|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> 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_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[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_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[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, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, array_real_pole, glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[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_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[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,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> array_real_pole,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_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_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_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_t[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, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, array_real_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_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_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> 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(t_end),convfloat(t_start),convfloat(array_t[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(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[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(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, 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(t_end), convfloat(t_start),
convfloat(array_t[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(t_end),
convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(array_t[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,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> 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 - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_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_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_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_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_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_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_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 - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_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_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_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_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_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_x1_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_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_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_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_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, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, array_real_pole, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_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_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_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 - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_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_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_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_x1_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_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_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,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> 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_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[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_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[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, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, 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_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> array_real_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_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_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_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_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 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, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, array_real_pole, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_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_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_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_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End 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_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
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,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> ALWAYS,
> INFO,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_trunc_err,
> glob_max_hours,
> glob_relerr,
> glob_hmin_init,
> glob_hmin,
> days_in_year,
> sec_in_min,
> glob_current_iter,
> glob_optimal_clock_start_sec,
> glob_abserr,
> glob_last_good_h,
> glob_reached_optimal_h,
> glob_log10relerr,
> glob_look_poles,
> glob_clock_start_sec,
> glob_unchanged_h_cnt,
> glob_optimal_start,
> glob_no_eqs,
> glob_max_order,
> glob_log10_abserr,
> glob_initial_pass,
> glob_not_yet_finished,
> glob_max_minutes,
> glob_iter,
> glob_start,
> hours_in_day,
> glob_dump,
> glob_max_opt_iter,
> glob_html_log,
> glob_log10abserr,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_max_rel_trunc_err,
> glob_hmax,
> min_in_hour,
> djd_debug,
> glob_optimal_expect_sec,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> centuries_in_millinium,
> glob_percent_done,
> glob_normmax,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_disp_incr,
> glob_not_yet_start_msg,
> glob_almost_1,
> years_in_century,
> MAX_UNCHANGED,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_dump_analytic,
> glob_large_float,
> glob_optimal_done,
> glob_clock_sec,
> djd_debug2,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_type_pole,
> array_pole,
> array_x1_init,
> array_t,
> array_x2,
> array_x1,
> array_last_rel_error,
> array_1st_rel_error,
> array_x2_init,
> array_norms,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher,
> array_complex_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_poles,
> array_x2_higher_work,
> array_real_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> glob_max_terms := 30;
> glob_max_trunc_err := 0.1e-10;
> glob_max_hours := 0.0;
> glob_relerr := 0.1e-10;
> glob_hmin_init := 0.001;
> glob_hmin := 0.00000000001;
> days_in_year := 365.0;
> sec_in_min := 60.0;
> glob_current_iter := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_reached_optimal_h := false;
> glob_log10relerr := 0.0;
> glob_look_poles := false;
> glob_clock_start_sec := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_optimal_start := 0.0;
> glob_no_eqs := 0;
> glob_max_order := 30;
> glob_log10_abserr := 0.1e-10;
> glob_initial_pass := true;
> glob_not_yet_finished := true;
> glob_max_minutes := 0.0;
> glob_iter := 0;
> glob_start := 0;
> hours_in_day := 24.0;
> glob_dump := false;
> glob_max_opt_iter := 10;
> glob_html_log := true;
> glob_log10abserr := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_hmax := 1.0;
> min_in_hour := 60.0;
> djd_debug := true;
> glob_optimal_expect_sec := 0.1;
> glob_log10_relerr := 0.1e-10;
> glob_h := 0.1;
> glob_log10normmin := 0.1;
> centuries_in_millinium := 10.0;
> glob_percent_done := 0.0;
> glob_normmax := 0.0;
> glob_orig_start_sec := 0.0;
> glob_warned := false;
> glob_small_float := 0.1e-50;
> glob_disp_incr := 0.1;
> glob_not_yet_start_msg := true;
> glob_almost_1 := 0.9990;
> years_in_century := 100.0;
> MAX_UNCHANGED := 10;
> glob_max_sec := 10000.0;
> glob_smallish_float := 0.1e-100;
> glob_max_iter := 1000;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> glob_optimal_done := false;
> glob_clock_sec := 0.0;
> djd_debug2 := true;
> glob_display_flag := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> 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/complicatedrev3postode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.00005 ;");
> 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_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_tmp10:= Array(1..(max_terms + 1),[]);
> array_tmp11:= Array(1..(max_terms + 1),[]);
> array_tmp12:= Array(1..(max_terms + 1),[]);
> array_tmp13:= Array(1..(max_terms + 1),[]);
> array_tmp14:= Array(1..(max_terms + 1),[]);
> array_tmp15:= Array(1..(max_terms + 1),[]);
> array_tmp16:= Array(1..(max_terms + 1),[]);
> array_tmp17:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 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_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_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_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_x1_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_x2_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_x2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_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_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[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_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> 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_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> 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
