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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> 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 - 3 - 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 - 3 - 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, glob_last;
n := glob_max_terms;
m := n - 4;
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 - 4;
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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, 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
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cos $eq_no = 1
> array_tmp1_g[1] := sin(array_x[1]);
> array_tmp1[1] := cos(array_x[1]);
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_m1[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if not array_y2_set_initial[1,4] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * (glob_h ^ (3)) * factorial_3(0,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,2] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,1] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp5[1] := (array_m1[1] * (array_y2[1]));
> #emit pre add $eq_no = 2 i = 1
> array_tmp6[1] := array_tmp5[1] + array_const_1D0[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_tmp6[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 cos $eq_no = 1
> array_tmp1_g[2] := (att(1,array_tmp1,array_x,1));
> array_tmp1[2] := (-att(1,array_tmp1_g,array_x,1));
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if not array_y2_set_initial[1,5] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * (glob_h ^ (3)) * factorial_3(1,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,3] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,2] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp5[2] := ats(2,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 2
> array_tmp6[2] := array_tmp5[2] + array_const_1D0[2];
> #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_tmp6[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 cos $eq_no = 1
> array_tmp1_g[3] := (att(2,array_tmp1,array_x,1));
> array_tmp1[3] := (-att(2,array_tmp1_g,array_x,1));
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if not array_y2_set_initial[1,6] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * (glob_h ^ (3)) * factorial_3(2,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,4] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,3] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp5[3] := ats(3,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 3
> array_tmp6[3] := array_tmp5[3] + array_const_1D0[3];
> #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_tmp6[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 cos $eq_no = 1
> array_tmp1_g[4] := (att(3,array_tmp1,array_x,1));
> array_tmp1[4] := (-att(3,array_tmp1_g,array_x,1));
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if not array_y2_set_initial[1,7] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * (glob_h ^ (3)) * factorial_3(3,6);
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,5] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,4] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp5[4] := ats(4,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 4
> array_tmp6[4] := array_tmp5[4] + array_const_1D0[4];
> #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_tmp6[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 cos $eq_no = 1
> array_tmp1_g[5] := (att(4,array_tmp1,array_x,1));
> array_tmp1[5] := (-att(4,array_tmp1_g,array_x,1));
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_m1,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if not array_y2_set_initial[1,8] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * (glob_h ^ (3)) * factorial_3(4,7);
> array_y2[8] := temporary;
> array_y2_higher[1,8] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,7] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[3,6] := temporary
> ;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[4,5] := temporary
> ;
> fi;# end if 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp5[5] := ats(5,array_m1,array_y2,1);
> #emit pre add $eq_no = 2 i = 5
> array_tmp6[5] := array_tmp5[5] + array_const_1D0[5];
> #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_tmp6[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 cos $eq_no = 1
> array_tmp1_g[kkk] := (att(kkk-1,array_tmp1,array_x,1));
> array_tmp1[kkk] := (-att(kkk-1,array_tmp1_g,array_x,1));
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_m1,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 3;
> 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_tmp3[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 mult $eq_no = 2
> array_tmp5[kkk] := ats(kkk,array_m1,array_y2,1);
> #emit add $eq_no = 2
> array_tmp6[kkk] := array_tmp5[kkk] + array_const_1D0[kkk];
> #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_tmp6[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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, glob_last;
array_tmp1_g[1] := sin(array_x[1]);
array_tmp1[1] := cos(array_x[1]);
array_tmp2[1] := array_m1[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y2_set_initial[1, 4] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*glob_h^3*factorial_3(0, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 2] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_m1[1]*array_y2[1];
array_tmp6[1] := array_tmp5[1] + array_const_1D0[1];
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp6[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_g[2] := att(1, array_tmp1, array_x, 1);
array_tmp1[2] := -att(1, array_tmp1_g, array_x, 1);
array_tmp2[2] := ats(2, array_m1, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
if not array_y2_set_initial[1, 5] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*glob_h^3*factorial_3(1, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 3] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := ats(2, array_m1, array_y2, 1);
array_tmp6[2] := array_tmp5[2] + array_const_1D0[2];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp6[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_g[3] := att(2, array_tmp1, array_x, 1);
array_tmp1[3] := -att(2, array_tmp1_g, array_x, 1);
array_tmp2[3] := ats(3, array_m1, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
if not array_y2_set_initial[1, 6] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*glob_h^3*factorial_3(2, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 4] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5[3] := ats(3, array_m1, array_y2, 1);
array_tmp6[3] := array_tmp5[3] + array_const_1D0[3];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp6[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_g[4] := att(3, array_tmp1, array_x, 1);
array_tmp1[4] := -att(3, array_tmp1_g, array_x, 1);
array_tmp2[4] := ats(4, array_m1, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
if not array_y2_set_initial[1, 7] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*glob_h^3*factorial_3(3, 6);
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5[4] := ats(4, array_m1, array_y2, 1);
array_tmp6[4] := array_tmp5[4] + array_const_1D0[4];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp6[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_g[5] := att(4, array_tmp1, array_x, 1);
array_tmp1[5] := -att(4, array_tmp1_g, array_x, 1);
array_tmp2[5] := ats(5, array_m1, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
if not array_y2_set_initial[1, 8] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*glob_h^3*factorial_3(4, 7);
array_y2[8] := temporary;
array_y2_higher[1, 8] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 7] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[3, 6] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[4, 5] := temporary
end if
end if;
kkk := 6;
array_tmp5[5] := ats(5, array_m1, array_y2, 1);
array_tmp6[5] := array_tmp5[5] + array_const_1D0[5];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp6[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_g[kkk] := att(kkk - 1, array_tmp1, array_x, 1);
array_tmp1[kkk] := -att(kkk - 1, array_tmp1_g, array_x, 1);
array_tmp2[kkk] := ats(kkk, array_m1, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
order_d := 3;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp3[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_tmp5[kkk] := ats(kkk, array_m1, array_y2, 1);
array_tmp6[kkk] := array_tmp5[kkk] + array_const_1D0[kkk];
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_tmp6[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_y2 := proc(x)
> 1.0 + cos(x);
> end;
exact_soln_y2 := proc(x) 1.0 + cos(x) end proc
> exact_soln_y2p := proc(x)
> -sin(x);
> end;
exact_soln_y2p := proc(x) -sin(x) end proc
> exact_soln_y2pp := proc(x)
> -cos(x);
> end;
exact_soln_y2pp := proc(x) -cos(x) end proc
> exact_soln_y1 := proc(x)
> 1.0 - sin(x);
> end;
exact_soln_y1 := proc(x) 1.0 - sin(x) end proc
>
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> glob_iolevel,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_iter,
> glob_start,
> glob_warned,
> glob_relerr,
> glob_dump_analytic,
> glob_look_poles,
> glob_hmin,
> glob_disp_incr,
> glob_display_flag,
> glob_dump,
> glob_subiter_method,
> glob_max_trunc_err,
> glob_large_float,
> djd_debug2,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> sec_in_min,
> MAX_UNCHANGED,
> glob_warned2,
> glob_h,
> days_in_year,
> glob_optimal_start,
> glob_no_eqs,
> glob_html_log,
> glob_log10relerr,
> glob_max_hours,
> glob_optimal_done,
> glob_not_yet_finished,
> glob_clock_sec,
> min_in_hour,
> glob_log10normmin,
> glob_normmax,
> glob_orig_start_sec,
> glob_max_sec,
> glob_log10_relerr,
> glob_almost_1,
> glob_max_opt_iter,
> glob_log10abserr,
> glob_max_iter,
> glob_abserr,
> glob_log10_abserr,
> glob_hmin_init,
> glob_clock_start_sec,
> djd_debug,
> glob_curr_iter_when_opt,
> glob_optimal_clock_start_sec,
> glob_initial_pass,
> years_in_century,
> glob_smallish_float,
> glob_small_float,
> glob_max_rel_trunc_err,
> hours_in_day,
> glob_max_minutes,
> glob_current_iter,
> glob_unchanged_h_cnt,
> glob_hmax,
> centuries_in_millinium,
> glob_optimal_expect_sec,
> glob_percent_done,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_3,
> array_const_0D0,
> array_const_1D0,
> #END CONST
> array_pole,
> array_y1_init,
> array_m1,
> array_y2,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_last_rel_error,
> array_y2_init,
> array_x,
> array_1st_rel_error,
> array_type_pole,
> array_norms,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_complex_pole,
> array_y1_higher_work,
> array_y2_set_initial,
> array_y1_higher_work2,
> array_poles,
> array_y1_set_initial,
> array_y1_higher,
> array_real_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> glob_iolevel := 5;
> INFO := 2;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_iter := 0;
> glob_start := 0;
> glob_warned := false;
> glob_relerr := 0.1e-10;
> glob_dump_analytic := false;
> glob_look_poles := false;
> glob_hmin := 0.00000000001;
> glob_disp_incr := 0.1;
> glob_display_flag := true;
> glob_dump := false;
> glob_subiter_method := 3;
> glob_max_trunc_err := 0.1e-10;
> glob_large_float := 9.0e100;
> djd_debug2 := true;
> glob_last_good_h := 0.1;
> glob_reached_optimal_h := false;
> glob_not_yet_start_msg := true;
> sec_in_min := 60.0;
> MAX_UNCHANGED := 10;
> glob_warned2 := false;
> glob_h := 0.1;
