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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> 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 not array_x2_set_initial[1,3] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x1_set_initial[2,2] then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x2_set_initial[1,4] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x1_set_initial[2,3] then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x2_set_initial[1,5] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x1_set_initial[2,4] then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x2_set_initial[1,6] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x1_set_initial[2,5] then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x2_set_initial[1,7] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> 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 2
> ;
> 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 not array_x1_set_initial[2,6] then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> 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 2
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_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
> if not array_x2_set_initial[1,kkk + order_d] then # if number 2
> 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 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
> if not array_x1_set_initial[2,kkk + order_d] then # if number 2
> 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 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 DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, 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 not array_x2_set_initial[1, 3] then
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
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 not array_x1_set_initial[2, 2] then
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
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 not array_x2_set_initial[1, 4] then
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
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 not array_x1_set_initial[2, 3] then
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
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 not array_x2_set_initial[1, 5] then
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
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 not array_x1_set_initial[2, 4] then
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
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 not array_x2_set_initial[1, 6] then
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
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 not array_x1_set_initial[2, 5] then
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
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 not array_x2_set_initial[1, 7] then
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
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 not array_x1_set_initial[2, 6] then
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
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
if not array_x2_set_initial[1, kkk + order_d] 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
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
if not array_x1_set_initial[2, kkk + order_d] 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
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 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> 1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; 1.0 + 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> - 6.0 * c3 * exp(-t);
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; -6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> 1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
1.0 + c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> 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 := 1.0; 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
> DEBUGMASSIVE,
> DEBUGL,
> glob_max_terms,
> ALWAYS,
> INFO,
> glob_iolevel,
> #Top Generate Globals Decl
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_hmin_init,
> glob_reached_optimal_h,
> glob_max_opt_iter,
> glob_log10normmin,
> glob_log10relerr,
> glob_smallish_float,
> glob_log10_abserr,
> glob_dump_analytic,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_subiter_method,
> glob_initial_pass,
> centuries_in_millinium,
> hours_in_day,
> glob_small_float,
> glob_max_iter,
> glob_unchanged_h_cnt,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_not_yet_finished,
> glob_percent_done,
> glob_max_sec,
> glob_no_eqs,
> glob_max_trunc_err,
> glob_h,
> glob_clock_start_sec,
> years_in_century,
> glob_current_iter,
> glob_relerr,
> glob_clock_sec,
> djd_debug2,
> glob_max_minutes,
> glob_start,
> glob_warned2,
> glob_warned,
> glob_look_poles,
> glob_almost_1,
> glob_orig_start_sec,
> glob_optimal_done,
> days_in_year,
> min_in_hour,
> sec_in_min,
> glob_optimal_expect_sec,
> MAX_UNCHANGED,
> glob_log10_relerr,
> glob_large_float,
> glob_hmax,
> glob_disp_incr,
> glob_display_flag,
> djd_debug,
> glob_dump,
> glob_log10abserr,
> glob_normmax,
> glob_iter,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_hmin,
> glob_html_log,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_0D0,
> array_const_4D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_m1,
> array_x2,
> array_x1,
> 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_last_rel_error,
> array_pole,
> array_x2_init,
> array_1st_rel_error,
> array_norms,
> array_x1_init,
> array_t,
> array_type_pole,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_set_initial,
> array_x1_higher,
> array_x2_set_initial,
> array_poles,
> array_x2_higher_work,
> array_x1_higher_work2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> DEBUGL := 3;
> glob_max_terms := 30;
> ALWAYS := 1;
> INFO := 2;
> glob_iolevel := 5;
> glob_curr_iter_when_opt := 0;
> glob_optimal_start := 0.0;
> glob_hmin_init := 0.001;
> glob_reached_optimal_h := false;
> glob_max_opt_iter := 10;
> glob_log10normmin := 0.1;
> glob_log10relerr := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_log10_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_last_good_h := 0.1;
> glob_not_yet_start_msg := true;
> glob_subiter_method := 3;
> glob_initial_pass := true;
> centuries_in_millinium := 10.0;
> hours_in_day := 24.0;
> glob_small_float := 0.1e-50;
> glob_max_iter := 1000;
> glob_unchanged_h_cnt := 0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_percent_done := 0.0;
> glob_max_sec := 10000.0;
> glob_no_eqs := 0;
> glob_max_trunc_err := 0.1e-10;
> glob_h := 0.1;
> glob_clock_start_sec := 0.0;
> years_in_century := 100.0;
> glob_current_iter := 0;
> glob_relerr := 0.1e-10;
> glob_clock_sec := 0.0;
> djd_debug2 := true;
> glob_max_minutes := 0.0;
> glob_start := 0;
> glob_warned2 := false;
> glob_warned := false;
> glob_look_poles := false;
> glob_almost_1 := 0.9990;
> glob_orig_start_sec := 0.0;
> glob_optimal_done := false;
> days_in_year := 365.0;
> min_in_hour := 60.0;
> sec_in_min := 60.0;
> glob_optimal_expect_sec := 0.1;
> MAX_UNCHANGED := 10;
> glob_log10_relerr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_disp_incr := 0.1;
> glob_display_flag := true;
> djd_debug := true;
> glob_dump := false;
> glob_log10abserr := 0.0;
> glob_normmax := 0.0;
> glob_iter := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_hmin := 0.00000000001;
> glob_html_log := 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_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/mtest6_revpostode.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,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"# was complicatedrev.ode");