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.00005 ;
> 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
> 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_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_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_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_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_t[1] <= t_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;
> sub_iter := 1;
> while sub_iter <= 3 + glob_max_terms do # do number 3
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;# end do number 3
> ;
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_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
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_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
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_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
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_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
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_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
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_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
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_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_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_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
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_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
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_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
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_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
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_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_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_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 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T02:12:37-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev3")
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[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 4
> 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 4
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 4
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 4
> ;
> log_revs(html_log_file," 076 | ")
> ;
> logitem_str(html_log_file,"complicatedrev3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev3 maple results")
> ;
> logitem_str(html_log_file,"sub iter tot order + max terms eqs reversed")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> 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 4
> 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 4
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 4
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 4
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3
> ;
> if glob_html_log then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, DEBUGMASSIVE, glob_iolevel, ALWAYS, INFO, glob_max_terms,
glob_max_trunc_err, glob_max_hours, glob_relerr, glob_hmin_init, glob_hmin,
days_in_year, sec_in_min, glob_current_iter, glob_optimal_clock_start_sec,
glob_abserr, glob_last_good_h, glob_reached_optimal_h, glob_log10relerr,
glob_look_poles, glob_clock_start_sec, glob_unchanged_h_cnt,
glob_optimal_start, glob_no_eqs, glob_max_order, glob_log10_abserr,
glob_initial_pass, glob_not_yet_finished, glob_max_minutes, glob_iter,
glob_start, hours_in_day, glob_dump, glob_max_opt_iter, glob_html_log,
glob_log10abserr, glob_curr_iter_when_opt, glob_warned2,
glob_max_rel_trunc_err, glob_hmax, min_in_hour, djd_debug,
glob_optimal_expect_sec, glob_log10_relerr, glob_h, glob_log10normmin,
centuries_in_millinium, glob_percent_done, glob_normmax,
glob_orig_start_sec, glob_warned, glob_small_float, glob_disp_incr,
glob_not_yet_start_msg, glob_almost_1, years_in_century, MAX_UNCHANGED,
glob_max_sec, glob_smallish_float, glob_max_iter, glob_dump_analytic,
glob_large_float, glob_optimal_done, glob_clock_sec, djd_debug2,
glob_display_flag, array_const_1, array_const_2, array_const_2D0,
array_const_3D0, array_const_0D0, array_const_4D0, array_m1, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_type_pole, array_pole, array_x1_init, array_t, array_x2, array_x1,
array_last_rel_error, array_1st_rel_error, array_x2_init, array_norms,
array_x1_higher_work2, array_x1_higher, array_x2_higher, array_complex_pole,
array_x1_higher_work, array_x2_higher_work2, array_poles,
array_x2_higher_work, array_real_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
glob_max_terms := 30;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_hours := 0.;
glob_relerr := 0.1*10^(-10);
glob_hmin_init := 0.001;
glob_hmin := 0.1*10^(-10);
days_in_year := 365.0;
sec_in_min := 60.0;
glob_current_iter := 0;
glob_optimal_clock_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_reached_optimal_h := false;
glob_log10relerr := 0.;
glob_look_poles := false;
glob_clock_start_sec := 0.;
glob_unchanged_h_cnt := 0;
glob_optimal_start := 0.;
glob_no_eqs := 0;
glob_max_order := 30;
glob_log10_abserr := 0.1*10^(-10);
glob_initial_pass := true;
glob_not_yet_finished := true;
glob_max_minutes := 0.;
glob_iter := 0;
glob_start := 0;
hours_in_day := 24.0;
glob_dump := false;
glob_max_opt_iter := 10;
glob_html_log := true;
glob_log10abserr := 0.;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_hmax := 1.0;
min_in_hour := 60.0;
djd_debug := true;
glob_optimal_expect_sec := 0.1;
glob_log10_relerr := 0.1*10^(-10);
glob_h := 0.1;
glob_log10normmin := 0.1;
centuries_in_millinium := 10.0;
glob_percent_done := 0.;
glob_normmax := 0.;
glob_orig_start_sec := 0.;
glob_warned := false;
glob_small_float := 0.1*10^(-50);
glob_disp_incr := 0.1;
glob_not_yet_start_msg := true;
glob_almost_1 := 0.9990;
years_in_century := 100.0;
MAX_UNCHANGED := 10;
glob_max_sec := 10000.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_iter := 1000;
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
glob_optimal_done := false;
glob_clock_sec := 0.;
djd_debug2 := true;
glob_display_flag := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
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/complicatedrev3postode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.00005 ;");
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_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_tmp10 := Array(1 .. max_terms + 1, []);
array_tmp11 := Array(1 .. max_terms + 1, []);
array_tmp12 := Array(1 .. max_terms + 1, []);
array_tmp13 := Array(1 .. max_terms + 1, []);
array_tmp14 := Array(1 .. max_terms + 1, []);
array_tmp15 := Array(1 .. max_terms + 1, []);
array_tmp16 := Array(1 .. max_terms + 1, []);
array_tmp17 := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[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_x2_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_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_x1_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_x2_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_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 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_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[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_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
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_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
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;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.00005;
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();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_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_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
sub_iter := 1;
while sub_iter <= 3 + glob_max_terms do
atomall(); sub_iter := sub_iter + 1
end do;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_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_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_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 (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T02:12:37-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev3");
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[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, " 076 | ");
logitem_str(html_log_file, "complicatedrev3 diffeq.mxt");
logitem_str(html_log_file, "complicatedrev3 maple results");
logitem_str(html_log_file,
"sub iter tot order + max terms eqs reversed");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
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/complicatedrev3postode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.00005 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 5e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 5e-05
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 5e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.20
NO POLE
NO POLE
t[1] = 0.50005