> days_in_year := 365.0;
> glob_optimal_start := 0.0;
> glob_no_eqs := 0;
> glob_html_log := true;
> glob_log10relerr := 0.0;
> glob_max_hours := 0.0;
> glob_optimal_done := false;
> glob_not_yet_finished := true;
> glob_clock_sec := 0.0;
> min_in_hour := 60.0;
> glob_log10normmin := 0.1;
> glob_normmax := 0.0;
> glob_orig_start_sec := 0.0;
> glob_max_sec := 10000.0;
> glob_log10_relerr := 0.1e-10;
> glob_almost_1 := 0.9990;
> glob_max_opt_iter := 10;
> glob_log10abserr := 0.0;
> glob_max_iter := 1000;
> glob_abserr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_clock_start_sec := 0.0;
> djd_debug := true;
> glob_curr_iter_when_opt := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_initial_pass := true;
> years_in_century := 100.0;
> glob_smallish_float := 0.1e-100;
> glob_small_float := 0.1e-50;
> glob_max_rel_trunc_err := 0.1e-10;
> hours_in_day := 24.0;
> glob_max_minutes := 0.0;
> glob_current_iter := 0;
> glob_unchanged_h_cnt := 0;
> glob_hmax := 1.0;
> centuries_in_millinium := 10.0;
> glob_optimal_expect_sec := 0.1;
> glob_percent_done := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_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/mtest4postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = m1 * cos(x) ;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> 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,"glob_h := 0.00001;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
> omniout_str(ALWAYS,"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_y2 := proc(x)");
> omniout_str(ALWAYS,"1.0 + cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"-sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"-cos(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"1.0 - sin(x);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_pole:= Array(1..(max_terms + 1),[]);
> array_y1_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_y2:= Array(1..(max_terms + 1),[]);
> array_y1:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1_g:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_y2_init:= Array(1..(max_terms + 1),[]);
> array_x:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_y2_higher := Array(1..(4+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work := Array(1..(4+ 1) ,(1..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(1..(4+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> 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_y1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp6[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_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_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_type_pole[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 <=4 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=4 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 <=4 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 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_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> 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 <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_y1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_y2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_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_3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3[1] := 3;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1D0[1] := 1.0;
> array_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;
> glob_h := 0.00001;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
> glob_max_iter := 20;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := 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 := 3;
> #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 <= 4 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 4 + 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 := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 4;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 4;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 4;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y1
> order_diff := 1;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 3 ) = m1 * cos(x) ;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
> 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,"2012-06-13T02:09:15-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest4")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 3 ) = m1 * cos(x) ;")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 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,"mtest4 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest4 maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;")
> ;
> 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 DEBUGL, glob_iolevel, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_iter, glob_start, glob_warned, glob_relerr, glob_dump_analytic,
glob_look_poles, glob_hmin, glob_disp_incr, glob_display_flag, glob_dump,
glob_subiter_method, glob_max_trunc_err, glob_large_float, djd_debug2,
glob_last_good_h, glob_reached_optimal_h, glob_not_yet_start_msg,
sec_in_min, MAX_UNCHANGED, glob_warned2, glob_h, days_in_year,
glob_optimal_start, glob_no_eqs, glob_html_log, glob_log10relerr,
glob_max_hours, glob_optimal_done, glob_not_yet_finished, glob_clock_sec,
min_in_hour, glob_log10normmin, glob_normmax, glob_orig_start_sec,
glob_max_sec, glob_log10_relerr, glob_almost_1, glob_max_opt_iter,
glob_log10abserr, glob_max_iter, glob_abserr, glob_log10_abserr,
glob_hmin_init, glob_clock_start_sec, djd_debug, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_initial_pass, years_in_century,
glob_smallish_float, glob_small_float, glob_max_rel_trunc_err, hours_in_day,
glob_max_minutes, glob_current_iter, glob_unchanged_h_cnt, glob_hmax,
centuries_in_millinium, glob_optimal_expect_sec, glob_percent_done,
array_const_1, array_const_3, array_const_0D0, array_const_1D0, array_pole,
array_y1_init, array_m1, array_y2, array_y1, array_tmp0, array_tmp1_g,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_last_rel_error, array_y2_init, array_x, array_1st_rel_error,
array_type_pole, array_norms, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_complex_pole, array_y1_higher_work,
array_y2_set_initial, array_y1_higher_work2, array_poles,
array_y1_set_initial, array_y1_higher, array_real_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
glob_iolevel := 5;
INFO := 2;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_terms := 30;
glob_iter := 0;
glob_start := 0;
glob_warned := false;
glob_relerr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_look_poles := false;
glob_hmin := 0.1*10^(-10);
glob_disp_incr := 0.1;
glob_display_flag := true;
glob_dump := false;
glob_subiter_method := 3;
glob_max_trunc_err := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
djd_debug2 := true;
glob_last_good_h := 0.1;
glob_reached_optimal_h := false;
glob_not_yet_start_msg := true;
sec_in_min := 60.0;
MAX_UNCHANGED := 10;
glob_warned2 := false;
glob_h := 0.1;
days_in_year := 365.0;
glob_optimal_start := 0.;
glob_no_eqs := 0;
glob_html_log := true;
glob_log10relerr := 0.;
glob_max_hours := 0.;
glob_optimal_done := false;
glob_not_yet_finished := true;
glob_clock_sec := 0.;
min_in_hour := 60.0;
glob_log10normmin := 0.1;
glob_normmax := 0.;
glob_orig_start_sec := 0.;
glob_max_sec := 10000.0;
glob_log10_relerr := 0.1*10^(-10);
glob_almost_1 := 0.9990;
glob_max_opt_iter := 10;
glob_log10abserr := 0.;
glob_max_iter := 1000;
glob_abserr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_clock_start_sec := 0.;
djd_debug := true;
glob_curr_iter_when_opt := 0;
glob_optimal_clock_start_sec := 0.;
glob_initial_pass := true;
years_in_century := 100.0;
glob_smallish_float := 0.1*10^(-100);
glob_small_float := 0.1*10^(-50);
glob_max_rel_trunc_err := 0.1*10^(-10);
hours_in_day := 24.0;
glob_max_minutes := 0.;
glob_current_iter := 0;
glob_unchanged_h_cnt := 0;
glob_hmax := 1.0;
centuries_in_millinium := 10.0;
glob_optimal_expect_sec := 0.1;
glob_percent_done := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_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/mtest4postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos(x) ;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
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, "glob_h := 0.00001;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
;
omniout_str(ALWAYS, "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_y2 := proc(x)");
omniout_str(ALWAYS, "1.0 + cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "-sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "-cos(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "1.0 - sin(x);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_pole := Array(1 .. max_terms + 1, []);
array_y1_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_y2 := Array(1 .. max_terms + 1, []);
array_y1 := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1_g := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_y2_init := Array(1 .. max_terms + 1, []);
array_x := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_y2_higher := Array(1 .. 5, 1 .. max_terms + 1, []);
array_y2_higher_work := Array(1 .. 5, 1 .. max_terms + 1, []);
array_y2_higher_work2 := Array(1 .. 5, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[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_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_1st_rel_error[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_norms[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 4 do
term := 1;
while term <= max_terms do
array_y2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 4 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 <= 4 do
term := 1;
while term <= max_terms do
array_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_const_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_3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3[term] := 0.; term := term + 1
end do;
array_const_3[1] := 3;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_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;
glob_h := 0.00001;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
array_y2_init[3] := exact_soln_y2pp(x_start);
glob_max_iter := 20;
glob_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := 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 := 3;
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 <= 4 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 4 + 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 := 3;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 4;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 2;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 4;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y2 , x , 3 ) = m1 * cos(x) ;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
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, "2012-06-13T02:09:15-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "mtest4")
;
logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos(x) ;");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 090 | ");
logitem_str(html_log_file,
"mtest4 diffeq.mxt");
logitem_str(html_log_file,
"mtest4 maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;");
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/mtest4postode.ode#################
diff ( y2 , x , 3 ) = m1 * cos(x) ;
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
!