> omniout_str(ALWAYS,"#");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x1_init[1 + 1] := exact_soln_x1p(t_start);");
> omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1 + 1] := 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 := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x1p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"- 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 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"1.0 + 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 := 1.0;");
> 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
> #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_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= 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_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_set_initial := 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_x1_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_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_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_pole[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_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> 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_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 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[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_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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 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_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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 <=3 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
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> 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_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_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_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_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #
> # was complicatedrev.ode
> #
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[0 + 1] := exact_soln_x1(t_start);
> array_x1_init[1 + 1] := exact_soln_x1p(t_start);
> array_x2_init[0 + 1] := exact_soln_x2(t_start);
> array_x2_init[1 + 1] := 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 := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_x2_set_initial[1,1] := true;
> array_x2_set_initial[1,2] := true;
> array_x2_set_initial[1,3] := false;
> array_x2_set_initial[1,4] := false;
> array_x2_set_initial[1,5] := false;
> array_x2_set_initial[1,6] := false;
> array_x2_set_initial[1,7] := false;
> array_x2_set_initial[1,8] := false;
> array_x2_set_initial[1,9] := false;
> array_x2_set_initial[1,10] := false;
> array_x2_set_initial[1,11] := false;
> array_x2_set_initial[1,12] := false;
> array_x2_set_initial[1,13] := false;
> array_x2_set_initial[1,14] := false;
> array_x2_set_initial[1,15] := false;
> array_x2_set_initial[1,16] := false;
> array_x2_set_initial[1,17] := false;
> array_x2_set_initial[1,18] := false;
> array_x2_set_initial[1,19] := false;
> array_x2_set_initial[1,20] := false;
> array_x2_set_initial[1,21] := false;
> array_x2_set_initial[1,22] := false;
> array_x2_set_initial[1,23] := false;
> array_x2_set_initial[1,24] := false;
> array_x2_set_initial[1,25] := false;
> array_x2_set_initial[1,26] := false;
> array_x2_set_initial[1,27] := false;
> array_x2_set_initial[1,28] := false;
> array_x2_set_initial[1,29] := false;
> array_x2_set_initial[1,30] := false;
> array_x1_set_initial[2,1] := true;
> array_x1_set_initial[2,2] := true;
> array_x1_set_initial[2,3] := false;
> array_x1_set_initial[2,4] := false;
> array_x1_set_initial[2,5] := false;
> array_x1_set_initial[2,6] := false;
> array_x1_set_initial[2,7] := false;
> array_x1_set_initial[2,8] := false;
> array_x1_set_initial[2,9] := false;
> array_x1_set_initial[2,10] := false;
> array_x1_set_initial[2,11] := false;
> array_x1_set_initial[2,12] := false;
> array_x1_set_initial[2,13] := false;
> array_x1_set_initial[2,14] := false;
> array_x1_set_initial[2,15] := false;
> array_x1_set_initial[2,16] := false;
> array_x1_set_initial[2,17] := false;
> array_x1_set_initial[2,18] := false;
> array_x1_set_initial[2,19] := false;
> array_x1_set_initial[2,20] := false;
> array_x1_set_initial[2,21] := false;
> array_x1_set_initial[2,22] := false;
> array_x1_set_initial[2,23] := false;
> array_x1_set_initial[2,24] := false;
> array_x1_set_initial[2,25] := false;
> array_x1_set_initial[2,26] := false;
> array_x1_set_initial[2,27] := false;
> array_x1_set_initial[2,28] := false;
> array_x1_set_initial[2,29] := false;
> array_x1_set_initial[2,30] := false;
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_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 := 2;
> #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;
> if glob_subiter_method = 1 then # if number 3
> atomall();
> elif glob_subiter_method = 2 then # if number 4
> subiter := 1;
> while subiter <= 3 do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> else
> subiter := 1;
> while subiter <= 3 + glob_max_terms do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3
> ;
> fi;# end if 4
> ;
> if (glob_look_poles) then # if number 4
> #left paren 0004C
> check_for_pole();
> fi;# end if 4
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x2
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> #BEFORE ADJUST SUBSERIES EQ =1
> 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
> 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
> 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
> 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
> 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
> 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
> 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
> 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
> 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
> 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
> 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
> 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
> #Jump Series array_x1
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[3,iii] := array_x1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 3;
> 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
> ord := 2;
> calc_term := 2;
> #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
> temp_sum := 0.0;
> ord := 2;
> 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
> 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
> 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
> ord := 1;
> calc_term := 3;
> #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
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #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
> 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
> 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
> 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
> 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 4
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 4
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 4
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (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 4
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-13T03:00:47-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest6_rev")
> ;
> 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 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 5