x2[1] (analytic) = 0.00082566083422809021229815693339498
x2[1] (numeric) = 0.00082566083695768288580953900132404
absolute error = 2.72959267351138206792906e-12
relative error = 3.3059490778235551390117036491830e-07 %
h = 5e-05
x1[1] (analytic) = 0.0012917006010880372652167092040327
x1[1] (numeric) = 0.0012917005956294101945681497523304
absolute error = 5.4586270706485594517023e-12
relative error = 4.2259228385049894096809262604668e-07 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.4MB, time=0.48
memory used=11.4MB, alloc=4.5MB, time=0.76
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 0.00082570611074256394598966051590164
x2[1] (numeric) = 0.00082570612166195819564280058730035
absolute error = 1.091939424965314007139871e-11
relative error = 1.3224310814211176964894105127815e-06 %
h = 5e-05
x1[1] (analytic) = 0.001291646017422585871235266471237
x1[1] (numeric) = 0.0012916459955876806646200645590095
absolute error = 2.18349052066152019122275e-11
relative error = 1.6904712987994689141068004837108e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.5MB, time=1.03
NO POLE
NO POLE
t[1] = 0.50015
x2[1] (analytic) = 0.00082575139314954126995470805844824
x2[1] (numeric) = 0.00082575141772058389758603430137354
absolute error = 2.457104262763132624292530e-11
relative error = 2.9755980833303394839523035700290e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012915914364862495213788540506512
x1[1] (numeric) = 0.0012915913873563234429827445767725
absolute error = 4.91299260783961094738787e-11
relative error = 3.8038287255955458736565201710781e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.6MB, time=1.30
memory used=22.8MB, alloc=4.6MB, time=1.57
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.00082579672513571925499813755054128
absolute error = 4.368617602056419589021638e-11
relative error = 5.2901854659770090598013732063872e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.0012915367709341102157994826101921
absolute error = 8.73447815475071200298711e-11
relative error = 6.7628562814616995542694166023323e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.6MB, time=1.84
NO POLE
NO POLE
t[1] = 0.50025
x2[1] (analytic) = 0.00082584197564309094518702663178858
x2[1] (numeric) = 0.0008258420439095239007238233415556
absolute error = 6.826643295553679670976702e-11
relative error = 8.2662827718798237035908373678726e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012914822828003761515000894181426
x1[1] (numeric) = 0.0012914821463198124849890774353521
absolute error = 1.364805636665110119827905e-10
relative error = 1.0567745720101895713651264456650e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.6MB, time=2.12
memory used=34.3MB, alloc=4.6MB, time=2.39
NO POLE
NO POLE
t[1] = 0.5003
x2[1] (analytic) = 0.00082588727573070556349803310856235
x2[1] (numeric) = 0.00082588737404415783715360011311766
absolute error = 9.831345227365556700455531e-11
relative error = 1.1903979533607964388943357952219e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012914277100505662472629969306448
x1[1] (numeric) = 0.0012914275135122015682182038172444
absolute error = 1.965383646790447931134004e-10
relative error = 1.5218688831707759568560980890415e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.6MB, time=2.67
NO POLE
NO POLE
t[1] = 0.50035
x2[1] (analytic) = 0.00082593258171290830618081821305085
x2[1] (numeric) = 0.00082593271554178143628376102029713
absolute error = 1.3382887313010294280724628e-10
relative error = 1.6203365273779871130867920442261e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012913731400293256187207719936699
x1[1] (numeric) = 0.0012913728725100485988737783832529
absolute error = 2.675192770198469936104170e-10
relative error = 2.0715877442965240424377310718147e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.6MB, time=2.94
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597806840455543977638267263934
absolute error = 1.7481433499419197391031263e-10
relative error = 2.1164529505062019082354776596102e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913182233121245260353213521031
absolute error = 3.494243933147849632618731e-10
relative error = 2.7059503417061277498442285575952e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.6MB, time=3.21
memory used=49.5MB, alloc=4.6MB, time=3.49
NO POLE
NO POLE
t[1] = 0.50045
x2[1] (analytic) = 0.00082602321136316330959838452294175
x2[1] (numeric) = 0.00082602343263464095901933332742376
absolute error = 2.2127147764942094880448201e-10
relative error = 2.6787561730167695380232448787849e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012912640081720064953294869263476
x1[1] (numeric) = 0.0012912635659172001144473141176543
absolute error = 4.422548063808821728086933e-10
relative error = 3.4249758653690466937391215708875e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=3.76
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 0.00082606880823419947518629053953756
absolute error = 2.7320194119352802852692030e-10
relative error = 3.3072551441855776740271661500744e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = 0.0012912089003240459444915526869146
absolute error = 5.460116092263455194610983e-10
relative error = 4.2286835089061730028678645513922e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.6MB, time=4.04
memory used=61.0MB, alloc=4.6MB, time=4.32
NO POLE
NO POLE
t[1] = 0.50055
x2[1] (analytic) = 0.00082611386459802680075087884886784
x2[1] (numeric) = 0.00082611419520539283929676826942815
absolute error = 3.3060736603854588942056031e-10
relative error = 4.0019588122929507801520963897019e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012911548872273274627521335501181
x1[1] (numeric) = 0.0012911542265314324121594969716558
absolute error = 6.606958950505926365784623e-10
relative error = 5.1170924695904982606510212787934e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.6MB, time=4.60
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615959355038327227615345059897
absolute error = 3.9348939291085637480598588e-10
relative error = 4.7628761246235280219858777252507e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.0012910995445381297290246159330063
absolute error = 7.863087572442792075132423e-10
relative error = 6.0902219483477805652389977664018e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.6MB, time=4.90
memory used=72.4MB, alloc=4.6MB, time=5.19
NO POLE
NO POLE
t[1] = 0.50065
x2[1] (analytic) = 0.0008262045414216705137705964508309
x2[1] (numeric) = 0.00082620500327133336501575201811287
absolute error = 4.6184966285124515556728197e-10
relative error = 5.5900160274661412510746576950557e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012910457771941973115410121980021
x1[1] (numeric) = 0.0012910448543429079222147285784005
absolute error = 9.228512893893262836196016e-10
relative error = 7.1480911497572117090493086975919e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.6MB, time=5.48
NO POLE
NO POLE
t[1] = 0.5007
x2[1] (analytic) = 0.00082624988868058886347644474630742
x2[1] (numeric) = 0.00082625042437040607843284439956772
absolute error = 5.3568981721495639965326030e-10
relative error = 6.4833874661136930641167696137183e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012909912262691220933319472376107
x1[1] (numeric) = 0.0012909901559445368343843408102628
absolute error = 1.0703245852589476064273479e-09
relative error = 8.2907192820520844778073521367501e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.6MB, time=5.76
NO POLE
NO POLE
memory used=83.9MB, alloc=4.6MB, time=6.03
t[1] = 0.50075
x2[1] (analytic) = 0.00082629524183826707178329997453724
x2[1] (numeric) = 0.00082629585684976474353075047000912
absolute error = 6.1501149767174745049547188e-10
relative error = 7.4429993848630349370736355705148e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012909366780715249413639121076118
x1[1] (numeric) = 0.0012909354493417861236869781258031
absolute error = 1.2287297388176769339818087e-09
relative error = 9.5181255571204600691116879333554e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.6MB, time=6.32
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634130071157306145890397224534
absolute error = 6.9981634620594351434441657e-10
relative error = 8.4688607270148454341961282132375e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908807345334252637475141673024
absolute error = 1.3980678442213953713502632e-09
relative error = 0.0001083032919050583563054479100121 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.6MB, time=6.59
NO POLE
NO POLE
t[1] = 0.50085
x2[1] (analytic) = 0.00082638596585198998708057987866837
x2[1] (numeric) = 0.00082638675595799510357293640402965
absolute error = 7.9010600511649235652536128e-10
relative error = 9.5609804348735084919648354747817e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012908275898582193609932004178204
x1[1] (numeric) = 0.0012908260115182235436344951222662
absolute error = 1.5783399958173587052955542e-09
relative error = 0.00012227349401407811917350286834454 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.6MB, time=6.88
memory used=99.1MB, alloc=4.7MB, time=7.18
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 0.00082643133670907829447576375839823
x2[1] (numeric) = 0.00082643222259119531149477037357576
absolute error = 8.8588211701701900661517753e-10