#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;
glob_h := 0.00001;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
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_y2 := proc(x)
1.0 + cos(x);
end;
exact_soln_y2p := proc(x)
-sin(x);
end;
exact_soln_y2pp := proc(x)
-cos(x);
end;
exact_soln_y1 := proc(x)
1.0 - sin(x);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1
y2[1] (analytic) = 1.9950041652780257660955619878039
y2[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 0.90016658335317184769318580158938
y1[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
h = 0.0001
x[1] = 0.1
y2[1] (analytic) = 1.9950041652780257660955619878039
y2[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
h = 0.0001
y1[1] (analytic) = 0.90016658335317184769318580158938
y1[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.52
NO POLE
NO POLE
x[1] = 0.1001
y2[1] (analytic) = 1.99499417696135689993881931509
y2[1] (numeric) = 1.9949941769611744232787116245154
absolute error = 1.824766601076905746e-13
relative error = 9.1467264523862895092208640632915e-12 %
h = 0.0001
y1[1] (analytic) = 0.90006708343597696196220785831547
y1[1] (numeric) = 0.9000670834359769665241056640093
absolute error = 4.56189780569383e-18
relative error = 5.0683975557454370671940508023476e-16 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.2MB, time=1.15
memory used=11.4MB, alloc=4.3MB, time=1.83
NO POLE
NO POLE
x[1] = 0.1002
y2[1] (analytic) = 1.9949841786947462724601257815688
y2[1] (numeric) = 1.9949841786932864293424290473843
absolute error = 1.4598431176967341845e-12
relative error = 7.3175673937016502868475485055980e-11 %
h = 0.0001
y1[1] (analytic) = 0.89996758451811124103868599099689
y1[1] (numeric) = 0.89996758451811131403024504725983
absolute error = 7.299155905626294e-17
relative error = 8.1104653447430954744631119827502e-15 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=2.46
NO POLE
NO POLE
x[1] = 0.1003
y2[1] (analytic) = 1.9949741704782938663255043431386
y2[1] (numeric) = 1.994974170473366795108886204824
absolute error = 4.9270712166181383146e-12
relative error = 2.4697418590822536474212144758846e-10 %
h = 0.0001
y1[1] (analytic) = 0.89986808660056967410044825122023
y1[1] (numeric) = 0.8998680866005700436262581048533
absolute error = 3.6952580985363307e-16
relative error = 4.1064442150581222368751418271897e-14 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=3.13
memory used=22.8MB, alloc=4.3MB, time=3.80
NO POLE
NO POLE
x[1] = 0.1004
y2[1] (analytic) = 1.9949641523120997636993956593421
y2[1] (numeric) = 1.9949641523004205414034965767649
absolute error = 1.16792222958990825772e-11
relative error = 5.8543519603413609177295971327085e-10 %
h = 0.0001
y1[1] (analytic) = 0.89976858968434724032208115905533
y1[1] (numeric) = 0.89976858968434840822521669394597
absolute error = 1.16790313553489064e-15
relative error = 1.2980038966959372876805633836775e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.3MB, time=4.44
NO POLE
NO POLE
x[1] = 0.1005
y2[1] (analytic) = 1.994954124196264146243657271722
y2[1] (numeric) = 1.9949541241734526990648649663917
absolute error = 2.28114471787923053303e-11
relative error = 1.1434572305256734194027721442207e-09 %
h = 0.0001
y1[1] (analytic) = 0.89966909377043890886497991131759
y1[1] (numeric) = 0.89966909377044176023760955369446
absolute error = 2.85137262964237687e-15
relative error = 3.1693570996114910933945414025662e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=5.08
memory used=34.3MB, alloc=4.3MB, time=5.74
NO POLE
NO POLE
x[1] = 0.1006
y2[1] (analytic) = 1.9949440861308872951165617872037
y2[1] (numeric) = 1.9949440860914683089547371917492
absolute error = 3.94189861618245954545e-11
relative error = 1.9759444104659650727992486352611e-09 %
h = 0.0001
y1[1] (analytic) = 0.8995695988598396388673986899624
y1[1] (numeric) = 0.89956959885984555157034048863801
absolute error = 5.91270294179867561e-15
relative error = 6.5728132089976547584843886895827e-13 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=6.39
NO POLE
NO POLE
x[1] = 0.1007
y2[1] (analytic) = 1.9949340381160695909717940665135
y2[1] (numeric) = 1.9949340380534724219679496771165
absolute error = 6.25971690038443893970e-11
relative error = 3.1378064541401318392960817288265e-09 %
h = 0.0001
y1[1] (analytic) = 0.89947010495354437943450107071087
y1[1] (numeric) = 0.89947010495355533362572555711659
absolute error = 1.095419122448640572e-14
relative error = 1.2178493942333041978804010386043e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=7.04
memory used=45.7MB, alloc=4.3MB, time=7.70
NO POLE
NO POLE
x[1] = 0.1008
y2[1] (analytic) = 1.9949239801519115139574474176422
y2[1] (numeric) = 1.9949239800584700990423789440502
absolute error = 9.34414149150684735920e-11
relative error = 4.6839586793654663998291634036852e-09 %
h = 0.0001
y1[1] (analytic) = 0.89937061205254806962841053200644
y1[1] (numeric) = 0.89937061205256675730048926473487
absolute error = 1.868767207873272843e-14
relative error = 2.0778610984501295371662388738465e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=8.33
NO POLE
NO POLE
x[1] = 0.1009
y2[1] (analytic) = 1.9949139122385136437150187943654
y2[1] (numeric) = 1.9949139121054664111688910019977
absolute error = 1.330472325461277923677e-10
relative error = 6.6693220058220010769330063871715e-09 %
h = 0.0001
y1[1] (analytic) = 0.89927112015784563845826106440201
y1[1] (numeric) = 0.89927112015787557298475976288216
absolute error = 2.993452649869848015e-14
relative error = 3.3287543464582946463493444904738e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=8.97
NO POLE
NO POLE
memory used=57.2MB, alloc=4.3MB, time=9.65
x[1] = 0.101
y2[1] (analytic) = 1.994903834375976659378402999829
y2[1] (numeric) = 1.9949038341934664394012906383798
absolute error = 1.825102199771123614492e-10
relative error = 9.1488229573834646568524884215014e-09 %
h = 0.0001
y1[1] (analytic) = 0.89917162927043200487024788047681
y1[1] (numeric) = 0.89917162927047763056106305231824
absolute error = 4.562569081517184143e-14
relative error = 5.0741915480798164168468314235371e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=10.29
NO POLE
NO POLE
x[1] = 0.1011
y2[1] (analytic) = 1.9948937465644013395728858952114
y2[1] (numeric) = 1.9948937463214752748662706080447
absolute error = 2.429260647066152871667e-10
relative error = 1.2177393664448628443366136222802e-08 %
h = 0.0001
y1[1] (analytic) = 0.89907213939130207773767822538281
y1[1] (numeric) = 0.89907213939136887940331619183528
absolute error = 6.680166563796645247e-14
relative error = 7.4300673673631037168863894606624e-12 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=10.98
NO POLE
NO POLE
x[1] = 0.1012
y2[1] (analytic) = 1.9948836488038885624141366134714
y2[1] (numeric) = 1.9948836484884980187733607219927
absolute error = 3.153905436407758914787e-10
relative error = 1.5809971866273041700968326349160e-08 %
h = 0.0001
y1[1] (analytic) = 0.8989726505214507558510222881199
y1[1] (numeric) = 0.89897265052154536837581951200581
absolute error = 9.461252479722388591e-14
relative error = 1.0524516484716605688813760799454e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=11.68
memory used=72.4MB, alloc=4.3MB, time=12.40
NO POLE
NO POLE
x[1] = 0.1013
y2[1] (analytic) = 1.9948735410945393055071987781922
y2[1] (numeric) = 1.9948735406935397824248768352726
absolute error = 4.009995230823219429196e-10
relative error = 2.0101500913301156645078880562496e-08 %
h = 0.0001
y1[1] (analytic) = 0.89887316266187292790796421363949
y1[1] (numeric) = 0.89887316266200324583224783402686
absolute error = 1.3031792428362038737e-13
relative error = 1.4497921363866748838717791351294e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.3MB, time=13.10
NO POLE
NO POLE
x[1] = 0.1014
y2[1] (analytic) = 1.9948634234364546459454807275319
y2[1] (numeric) = 1.9948634229356056872258697339501
absolute error = 5.008489587196109935818e-10
relative error = 2.5106929769498843137019778003200e-08 %
h = 0.0001
y1[1] (analytic) = 0.89877367581356347250345321587596
y1[1] (numeric) = 0.89877367581373875961464069367038
absolute error = 1.7528711118747779442e-13
relative error = 1.9502920023643233769177408139558e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.3MB, time=13.81
memory used=83.9MB, alloc=4.3MB, time=14.49
NO POLE
NO POLE
x[1] = 0.1015
y2[1] (analytic) = 1.9948532958297357603097447432905
y2[1] (numeric) = 1.9948532952137008646940739210493
absolute error = 6.160348956156708222412e-10
relative error = 3.0881213014686293241474724043789e-08 %
h = 0.0001
y1[1] (analytic) = 0.89867418997751725811975479180544
y1[1] (numeric) = 0.89867418997774825705239157035
absolute error = 2.3099893263677854456e-13
relative error = 2.5704413814594764490762267468424e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.3MB, time=15.15
NO POLE
NO POLE
x[1] = 0.1016
y2[1] (analytic) = 1.9948431582744839246670952851026
y2[1] (numeric) = 1.9948431575268304564698563013668
absolute error = 7.476534681972389837358e-10
relative error = 3.7479310846871315804223605312719e-08 %
h = 0.0001
y1[1] (analytic) = 0.89857470515472914311650203663147
y1[1] (numeric) = 0.89857470515502818496123612131424
absolute error = 2.9904184473408468277e-13