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 5
> ;
> log_revs(html_log_file," 090 | ")
> ;
> logitem_str(html_log_file,"mtest6_rev diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest6_rev maple results")
> ;
> logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (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 5
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 5
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 5
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 5
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 4
> ;
> if glob_html_log then # if number 4
> fclose(html_log_file);
> fi;# end if 4
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
Warning, `subiter` is implicitly declared local to procedure `mainprog`
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp,
subiter;
global DEBUGMASSIVE, DEBUGL, glob_max_terms, ALWAYS, INFO, glob_iolevel,
glob_curr_iter_when_opt, glob_optimal_start, glob_hmin_init,
glob_reached_optimal_h, glob_max_opt_iter, glob_log10normmin,
glob_log10relerr, glob_smallish_float, glob_log10_abserr,
glob_dump_analytic, glob_last_good_h, glob_not_yet_start_msg,
glob_subiter_method, glob_initial_pass, centuries_in_millinium,
hours_in_day, glob_small_float, glob_max_iter, glob_unchanged_h_cnt,
glob_max_rel_trunc_err, glob_abserr, glob_not_yet_finished,
glob_percent_done, glob_max_sec, glob_no_eqs, glob_max_trunc_err, glob_h,
glob_clock_start_sec, years_in_century, glob_current_iter, glob_relerr,
glob_clock_sec, djd_debug2, glob_max_minutes, glob_start, glob_warned2,
glob_warned, glob_look_poles, glob_almost_1, glob_orig_start_sec,
glob_optimal_done, days_in_year, min_in_hour, sec_in_min,
glob_optimal_expect_sec, MAX_UNCHANGED, glob_log10_relerr, glob_large_float,
glob_hmax, glob_disp_incr, glob_display_flag, djd_debug, glob_dump,
glob_log10abserr, glob_normmax, glob_iter, glob_optimal_clock_start_sec,
glob_max_hours, glob_hmin, glob_html_log, array_const_1, array_const_2,
array_const_0D0, array_const_4D0, array_const_2D0, array_const_3D0,
array_m1, array_x2, array_x1, 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_last_rel_error, array_pole,
array_x2_init, array_1st_rel_error, array_norms, array_x1_init, array_t,
array_type_pole, array_real_pole, array_x1_higher_work, array_x2_higher,
array_x2_higher_work2, array_complex_pole, array_x1_set_initial,
array_x1_higher, array_x2_set_initial, array_poles, array_x2_higher_work,
array_x1_higher_work2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
DEBUGL := 3;
glob_max_terms := 30;
ALWAYS := 1;
INFO := 2;
glob_iolevel := 5;
glob_curr_iter_when_opt := 0;
glob_optimal_start := 0.;
glob_hmin_init := 0.001;
glob_reached_optimal_h := false;
glob_max_opt_iter := 10;
glob_log10normmin := 0.1;
glob_log10relerr := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_log10_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_last_good_h := 0.1;
glob_not_yet_start_msg := true;
glob_subiter_method := 3;
glob_initial_pass := true;
centuries_in_millinium := 10.0;
hours_in_day := 24.0;
glob_small_float := 0.1*10^(-50);
glob_max_iter := 1000;
glob_unchanged_h_cnt := 0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_percent_done := 0.;
glob_max_sec := 10000.0;
glob_no_eqs := 0;
glob_max_trunc_err := 0.1*10^(-10);
glob_h := 0.1;
glob_clock_start_sec := 0.;
years_in_century := 100.0;
glob_current_iter := 0;
glob_relerr := 0.1*10^(-10);
glob_clock_sec := 0.;
djd_debug2 := true;
glob_max_minutes := 0.;
glob_start := 0;
glob_warned2 := false;
glob_warned := false;
glob_look_poles := false;
glob_almost_1 := 0.9990;
glob_orig_start_sec := 0.;
glob_optimal_done := false;
days_in_year := 365.0;
min_in_hour := 60.0;
sec_in_min := 60.0;
glob_optimal_expect_sec := 0.1;
MAX_UNCHANGED := 10;
glob_log10_relerr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_disp_incr := 0.1;
glob_display_flag := true;
djd_debug := true;
glob_dump := false;
glob_log10abserr := 0.;
glob_normmax := 0.;
glob_iter := 0;
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_hmin := 0.1*10^(-10);
glob_html_log := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest6_revpostode.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, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "# was complicatedrev.ode");
omniout_str(ALWAYS, "#");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x1_init[1 + 1] := exact_soln_x1p(t_start);")
;
omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[1 + 1] := 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 := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x1p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "- 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 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "1.0 + 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 := 1.0;");
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_x2 := Array(1 .. max_terms + 1, []);
array_x1 := 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_last_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_set_initial := 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_x1_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_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_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[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_type_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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[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_complex_pole[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_x1_set_initial[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_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_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_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 <= 3 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;
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_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_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_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[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_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_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_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_x1_init[2] := exact_soln_x1p(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 := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
array_x2_set_initial[1, 1] := true;
array_x2_set_initial[1, 2] := true;
array_x2_set_initial[1, 3] := false;
array_x2_set_initial[1, 4] := false;
array_x2_set_initial[1, 5] := false;
array_x2_set_initial[1, 6] := false;
array_x2_set_initial[1, 7] := false;
array_x2_set_initial[1, 8] := false;
array_x2_set_initial[1, 9] := false;
array_x2_set_initial[1, 10] := false;
array_x2_set_initial[1, 11] := false;
array_x2_set_initial[1, 12] := false;
array_x2_set_initial[1, 13] := false;
array_x2_set_initial[1, 14] := false;
array_x2_set_initial[1, 15] := false;
array_x2_set_initial[1, 16] := false;
array_x2_set_initial[1, 17] := false;
array_x2_set_initial[1, 18] := false;
array_x2_set_initial[1, 19] := false;
array_x2_set_initial[1, 20] := false;
array_x2_set_initial[1, 21] := false;
array_x2_set_initial[1, 22] := false;
array_x2_set_initial[1, 23] := false;
array_x2_set_initial[1, 24] := false;
array_x2_set_initial[1, 25] := false;
array_x2_set_initial[1, 26] := false;
array_x2_set_initial[1, 27] := false;
array_x2_set_initial[1, 28] := false;
array_x2_set_initial[1, 29] := false;
array_x2_set_initial[1, 30] := false;