relative error = 0.00010719367449746991777942651841703 %
h = 5e-05
x1[1] (analytic) = 0.0012907730498422382120572030903234
x1[1] (numeric) = 0.0012907712802949500678324599728227
absolute error = 1.7695472881442247431175007e-09
relative error = 0.00013709205412682761069697657808744 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.7MB, time=7.47
NO POLE
NO POLE
t[1] = 0.50095
x2[1] (analytic) = 0.00082647671346701366129224988326191
x2[1] (numeric) = 0.00082647770061333849717272242487194
absolute error = 9.8714632483588047254161003e-10
relative error = 0.00011944030711946725124538121355859 %
h = 5e-05
x1[1] (analytic) = 0.0012907185125531896882949122564762
x1[1] (numeric) = 0.0012907165408623737562142565937436
absolute error = 1.9716908159320806556627326e-09
relative error = 0.00015275916450844494509555417111334 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.7MB, time=7.76
memory used=110.6MB, alloc=4.7MB, time=8.05
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652319002658984294161533425997
absolute error = 1.09390027181622046360638811e-09
relative error = 0.00013234979160787479037677949812843 %
h = 5e-05
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906617932192633440133536984651
absolute error = 2.1847716741024703245035700e-09
relative error = 0.00016927501746064930957193758540632 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.7MB, time=8.35
NO POLE
NO POLE
t[1] = 0.50105
x2[1] (analytic) = 0.0008265674846875133855587774461534
x2[1] (numeric) = 0.00082656869083311490158289987974494
absolute error = 1.20614560151602412243359154e-09
relative error = 0.0001459222173458724328038709032973 %
h = 5e-05
x1[1] (analytic) = 0.0012906094461553451502178419190542
x1[1] (numeric) = 0.0012906070373643873817961486324857
absolute error = 2.4087909577684216932865685e-09
relative error = 0.00018663980532174764567337684769861 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.7MB, time=8.65
NO POLE
NO POLE
memory used=122.0MB, alloc=4.7MB, time=8.93
t[1] = 0.5011
x2[1] (analytic) = 0.00082661287915112178821202023981947
x2[1] (numeric) = 0.00082661420303507959638478608450251
absolute error = 1.32388395780817276584468304e-09
relative error = 0.0001601576737066710553127480587017 %
h = 5e-05
x1[1] (analytic) = 0.0012905549170462764699083942648711
x1[1] (numeric) = 0.0012905522732965142354342710135191
absolute error = 2.6437497622344741232513520e-09
relative error = 0.00020485372046664133184991620318868 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.7MB, time=9.22
NO POLE
NO POLE
t[1] = 0.50115
x2[1] (analytic) = 0.00082665827951766534070374927443031
x2[1] (numeric) = 0.00082665972663465022120238393605014
absolute error = 1.44711698488049863466161983e-09
relative error = 0.0001750562500535113011792510313945 %
h = 5e-05
x1[1] (analytic) = 0.0012905003906635950827826351381346
x1[1] (numeric) = 0.001290497501014412086076882217778
absolute error = 2.8896491829967057529203566e-09
relative error = 0.00022391695530683286720956534625808 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.7MB, time=9.50
NO POLE
NO POLE
t[1] = 0.5012
x2[1] (analytic) = 0.00082670368578766620467820114309252
x2[1] (numeric) = 0.00082670526163399344051785358254924
absolute error = 1.57584632723583965243945672e-09
relative error = 0.00019061803573966236825189924298533 %
h = 5e-05
x1[1] (analytic) = 0.0012904458670071646728838326718726
x1[1] (numeric) = 0.0012904427205168489301229707117668
absolute error = 3.1464903157427608619601058e-09
relative error = 0.00024382970229043255647060577143722 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.7MB, time=9.78
memory used=137.3MB, alloc=4.7MB, time=10.07
NO POLE
NO POLE
t[1] = 0.50125
x2[1] (analytic) = 0.00082674909796164659740637187785192
x2[1] (numeric) = 0.0008267508080352762895005650077053
absolute error = 1.71007362969209419312985338e-09
relative error = 0.00020684312010842079778383474863105 %
h = 5e-05
x1[1] (analytic) = 0.0012903913460768489310708824436005
x1[1] (numeric) = 0.0012903879318025925791936432289599
absolute error = 3.4142742563518772392146406e-09
relative error = 0.00026459215390216519611124255607596 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.7MB, time=10.35
NO POLE
NO POLE
t[1] = 0.5013
x2[1] (analytic) = 0.00082679451604012879179140950883443
x2[1] (numeric) = 0.00082679636584066617406726718573338
absolute error = 1.84980053738227585767689895e-09
relative error = 0.00022373159249310926401376062668334 %
h = 5e-05
x1[1] (analytic) = 0.0012903368278725115550179667024679
x1[1] (numeric) = 0.0012903331348704106601044117907419
absolute error = 3.6930021008949135549117260e-09
relative error = 0.00028620450266337676171681175223814 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.7MB, time=10.64
memory used=148.7MB, alloc=4.7MB, time=10.94
NO POLE
NO POLE
t[1] = 0.50135
x2[1] (analytic) = 0.00082683994002363511637400717118929
x2[1] (numeric) = 0.00082684193505233087094226671785644
absolute error = 1.99502869575456825954666715e-09
relative error = 0.00024128354221707536449585813005146 %
h = 5e-05
x1[1] (analytic) = 0.0012902823123940162492142136134444
x1[1] (numeric) = 0.0012902783297190706148374765709874
absolute error = 3.9826749456343767370424570e-09
relative error = 0.00030866694113204109652475371810161 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.7MB, time=11.23
NO POLE
NO POLE
t[1] = 0.5014
x2[1] (analytic) = 0.00082688536991268795533779675988916
x2[1] (numeric) = 0.00082688751567243852771761595180433
absolute error = 2.14575975057237981919191517e-09
relative error = 0.00025949905859369041117866616712503 %
h = 5e-05
x1[1] (analytic) = 0.0012902277996412267249633565185424
x1[1] (numeric) = 0.0012902235163473397005140046036559
absolute error = 4.2832938870244493519148865e-09
relative error = 0.00033197966190276660116756269369389 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.7MB, time=11.51
memory used=160.2MB, alloc=4.7MB, time=11.79
NO POLE
NO POLE
t[1] = 0.50145
x2[1] (analytic) = 0.00082693080570780974851474313244131
x2[1] (numeric) = 0.00082693310770315766291331058578142
absolute error = 2.30199534791439856745334011e-09
relative error = 0.00027837823092634822223290664165133 %
h = 5e-05
x1[1] (analytic) = 0.0012901732896140067003833932150759
x1[1] (numeric) = 0.0012901686947539849893664043327792
absolute error = 4.5948600217110169888822967e-09
relative error = 0.00035614285760680292461392289257297 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.7MB, time=12.07
NO POLE
NO POLE
t[1] = 0.5015
x2[1] (analytic) = 0.00082697624740952299139053885956424
x2[1] (numeric) = 0.00082697871114665716603749675837113
absolute error = 2.46373713417464695789880689e-09
relative error = 0.0002979211485084639146282391013914 %
h = 5e-05
x1[1] (analytic) = 0.0012901187823122199004062452509559
x1[1] (numeric) = 0.0012901138649377733687105960042176
absolute error = 4.9173744465316956492467383e-09
relative error = 0.00038115672091204765630824161911299 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.7MB, time=12.35
NO POLE
NO POLE
t[1] = 0.50155
x2[1] (analytic) = 0.00082702169501835023510999952388432
x2[1] (numeric) = 0.00082702432600510629764668762584572
absolute error = 2.63098675606253668810196140e-09
relative error = 0.00031812790062347269745892802955144 %
h = 5e-05
x1[1] (analytic) = 0.0012900642777357300567774172370197
x1[1] (numeric) = 0.0012900590268974715409182778985608
absolute error = 5.2508382585158591393384589e-09
relative error = 0.00040702144452305301950878972510061 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.7MB, time=12.62
memory used=175.4MB, alloc=4.7MB, time=12.90
NO POLE
NO POLE
t[1] = 0.5016
x2[1] (analytic) = 0.00082706714853481408648245956670656
x2[1] (numeric) = 0.00082706995228067468940598942835014
absolute error = 2.80374586060292352986164358e-09
relative error = 0.00033899857654482866601840612656375 %
h = 5e-05
x1[1] (analytic) = 0.001290009775884400908055656176395
x1[1] (numeric) = 0.0012900041806318460233891884045503
absolute error = 5.5952525548846664677718447e-09
relative error = 0.00043373722118103256582465995741464 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.7MB, time=13.19
NO POLE
NO POLE
t[1] = 0.50165
x2[1] (analytic) = 0.00082711260795943720798716868291399
x2[1] (numeric) = 0.00082711558997553234414933704642873
absolute error = 2.98201609513616216836351474e-09
relative error = 0.00036053326553600359662271678616608 %
h = 5e-05
x1[1] (analytic) = 0.0012899552767580961996126108108966
x1[1] (numeric) = 0.0012899493261396631485233639323994
absolute error = 5.9506184330510892468784972e-09
relative error = 0.00046130424366386787095175359134877 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.7MB, time=13.46
memory used=186.9MB, alloc=4.7MB, time=13.74
NO POLE
NO POLE
t[1] = 0.5017
x2[1] (analytic) = 0.00082715807329274231777868876405026
x2[1] (numeric) = 0.00082716123909184963593973904936392
absolute error = 3.16579910731816105028531366e-09
relative error = 0.0003827320568504857421828188998968 %
h = 5e-05
x1[1] (analytic) = 0.0012899007803566796836324909844552
x1[1] (numeric) = 0.0012898944634196890636933926663862
absolute error = 6.3169369906199390983180690e-09
relative error = 0.00048972270478611523160800595897644 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.7MB, time=14.02
NO POLE
NO POLE
t[1] = 0.50175