relative error = 3.3279575200438285343181335819351e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.3MB, time=15.87
memory used=95.3MB, alloc=4.4MB, time=16.61
NO POLE
NO POLE
x[1] = 0.1017
y2[1] (analytic) = 1.9948330107708005145699662297676
y2[1] (numeric) = 1.9948330098739996143261647650598
absolute error = 8.968009002438014647078e-10
relative error = 4.4956189084583021208015155203357e-08 %
h = 0.0001
y1[1] (analytic) = 0.89847522134619397572074706019696
y1[1] (numeric) = 0.89847522134657508964223942097632
absolute error = 3.8111392149236077936e-13
relative error = 4.2417855544344802674925343665021e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=17.29
NO POLE
NO POLE
x[1] = 0.1018
y2[1] (analytic) = 1.9948228533187870050551071157262
y2[1] (numeric) = 1.9948228522542135001784766699085
absolute error = 1.0645735048766304458177e-09
relative error = 5.3366819169205896464382129553377e-08 %
h = 0.0001
y1[1] (analytic) = 0.89837573855290659401701250472195
y1[1] (numeric) = 0.89837573855338561688078220539064
absolute error = 4.7902286376970066869e-13
relative error = 5.3320992900064870513032294759163e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.4MB, time=17.98
memory used=106.8MB, alloc=4.4MB, time=18.71
NO POLE
NO POLE
x[1] = 0.1019
y2[1] (analytic) = 1.9948126859185449706425683926936
y2[1] (numeric) = 1.9948126846664772860947472221527
absolute error = 1.2520676845478211705409e-09
relative error = 6.2766178167314270799339786596333e-08 %
h = 0.0001
y1[1] (analytic) = 0.89827625677586182593734316396666
y1[1] (numeric) = 0.89827625677645651194554612188617
absolute error = 5.9468600820295791951e-13
relative error = 6.6203019807896821576767887482565e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=19.41
NO POLE
NO POLE
x[1] = 0.102
y2[1] (analytic) = 1.9948025085701760853346856764599
y2[1] (numeric) = 1.9948025071097961543053577558044
absolute error = 1.4603799310293279206555e-09
relative error = 7.3209248773007171890854485583811e-08 %
h = 0.0001
y1[1] (analytic) = 0.89817677601605448925135770391935
y1[1] (numeric) = 0.89817677601678461958749798386676
absolute error = 7.3013033614027994741e-13
relative error = 8.1290271095500827063755351573316e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=20.11
memory used=118.2MB, alloc=4.4MB, time=20.86
NO POLE
NO POLE
x[1] = 0.1021
y2[1] (analytic) = 1.9947923212737821226150630088674
y2[1] (numeric) = 1.9947923195831752972130639103354
absolute error = 1.6906068254019990985320e-09
relative error = 8.4751019310243572916105746994516e-08 %
h = 0.0001
y1[1] (analytic) = 0.89807729627447939155630048510842
y1[1] (numeric) = 0.89807729627536688403887303078865
absolute error = 8.8749248257254568023e-13
relative error = 9.8821391683561870782388740917658e-11 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=21.55
NO POLE
NO POLE
x[1] = 0.1022
y2[1] (analytic) = 1.9947821240294649554475551229758
y2[1] (numeric) = 1.9947821220856199174029437066414
absolute error = 1.9438450380446114163344e-09
relative error = 9.7446483735178030566541248191329e-08 %
h = 0.0001
y1[1] (analytic) = 0.89797781755213133026709348663827
y1[1] (numeric) = 0.89797781755320034901215719332527
absolute error = 1.06901874506370668700e-12
relative error = 1.1904734439630472527998256181427e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=22.25
NO POLE
NO POLE
memory used=129.7MB, alloc=4.4MB, time=22.93
x[1] = 0.1023
y2[1] (analytic) = 1.9947719168373265562752487134242
y2[1] (numeric) = 1.9947719146161352276523455211831
absolute error = 2.2211913286229031922411e-09
relative error = 1.1135064163849671418870538602525e-07 %
h = 0.0001
y1[1] (analytic) = 0.89787833985000509260638833204834
y1[1] (numeric) = 0.89787833985128215769906836372953
absolute error = 1.27706509268003168119e-12
relative error = 1.4223141777686401974782330864558e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=23.60
NO POLE
NO POLE
x[1] = 0.1024
y2[1] (analytic) = 1.9947616996974689970194427120013
y2[1] (numeric) = 1.9947616971737264509408359582044
absolute error = 2.5237425460786067537969e-09
relative error = 1.2651849824775382620900373453923e-07 %
h = 0.0001
y1[1] (analytic) = 0.89777886316909545559461841709491
y1[1] (numeric) = 0.89777886317060955276953667140383
absolute error = 1.51409717491825430892e-12
relative error = 1.6864923390751249157970631216319e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=24.27
NO POLE
NO POLE
x[1] = 0.1025
y2[1] (analytic) = 1.9947514726099944490786275684329
y2[1] (numeric) = 1.9947514697573988204601476199284
absolute error = 2.8525956286184799485045e-09
relative error = 1.4300506442970841400045668259641e-07 %
h = 0.0001
y1[1] (analytic) = 0.89767938751039718604005113955504
y1[1] (numeric) = 0.8976793875121798763706837636879
absolute error = 1.78269033063262413286e-12
relative error = 1.9858875623475051558089266390322e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=24.97
memory used=144.9MB, alloc=4.4MB, time=25.72
NO POLE
NO POLE
x[1] = 0.1026
y2[1] (analytic) = 1.9947412355750051833274635363984
y2[1] (numeric) = 1.9947412323661575796241267746318
absolute error = 3.2088476037033367617666e-09
relative error = 1.6086535669266157334966724075990e-07 %
h = 0.0001
y1[1] (analytic) = 0.89757991287490504052884023115219
y1[1] (numeric) = 0.89757991287699057012580109187476
absolute error = 2.08552959696086072257e-12
relative error = 2.3235029739926000693965212389151e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=26.43
NO POLE
NO POLE
x[1] = 0.1027
y2[1] (analytic) = 1.9947309885926035701157579647845
y2[1] (numeric) = 1.9947309849990079820786809224982
absolute error = 3.5935955880370770422863e-09
relative error = 1.8015439718879404368209392822332e-07 %
h = 0.0001
y1[1] (analytic) = 0.89748043926361376541507819170298
y1[1] (numeric) = 0.89748043926603917513332720246495
absolute error = 2.42540971824901076197e-12
relative error = 2.7024652707072579618143422490288e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=27.14
memory used=156.4MB, alloc=4.4MB, time=27.86
NO POLE
NO POLE
x[1] = 0.1028
y2[1] (analytic) = 1.9947207316628920792674415941882
y2[1] (numeric) = 1.9947207276549552917117262591505
absolute error = 4.0079367875557153350377e-09
relative error = 2.0092721371650419520396658627643e-07 %
h = 0.0001
y1[1] (analytic) = 0.89738096667751809681084882558455
y1[1] (numeric) = 0.89738096668032333196582403366934
absolute error = 2.80523515497520808479e-12
relative error = 3.1260247978752757645965323298269e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=28.56
NO POLE
NO POLE
x[1] = 0.1029
y2[1] (analytic) = 1.9947104647859732800795438586784
y2[1] (numeric) = 1.9947104603330047826631350367639
absolute error = 4.4529684974164088219145e-09
relative error = 2.2323883972274640811901382610085e-07 %
h = 0.0001
y1[1] (analytic) = 0.89728149511761276057627988062199
y1[1] (numeric) = 0.89728149512084078066895221717064
absolute error = 3.22802009267233654865e-12
relative error = 3.5975556280130552563247192871495e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=29.26
memory used=167.8MB, alloc=4.4MB, time=29.98
NO POLE
NO POLE
x[1] = 0.103
y2[1] (analytic) = 1.9947001879619498413211671928266
y2[1] (numeric) = 1.9947001830321617393346828226584
absolute error = 4.9297881019864843701682e-09
relative error = 2.4714431430536984407839773636823e-07 %
h = 0.0001
y1[1] (analytic) = 0.89718202458489247230959578949541
y1[1] (numeric) = 0.89718202458858936076044538515399
absolute error = 3.69688845084959565858e-12
relative error = 4.1205556392640270771203238752033e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=30.69
NO POLE
NO POLE
x[1] = 0.1031
y2[1] (analytic) = 1.9946899011909245312324603440163
y2[1] (numeric) = 1.994689895751431456399995655273
absolute error = 5.4394930748324646887433e-09
relative error = 2.7269868221545761002207735415589e-07 %
h = 0.0001
y1[1] (analytic) = 0.89708255508035193733717051376591
y1[1] (numeric) = 0.89708255508456701122908348261677
absolute error = 4.21507389191296885086e-12
relative error = 4.6986465939418736040119216279093e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=31.40
memory used=179.2MB, alloc=4.4MB, time=32.13
NO POLE
NO POLE
x[1] = 0.1032
y2[1] (analytic) = 1.9946796044730002175235906900428
y2[1] (numeric) = 1.9946795984898192388144970974212
absolute error = 5.9831809787090935926216e-09
relative error = 2.9995699385966631457009447431168e-07 %
h = 0.0001
y1[1] (analytic) = 0.89698308660498585070358049062019
y1[1] (numeric) = 0.896983086609771770533665084968
absolute error = 4.78591983008459434781e-12
relative error = 5.3355742171225817752733014021050e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=32.83
NO POLE
NO POLE
x[1] = 0.1033
y2[1] (analytic) = 1.994669297808279867373715562012
y2[1] (numeric) = 1.9946692912463304018253551867284
absolute error = 6.5619494655483603752836e-09
relative error = 3.2897430530256601712210629546185e-07 %
h = 0.0001
y1[1] (analytic) = 0.89688361915978889716165768243304
y1[1] (numeric) = 0.89688361916520177660197872092749
absolute error = 5.41287944032103849445e-12
relative error = 6.0352082752853569733903710267088e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.4MB, time=33.53
memory used=190.7MB, alloc=4.4MB, time=34.25
NO POLE
NO POLE
x[1] = 0.1034