array_x1_set_initial[2, 1] := true;
array_x1_set_initial[2, 2] := true;
array_x1_set_initial[2, 3] := false;
array_x1_set_initial[2, 4] := false;
array_x1_set_initial[2, 5] := false;
array_x1_set_initial[2, 6] := false;
array_x1_set_initial[2, 7] := false;
array_x1_set_initial[2, 8] := false;
array_x1_set_initial[2, 9] := false;
array_x1_set_initial[2, 10] := false;
array_x1_set_initial[2, 11] := false;
array_x1_set_initial[2, 12] := false;
array_x1_set_initial[2, 13] := false;
array_x1_set_initial[2, 14] := false;
array_x1_set_initial[2, 15] := false;
array_x1_set_initial[2, 16] := false;
array_x1_set_initial[2, 17] := false;
array_x1_set_initial[2, 18] := false;
array_x1_set_initial[2, 19] := false;
array_x1_set_initial[2, 20] := false;
array_x1_set_initial[2, 21] := false;
array_x1_set_initial[2, 22] := false;
array_x1_set_initial[2, 23] := false;
array_x1_set_initial[2, 24] := false;
array_x1_set_initial[2, 25] := false;
array_x1_set_initial[2, 26] := false;
array_x1_set_initial[2, 27] := false;
array_x1_set_initial[2, 28] := false;
array_x1_set_initial[2, 29] := false;
array_x1_set_initial[2, 30] := false;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_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 := 2;
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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 3 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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;
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;
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)!;
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;
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)!;
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;
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)!;
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;
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)!;
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;
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)!;
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;
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 := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[3, iii] := array_x1_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_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)!;
ord := 2;
calc_term := 2;
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;
temp_sum := 0.;
ord := 2;
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)!;
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;
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)!;
ord := 1;
calc_term := 3;
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;
temp_sum := 0.;
ord := 1;
calc_term := 3;
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)!;
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;
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)!;
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;
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, "2012-06-13T03:00:47-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest6_rev");
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, " 090 | ");
logitem_str(html_log_file, "mtest6_rev diffeq.mxt");
logitem_str(html_log_file, "mtest6_rev maple results");
logitem_str(html_log_file,
"Test of revised logic - mostly affecting systems of eqs");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff (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/mtest6_revpostode.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
#
# was complicatedrev.ode
#
t_start := 0.5;
t_end := 5.0;
array_x1_init[0 + 1] := exact_soln_x1(t_start);
array_x1_init[1 + 1] := exact_soln_x1p(t_start);
array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := 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 := 0.0001 ;
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 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
1.0 + 2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
- 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
1.0 + c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 1.0;
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) = 2.0007256155636055990741531973548
x2[1] (numeric) = 2.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
h = 0.0001
x1[1] (analytic) = 3.001091755187482740162486839163
x1[1] (numeric) = 3.001091755187482740162486839163
absolute error = 0
relative error = 0 %
h = 0.0001
t[1] = 0.5
x2[1] (analytic) = 2.0007256155636055990741531973548
x2[1] (numeric) = 2.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
h = 0.0001
x1[1] (analytic) = 3.001091755187482740162486839163
x1[1] (numeric) = 3.001091755187482740162486839163
absolute error = 0
relative error = 0 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.21
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 2.0007257061107425639459896605159
x2[1] (numeric) = 2.0007257011153643353864612335881
absolute error = 4.9953782285595284269278e-09
relative error = 2.4967831488855915461522379994911e-07 %
h = 0.0001
x1[1] (analytic) = 3.0010916460174225858712352664712
x1[1] (numeric) = 3.0010916560067727215008266624966
absolute error = 9.9893501356295913960254e-09
relative error = 3.3285721710251293877171755932824e-07 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.4MB, time=0.48
memory used=11.4MB, alloc=4.5MB, time=0.77
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 2.0007257966814495432344339416603
x2[1] (numeric) = 2.0007257766964922309278518366111
absolute error = 1.99849573123065821050492e-08
relative error = 9.9888537177133903968906655509262e-07 %
h = 0.0001
x1[1] (analytic) = 3.0010915368582788917633066026401
x1[1] (numeric) = 3.0010915768291406277631439384486
absolute error = 3.99708617359998373358085e-08
relative error = 1.3318774600871958952379931288251e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.5MB, time=1.04
NO POLE
NO POLE
t[1] = 0.5003
x2[1] (analytic) = 2.0007258872757307055634980331085
x2[1] (numeric) = 2.0007258423019961384481191417913
absolute error = 4.49737345671153788913172e-08
relative error = 2.2478708779218843915256838296736e-06 %
h = 0.0001
x1[1] (analytic) = 3.0010914277100505662472629969306
x1[1] (numeric) = 3.0010915176565853304214059875617
absolute error = 8.99465347641741429906311e-08
relative error = 2.9971274428252539409122863375084e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.6MB, time=1.31
memory used=22.8MB, alloc=4.6MB, time=1.60
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 2.0007259778935902204455844087623
x2[1] (numeric) = 2.0007258979268816125707643515641
absolute error = 7.99667086078748200571982e-08
relative error = 3.9968846054603433631685930316760e-06 %
h = 0.0001
x1[1] (analytic) = 3.001091318572736517840820284614
x1[1] (numeric) = 3.0010914784911059004451523859818
absolute error = 1.599183693826043321013678e-07
relative error = 5.3286738858269247387356422877830e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.6MB, time=1.88
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 2.0007260685350322582816582620126
x2[1] (numeric) = 2.0007259435661529095035171680427
absolute error = 1.249688793487781410939699e-07
relative error = 6.2461763913678902738712398140542e-06 %
h = 0.0001
x1[1] (analytic) = 3.001091209446335655170837072148
x1[1] (numeric) = 3.0010914593347016083213566057672
absolute error = 2.498883659531505195336192e-07
relative error = 8.3265835162421419242860776700606e-06 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.6MB, time=2.15
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 2.0007261592000609903614197786446