x2[1] (analytic) = 0.0008272035445352521896922913896394
x2[1] (numeric) = 0.00082720689963179731012953223679634
absolute error = 3.35509654512043724084715694e-09
relative error = 0.00040559503973177862852573713892529 %
h = 5e-05
x1[1] (analytic) = 0.0012898462866800151191117270235781
x1[1] (numeric) = 0.0012898395924706897312166641560967
absolute error = 6.6942093253878950628674814e-09
relative error = 0.00051899279739901236366806140226071 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.7MB, time=14.29
memory used=198.3MB, alloc=4.7MB, time=14.57
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 0.00082724902168748965324935586679766
x2[1] (numeric) = 0.00082725257159754648342064567509583
absolute error = 3.54991005683017128980829817e-09
relative error = 0.00042912230341339985146454065569276 %
h = 5e-05
x1[1] (analytic) = 0.0012897917957279662718586291348401
x1[1] (numeric) = 0.001289784713291430928327614745693
absolute error = 7.0824365353435310143891471e-09
relative error = 0.00054911471439048510149760825594077 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.7MB, time=14.84
NO POLE
NO POLE
t[1] = 0.50185
x2[1] (analytic) = 0.00082729450474997759366276781819127
x2[1] (numeric) = 0.00082729825499126864392487422995316
absolute error = 3.75024129105026210641176189e-09
relative error = 0.00045331393711887987461713321948834 %
h = 5e-05
x1[1] (analytic) = 0.0012897373075003969144930468194044
x1[1] (numeric) = 0.0012897298258806782471499688405826
absolute error = 7.4816197186673430779788218e-09
relative error = 0.00058008864868515409848758453282111 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.7MB, time=15.11
NO POLE
NO POLE
t[1] = 0.5019
x2[1] (analytic) = 0.00082733999372323895184231831839524
x2[1] (numeric) = 0.00082734394981513565122416159666257
absolute error = 3.95609189669938184327826733e-09
relative error = 0.00047817003006176082797383758400603 %
h = 5e-05
x1[1] (analytic) = 0.0012896828219971708264460283045716
x1[1] (numeric) = 0.0012896749302371970946689760108651
absolute error = 7.8917599737317770522937065e-09
relative error = 0.00061191479324434152878846485785581 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.7MB, time=15.39
memory used=213.6MB, alloc=4.7MB, time=15.66
NO POLE
NO POLE
t[1] = 0.50195
x2[1] (analytic) = 0.00082738548860779672440010357870682
x2[1] (numeric) = 0.00082738965607131973643089282956524
absolute error = 4.16746352301203078925085842e-09
relative error = 0.00050369067144559530721375696867321 %
h = 5e-05
x1[1] (analytic) = 0.0012896283392181517939594799923581
x1[1] (numeric) = 0.0012896200263597526927036439309307
absolute error = 8.3128583991012558360614274e-09
relative error = 0.0006445933410660777902448396216737 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.7MB, time=15.94
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.0008274353737619935022481963721243
absolute error = 4.38435781953859227119165560e-09
relative error = 0.00052987595046394517376989632191381 %
h = 5e-05
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895651142471100778789671545872
absolute error = 8.7449160935322068587705128e-09
relative error = 0.00067812448518510820853049677153328 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.7MB, time=16.22
memory used=225.0MB, alloc=4.7MB, time=16.49
NO POLE
NO POLE
t[1] = 0.50205
x2[1] (analytic) = 0.00082747649611289377764269085695601
x2[1] (numeric) = 0.00082748110288932992303025558910194
absolute error = 4.60677643614538756473214593e-09
relative error = 0.0005567259563003803556430260542053 %
h = 5e-05
x1[1] (analytic) = 0.0012895193818321900746876672680847
x1[1] (numeric) = 0.0012895101938980341015981517250904
absolute error = 9.1879341559730895155429943e-09
relative error = 0.00071250841867289974248421729905844 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.7MB, time=16.76
NO POLE
NO POLE
t[1] = 0.5021
x2[1] (analytic) = 0.00082752200873447933011181582388164
x2[1] (numeric) = 0.0008275268434555023448426298023097
absolute error = 4.83472102301473081397842806e-09
relative error = 0.00058424077812847764896427083848272 %
h = 5e-05
x1[1] (analytic) = 0.0012894649072249749944374418092067
x1[1] (numeric) = 0.0012894552653112894300148356194531
absolute error = 9.6419136855644226061897536e-09
relative error = 0.00074774533463764769064649504774226 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=232.6MB, alloc=4.7MB, time=17.04
memory used=236.5MB, alloc=4.7MB, time=17.31
NO POLE
NO POLE
t[1] = 0.50215
x2[1] (analytic) = 0.00082756752726945384053862465857453
x2[1] (numeric) = 0.00082757259546268448552258483140294
absolute error = 5.06819323064498396017282841e-09
relative error = 0.00061242050511181952030640595253393 %
h = 5e-05
x1[1] (analytic) = 0.0012894104353414221828170834756492
x1[1] (numeric) = 0.0012894003284856405440053050264081
absolute error = 1.01068557816388117784492411e-08
relative error = 0.00078383542622428239899739187200994 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.7MB, time=17.59
NO POLE
NO POLE
t[1] = 0.5022
x2[1] (analytic) = 0.0008276130517183405841277537278848
x2[1] (numeric) = 0.00082761835891305043473943304119095
absolute error = 5.30719470985061167931330615e-09
relative error = 0.00064126522640399290974384369036098 %
h = 5e-05
x1[1] (analytic) = 0.0012893559661813954601176818675888
x1[1] (numeric) = 0.0012893453834198517391407064574005
absolute error = 1.05827615437209769754101883e-08
relative error = 0.0008207788866144759698957388828087 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.7MB, time=17.86
NO POLE
NO POLE
t[1] = 0.50225
x2[1] (analytic) = 0.00082765858208166289181855416487103
x2[1] (numeric) = 0.00082766413380877465405488289693428
absolute error = 5.55172711176223632873206325e-09
relative error = 0.00067077503114858803466129211245632 %
h = 5e-05
x1[1] (analytic) = 0.0012893014997447586534391418089226
x1[1] (numeric) = 0.0012892904301126871256592546899842
absolute error = 1.10696320715277798871189384e-08
relative error = 0.00085857590902664897221989472964876 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.7MB, time=18.14
memory used=251.7MB, alloc=4.7MB, time=18.43
NO POLE
NO POLE
t[1] = 0.5023
x2[1] (analytic) = 0.00082770411835994415029049539432325
x2[1] (numeric) = 0.00082770992015203197698339802910111
absolute error = 5.80179208782669290263477786e-09
relative error = 0.00070095000847919719431106854792435 %
h = 5e-05
x1[1] (analytic) = 0.0012892470360313755966898429150187
x1[1] (numeric) = 0.0012892354685629106284384365429973
absolute error = 1.15674684649682514063720214e-08
relative error = 0.00089722668671597715271027204526737 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.7MB, time=18.70
NO POLE
NO POLE
t[1] = 0.50235
x2[1] (analytic) = 0.00082774966055370780196856920717682
x2[1] (numeric) = 0.00082775571794499760905256580905472
absolute error = 6.05739128980708399660187790e-09
relative error = 0.00073179024751941357511904999713522 %
h = 5e-05
x1[1] (analytic) = 0.0012891925750411101305862991774863
x1[1] (numeric) = 0.0012891804987692859869672104828916
absolute error = 1.20762718241436190886945947e-08
relative error = 0.00093673141297439814851384279690749 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.7MB, time=18.98
memory used=263.2MB, alloc=4.8MB, time=19.26
NO POLE
NO POLE
t[1] = 0.5024
x2[1] (analytic) = 0.00082779520866347734502869438387111
x2[1] (numeric) = 0.00082780152718984712786347543714429
absolute error = 6.31852636978283478105327318e-09
relative error = 0.00076329583738283005673924266012828 %
h = 5e-05
x1[1] (analytic) = 0.0012891381167738261026528185659675
x1[1] (numeric) = 0.001289125520730576755318202060591
absolute error = 1.25960432493473346165053765e-08
relative error = 0.00097709028113061820093083380568895 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.8MB, time=19.53
NO POLE
NO POLE
t[1] = 0.50245
x2[1] (analytic) = 0.00082784076268977633340312186670805
x2[1] (numeric) = 0.00082784734788875648315110554467163
absolute error = 6.58519898014974798367796358e-09
relative error = 0.00079546686717303801885695262307471 %
h = 5e-05
x1[1] (analytic) = 0.0012890836612293873672211626469477
x1[1] (numeric) = 0.0012890705344455463021198951782532
absolute error = 1.31267838410651012674686945e-08
relative error = 0.0010183034845501188703638233521533 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.8MB, time=19.80
memory used=274.6MB, alloc=4.8MB, time=20.09
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 0.00082788632263312837678584048126422
x2[1] (numeric) = 0.00082789318004390199684472131120643
absolute error = 6.85741077362005888082994221e-09
relative error = 0.00082830342598362614874053980559543 %
h = 5e-05
x1[1] (analytic) = 0.0012890292084076577854302062195851
x1[1] (numeric) = 0.0012890155399129578105288191853093
absolute error = 1.36684946999749013870342758e-08
relative error = 0.0010603712166351637524694500786599 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.8MB, time=20.36
NO POLE
NO POLE
t[1] = 0.50255
x2[1] (analytic) = 0.00082793188849405714063798320691191
x2[1] (numeric) = 0.0008279390236574603631282810987231
absolute error = 7.13516340322249029789181119e-09
relative error = 0.00086180560289817924954173701966705 %
h = 5e-05
x1[1] (analytic) = 0.0012889747583085012252255969685576
x1[1] (numeric) = 0.0012889605371315742782017318031562