y2[1] (analytic) = 1.9946589811968665474299525725501
y2[1] (numeric) = 1.9946589740199702709814292831519
absolute error = 7.1768962764485232893982e-09
relative error = 3.5980567826898056982368630812027e-07 %
h = 0.0001
y1[1] (analytic) = 0.89678415274575575116254272924732
y1[1] (numeric) = 0.89678415275185526682977320073513
absolute error = 6.09951566723047148781e-12
relative error = 6.8015426550024290974140545197743e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=34.95
NO POLE
NO POLE
x[1] = 0.1035
y2[1] (analytic) = 1.9946486546388634238063489493329
y2[1] (numeric) = 1.994648646809744182143216813484
absolute error = 7.8291192416631321358489e-09
relative error = 3.9250618014632835255780092980491e-07 %
h = 0.0001
y1[1] (analytic) = 0.89668468736388107684573820427085
y1[1] (numeric) = 0.8966846873707305780797269496806
absolute error = 6.84950123398874540975e-12
relative error = 7.6386954416777819768161791784521e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.4MB, time=35.66
NO POLE
NO POLE
x[1] = 0.1036
y2[1] (analytic) = 1.9946383181343737620828498739466
y2[1] (numeric) = 1.9946383096146574814927999127389
absolute error = 8.5197162805900499612077e-09
relative error = 4.2713088398696340112005630734011e-07 %
h = 0.0001
y1[1] (analytic) = 0.89658522301515952802916197248966
y1[1] (numeric) = 0.89658522302282614668041634696372
absolute error = 7.66661865125437447406e-12
relative error = 8.5509089983348373001513652066981e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.4MB, time=36.36
memory used=205.9MB, alloc=4.4MB, time=37.09
NO POLE
NO POLE
x[1] = 0.1037
y2[1] (analytic) = 1.9946279716835009273042658260886
y2[1] (numeric) = 1.9946279624337155255437919623233
absolute error = 9.2497854017604738637653e-09
relative error = 4.6373486851051692873621589111174e-07 %
h = 0.0001
y1[1] (analytic) = 0.8964857597005857481992006524971
y1[1] (numeric) = 0.89648575970914050842528306989589
absolute error = 8.55476022608241739879e-12
relative error = 9.5425500444531242533307129742170e-10 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.4MB, time=37.81
NO POLE
NO POLE
x[1] = 0.1038
y2[1] (analytic) = 1.9946176152863483839792389331209
y2[1] (numeric) = 1.9946176052659236811512840248924
absolute error = 1.00204247028279549082285e-08
relative error = 5.0237321810623924108064124209519e-07 %
h = 0.0001
y1[1] (analytic) = 0.8963862974211543705007631816383
y1[1] (numeric) = 0.89638629743067229857160044345283
absolute error = 9.51792807083726181453e-12
relative error = 1.0618109734853966083374378555839e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.4MB, time=38.50
memory used=217.4MB, alloc=4.4MB, time=39.23
NO POLE
NO POLE
x[1] = 0.1039
y2[1] (analytic) = 1.9946072489430196960792083249843
y2[1] (numeric) = 1.9946072381102873255217911757902
absolute error = 1.08327323705574171491941e-08
relative error = 5.4310102283534204495426488312609e-07 %
h = 0.0001
y1[1] (analytic) = 0.8962868361778600177273344845693
y1[1] (numeric) = 0.89628683618842025183943879518901
absolute error = 1.056023411210431061971e-11
relative error = 1.1782203738635214825233999142496e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=39.93
NO POLE
NO POLE
x[1] = 0.104
y2[1] (analytic) = 1.9945968726536185270373744944846
y2[1] (numeric) = 1.9945968609658118462231987309764
absolute error = 1.16878066808141757635082e-08
relative error = 5.8597337843334115078072053175156e-07 %
h = 0.0001
y1[1] (analytic) = 0.89618737597169730231102924533054
y1[1] (numeric) = 0.89618737598338320241062981552416
absolute error = 1.168590009960057019362e-11
relative error = 1.3039572318155065450212517161209e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.4MB, time=40.65
memory used=228.8MB, alloc=4.4MB, time=41.36
NO POLE
NO POLE
x[1] = 0.1041
y2[1] (analytic) = 1.994586486418248639747662662962
y2[1] (numeric) = 1.9945864738315026411947083713392
absolute error = 1.25867459985529542916228e-08
relative error = 6.3104538631239956907944305475863e-07 %
h = 0.0001
y1[1] (analytic) = 0.89608791680366082631264578303401
y1[1] (numeric) = 0.89608791681656008392772992341208
absolute error = 1.289925761508414037807e-11
relative error = 1.4395080408064980716119286837914e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.4MB, time=42.06
NO POLE
NO POLE
x[1] = 0.1042
y2[1] (analytic) = 1.994576090237013896563685151352
y2[1] (numeric) = 1.994576076706365118756784163295
absolute error = 1.35306487778069009880570e-08
relative error = 6.7837215356367100107435647737993e-07 %
h = 0.0001
y1[1] (analytic) = 0.8959884586747451814117200312635
y1[1] (numeric) = 0.8959884586889499294929826374023
absolute error = 1.420474808126260613880e-11
relative error = 1.5853717694391758020891199253046e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.4MB, time=42.77
memory used=240.3MB, alloc=4.4MB, time=43.50
NO POLE
NO POLE
x[1] = 0.1043
y2[1] (analytic) = 1.9945656841100182592977027566508
y2[1] (numeric) = 1.9945656695894046976210984755754
absolute error = 1.45206135616766042810754e-08
relative error = 7.2800879295964372359707072737318e-07 %
h = 0.0001
y1[1] (analytic) = 0.89588900158594494889657962128759
y1[1] (numeric) = 0.89588900160155187166727995210479
absolute error = 1.560692277070033081720e-11
relative error = 1.7420598693668769582193398419192e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.4MB, time=44.22
NO POLE
NO POLE
x[1] = 0.1044
y2[1] (analytic) = 1.9945552680373657892195851337935
y2[1] (numeric) = 1.9945552524796268069004777921022
absolute error = 1.55577389823191073416913e-08
relative error = 7.8001042295648486844329376444174e-07 %
h = 0.0001
y1[1] (analytic) = 0.89578954553825469965439806918463
y1[1] (numeric) = 0.89578954555536514246912272006822
absolute error = 1.711044281472465088359e-11
relative error = 1.9100962832116407287695417862346e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.4MB, time=44.91
memory used=251.7MB, alloc=4.4MB, time=45.63
NO POLE
NO POLE
x[1] = 0.1045
y2[1] (analytic) = 1.9945448420191606470557701829557
y2[1] (numeric) = 1.9945448253760368861188484208509
absolute error = 1.66431237609369217621048e-08
relative error = 8.3443216769638509634132774606047e-07 %
h = 0.0001
y1[1] (analytic) = 0.89569009053266899416124906697927
y1[1] (numeric) = 0.89569009055138907337358003908216
absolute error = 1.872007921233097210289e-11
relative error = 2.0900174524871763581678118234067e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.4MB, time=46.32
NO POLE
NO POLE
x[1] = 0.1046
y2[1] (analytic) = 1.9945344060555070929882224422906
y2[1] (numeric) = 1.9945343882776403852211820986031
absolute error = 1.77778667077670403436875e-08
relative error = 8.9132915700990366569163478039905e-07 %
h = 0.0001
y1[1] (analytic) = 0.89559063657018238247216087789009
y1[1] (numeric) = 0.89559063659062309531124764491352
absolute error = 2.044071283908676702343e-11
relative error = 2.2823723255267579774981332104502e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.4MB, time=47.02
NO POLE
NO POLE
memory used=263.2MB, alloc=4.4MB, time=47.71
x[1] = 0.1047
y2[1] (analytic) = 1.9945239601465094866533904861099
y2[1] (numeric) = 1.9945239411834427645834414914885
absolute error = 1.89630667220699489946214e-08
relative error = 9.5075652641831389623628895443660e-07 %
h = 0.0001
y1[1] (analytic) = 0.89549118365178940421117083578751
y1[1] (numeric) = 0.89549118367406673866720530948782
absolute error = 2.227733445603447370031e-11
relative error = 2.4877223654160493187498738235876e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.4MB, time=48.40
NO POLE
NO POLE
x[1] = 0.1048
y2[1] (analytic) = 1.9945135042922722871411633285203
y2[1] (numeric) = 1.9945134840924494950225255912171
absolute error = 2.01998227921186377373032e-08
relative error = 1.0127694171359490278173485286054e-06 %
h = 0.0001
y1[1] (analytic) = 0.89539173177848458856137994896177
y1[1] (numeric) = 0.89539173180271963327997324452555
absolute error = 2.423504471859329556378e-11
relative error = 2.7066415579308614552852743374823e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.4MB, time=49.08
NO POLE
NO POLE
x[1] = 0.1049
y2[1] (analytic) = 1.9945030384929000529938258325255
y2[1] (numeric) = 1.9945030170036660578062150069017
absolute error = 2.14892339951876108256238e-08
relative error = 1.0774229760725484743831487285138e-06 %
h = 0.0001
y1[1] (analytic) = 0.89529228095126245425500760830018
y1[1] (numeric) = 0.89529228097758150844046751064416
absolute error = 2.631905418545990234398e-11
relative error = 2.9397164194798467137344885385773e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.4MB, time=49.73
memory used=278.4MB, alloc=4.4MB, time=50.42
NO POLE
NO POLE
x[1] = 0.105
y2[1] (analytic) = 1.9944925627484974422050131246041
y2[1] (numeric) = 1.994492539916097944663117152372
absolute error = 2.28323994975418959722321e-08
relative error = 1.1447723558356044734015172133317e-06 %
h = 0.0001
y1[1] (analytic) = 0.89519283117111750956344639997322
y1[1] (numeric) = 0.89519283119965219289095443193607
absolute error = 2.853468332750803196285e-11
relative error = 3.1875460050521319046192925243014e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.4MB, time=51.10
NO POLE
NO POLE
x[1] = 0.1051
y2[1] (analytic) = 1.9944820770591692122186640147742