x2[1] (numeric) = 2.0007259792148129867487963653838
absolute error = 1.799852480036126234132608e-07
relative error = 8.9959961375011513730950786241284e-06 %
h = 0.0001
x1[1] (analytic) = 3.0010911003308468869733038234462
x1[1] (numeric) = 3.0010914601893719240742896227248
absolute error = 3.598585250371009857992786e-07
relative error = 1.1990923067861198552416354341961e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.6MB, time=2.42
memory used=38.1MB, alloc=4.6MB, time=2.72
NO POLE
NO POLE
t[1] = 0.5007
x2[1] (analytic) = 2.0007262498886805888634764447463
x2[1] (numeric) = 2.0007260048678635028141094894452
absolute error = 2.450208170860493669553011e-07
relative error = 1.2246593810606633619644383900098e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010909912262691220933319472376
x1[1] (numeric) = 3.0010914810571165172853854919654
absolute error = 4.898308473951920535447278e-07
relative error = 1.6321759281115410609326674455606e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.6MB, time=2.99
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 2.0007263406008952268555153896278
x2[1] (numeric) = 2.0007260205203048169223916722684
absolute error = 3.200805904099331237173594e-07
relative error = 1.5998219442335156476547231962628e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010908821326012694851428855176
x1[1] (numeric) = 3.0010915219399352571131088913724
absolute error = 6.398073339876279660058548e-07
relative error = 2.1319158903077780590078737915743e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.6MB, time=3.27
memory used=49.5MB, alloc=4.6MB, time=3.55
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 2.0007264313367090782944757637584
x2[1] (numeric) = 2.000726026167135988722283548917
absolute error = 4.051695730895721922148414e-07
relative error = 2.0251123129256286722292177246485e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010907730498422382120572030903
x1[1] (numeric) = 3.0010915828398282123128246331756
absolute error = 8.097899859741007674300853e-07
relative error = 2.6983188687463661141557572960993e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=3.83
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 2.0007265220961263180267211517279
x2[1] (numeric) = 2.0007260218033547779983482641991
absolute error = 5.002927715400283728875288e-07
relative error = 2.5005555032872776279030240107841e-05 %
h = 0.0001
x1[1] (analytic) = 3.001090663977990937446483678202
x1[1] (numeric) = 3.001091663758795651256669143824
absolute error = 9.997808047138101854656220e-07
relative error = 3.3313915394631418770887620633644e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.6MB, time=4.10
NO POLE
NO POLE
t[1] = 0.5011
x2[1] (analytic) = 2.0007266128791511217882120202398
x2[1] (numeric) = 2.0007260074239576443812275567997
absolute error = 6.054551934774069844634401e-07
relative error = 3.0261765379635003058351992003446e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010905549170462764699083942649
x1[1] (numeric) = 3.0010917646988380419534239123498
absolute error = 1.2097817917654835155180849e-06
relative error = 4.0311405791583097619309527245136e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.6MB, time=4.38
memory used=64.8MB, alloc=4.6MB, time=4.67
NO POLE
NO POLE
t[1] = 0.5012
x2[1] (analytic) = 2.000726703685787666204678201143
x2[1] (numeric) = 2.0007259830239397470577369083458
absolute error = 7.206618479191469412927972e-07
relative error = 3.6020004460955414825249627419352e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010904458670071646728838326719
x1[1] (numeric) = 3.0010918856619560520683909074176
absolute error = 1.4397949488873955070747457e-06
relative error = 4.7975726651965083301524095610830e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.6MB, time=4.95
NO POLE
NO POLE
t[1] = 0.5013
x2[1] (analytic) = 2.0007267945160401287917914095088
x2[1] (numeric) = 2.0007259485982949444808997449253
absolute error = 8.459177451843108916645835e-07
relative error = 4.2280522633222976080873995512731e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010903368278725115550179667025
x1[1] (numeric) = 3.0010920266501505489432699632507
absolute error = 1.6898222780373882519965482e-06
relative error = 5.6306944756068766810509805840835e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.6MB, time=5.22
memory used=76.2MB, alloc=4.6MB, time=5.51
NO POLE
NO POLE
t[1] = 0.5014
x2[1] (analytic) = 2.0007268853699126879553377967599
x2[1] (numeric) = 2.0007259041420157940799206785779
absolute error = 9.812278968938754171181820e-07
relative error = 4.9043570317817617964696697995377e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010902277996412267249633565185
x1[1] (numeric) = 3.0010921876654225996160381346285
absolute error = 1.9598657813728910747781100e-06
relative error = 6.5305126890831208487820429764471e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.6MB, time=5.79
NO POLE
NO POLE
t[1] = 0.5015
x2[1] (analytic) = 2.0007269762474095229913905388596
x2[1] (numeric) = 2.0007258496500935519700977762729
absolute error = 1.1265973159710212927625867e-06
relative error = 5.6309398001124691176687593313273e-05 %
h = 0.0001
x1[1] (analytic) = 3.001090118782312219900406245251
x1[1] (numeric) = 3.0010923687097734708408310211475
absolute error = 2.2499274612509404247758965e-06
relative error = 7.4970339849835802059369119783263e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.6MB, time=6.06
NO POLE
NO POLE
memory used=87.7MB, alloc=4.6MB, time=6.34
t[1] = 0.5016
x2[1] (analytic) = 2.0007270671485348140864824595667
x2[1] (numeric) = 2.0007257851175181726626738438882
absolute error = 1.2820310166414238086156785e-06
relative error = 6.4078256234549421920117935825066e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010900097758844009080556561764
x1[1] (numeric) = 3.0010925697852046291078260609394
absolute error = 2.5600093202281997704047630e-06
relative error = 8.5302650433312938736705512887943e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.6MB, time=6.64
NO POLE
NO POLE
t[1] = 0.5017
x2[1] (analytic) = 2.000727158073292742317778688764
x2[1] (numeric) = 2.0007257105392783087746267126998
absolute error = 1.4475340144335431519760642e-06
relative error = 7.2350395634531370865599742155319e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010899007803566796836324909845
x1[1] (numeric) = 3.001092790893717740663127794039
absolute error = 2.8901133610609794953030545e-06
relative error = 9.6302125448140671383792183981859e-05 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.6MB, time=6.91
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 2.0007272490216874896532493558668
x2[1] (numeric) = 2.000725625910361310738398515891
absolute error = 1.6231113261789148508399758e-06
relative error = 8.1126066882558895136971900528569e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010897917957279662718586291348
x1[1] (numeric) = 3.0010930320373146715286550955952
absolute error = 3.2402415867052567964664604e-06
relative error = 0.00010796883170784537874928703589327 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.6MB, time=7.19
memory used=102.9MB, alloc=4.6MB, time=7.48
NO POLE
NO POLE
t[1] = 0.5019
x2[1] (analytic) = 2.0007273399937232389518423183184
x2[1] (numeric) = 2.0007255312257532265115639425858
absolute error = 1.8087679700124402783757326e-06
relative error = 9.0405520725183613319643797395834e-05 %
h = 0.0001
x1[1] (analytic) = 3.0010896828219971708264460283046
x1[1] (numeric) = 3.0010932932179974875220303791187
absolute error = 3.6103960003166955843508141e-06