absolute error = 1.42211769269470238651654014e-08
relative error = 0.001103293670824805195512945234286 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.8MB, time=20.64
NO POLE
NO POLE
t[1] = 0.5026
x2[1] (analytic) = 0.00082797746027308634619323399650282
x2[1] (numeric) = 0.00082798487873160864850085260403231
absolute error = 7.41845852230230761860752949e-09
relative error = 0.00089597348699027704934451611087957 %
h = 5e-05
x1[1] (analytic) = 0.001288920310931781561359415133927
x1[1] (numeric) = 0.0012889055261001585172677978778756
absolute error = 1.47848316230440916172560514e-08
relative error = 0.0011470710405948910189256995462205 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.8MB, time=20.92
memory used=289.9MB, alloc=4.8MB, time=21.20
NO POLE
NO POLE
t[1] = 0.50265
x2[1] (analytic) = 0.00082802303797073977046323514526932
x2[1] (numeric) = 0.00082803074526852429183703853098066
absolute error = 7.70729778452137380338571134e-09
relative error = 0.0009308071673234930109624829430547 %
h = 5e-05
x1[1] (analytic) = 0.0012888658662773626753898331980192
x1[1] (numeric) = 0.0012888505068174731543007639603542
absolute error = 1.53594598895210890692376650e-08
relative error = 0.0011917035194580712330660758754047 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.8MB, time=21.46
NO POLE
NO POLE
t[1] = 0.5027
x2[1] (analytic) = 0.00082806862158754124624299520899781
x2[1] (numeric) = 0.0008280766232703851044474117838921
absolute error = 8.00168284385820441657489429e-09
relative error = 0.00096630673295139314248478295870496 %
h = 5e-05
x1[1] (analytic) = 0.0012888114243451084556807755893193
x1[1] (numeric) = 0.0012887954792822806302911287131794
absolute error = 1.59450628278253896468761399e-08
relative error = 0.0012371913009638047601836788818509 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.8MB, time=21.73
memory used=301.3MB, alloc=4.8MB, time=22.03
NO POLE
NO POLE
t[1] = 0.50275
x2[1] (analytic) = 0.00082811421112401466211629747152829
x2[1] (numeric) = 0.00082812251273936927013896018372495
absolute error = 8.30161535460802266271219666e-09
relative error = 0.0010024722729175348085704990301445 %
h = 5e-05
x1[1] (analytic) = 0.0012887569851348827974015784033818
x1[1] (numeric) = 0.0012887404434933432006183091436844
absolute error = 1.65416415395967832692596974e-08
relative error = 0.0012835345786983661565872930858802 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.8MB, time=22.30
NO POLE
NO POLE
t[1] = 0.5028
x2[1] (analytic) = 0.00082815980658068396246110896163522
x2[1] (numeric) = 0.00082816841367765534527554070841859
absolute error = 8.60709697138281443174678337e-09
relative error = 0.0010393038762554655424915231281195 %
h = 5e-05
x1[1] (analytic) = 0.0012887025486465496025266491407532
x1[1] (numeric) = 0.0012886853994494229350228026625168
absolute error = 1.71491971266675038464782364e-08
relative error = 0.001330733546284852336016700499918 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.8MB, time=22.58
memory used=312.8MB, alloc=4.8MB, time=22.86
NO POLE
NO POLE
t[1] = 0.50285
x2[1] (analytic) = 0.0008282054079580731474549900193436
x2[1] (numeric) = 0.00082821432608742225883834325890416
absolute error = 8.91812934911138335323956056e-09
relative error = 0.0010768016319887218589238834089685 %
h = 5e-05
x1[1] (analytic) = 0.0012886481148799727798351264619085
x1[1] (numeric) = 0.0012886303471492817175783449671047
absolute error = 1.77677306910622567814948038e-08
relative error = 0.0013787883973831892942185893680331 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.8MB, time=23.14
NO POLE
NO POLE
t[1] = 0.5029
x2[1] (analytic) = 0.0008282510152567062730805044117353
x2[1] (numeric) = 0.00082826024997084931248636395225375
absolute error = 9.23471414303940585954051845e-09
relative error = 0.0011149656291308280674875081080501 %
h = 5e-05
x1[1] (analytic) = 0.0012885936838350162449105399591989
x1[1] (numeric) = 0.0012885752865916812466640637493939
absolute error = 1.83972433349982464762098050e-08
relative error = 0.0014276993256901388347267652844964 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.8MB, time=23.41
NO POLE
NO POLE
memory used=324.2MB, alloc=4.8MB, time=23.69
t[1] = 0.50295
x2[1] (analytic) = 0.00082829662847710745113062999829971
x2[1] (numeric) = 0.00082830618533011618061688794344289
absolute error = 9.55685300872948625794514318e-09
relative error = 0.0011537959566852950870344076856271 %
h = 5e-05
x1[1] (analytic) = 0.0012885392555115439201404699458103
x1[1] (numeric) = 0.0012885202177753830349366282272301
absolute error = 1.90377361608852038417185802e-08
relative error = 0.0014774665249393052958468761467348 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.8MB, time=23.97
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082835213216740291042598177720128
absolute error = 9.88454760206121181183131758e-09
relative error = 0.0011932927036456192606852564786948 %
h = 5e-05
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884651406991484093023944987599
absolute error = 1.96892102713254138127629724e-08
relative error = 0.0015280901889011422788458624425162 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.8MB, time=24.24
NO POLE
NO POLE
t[1] = 0.50305
x2[1] (analytic) = 0.00082838787268531069076116449329504
x2[1] (numeric) = 0.00082839809048488992196899527142696
absolute error = 1.021779957923120783077813192e-08
relative error = 0.0012334559589952811716143551477617 %
h = 5e-05
x1[1] (analytic) = 0.0012884304070285076246324130967366
x1[1] (numeric) = 0.0012884100553617385108895467192237
absolute error = 2.03516667691137428663775129e-08
relative error = 0.0015795705113829593773463443923874 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.8MB, time=24.51
memory used=339.5MB, alloc=4.8MB, time=24.80
NO POLE
NO POLE
t[1] = 0.5031
x2[1] (analytic) = 0.00082843350367416125502830326561401
x2[1] (numeric) = 0.00082844406028475800822107293363943
absolute error = 1.055661059675319276966802542e-08
relative error = 0.0012742858117077444595829550777008 %
h = 5e-05
x1[1] (analytic) = 0.0012883759868686715326867788303632
x1[1] (numeric) = 0.0012883549617619142950202340995143
absolute error = 2.10251067572376665447308489e-08
relative error = 0.0016319076862289289079261574041971 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.8MB, time=25.07
NO POLE
NO POLE
t[1] = 0.50315
x2[1] (analytic) = 0.0008284791405868768771043381382677
x2[1] (numeric) = 0.00082849004156918833513767491194727
absolute error = 1.090098231145803333677367957e-08
relative error = 0.0013157823507464546382209258271202 %
h = 5e-05
x1[1] (analytic) = 0.0012883215694297754084796858889148
x1[1] (numeric) = 0.0012882998598984365311827037258745
absolute error = 2.17095313388772969821630403e-08
relative error = 0.0016851019073200926419232475194978 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.8MB, time=25.34
memory used=350.9MB, alloc=4.8MB, time=25.62
NO POLE
NO POLE
t[1] = 0.5032
x2[1] (analytic) = 0.00082852478342398194791549665092172
x2[1] (numeric) = 0.00082853603434036244171510748200624
absolute error = 1.125091638049379961083108452e-08
relative error = 0.0013579456650648379130567466487991 %
h = 5e-05
x1[1] (analytic) = 0.0012882671547116832084138656194575
x1[1] (numeric) = 0.001288244749770065803003429200107
absolute error = 2.24049416174054104364193505e-08
relative error = 0.0017391533685743685384461383820764 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.8MB, time=25.90
NO POLE
NO POLE
t[1] = 0.50325
x2[1] (analytic) = 0.00082857043218600091423089597124342
x2[1] (numeric) = 0.0008285820386004622400510630714439
absolute error = 1.160641446132582016710020048e-08
relative error = 0.0014007758436063000002958030885695 %
h = 5e-05
x1[1] (analytic) = 0.0012882127427142588956940591808277
x1[1] (numeric) = 0.0012881896313755625082192350996694
absolute error = 2.31113386963874748240811583e-08
relative error = 0.0017940622639465574785901814663308 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.8MB, time=26.17
NO POLE
NO POLE
memory used=362.4MB, alloc=4.8MB, time=26.45
t[1] = 0.5033
x2[1] (analytic) = 0.00082861608687345827866795740859187
x2[1] (numeric) = 0.00082862805435167001540516982322714
absolute error = 1.196747821173673721241463527e-08
relative error = 0.0014442729753042249463469694762306 %
h = 5e-05
x1[1] (analytic) = 0.0012881583334373664403266774516441
x1[1] (numeric) = 0.001288134504713686858649417257028
absolute error = 2.38287236795816772601946161e-08
relative error = 0.0018498287874283500008598011847003 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.8MB, time=26.72
NO POLE
NO POLE
t[1] = 0.50335
x2[1] (analytic) = 0.0008286617474868785996978214776885
x2[1] (numeric) = 0.00082867408159616842625955069944916
absolute error = 1.233410928982656172922176066e-08
relative error = 0.0014884371490819739480974582059198 %
h = 5e-05
x1[1] (analytic) = 0.0012881039268808698191194609553229
x1[1] (numeric) = 0.001288079369783198880167858857643
absolute error = 2.45570976709389516020976799e-08
relative error = 0.001906453133048333037796946545594 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.8MB, time=27.00
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 0.00082870741402678649165076351232339
x2[1] (numeric) = 0.00082872012033614050437939212701268
absolute error = 1.270630935401272862861468929e-08
relative error = 0.0015332684538528841739359165035621 %