y2[1] (numeric) = 1.9944820528287506577926113288801
absolute error = 2.42304185544260526858941e-08
relative error = 1.2148727147327091308390463239344e-06 %
h = 0.0001
y1[1] (analytic) = 0.89509338243904425228731702272891
y1[1] (numeric) = 0.89509338246993161482400401603321
absolute error = 3.088736253668699330430e-11
relative error = 3.4507419161698940211901659228082e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.4MB, time=51.75
memory used=289.9MB, alloc=4.4MB, time=52.42
NO POLE
NO POLE
x[1] = 0.1052
y2[1] (analytic) = 1.9944715814250202199279734221549
y2[1] (numeric) = 1.9944715557406297098747937030986
absolute error = 2.56843905100531797190563e-08
relative error = 1.2877792167739018618654927179009e-06 %
h = 0.0001
y1[1] (analytic) = 0.89499393475603716974652330989487
y1[1] (numeric) = 0.89499393478941980188144237966848
absolute error = 3.338263213491906977361e-11
relative error = 3.7299283088458815581019609711825e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.4MB, time=53.11
NO POLE
NO POLE
x[1] = 0.1053
y2[1] (analytic) = 1.9944610758461554216743438060354
y2[1] (numeric) = 1.9944610486507406240804221803111
absolute error = 2.71954147975939216257243e-08
relative error = 1.3635470316740172274425070557493e-06 %
h = 0.0001
y1[1] (analytic) = 0.89489448812309073877030735618759
y1[1] (numeric) = 0.89489448815911688115330317974469
absolute error = 3.602614238299582355710e-11
relative error = 4.0257419015458846037166955065570e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.4MB, time=53.79
memory used=301.3MB, alloc=4.4MB, time=54.48
NO POLE
NO POLE
x[1] = 0.1054
y2[1] (analytic) = 1.9944505603226798732463356024613
y2[1] (numeric) = 1.9944505315580889340808611726966
absolute error = 2.87645909391654744297647e-08
relative error = 1.4422313348550331669557928272315e-06 %
h = 0.0001
y1[1] (analytic) = 0.89479504254119942568730474942828
y1[1] (numeric) = 0.89479504258002307917677804992142
absolute error = 3.882365348947330049314e-11
relative error = 4.3388319831561568619824542926901e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.4MB, time=55.13
NO POLE
NO POLE
x[1] = 0.1055
y2[1] (analytic) = 1.9944400348546987298786166663504
y2[1] (numeric) = 1.9944400044616801840580262626074
absolute error = 3.03930185458205904037430e-08
relative error = 1.5238873074484196270500608722426e-06 %
h = 0.0001
y1[1] (analytic) = 0.89469559801135768631559990726483
y1[1] (numeric) = 0.89469559805313872193516604273027
absolute error = 4.178103561956613546544e-11
relative error = 4.6698604209557927619815435485522e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.4MB, time=55.81
memory used=312.8MB, alloc=4.4MB, time=56.47
NO POLE
NO POLE
x[1] = 0.1056
y2[1] (analytic) = 1.9944294994423172462509107191469
y2[1] (numeric) = 1.9944294673605199287143287607417
absolute error = 3.20817973175365819584052e-08
relative error = 1.6085701362974875868259323034508e-06 %
h = 0.0001
y1[1] (analytic) = 0.8945961545345599659527815189992
y1[1] (numeric) = 0.89459615457946423485682207722908
absolute error = 4.490426890404055822988e-11
relative error = 5.0195016685940628154370846509922e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.4MB, time=57.12
NO POLE
NO POLE
x[1] = 0.1057
y2[1] (analytic) = 1.9944189540856407764869448020247
y2[1] (numeric) = 1.9944189202536137332826201591112
absolute error = 3.38320270432043246429135e-08
relative error = 1.6963350139597384795581147722653e-06 %
h = 0.0001
y1[1] (analytic) = 0.89449671211180069936599809261988
y1[1] (numeric) = 0.89449671216000014281410439220554
absolute error = 4.819944344810629958566e-11
relative error = 5.3884427740727103845754685397635e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.4MB, time=57.78
memory used=324.2MB, alloc=4.4MB, time=58.44
NO POLE
NO POLE
x[1] = 0.1058
y2[1] (analytic) = 1.994408398784774774153395734651
y2[1] (numeric) = 1.9944083631399671735361364787042
absolute error = 3.56448076006172592559468e-08
relative error = 1.7872371387092140110942289407859e-06 %
h = 0.0001
y1[1] (analytic) = 0.89439727074407431078201360713865
y1[1] (numeric) = 0.89439727079574707012232100494082
absolute error = 5.167275934030739780217e-11
relative error = 5.7773833877332130249748577961275e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.4MB, time=59.12
NO POLE
NO POLE
x[1] = 0.1059
y2[1] (analytic) = 1.994397833539824792258835579521
y2[1] (numeric) = 1.9943977960185858357984425117452
absolute error = 3.75212389564603930677758e-08
relative error = 1.8813317145388463750936537921124e-06 %
h = 0.0001
y1[1] (analytic) = 0.89429783043237521387726327033124
y1[1] (numeric) = 0.89429783048770574053867517554369
absolute error = 5.533052666141190521245e-11
relative error = 6.1870357702490115701357626305076e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.4MB, time=59.80
NO POLE
NO POLE
x[1] = 0.106
y2[1] (analytic) = 1.9943872583508964832526761118722
y2[1] (numeric) = 1.9943872188884753169533759584507
absolute error = 3.94624211662993001534215e-08
relative error = 1.9786739511628088652657461814442e-06 %
h = 0.0001
y1[1] (analytic) = 0.89419839117769781176790938198128
y1[1] (numeric) = 0.89419839123687697726120987686564
absolute error = 5.917916549330049488436e-11
relative error = 6.6181248006227101267043242175504e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.4MB, time=60.46
memory used=339.5MB, alloc=4.4MB, time=61.12
NO POLE
NO POLE
x[1] = 0.1061
y2[1] (analytic) = 1.994376673218095599024112295192
y2[1] (numeric) = 1.9943766317486412244549914581827
absolute error = 4.14694543745691208370093e-08
relative error = 2.0793190640188668847669974348900e-06 %
h = 0.0001
y1[1] (analytic) = 0.89409895298103649699989730272694
y1[1] (numeric) = 0.89409895304426170292775127000769
absolute error = 6.322520592785396728075e-11
relative error = 7.0713879841882501514662259609813e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.4MB, time=61.77
NO POLE
NO POLE
x[1] = 0.1062
y2[1] (analytic) = 1.9943660781415279909010647623259
y2[1] (numeric) = 1.9943660345980891763375045148999
absolute error = 4.35434388145635602474260e-08
relative error = 2.1833222742707293529164810597531e-06 %
h = 0.0001
y1[1] (analytic) = 0.89399951584338565153901152860976
y1[1] (numeric) = 0.89399951591086093961485118542928
absolute error = 6.747528807583965681952e-11
relative error = 7.5475754606180617833543018355690e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.4MB, time=62.43
memory used=350.9MB, alloc=4.4MB, time=63.11
NO POLE
NO POLE
x[1] = 0.1063
y2[1] (analytic) = 1.9943554731212996096491213021998
y2[1] (numeric) = 1.994355427435824801225235316807
absolute error = 4.56854748084238859853928e-08
relative error = 2.2907388088104005093892734058765e-06 %
h = 0.0001
y1[1] (analytic) = 0.89390007976573964676093187142512
y1[1] (numeric) = 0.89390007983767580883672860966998
absolute error = 7.193616207579673824486e-11
relative error = 8.0474500119351956059291122895103e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.4MB, time=63.77
NO POLE
NO POLE
x[1] = 0.1064
y2[1] (analytic) = 1.9943448581575165054704773521646
y2[1] (numeric) = 1.9943448102608537383425524501035
absolute error = 4.78966627671279249020611e-08
relative error = 2.4016239002605321160472502083941e-06 %
h = 0.0001
y1[1] (analytic) = 0.89380064474909284344128974497372
y1[1] (numeric) = 0.89380064482570753154421017769447
absolute error = 7.661468810292043272075e-11
relative error = 8.5717870705304380179413597925105e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.4MB, time=64.43
memory used=362.4MB, alloc=4.4MB, time=65.09
NO POLE
NO POLE
x[1] = 0.1065
y2[1] (analytic) = 1.9943342332502848280028754959752
y2[1] (numeric) = 1.9943341830721816375238165067316
absolute error = 5.01781031904790589892436e-08
relative error = 2.5160327869767760565669847389794e-06 %
h = 0.0001
y1[1] (analytic) = 0.89370121079443959174572455731352
y1[1] (numeric) = 0.89370121087595742812366967087148
absolute error = 8.151783637794511355796e-11
relative error = 9.1213747271844133917775997113632e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.4MB, time=65.74
NO POLE
NO POLE
x[1] = 0.1066
y2[1] (analytic) = 1.9943235983997108263185439674139
y2[1] (numeric) = 1.9943235458688141592233235860243
absolute error = 5.25308966670952203813896e-08
relative error = 2.6340207130501373340243297961610e-06 %
h = 0.0001
y1[1] (analytic) = 0.89360177790277423121994020911169
y1[1] (numeric) = 0.89360177798942691839596652059725
absolute error = 8.665268717602631148556e-11
relative error = 9.6970137390946762017412660385115e-09 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.4MB, time=66.41
memory used=373.8MB, alloc=4.4MB, time=67.08
NO POLE
NO POLE
x[1] = 0.1067
y2[1] (analytic) = 1.9943129536059008489231341595696
y2[1] (numeric) = 1.9943128986497569745252486901542
absolute error = 5.49561438743978854694154e-08
relative error = 2.7556429283093274665954030751268e-06 %
h = 0.0001
y1[1] (analytic) = 0.89350234607509109077976169819579
y1[1] (numeric) = 0.89350234616711752161538331757413
absolute error = 9.202643083562161937834e-11
relative error = 1.0299517537907796306342566637091e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.4MB, time=67.75
NO POLE
NO POLE
x[1] = 0.1068
y2[1] (analytic) = 1.994302298868961343754657139781