relative error = 0.00012030283603260242976433797354466 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.6MB, time=7.76
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 2.0007274309894041739636559251805
x2[1] (numeric) = 2.0007254264804388012864374569104
absolute error = 2.0045089653726772184682701e-06
relative error = 0.00010018900797403487349200730423701 %
h = 0.0001
x1[1] (analytic) = 3.0010895738591632036100858259251
x1[1] (numeric) = 3.0010935744377684542764707699585
absolute error = 4.0005786052506663849440334e-06
relative error = 0.00013330420524923684790589640634121 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.6MB, time=8.04
memory used=114.4MB, alloc=4.6MB, time=8.32
NO POLE
NO POLE
t[1] = 0.5021
x2[1] (analytic) = 2.0007275220087344793301118158238
x2[1] (numeric) = 2.0007253116694014771996194695823
absolute error = 2.2103393330021304923462415e-06
relative error = 0.0001104767795058342242805280509864 %
h = 0.0001
x1[1] (analytic) = 3.0010894649072249749944374418092
x1[1] (numeric) = 3.0010938756986300372606812492015
absolute error = 4.4107914050622662438073923e-06
relative error = 0.00014697300619122397562555594623657 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.6MB, time=8.60
NO POLE
NO POLE
t[1] = 0.5022
x2[1] (analytic) = 2.0007276130517183405841277537279
x2[1] (numeric) = 2.0007251867876233930414814495262
absolute error = 2.4262640949475426463042017e-06
relative error = 0.00012126908626240988893912711104737 %
h = 0.0001
x1[1] (analytic) = 3.0010893559661813954601176818676
x1[1] (numeric) = 3.0010941970025849017987497681878
absolute error = 4.8410364035063386320863202e-06
relative error = 0.00016130930569869013884392284886742 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.6MB, time=8.88
NO POLE
NO POLE
t[1] = 0.5023
x2[1] (analytic) = 2.0007277041183599441502904953943
x2[1] (numeric) = 2.0007250518300853839655899630107
absolute error = 2.6522882745601847005323836e-06
relative error = 0.00013256617925071124245346421145519 %
h = 0.0001
x1[1] (analytic) = 3.001089247036031375596689842915
x1[1] (numeric) = 3.0010945383516359130900443338351
absolute error = 5.2913156045374933544909201e-06
relative error = 0.00017631317061841331151052459853348 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.6MB, time=9.15
memory used=129.7MB, alloc=4.6MB, time=9.44
NO POLE
NO POLE
t[1] = 0.5024
x2[1] (analytic) = 2.0007277952086634773450286943839
x2[1] (numeric) = 2.0007249067917669811980696277997
absolute error = 2.8884168964961469590665842e-06
relative error = 0.00014436830954282329167073396019443 %
h = 0.0001
x1[1] (analytic) = 3.001089138116773826102652818566
x1[1] (numeric) = 3.0010948997477861362291120649652
absolute error = 5.7616310123101264592463992e-06
relative error = 0.00019198466780382378022926309777651 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.6MB, time=9.73
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 2.0007278863226331283767858404813
x2[1] (numeric) = 2.0007247516676464117469049698087
absolute error = 3.1346549867166298808706726e-06
relative error = 0.00015667572827598115845558630636137 %
h = 0.0001
x1[1] (analytic) = 3.0010890292084076577854302062196
x1[1] (numeric) = 3.0010952811930388362255802198265
absolute error = 6.2519846311784401500136069e-06
relative error = 0.0002083238641150048089494189756244 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.6MB, time=10.00
memory used=141.1MB, alloc=4.6MB, time=10.28
NO POLE
NO POLE
t[1] = 0.5026
x2[1] (analytic) = 2.0007279774602730863461932339965
x2[1] (numeric) = 2.0007245864527005981111811697531
absolute error = 3.3910075724882350120642434e-06
relative error = 0.00016948868665258456587278301223639 %
h = 0.0001
x1[1] (analytic) = 3.0010889203109317815613594151339
x1[1] (numeric) = 3.0010956826893974780240591950046
absolute error = 6.7623784656964626997798707e-06
relative error = 0.00022533082641869330372221337861953 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.6MB, time=10.56
NO POLE
NO POLE
t[1] = 0.5027
x2[1] (analytic) = 2.000728068621587541246242995209
x2[1] (numeric) = 2.0007244111419051579902636872749
absolute error = 3.6574796823832559793079341e-06
relative error = 0.00018280743594021232739720166500053 %
h = 0.0001
x1[1] (analytic) = 3.0010888114243451084556807755893
x1[1] (numeric) = 3.0010961042388657265240474959158
absolute error = 7.2928145206180683667203265e-06
relative error = 0.00024300562158828047752293380867672 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.6MB, time=10.84
NO POLE
NO POLE
t[1] = 0.5028
x2[1] (analytic) = 2.0007281598065806839624611089617
x2[1] (numeric) = 2.0007242257302344039929167500296
absolute error = 3.9340763462799695443589321e-06
relative error = 0.00019663222747163683915179909927934 %
h = 0.0001
x1[1] (analytic) = 3.0010887025486465496025266491408
x1[1] (numeric) = 3.0010965458434474465998386790756
absolute error = 7.8432948008969973120299348e-06
relative error = 0.00026134831650381251513863040520838 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.6MB, time=11.11
memory used=156.4MB, alloc=4.7MB, time=11.40
NO POLE
NO POLE
t[1] = 0.5029
x2[1] (analytic) = 2.0007282510152567062730805044118
x2[1] (numeric) = 2.0007240302126613433463606952141
absolute error = 4.2208025953629267198091977e-06
relative error = 0.00021096331264483857517414613525726 %
h = 0.0001
x1[1] (analytic) = 3.0010885936838350162449105399592
x1[1] (numeric) = 3.001097007505146703120430266336
absolute error = 8.4138213116868755197263768e-06
relative error = 0.00028035897805199123812138915225629 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.7MB, time=11.68
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 2.0007283422476198008492141699459
x2[1] (numeric) = 2.0007238245841576776052681510129
absolute error = 4.5176634621232439460189330e-06
relative error = 0.00022580094292302058571214570561259 %
h = 0.0001
x1[1] (analytic) = 3.0010884848299094197347162072617
x1[1] (numeric) = 3.001097489225967760969434631285
absolute error = 9.0043960583412347184240233e-06
relative error = 0.00030003767312617476980718845471468 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.7MB, time=11.95
memory used=167.8MB, alloc=4.7MB, time=12.23
NO POLE
NO POLE
t[1] = 0.5031
x2[1] (analytic) = 2.0007284335036741612550283032656
x2[1] (numeric) = 2.0007236088396938023606990454384
absolute error = 4.8246639803588943292578272e-06
relative error = 0.00024114536983462299854954646808129 %
h = 0.0001
x1[1] (analytic) = 3.0010883759868686715326867788304
x1[1] (numeric) = 3.0010979910079150850649918580018
absolute error = 9.6150210464135323050791714e-06
relative error = 0.00032038446862637820040034559770259 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.7MB, time=12.51
NO POLE
NO POLE
t[1] = 0.5032
x2[1] (analytic) = 2.0007285247834239819479154966509
x2[1] (numeric) = 2.000723382974238806948974430037
absolute error = 5.1418091851749989410666139e-06
relative error = 0.00025699684497333752336186424893023 %
h = 0.0001
x1[1] (analytic) = 3.0010882671547116832084138656195
x1[1] (numeric) = 3.0010985128529933403796845723605
absolute error = 1.02456982816571712707067410e-05
relative error = 0.00034139943145927425212355950317828 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.7MB, time=12.79
NO POLE
NO POLE
t[1] = 0.5033
x2[1] (analytic) = 2.0007286160868734582786679574086
x2[1] (numeric) = 2.0007231469827604741604891059317
absolute error = 5.4691041129841181788514769e-06
relative error = 0.00027335561999812195910332370116704 %
h = 0.0001
x1[1] (analytic) = 3.0010881583334373664403266774516