h = 5e-05
x1[1] (analytic) = 0.0012880495230446330156811398020981
x1[1] (numeric) = 0.0012880242265828584126751423559577
absolute error = 2.52964617746030059974461404e-08
relative error = 0.0019639354948719966538159613572247 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.8MB, time=27.27
memory used=377.6MB, alloc=4.8MB, time=27.55
NO POLE
NO POLE
t[1] = 0.50345
x2[1] (analytic) = 0.00082875308649370662472160982915166
x2[1] (numeric) = 0.00082876617057376965487352218668642
absolute error = 1.308408006303015191235753476e-08
relative error = 0.001578766978520267585523751378386 %
h = 5e-05
x1[1] (analytic) = 0.0012879951219285200204210936480425
x1[1] (numeric) = 0.0012879690751114251100706572087652
absolute error = 2.60468170949103504364392773e-08
relative error = 0.0020222760670017407842450844428122 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.8MB, time=27.82
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 0.00082879876488816372497515444163463
x2[1] (numeric) = 0.00082881223231123965625499834701206
absolute error = 1.346742307593127984390537743e-08
relative error = 0.0016249328119774097603146633522819 %
h = 5e-05
x1[1] (analytic) = 0.0012879407235323948305490116710912
x1[1] (numeric) = 0.0012879139153676584402247034253248
absolute error = 2.68081647363903243082457664e-08
relative error = 0.0020814750435768819755747919438021 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.8MB, time=28.09
memory used=389.1MB, alloc=4.8MB, time=28.38
NO POLE
NO POLE
t[1] = 0.50355
x2[1] (analytic) = 0.00082884444921068257435157632418004
x2[1] (numeric) = 0.00082885830555073466050170474453918
absolute error = 1.385634005208615012842035914e-08
relative error = 0.0016717660431075687148223695444627 %
h = 5e-05
x1[1] (analytic) = 0.0012878863278561214500745525640661
x1[1] (numeric) = 0.0012878587473503176849505909336008
absolute error = 2.75805058037651239616304653e-08
relative error = 0.0021415326187736601269131935217596 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.8MB, time=28.65
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 0.00082889013946178801067185722653652
x2[1] (numeric) = 0.00082890439029443919311695901186586
absolute error = 1.425083265118244510178532934e-08
relative error = 0.001719266760783973728636496504857 %
h = 5e-05
x1[1] (analytic) = 0.0012878319348995638898070045446997
x1[1] (numeric) = 0.0012878035710581619399767347619963
absolute error = 2.83638414019498302697827034e-08
relative error = 0.0022024489868052452326486942908023 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.8MB, time=28.93
NO POLE
NO POLE
memory used=400.5MB, alloc=4.8MB, time=29.21
t[1] = 0.50365
x2[1] (analytic) = 0.00082893583564200492764320003849618
x2[1] (numeric) = 0.00082895048654453815319012865496285
absolute error = 1.465090253322554692861646667e-08
relative error = 0.0017674350538698241691866232795569 %
h = 5e-05
x1[1] (analytic) = 0.0012877775446625861673549453826583
x1[1] (numeric) = 0.0012877483864899501149187460359543
absolute error = 2.91581726360524361993467040e-08
relative error = 0.0022642243419217441263201345044724 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.8MB, time=29.48
NO POLE
NO POLE
t[1] = 0.5037
x2[1] (analytic) = 0.00082898153775185827486444770496057
x2[1] (numeric) = 0.00082899659430321681345725698125947
absolute error = 1.505655135853859280927629890e-08
relative error = 0.0018162710112182883172544549581695 %
h = 5e-05
x1[1] (analytic) = 0.0012877231571450523071259024435631
x1[1] (numeric) = 0.0012876931936444409332515187887983
absolute error = 2.99635006113738743836547648e-08
relative error = 0.0023268588784102072256946189334907 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.8MB, time=29.77
NO POLE
NO POLE
t[1] = 0.50375
x2[1] (analytic) = 0.00082902724579187305783150269142413
x2[1] (numeric) = 0.0008290427135726608203616985799696
absolute error = 1.546778078776253019588854547e-08
relative error = 0.0018657747216725021932341070162811 %
h = 5e-05
x1[1] (analytic) = 0.0012876687723468263403260127500097
x1[1] (numeric) = 0.0012876379925203929322813125861852
absolute error = 3.07798264334080447001638245e-08
relative error = 0.0023903527905946352790532480085461 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=411.9MB, alloc=4.8MB, time=30.05
memory used=415.8MB, alloc=4.8MB, time=30.33
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 0.0008290729597625743379427469999303
x2[1] (numeric) = 0.0008290888443550561941147643561364
absolute error = 1.588459248185617201735620610e-08
relative error = 0.0019159462740655683841404805762492 %
h = 5e-05
x1[1] (analytic) = 0.0012876143902677723049596830595824
x1[1] (numeric) = 0.0012875827831165644631178309635421
absolute error = 3.16071512078418418520960403e-08
relative error = 0.0024547062728359861126849626060819 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.8MB, time=30.60
NO POLE
NO POLE
t[1] = 0.50385
x2[1] (analytic) = 0.00082911867966448723250446273555416
x2[1] (numeric) = 0.00082913498665258932875637611987449
absolute error = 1.630698810209625191338432033e-08
relative error = 0.0019667857572205548713657087801367 %
h = 5e-05
x1[1] (analytic) = 0.0012875600109077542458292499598661
x1[1] (numeric) = 0.0012875275654317136906462956758588
absolute error = 3.24454760405551829542840073e-08
relative error = 0.0025199195195321813795887148655157 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.8MB, time=30.89
memory used=427.2MB, alloc=4.8MB, time=31.17
NO POLE
NO POLE
t[1] = 0.5039
x2[1] (analytic) = 0.00082916440549813691473625322346704
x2[1] (numeric) = 0.00082918114046744699221573073228877
absolute error = 1.673496931007747947750882173e-08
relative error = 0.0020182932599504938591836542364237 %
h = 5e-05
x1[1] (analytic) = 0.0012875056342666362145346399804511
x1[1] (numeric) = 0.0012874723394645985934995167592088
absolute error = 3.32948020376210351232212423e-08
relative error = 0.0025859927251181133093841767952675 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.8MB, time=31.45
NO POLE
NO POLE
t[1] = 0.50395
x2[1] (analytic) = 0.00082921013726404861377646467663714
x2[1] (numeric) = 0.00082922730580181632637197380954903
absolute error = 1.716853776771259550913291189e-08
relative error = 0.0020704688710583806040024375703374 %
h = 5e-05
x1[1] (analytic) = 0.0012874512603442822694730297219339
x1[1] (numeric) = 0.00128741710521397696402995840337
absolute error = 3.41551303053054430713185639e-08
relative error = 0.0026529260840656514594311991839808 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.8MB, time=31.72
memory used=438.6MB, alloc=4.8MB, time=32.01
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082927348265788484711488298659999
absolute error = 1.760769513723242727457237897e-08
relative error = 0.0021233126793371722443649769707826 %
h = 5e-05
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.001287361862678606408281800634917
absolute error = 3.50264619500675567053669921e-08
relative error = 0.002720719790883649467158232686697 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.8MB, time=32.28
NO POLE
NO POLE
t[1] = 0.50405
x2[1] (analytic) = 0.00082930161859475925846178363070083
x2[1] (numeric) = 0.00082931967103784044440556074198634
absolute error = 1.805244308118594377711128551e-08
relative error = 0.0021768247735697866316975185201854 %
h = 5e-05
x1[1] (analytic) = 0.0012873425206553229056217260179551
x1[1] (numeric) = 0.0012873066118572443459629968101567
absolute error = 3.59087980785596587292077984e-08
relative error = 0.0027893740401179518035999235905492 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=446.3MB, alloc=4.8MB, time=32.55
NO POLE
NO POLE
t[1] = 0.5041
x2[1] (analytic) = 0.00082934736816060894202610071582133
x2[1] (numeric) = 0.00082936587094387138233713678527289
absolute error = 1.850278326244031103606945156e-08
relative error = 0.0022310052425291011618061371605633 %
h = 5e-05
x1[1] (analytic) = 0.0012872881548884456376095775276106
x1[1] (numeric) = 0.0012872513527486480104173269172787
absolute error = 3.68021397976271922506103319e-08
relative error = 0.0028588890263514005281440963664259 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=450.1MB, alloc=4.8MB, time=32.84
memory used=453.9MB, alloc=4.8MB, time=33.11
NO POLE
NO POLE
t[1] = 0.50415
x2[1] (analytic) = 0.00082939312366082211824810512538206
x2[1] (numeric) = 0.00082941208237816629919548000853992
absolute error = 1.895871734418094737488315786e-08
relative error = 0.0022858541749779516071211878917311 %
h = 5e-05
x1[1] (analytic) = 0.0012872337918397887573848390453416
x1[1] (numeric) = 0.0012871960853515744485964466870922
absolute error = 3.77064882143087883923582494e-08
relative error = 0.0029292649442038420444883353362457 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=457.7MB, alloc=4.8MB, time=33.38
NO POLE
NO POLE
t[1] = 0.5042
x2[1] (analytic) = 0.00082943888509592429594120180293885
x2[1] (numeric) = 0.0008294583053429142075199200034342
absolute error = 1.942024698991157871820049535e-08
relative error = 0.0023413716596691309496896868874888 %
h = 5e-05
x1[1] (analytic) = 0.0012871794315092163573258400564985
x1[1] (numeric) = 0.0012871408096647805210319325117205
absolute error = 3.86218444358362939075447780e-08
relative error = 0.0030005019883321338578063778533837 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.8MB, time=33.65