y2[1] (numeric) = 1.9943022414140157651535890132834
absolute error = 5.74549455786010681264976e-08
relative error = 2.8809546883231182815335770601424e-06 %
h = 0.0001
y1[1] (analytic) = 0.89340291531238448870119183040385
y1[1] (numeric) = 0.89340291541003085646856232675495
absolute error = 9.764636776737049635110e-11
relative error = 1.0929712237756440570901086788794e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.4MB, time=68.43
memory used=385.2MB, alloc=4.4MB, time=69.10
NO POLE
NO POLE
x[1] = 0.1069
y2[1] (analytic) = 1.9942916341889988581824191702586
y2[1] (numeric) = 1.9942915741605962234821071243154
absolute error = 6.00284026347003120459432e-08
relative error = 3.0100112544026961075824175111837e-06 %
h = 0.0001
y1[1] (analytic) = 0.89330348561564873261046803683264
y1[1] (numeric) = 0.8933034857191686410734410079638
absolute error = 1.0351990846297297113116e-10
relative error = 1.1588436643301454018989697965700e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=389.1MB, alloc=4.4MB, time=69.78
NO POLE
NO POLE
x[1] = 0.107
y2[1] (analytic) = 1.9942809595661200390059562343918
y2[1] (numeric) = 1.9942808968885040525442740431489
absolute error = 6.26776159864616821912429e-08
relative error = 3.1428678936040163659841756261263e-06 %
h = 0.0001
y1[1] (analytic) = 0.89320405698587811947411929758354
y1[1] (numeric) = 0.89320405709553269297818654220386
absolute error = 1.0965457350406724462032e-10
relative error = 1.2276542257778943703417683844300e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.4MB, time=70.46
NO POLE
NO POLE
memory used=396.7MB, alloc=4.4MB, time=71.12
x[1] = 0.1071
y2[1] (analytic) = 1.9942702750004316324539675687545
y2[1] (numeric) = 1.9942702095967449660432122103351
absolute error = 6.54036866664107553584194e-08
relative error = 3.2795798787301585602437468211860e-06 %
h = 0.0001
y1[1] (analytic) = 0.89310462942406693558902317210554
y1[1] (numeric) = 0.89310462954012492916012936366292
absolute error = 1.1605799357110619155738e-10
relative error = 1.2994893291052368489621909576562e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.4MB, time=71.78
NO POLE
NO POLE
x[1] = 0.1072
y2[1] (analytic) = 1.9942595804920404841832482008192
y2[1] (numeric) = 1.994259512284324688361638350038
absolute error = 6.82077157958216098507812e-08
relative error = 3.4202024883336816648079809990039e-06 %
h = 0.0001
y1[1] (analytic) = 0.89300520293120945657246293623481
y1[1] (numeric) = 0.89300520305394736602469569742728
absolute error = 1.2273790945223276119247e-10
relative error = 1.3744366667669637946536489673021e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.4MB, time=72.48
NO POLE
NO POLE
x[1] = 0.1073
y2[1] (analytic) = 1.99424887604105353927762049239
y2[1] (numeric) = 1.994248804950248954571806226199
absolute error = 7.10908045847058142661910e-08
relative error = 3.5647910067189799128201960995143e-06 %
h = 0.0001
y1[1] (analytic) = 0.89290577750829994735218482603007
y1[1] (numeric) = 0.8929057776380021194043391029147
absolute error = 1.2970217205215427688463e-10
relative error = 1.4525852034925223542220269510775e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.4MB, time=73.15
memory used=411.9MB, alloc=4.4MB, time=73.85
NO POLE
NO POLE
x[1] = 0.1074
y2[1] (analytic) = 1.9942381616475778422468646887649
y2[1] (numeric) = 1.9942380875935235104454492918062
absolute error = 7.40540543318014153969587e-08
relative error = 3.7134007239446389831098289999440e-06 %
h = 0.0001
y1[1] (analytic) = 0.89280635315633266215645538850346
y1[1] (numeric) = 0.89280635329329140455747102303704
absolute error = 1.3695874240101563453358e-10
relative error = 1.5340251770927285343654648280971e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.4MB, time=74.53
NO POLE
NO POLE
x[1] = 0.1075
y2[1] (analytic) = 1.9942274373117205370256484736392
y2[1] (numeric) = 1.9942273602131541124637232311685
absolute error = 7.70985664245619252424707e-08
relative error = 3.8660869358257925865772802360662e-06 %
h = 0.0001
y1[1] (analytic) = 0.89270692987630184450411893934616
y1[1] (numeric) = 0.89270693002081753616739033910338
absolute error = 1.4451569166327139975722e-10
relative error = 1.6188480992669817422382266108716e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.4MB, time=75.18
memory used=423.4MB, alloc=4.4MB, time=75.85
NO POLE
NO POLE
x[1] = 0.1076
y2[1] (analytic) = 1.9942167030335888669724555297596
y2[1] (numeric) = 1.9942166228081465278271483950961
absolute error = 8.02254423391453071346635e-08
relative error = 4.0229049439364794521338606603488e-06 %
h = 0.0001
y1[1] (analytic) = 0.89260750766920172719465512774823
y1[1] (numeric) = 0.89260750782158292834121193147423
absolute error = 1.5238120114655680372600e-10
relative error = 1.7071467564109815169804727814343e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.4MB, time=76.50
NO POLE
NO POLE
x[1] = 0.1077
y2[1] (analytic) = 1.9942059588132901748685131053403
y2[1] (numeric) = 1.9942058753775065344655521288868
absolute error = 8.34357836404029609764535e-08
relative error = 4.1839100556120007123569809078341e-06 %
h = 0.0001
y1[1] (analytic) = 0.89250808653602653229823660841207
y1[1] (numeric) = 0.89250808669659009460879424597757
absolute error = 1.6056356231055763756550e-10
relative error = 1.7990152104249467728173986988878e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.4MB, time=77.15
memory used=434.8MB, alloc=4.4MB, time=77.83
NO POLE
NO POLE
x[1] = 0.1078
y2[1] (analytic) = 1.9941952046509319029167185862516
y2[1] (numeric) = 1.9941951179202399210480109930193
absolute error = 8.67306919818687075932323e-08
relative error = 4.3491575839512776890206313758693e-06 %
h = 0.0001
y1[1] (analytic) = 0.89240866647777047114578682085902
y1[1] (numeric) = 0.89240866664684164792166586609748
absolute error = 1.6907117677587904523846e-10
relative error = 1.8945487995223378745496492211458e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.4MB, time=78.52
NO POLE
NO POLE
x[1] = 0.1079
y2[1] (analytic) = 1.9941844405466215927405650739918
y2[1] (numeric) = 1.9941843504353524869927928764546
absolute error = 9.01112691057477721975372e-08
relative error = 4.5187028478192100786612577068235e-06 %
h = 0.0001
y1[1] (analytic) = 0.89230924749542774431903787612839
y1[1] (numeric) = 0.89230924767334030065195109094608
absolute error = 1.7791255633291321481769e-10
relative error = 1.9938441390390818664787786779588e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.4MB, time=79.20
memory used=446.3MB, alloc=4.4MB, time=79.87
NO POLE
NO POLE
x[1] = 0.108
y2[1] (analytic) = 1.9941736665004668853830659694533
y2[1] (numeric) = 1.9941735729218500424772990024445
absolute error = 9.35786168429057669670088e-08
relative error = 4.6926011718490345383392843264975e-06 %
h = 0.0001
y1[1] (analytic) = 0.89220982958999254164058855096841
y1[1] (numeric) = 0.89220982977708886459129451902946
absolute error = 1.8709632295070596806105e-10
relative error = 2.0969991222433011760287293246426e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=450.1MB, alloc=4.4MB, time=80.54
NO POLE
NO POLE
x[1] = 0.1081
y2[1] (analytic) = 1.9941628825125755213056785624931
y2[1] (numeric) = 1.9941627853787384084480058267497
absolute error = 9.71338371128576727357434e-08
relative error = 4.8709078864446836717563652398303e-06 %
h = 0.0001
y1[1] (analytic) = 0.89211041276245904216396238961858
y1[1] (numeric) = 0.89211041295909025094978463781848
absolute error = 1.9663120878582224819990e-10
relative error = 2.2041129211455461135467094471689e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.4MB, time=81.21
memory used=457.7MB, alloc=4.4MB, time=81.88
NO POLE
NO POLE
x[1] = 0.1082
y2[1] (analytic) = 1.9941520885830553403872266273193
y2[1] (numeric) = 1.9941519878050234166304068281667
absolute error = 1.007780319237568197991526e-07
relative error = 5.0536783277831454158887142457739e-06 %
h = 0.0001
y1[1] (analytic) = 0.89201099701382141416366591328264
y1[1] (numeric) = 0.89201099722034747035487641913507
absolute error = 2.0652605619121050585243e-10
relative error = 2.3152859873095314899871832224814e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.4MB, time=82.57
NO POLE
NO POLE
x[1] = 0.1083
y2[1] (analytic) = 1.9941412847120142819228220237039
y2[1] (numeric) = 1.9941411801997109095389541912644
absolute error = 1.045123033723838678324395e-07
relative error = 5.2409678378168228282967535904767e-06 %
h = 0.0001
y1[1] (analytic) = 0.89191158234507381512524693739185
y1[1] (numeric) = 0.8919115825618636328503129203649
absolute error = 2.1678981772506598297305e-10
relative error = 2.4306200526633776744004874213524e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=465.4MB, alloc=4.4MB, time=83.23
NO POLE
NO POLE
memory used=469.2MB, alloc=4.4MB, time=83.91
x[1] = 0.1084
y2[1] (analytic) = 1.9941304708995603846227853040322
y2[1] (numeric) = 1.9941303625618067404870003812313
absolute error = 1.083377536441357849228009e-07
relative error = 5.4328317642758942752713573860206e-06 %
h = 0.0001
y1[1] (analytic) = 0.89181216875721039173535299675779
y1[1] (numeric) = 0.89181216898464194789504589150716
absolute error = 2.2743155615969289474937e-10
relative error = 2.5502181303113564133720569665738e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.4MB, time=84.57