x1[1] (numeric) = 3.0010990547632073919604547460762
absolute error = 1.08964297700255201280686246e-05
relative error = 0.00036308262853819394443355624786891 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.7MB, time=13.06
memory used=183.1MB, alloc=4.7MB, time=13.36
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 2.0007287074140267864916507635123
x2[1] (numeric) = 2.000722900860225279948463039669
absolute error = 5.8065538015065431877238433e-06
relative error = 0.00029022194663321470442543266983201 %
h = 0.0001
x1[1] (analytic) = 3.0010880495230446330156811398021
x1[1] (numeric) = 3.0010996167405623049485224736871
absolute error = 1.15672175176719328413338850e-05
relative error = 0.00038543412678312725930234384324101 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.7MB, time=13.63
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 2.0007287987648881637249751544417
x2[1] (numeric) = 2.0007226446015983931376315563345
absolute error = 6.1541632897705873435981072e-06
relative error = 0.0003075960766681492711278019751926 %
h = 0.0001
x1[1] (analytic) = 3.0010879407235323948305490116711
x1[1] (numeric) = 3.0011001987870633445993067226653
absolute error = 1.22580635309497687577109942e-05
relative error = 0.00040845399312072380656408273491791 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.7MB, time=13.91
memory used=194.5MB, alloc=4.7MB, time=14.20
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 2.0007288901394617880106718572265
x2[1] (numeric) = 2.0007223782018436751328742973996
absolute error = 6.5119376181128777975598269e-06
relative error = 0.00032547826195776880064182329822305 %
h = 0.0001
x1[1] (analytic) = 3.0010878319348995638898070045447
x1[1] (numeric) = 3.0011008009047159763023480568508
absolute error = 1.29689698164124125410523061e-05
relative error = 0.00043214229448429348932757845562427 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.7MB, time=14.47
NO POLE
NO POLE
t[1] = 0.5037
x2[1] (analytic) = 2.0007289815377518582748644477049
x2[1] (numeric) = 2.0007221016559236796277829307605
absolute error = 6.8798818281786470815169444e-06
relative error = 0.00034386875442224058354781814119526 %
h = 0.0001
x1[1] (analytic) = 3.0010877231571450523071259024436
x1[1] (numeric) = 3.001101423095525865601233333401
absolute error = 1.36999383808132941074309574e-05
relative error = 0.0004564990978138071694544029257146 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.7MB, time=14.75
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 2.0007290729597625743379427469999
x2[1] (numeric) = 2.0007218149587996523131676004251
absolute error = 7.2580009629220247751465748e-06
relative error = 0.00036276780604707058212627076977874 %
h = 0.0001
x1[1] (analytic) = 3.0010876143902677723049596830596
x1[1] (numeric) = 3.0011020653614988782135223734502
absolute error = 1.44509712311059085626903906e-05
relative error = 0.00048152447005589733310265087868094 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.7MB, time=15.02
memory used=209.8MB, alloc=4.7MB, time=15.31
NO POLE
NO POLE
t[1] = 0.5039
x2[1] (analytic) = 2.0007291644054981369147362532235
x2[1] (numeric) = 2.0007215181054315305855021033043
absolute error = 7.6463000666063292341499192e-06
relative error = 0.00038217566888311795594375833648284 %
h = 0.0001
x1[1] (analytic) = 3.0010875056342666362145346399805
x1[1] (numeric) = 3.001102727704641080050676606672
absolute error = 1.52220703744438361419666915e-05
relative error = 0.00050721847816385875633633783905114 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.7MB, time=15.58
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 2.0007292558749627476146876084142
x2[1] (numeric) = 2.0007212110907779432553077805589
absolute error = 8.0447841848043593798278553e-06
relative error = 0.00040209259504660959047419140880803 %
h = 0.0001
x1[1] (analytic) = 3.0010873968891405564758385060019
x1[1] (numeric) = 3.0011034101269587372379896899386
absolute error = 1.60132378181807621511839367e-05
relative error = 0.00053358118909764917080044618338419 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.7MB, time=15.86
memory used=221.2MB, alloc=4.7MB, time=16.14
NO POLE
NO POLE
t[1] = 0.5041
x2[1] (analytic) = 2.0007293473681606089420261007159
x2[1] (numeric) = 2.0007208939097962102554761109527
absolute error = 8.4534583643986865499897632e-06
relative error = 0.00042251883671915462875597828395208 %
h = 0.0001
x1[1] (analytic) = 3.0010872881548884456376095775276
x1[1] (numeric) = 3.0011041126304583161345201002703
absolute error = 1.68244755698704969105227427e-05
relative error = 0.00056061266982388992946162568511453 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.7MB, time=16.42
NO POLE
NO POLE
t[1] = 0.5042
x2[1] (analytic) = 2.0007294388850959242959412018029
x2[1] (numeric) = 2.0007205665574423423495299936585
absolute error = 8.8723276535819464112081444e-06
relative error = 0.00044345464614775900608572649044672 %
h = 0.0001
x1[1] (analytic) = 3.0010871794315092163573258400565
x1[1] (numeric) = 3.0011048352171464833530257022683
absolute error = 1.76557856372669956998622118e-05
relative error = 0.0005883129873158666724145550639524 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.7MB, time=16.70
NO POLE
NO POLE
memory used=232.7MB, alloc=4.7MB, time=16.98
t[1] = 0.5043
x2[1] (analytic) = 2.0007295304257728979707561395621
x2[1] (numeric) = 2.0007202290286710408398237079618
absolute error = 9.3013971018571309324316003e-06
relative error = 0.00046490027564483998774909528548233 %
h = 0.0001
x1[1] (analytic) = 3.0010870707190017814011940947576
x1[1] (numeric) = 3.0011055778890301057799002902256
absolute error = 1.85071700283243787061954680e-05
relative error = 0.00061668220855352999275397099390363 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.7MB, time=17.26
NO POLE
NO POLE
t[1] = 0.5044
x2[1] (analytic) = 2.000729621990195735156101506034
x2[1] (numeric) = 2.0007198813184356972756815373051
absolute error = 9.7406717600378804199687289e-06
relative error = 0.00048685597758824070978941257035049 %
h = 0.0001
x1[1] (analytic) = 3.001086962017365053644139086132
x1[1] (numeric) = 3.0011063406481162505951121051085
absolute error = 1.93786307511969509730189765e-05
relative error = 0.00064572040052349610251237103729905 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.7MB, time=17.54
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 2.0007297135783686419370889006249
x2[1] (numeric) = 2.0007195234216883931614750451113
absolute error = 1.01901566802487756138555136e-05
relative error = 0.00050932200442124472281467039968436 %
h = 0.0001
x1[1] (analytic) = 3.0010868533265979460697926307621
x1[1] (numeric) = 3.0011071234964121852921443266027
absolute error = 2.02701698142392223516958406e-05
relative error = 0.000675427630219047498663396978887 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.7MB, time=17.82
memory used=247.9MB, alloc=4.7MB, time=18.10
NO POLE
NO POLE
t[1] = 0.5046
x2[1] (analytic) = 2.0007298051902958252944846085935
x2[1] (numeric) = 2.0007191553333798996646389898241
absolute error = 1.06498569159256298456187694e-05
relative error = 0.00053229860865259053884351282386162 %
h = 0.0001
x1[1] (analytic) = 3.0010867446466993717704827471482
x1[1] (numeric) = 3.0011079264359253776979375404177
absolute error = 2.11817892260059274547932695e-05
relative error = 0.00070580396464013362919090502404427 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.7MB, time=18.38
NO POLE
NO POLE
t[1] = 0.5047
x2[1] (analytic) = 2.0007298968259814931048833148203
x2[1] (numeric) = 2.0007187770484596773236258665998