memory used=465.4MB, alloc=4.8MB, time=33.93
NO POLE
NO POLE
t[1] = 0.50425
x2[1] (analytic) = 0.00082948465246644103987008015246953
x2[1] (numeric) = 0.00082950453984030449416397814525622
absolute error = 1.988737386345429389799278669e-08
relative error = 0.0023975577853453882149156020463035 %
h = 5e-05
x1[1] (analytic) = 0.0012871250738965925366061212482615
x1[1] (numeric) = 0.0012870855256870229018073221706243
absolute error = 3.95482095696347987990776372e-08
relative error = 0.0030726003534301513331245313063218 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.8MB, time=34.20
NO POLE
NO POLE
t[1] = 0.5043
x2[1] (analytic) = 0.00082953042577289797075613956205843
x2[1] (numeric) = 0.00082955078587252692035610824556464
absolute error = 2.036009962894959996868350621e-08
relative error = 0.0024544126407394273060480324852624 %
h = 5e-05
x1[1] (analytic) = 0.0012870707190017814011940947575749
x1[1] (numeric) = 0.0012870302334170580785301513633258
absolute error = 4.04855847233226639433942491e-08
relative error = 0.0031455602342287944549083264089309 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.8MB, time=34.48
memory used=476.8MB, alloc=4.8MB, time=34.76
NO POLE
NO POLE
t[1] = 0.50435
x2[1] (analytic) = 0.00082957620501582076528291547865441
x2[1] (numeric) = 0.00082959704344177162176044677477891
absolute error = 2.083842595085647753129612450e-08
relative error = 0.0025119363145739058394172563638025 %
h = 5e-05
x1[1] (analytic) = 0.0012870163668246470638527044360674
x1[1] (numeric) = 0.0012869749328536423523039860482033
absolute error = 4.14339710047115487183878641e-08
relative error = 0.0032193818254959945878596191766395 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.8MB, time=35.03
NO POLE
NO POLE
t[1] = 0.5044
x2[1] (analytic) = 0.00082962199019573515610150603395714
x2[1] (numeric) = 0.00082964331255022910853757265626147
absolute error = 2.132235449395243606662230433e-08
relative error = 0.0025701288955614339804186263846646 %
h = 5e-05
x1[1] (analytic) = 0.00128696201736505364413908613196
x1[1] (numeric) = 0.0012869196239955318377004505867286
absolute error = 4.23933695218064386355452314e-08
relative error = 0.0032940653220367212389243541644111 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=484.4MB, alloc=4.8MB, time=35.30
NO POLE
NO POLE
t[1] = 0.50445
x2[1] (analytic) = 0.00082966778131316693183599922148616
x2[1] (numeric) = 0.00082968959320009026540527663336103
absolute error = 2.181188692333356927741187487e-08
relative error = 0.0026289904724045732802442922563442 %
h = 5e-05
x1[1] (analytic) = 0.0012869076706228652684042279889585
x1[1] (numeric) = 0.0012868643068414824627312516925175
absolute error = 4.33637813828056729762964410e-08
relative error = 0.0033696109186929888205112013695244 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.8MB, time=35.57
memory used=492.1MB, alloc=4.8MB, time=35.86
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 0.00082971357836864193708890062488759
x2[1] (numeric) = 0.00082973588539354635169934021089874
absolute error = 2.230702490441461043958601115e-08
relative error = 0.0026885211337958355133627293007885 %
h = 5e-05
x1[1] (analytic) = 0.0012868533265979460697926307621308
x1[1] (numeric) = 0.0012868089813902499688201981845643
absolute error = 4.43452076961009724325775665e-08
relative error = 0.0034460188103438634149212794332203 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.8MB, time=36.13
NO POLE
NO POLE
t[1] = 0.50455
x2[1] (analytic) = 0.00082975938136268607244656169753319
x2[1] (numeric) = 0.00082978218913278900143432417257916
absolute error = 2.280777010292898776247504597e-08
relative error = 0.0027487209684176815157460523257469 %
h = 5e-05
x1[1] (analytic) = 0.0012867989852901601882419681507683
x1[1] (numeric) = 0.0012867536476405899107752165440308
absolute error = 4.53376495702774667516067375e-08
relative error = 0.0035232891919054695399891777655242 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.8MB, time=36.40
memory used=503.5MB, alloc=4.8MB, time=36.67
NO POLE
NO POLE
t[1] = 0.5046
x2[1] (analytic) = 0.00082980519029582529448460859346626
x2[1] (numeric) = 0.00082982850442001022336436667580839
absolute error = 2.331412418492887975808234213e-08
relative error = 0.002809590064942520023845093863846 %
h = 5e-05
x1[1] (analytic) = 0.0012867446466993717704827471482299
x1[1] (numeric) = 0.0012866983055912576567603622739612
absolute error = 4.63411081141137223848742687e-08
relative error = 0.0036014222583309969159354901145294 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.8MB, time=36.94
NO POLE
NO POLE
t[1] = 0.50465
x2[1] (analytic) = 0.00082985100516858561577337154974936
x2[1] (numeric) = 0.00082987483125740240104399092540168
absolute error = 2.382608881678527061937565232e-08
relative error = 0.002871128512032706514312225719712 %
h = 5e-05
x1[1] (analytic) = 0.001286690310825444970037968408768
x1[1] (numeric) = 0.0012866429552410083882678270612921
absolute error = 4.73555844365817701413474759e-08
relative error = 0.0036804182046107072334310723714021 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=511.1MB, alloc=4.8MB, time=37.21
memory used=514.9MB, alloc=4.8MB, time=37.49
NO POLE
NO POLE
t[1] = 0.5047
x2[1] (analytic) = 0.00082989682598149310488331482026843
x2[1] (numeric) = 0.00082992116964715829288892242766328
absolute error = 2.434366566518800560760739485e-08
relative error = 0.0029333363983405420444719027708556 %
h = 5e-05
x1[1] (analytic) = 0.0012866359776682439472227866313365
x1[1] (numeric) = 0.0012865875965885971000899417405297
absolute error = 4.83810796468471328448908068e-08
relative error = 0.0037602772257719409228732372527364 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.8MB, time=37.77
NO POLE
NO POLE
t[1] = 0.50475
x2[1] (analytic) = 0.00082994265273507388639046716104801
x2[1] (numeric) = 0.00082996751959147103223691582632143
absolute error = 2.486685639714584644866527342e-08
relative error = 0.0029962138125082720935389078735937 %
h = 5e-05
x1[1] (analytic) = 0.001286581647227632869144170960378
x1[1] (numeric) = 0.0012865322296327786002911750584629
absolute error = 4.94175948542688529959019151e-08
relative error = 0.0038409995168791239248740985776043 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.8MB, time=38.04
NO POLE
NO POLE
t[1] = 0.5048
x2[1] (analytic) = 0.00082998848542985414088185286713247
x2[1] (numeric) = 0.00083001388109253412740859132180156
absolute error = 2.539566267998652673845466909e-08
relative error = 0.0030597608431680854045842766236431 %
h = 5e-05
x1[1] (analytic) = 0.0012865273195034759097005654035915
x1[1] (numeric) = 0.0012864768543723075101801282392837
absolute error = 5.04651311683995204371643078e-08
relative error = 0.0039225852730337744619612779945469 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.8MB, time=38.31
memory used=530.2MB, alloc=4.8MB, time=38.59
NO POLE
NO POLE
t[1] = 0.50485
x2[1] (analytic) = 0.00083003432406636010496092336108762
x2[1] (numeric) = 0.00083006025415254146176828067532113
absolute error = 2.593008618135680735731423351e-08
relative error = 0.0031239775789421128272488807326534 %
h = 5e-05
x1[1] (analytic) = 0.0012864729944956372495815492666783
x1[1] (numeric) = 0.0012864214708059382642815253494848
absolute error = 5.15236896989853000239171935e-08
relative error = 0.0040050346893745098114911868796541 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.8MB, time=38.87
NO POLE
NO POLE
t[1] = 0.5049
x2[1] (analytic) = 0.00083008016864511807125298933317795
x2[1] (numeric) = 0.00083010663877368729378488279928968
absolute error = 2.647012856922253189346611173e-08
relative error = 0.0031888641084424261612046485959821 %
h = 5e-05
x1[1] (analytic) = 0.001286418672203981076267497605066
x1[1] (numeric) = 0.0012863660789324251103081994619038
absolute error = 5.25932715559659592981431622e-08
relative error = 0.0040883479610770530797750963658383 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.8MB, time=39.14
memory used=541.6MB, alloc=4.8MB, time=39.41
NO POLE
NO POLE
t[1] = 0.50495
x2[1] (analytic) = 0.00083012601916665438841065343327373
x2[1] (numeric) = 0.00083015303495816625709272893549786
absolute error = 2.701579151186868207550222413e-08
relative error = 0.0032544205202710370003634016772257 %
h = 5e-05
x1[1] (analytic) = 0.0012863643526283715840292416926091
x1[1] (numeric) = 0.001286310678750522109133074618285
absolute error = 5.36738778494748961670743241e-08
relative error = 0.0041725252833542399774182082593455 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=545.5MB, alloc=4.8MB, time=39.70
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.00083019944270817336055245742257955
absolute error = 2.756707667789943321390803641e-08
relative error = 0.0033206469030198955778332851659561 %
h = 5e-05
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012862552702589831347611435897279
absolute error = 5.47655096898391665859175385e-08
relative error = 0.0042575668514560255958719399084856 %
h = 5e-05
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations = 100
Total Elapsed Time = 39 Seconds
Elapsed Time(since restart) = 39 Seconds
Expected Time Remaining = 9 Hours 51 Minutes 3 Seconds
Optimized Time Remaining = 9 Hours 50 Minutes 54 Seconds
Time to Timeout = 14 Minutes 20 Seconds
Percent Done = 0.1122 %
> quit
memory used=548.1MB, alloc=4.8MB, time=39.88