NO POLE
NO POLE
x[1] = 0.1085
y2[1] (analytic) = 1.9941196471458017866115653262008
y2[1] (numeric) = 1.994119534890316773596739610734
absolute error = 1.122554850130148257154668e-07
relative error = 5.6293254606706740209770987268510e-06 %
h = 0.0001
y1[1] (analytic) = 0.89171275625122527987178987871414
y1[1] (numeric) = 0.89171275648968572436215538807225
absolute error = 2.3846044449036550935811e-10
relative error = 2.6741845153461417347768195062293e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.4MB, time=85.22
NO POLE
NO POLE
x[1] = 0.1086
y2[1] (analytic) = 1.994108813450846725426657872374
y2[1] (numeric) = 1.9941086971842468838091491986866
absolute error = 1.162665998416175086736874e-07
relative error = 5.8305042862939732177528916190998e-06 %
h = 0.0001
y1[1] (analytic) = 0.89161334482811260459358026434694
y1[1] (numeric) = 0.89161334507799837053776838983819
absolute error = 2.4988576594418812549125e-10
relative error = 2.8026247856615662584338528494158e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.4MB, time=85.87
memory used=484.4MB, alloc=4.4MB, time=86.34
NO POLE
NO POLE
x[1] = 0.1087
y2[1] (analytic) = 1.9940979698148035380175232736096
y2[1] (numeric) = 1.9940978494426029568939308208328
absolute error = 1.203722005811235924527768e-07
relative error = 6.0364236062234612977304060498383e-06 %
h = 0.0001
y1[1] (analytic) = 0.89151393448886648013102247791261
y1[1] (numeric) = 0.89151393475058339411997642547659
absolute error = 2.6171691398895394756398e-10
relative error = 2.9356458027658832364702364940755e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.4MB, time=86.61
NO POLE
NO POLE
x[1] = 0.1088
y2[1] (analytic) = 1.9940871162377806607445030403653
y2[1] (numeric) = 1.9940869916643908894594516520406
absolute error = 1.245733897712850513883247e-07
relative error = 6.2471387913240277659307772089501e-06 %
h = 0.0001
y1[1] (analytic) = 0.89141452523448100987574934454329
y1[1] (numeric) = 0.89141452550844440221775220305892
absolute error = 2.7396339234200285851563e-10
relative error = 3.0733557125955346464199646919138e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.4MB, time=86.88
memory used=495.9MB, alloc=4.4MB, time=87.17
NO POLE
NO POLE
x[1] = 0.1089
y2[1] (analytic) = 1.9940762527198866293777354988961
y2[1] (numeric) = 1.9940761238486165889626854002105
absolute error = 1.288712700404150500986856e-07
relative error = 6.4627052182501443950000770045207e-06 %
h = 0.0001
y1[1] (analytic) = 0.89131511706595028637078715633878
y1[1] (numeric) = 0.89131511735258510134986524645401
absolute error = 2.8663481497907809011523e-10
relative error = 3.2158639463294256603104204723759e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.4MB, time=87.44
NO POLE
NO POLE
x[1] = 0.109
y2[1] (analytic) = 1.9940653792612300790960704335539
y2[1] (numeric) = 1.9940652459942859737191532316971
absolute error = 1.332669441053769172018568e-07
relative error = 6.6831782694482278217441436888072e-06 %
h = 0.0001
y1[1] (analytic) = 0.89121570998426839130061474694456
y1[1] (numeric) = 0.89121571028400929744379653762757
absolute error = 2.9974090614318179068301e-10
relative error = 3.3632812212037058132066223069484e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=503.5MB, alloc=4.4MB, time=87.72
memory used=507.3MB, alloc=4.4MB, time=88.01
NO POLE
NO POLE
x[1] = 0.1091
y2[1] (analytic) = 1.994054495861919744485982735
y2[1] (numeric) = 1.9940543581004049729128645881459
absolute error = 1.377615147715731181468541e-07
relative error = 6.9086133331590025456232824829970e-06 %
h = 0.0001
y1[1] (analytic) = 0.89111630399042939548122267471527
y1[1] (numeric) = 0.8911163043037208958346521648546
absolute error = 3.1329150035342949013933e-10
relative error = 3.5157195413270571949071627343929e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=511.1MB, alloc=4.4MB, time=88.28
NO POLE
NO POLE
x[1] = 0.1092
y2[1] (analytic) = 1.9940436025220644595404850543411
y2[1] (numeric) = 1.994043460165979526606257894645
absolute error = 1.423560849329342271596961e-07
relative error = 7.1390658034198643293674878280466e-06 %
h = 0.0001
y1[1] (analytic) = 0.89101689908542735885017251456312
y1[1] (numeric) = 0.89101689941272390126407597685554
absolute error = 3.2729654241390346229242e-10
relative error = 3.6732921984964899887063771872081e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.4MB, time=88.55
memory used=518.8MB, alloc=4.4MB, time=88.84
NO POLE
NO POLE
x[1] = 0.1093
y2[1] (analytic) = 1.9940326992417731576580394631999
y2[1] (numeric) = 1.994032552190015585750141159092
absolute error = 1.470517575719078983041079e-07
relative error = 7.3745910800672440018728703353784e-06 %
h = 0.0001
y1[1] (analytic) = 0.89091749527025633045665625859053
y1[1] (numeric) = 0.89091749561202241787916124286705
absolute error = 3.4176608742250498427652e-10
relative error = 3.8361137730136456813616548355275e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.4MB, time=89.12
NO POLE
NO POLE
x[1] = 0.1094
y2[1] (analytic) = 1.9940217860211548716414681197318
y2[1] (numeric) = 1.9940216341715191121936324626781
absolute error = 1.518496357594478356570537e-07
relative error = 7.6152445687389716635399437942642e-06 %
h = 0.0001
y1[1] (analytic) = 0.89081809254591034845155582560653
y1[1] (numeric) = 0.89081809290262064923136131865832
absolute error = 3.5671030077980549305179e-10
relative error = 4.0043001345016082686245164072221e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.4MB, time=89.39
memory used=530.2MB, alloc=4.4MB, time=89.67
NO POLE
NO POLE
x[1] = 0.1095
y2[1] (analytic) = 1.9940108628603187336968629405976
y2[1] (numeric) = 1.9940107061094960786941003413884
absolute error = 1.567508226550027625992092e-07
relative error = 7.8610816808766412942145352947692e-06 %
h = 0.0001
y1[1] (analytic) = 0.89071869091338344007750267962617
y1[1] (numeric) = 0.89071869128552289827539931850373
absolute error = 3.7213945819789663887756e-10
relative error = 4.1779684427222237809186742548651e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.4MB, time=89.94
NO POLE
NO POLE
x[1] = 0.1096
y2[1] (analytic) = 1.9939999297593739754324942789029
y2[1] (numeric) = 1.99399976800295246892710405842
absolute error = 1.617564215065053902204829e-07
relative error = 8.1121578337279757638920287658771e-06 %
h = 0.0001
y1[1] (analytic) = 0.89061929037366962165893755745254
y1[1] (numeric) = 0.89061929076173356736817679312284
absolute error = 3.8806394570923923567030e-10
relative error = 4.3572371483939284539686680176220e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.4MB, time=90.21
NO POLE
NO POLE
x[1] = 0.1097
y2[1] (analytic) = 1.9939889867184299278577186081169
y2[1] (numeric) = 1.9939888198508942774963337674181
absolute error = 1.668675356503613848406988e-07
relative error = 8.3685284503491922463458602652124e-06 %
h = 0.0001
y1[1] (analytic) = 0.89051989092776289859217030544061
y1[1] (numeric) = 0.89051989133225715826768141359862
absolute error = 4.0449425967551110815801e-10
relative error = 4.5422259940100858694089367709856e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=541.6MB, alloc=4.4MB, time=90.48
memory used=545.5MB, alloc=4.4MB, time=90.76
NO POLE
NO POLE
x[1] = 0.1098
y2[1] (analytic) = 1.9939780337375960213818852119796
y2[1] (numeric) = 1.9939778616523275099435505664308
absolute error = 1.720852685114383346455488e-07
relative error = 8.6302489596073680358410102711020e-06 %
h = 0.0001
y1[1] (analytic) = 0.89042049257665726533543982554245
y1[1] (numeric) = 0.89042049299809827213189366128477
absolute error = 4.2144100679645383574232e-10
relative error = 4.7330560146578333906214260871920e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=549.3MB, alloc=4.4MB, time=91.04
NO POLE
NO POLE
x[1] = 0.1099
y2[1] (analytic) = 1.993967070816981785813241880409
y2[1] (numeric) = 1.9939668934062581827585264424833
absolute error = 1.774107236030547154379257e-07
relative error = 8.8973747961828067670934061770431e-06 %
h = 0.0001
y1[1] (analytic) = 0.89032109532134670539897413073309
y1[1] (numeric) = 0.89032109576026160951769252371317
absolute error = 4.3891490411871839298008e-10
relative error = 4.9298495388374382192783349283567e-08 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=553.1MB, alloc=4.4MB, time=91.31
memory used=556.9MB, alloc=4.4MB, time=91.59
NO POLE
NO POLE
x[1] = 0.11
y2[1] (analytic) = 1.9939560979566968503578396114198
y2[1] (numeric) = 1.9939559151116923233889841066717
absolute error = 1.828450045269688555047481e-07
relative error = 9.1699614005714050386362058277292e-06 %
h = 0.0001
y1[1] (analytic) = 0.89022169916282519133505050991655
y1[1] (numeric) = 0.89022169961975197037976019651228
absolute error = 4.5692677904470968659573e-10
relative error = 5.1327301892821633982842758414925e-08 %
h = 0.0001
Finished!
Maximum Iterations Reached before Solution Completed!
diff ( y2 , x , 3 ) = m1 * cos(x) ;
diff ( y1 , x , 1 ) = m1 * y2 + 1.0;
Iterations = 100
Total Elapsed Time = 1 Minutes 31 Seconds
Elapsed Time(since restart) = 1 Minutes 31 Seconds
Expected Time Remaining = 12 Hours 19 Minutes 2 Seconds
Optimized Time Remaining = 12 Hours 18 Minutes 48 Seconds
Time to Timeout = 13 Minutes 28 Seconds
Percent Done = 0.2061 %
> quit
memory used=558.4MB, alloc=4.4MB, time=91.69