059782139788451283585318802682
y1[1] (numeric) = 1.0059782139788451283585364246877
absolute error = 4.5444195e-24
relative error = 4.5174134358495812329657880335896e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.3MB, time=59.16
NO POLE
NO POLE
x[1] = 0.1095
y2[1] (analytic) = 1.0059891371396812663031370594024
y2[1] (numeric) = 1.0069819671624903263328360501892
absolute error = 0.0009928300228090600296989907868
relative error = 0.098691922820554860739448030082325 %
h = 0.0001
y1[1] (analytic) = 1.0059891371396812663031370594024
y1[1] (numeric) = 1.0059891371396812663031416521423
absolute error = 4.5927399e-24
relative error = 4.5653971106074672756766218309236e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.3MB, time=59.84
NO POLE
NO POLE
x[1] = 0.1096
y2[1] (analytic) = 1.0060000702406260245675057210971
y2[1] (numeric) = 1.0070038283943498195078862022317
absolute error = 0.0010037581537237949403804811346
relative error = 0.099777145491024186684051955214565 %
h = 0.0001
y1[1] (analytic) = 1.0060000702406260245675057210971
y1[1] (numeric) = 1.0060000702406260245675103621569
absolute error = 4.6410598e-24
relative error = 4.6133792007488636686689137336489e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.3MB, time=60.51
NO POLE
NO POLE
x[1] = 0.1097
y2[1] (analytic) = 1.0060110132815700721422813918831
y2[1] (numeric) = 1.0070257095062625788974146439307
absolute error = 0.0010146962246925067551332520476
relative error = 0.10086333164312047143171873019858 %
h = 0.0001
y1[1] (analytic) = 1.0060110132815700721422813918831
y1[1] (numeric) = 1.0060110132815700721422860812622
absolute error = 4.6893791e-24
relative error = 4.6613596055011583055084532430424e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.3MB, time=61.20
NO POLE
NO POLE
x[1] = 0.1098
y2[1] (analytic) = 1.0060219662624039786181147880204
y2[1] (numeric) = 1.0070476104980097933824761239902
absolute error = 0.0010256442356058147643613359698
relative error = 0.10195048120234510321478101690938 %
h = 0.0001
y1[1] (analytic) = 1.0060219662624039786181147880204
y1[1] (numeric) = 1.0060219662624039786181195257183
absolute error = 4.7376979e-24
relative error = 4.7093384228990591058049808797048e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.3MB, time=61.85
NO POLE
NO POLE
x[1] = 0.1099
y2[1] (analytic) = 1.006032929183018214186758119591
y2[1] (numeric) = 1.007069531369372453045781005824
absolute error = 0.001036602186354238859022886233
relative error = 0.10303859409413620338749923105644 %
h = 0.0001
y1[1] (analytic) = 1.006032929183018214186758119591
y1[1] (numeric) = 1.0060329291830182141867629056072
absolute error = 4.7860162e-24
relative error = 4.7573156515727971615195838655554e-22 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.3MB, time=62.51
NO POLE
NO POLE
x[1] = 0.11
y2[1] (analytic) = 1.0060439020433031496421603885802
y2[1] (numeric) = 1.0070914721201313491738853667271
absolute error = 0.0010475700768281995317249781469
relative error = 0.10412767024386863893146289305392 %
h = 0.0001
y1[1] (analytic) = 1.0060439020433031496421603885802
y1[1] (numeric) = 1.0060439020433031496421652229141
absolute error = 4.8343339e-24
relative error = 4.8052911907535380662668580645539e-22 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;
diff ( y1 , x , 1 ) = sin ( x ) ;
Iterations = 100
Total Elapsed Time = 1 Minutes 2 Seconds
Elapsed Time(since restart) = 1 Minutes 2 Seconds
Expected Time Remaining = 8 Hours 24 Minutes 12 Seconds
Optimized Time Remaining = 8 Hours 23 Minutes 59 Seconds
Time to Timeout = 13 Minutes 57 Seconds
Percent Done = 0.2061 %
> quit
memory used=366.8MB, alloc=4.3MB, time=62.59