absolute error = 1.11197775218157812574482205e-05
relative error = 0.00055578604285648618119083023229862 %
h = 0.0001
x1[1] (analytic) = 3.0010866359776682439472227866313
x1[1] (numeric) = 3.0011087494686634959928341810434
absolute error = 2.21134909952520456113944121e-05
relative error = 0.0007368494707933715592237293784739 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.7MB, time=18.66
NO POLE
NO POLE
memory used=259.4MB, alloc=4.7MB, time=18.94
t[1] = 0.5048
x2[1] (analytic) = 2.0007299884854298541408818528671
x2[1] (numeric) = 2.0007183885618758757557990630827
absolute error = 1.15999235539783850827897844e-05
relative error = 0.00057978455967262373739357441386523 %
h = 0.0001
x1[1] (analytic) = 3.0010865273195034759097005654036
x1[1] (numeric) = 3.0011095925966344087305249501521
absolute error = 2.30652771309328208243847485e-05
relative error = 0.000768564215692046637236145613464 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.7MB, time=19.23
NO POLE
NO POLE
t[1] = 0.5049
x2[1] (analytic) = 2.0007300801686451180712529893331
x2[1] (numeric) = 2.0007179898685753333652646166927
absolute error = 1.20903000697847059883726404e-05
relative error = 0.00060429441180619391517740868411672 %
h = 0.0001
x1[1] (analytic) = 3.0010864186722039810762674976051
x1[1] (numeric) = 3.0011104558218461848579972108397
absolute error = 2.40371496422037817297132346e-05
relative error = 0.00080094826635611316131404034406985 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.7MB, time=19.52
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 2.0007301718756314954611192435145
x2[1] (numeric) = 2.0007175809635035770506415608534
absolute error = 1.25909121279184104776826611e-05
relative error = 0.00062931585202790060146480745754155 %
h = 0.0001
x1[1] (analytic) = 3.0010863100357686729739277295073
x1[1] (numeric) = 3.0011113391463070937354853579002
absolute error = 2.50291105384207615576283929e-05
relative error = 0.00083400168981219504548679367094041 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.7MB, time=19.79
memory used=274.6MB, alloc=4.7MB, time=20.07
NO POLE
NO POLE
t[1] = 0.5051
x2[1] (analytic) = 2.0007302636063931977721267423749
x2[1] (numeric) = 2.0007171618416048219127708475841
absolute error = 1.31017647883758593558947908e-05
relative error = 0.00065484913317397542442521990143891 %
h = 0.0001
x1[1] (analytic) = 3.0010862014101964652383272747832
x1[1] (numeric) = 3.0011122425720256051564231643269
absolute error = 2.60411618291399180958895437e-05
relative error = 0.00086772455309358648612488087316308 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.7MB, time=20.35
NO POLE
NO POLE
t[1] = 0.5052
x2[1] (analytic) = 2.0007303553609344373626191108334
x2[1] (numeric) = 2.0007167324978219709623628338777
absolute error = 1.36228631124664002562769557e-05
relative error = 0.00068089450814619231856791235153157 %
h = 0.0001
x1[1] (analytic) = 3.0010860927954862716137431508637
x1[1] (numeric) = 3.0011131661010103893673981042343
absolute error = 2.70733055241177536549533706e-05
relative error = 0.00090211692324025262840319982950248 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.7MB, time=20.62
memory used=286.1MB, alloc=4.7MB, time=20.91
NO POLE
NO POLE
t[1] = 0.5053
x2[1] (analytic) = 2.0007304471392594274878113973781
x2[1] (numeric) = 2.0007162929270966148275833192844
absolute error = 1.41542121628126602280780937e-05
relative error = 0.00070745222991188209287810430787265 %
h = 0.0001
x1[1] (analytic) = 3.0010859841916370059530725163803
x1[1] (numeric) = 3.0011141097352703170881076523941
absolute error = 2.81255436333111350351360138e-05
relative error = 0.00093717886729883023283013063207923 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.7MB, time=21.18
NO POLE
NO POLE
t[1] = 0.5054
x2[1] (analytic) = 2.0007305389413723822999640350102
x2[1] (numeric) = 2.0007158431243690314615781221169
absolute error = 1.46958170033508383859128933e-05
relative error = 0.00073452255150394700199701290807868 %
h = 0.0001
x1[1] (analytic) = 3.0010858755986475822178218096944
x1[1] (numeric) = 3.0011150734768144595313175605793
absolute error = 2.91978781668773134957508849e-05
relative error = 0.0009729104523226283418423338631974 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.7MB, time=21.47
NO POLE
NO POLE
t[1] = 0.5055
x2[1] (analytic) = 2.000730630767277516848556837528
x2[1] (numeric) = 2.0007153830845781858499361816928
absolute error = 1.52476826993309986206558352e-05
relative error = 0.00076210572602087532044642097334608 %
h = 0.0001
x1[1] (analytic) = 3.0010857670165169144780958885117
x1[1] (numeric) = 3.0011160573276520884228221109106
absolute error = 3.02903111351739447262223989e-05
relative error = 0.0010093117453716289464652940726711 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.7MB, time=21.75
memory used=301.3MB, alloc=4.7MB, time=22.03
NO POLE
NO POLE
t[1] = 0.5056
x2[1] (analytic) = 2.0007307226169790470804630311551
x2[1] (numeric) = 2.0007149128026617297180911740239
absolute error = 1.58098143173173623718571312e-05
relative error = 0.00079020200662675591989838376618953 %
h = 0.0001
x1[1] (analytic) = 3.001085658445243916912587170584
x1[1] (numeric) = 3.0011170612897926760214063463982
absolute error = 3.14028445487591088191758142e-05
relative error = 0.0010463828135124876530396148297237 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.7MB, time=22.32
NO POLE
NO POLE
t[1] = 0.5057
x2[1] (analytic) = 2.0007308144904811898401233215242
x2[1] (numeric) = 2.0007144322735560012386616283639
absolute error = 1.63822169251886014616931603e-05
relative error = 0.00081881164655129284949068985723696 %
h = 0.0001
x1[1] (analytic) = 3.0010855498848275038085647754956
x1[1] (numeric) = 3.0011180853652458951388102788737
absolute error = 3.25354804183913302455033781e-05
relative error = 0.0010841237238185343500130719467869 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.7MB, time=22.59
memory used=312.8MB, alloc=4.7MB, time=22.88
NO POLE
NO POLE
t[1] = 0.5058
x2[1] (analytic) = 2.0007309063877881628697199960171
x2[1] (numeric) = 2.0007139414921960247387295320188
absolute error = 1.69648955921381309904639983e-05
relative error = 0.0008479348990898199191886913119778 %
h = 0.0001
x1[1] (analytic) = 3.001085441335266589561863667536
x1[1] (numeric) = 3.0011191295560216191596950745048
absolute error = 3.36882207550295978314069688e-05
relative error = 0.0011225345433697738747984312559335 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.7MB, time=23.16
NO POLE
NO POLE
t[1] = 0.5059
x2[1] (analytic) = 2.0007309983089041848093510614748
x2[1] (numeric) = 2.0007134404535155104070574108255
absolute error = 1.75578553886744022936506493e-05
relative error = 0.00087757201760331528619411900662502 %
h = 0.0001
x1[1] (analytic) = 3.0010853327965600886768737996586
x1[1] (numeric) = 3.001120193864129922061611217088
absolute error = 3.48610675698333847374174294e-05
relative error = 0.0011616153392528866806970374686261 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.7MB, time=23.44
NO POLE
NO POLE
t[1] = 0.506
x2[1] (analytic) = 2.0007310902538334751972044172794
x2[1] (numeric) = 2.0007129291524468540012438726996
absolute error = 1.81611013866211959605445798e-05
relative error = 0.00090772325551841604440149849088332 %
h = 0.0001
x1[1] (analytic) = 3.0010852242687069157665292585244
x1[1] (numeric) = 3.0011212782915810784349686493126
absolute error = 3.60540228741626684393907882e-05
relative error = 0.0012013661785612295038881806094736 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.7MB, time=23.73
memory used=328.0MB, alloc=4.7MB, time=24.01
NO POLE
NO POLE
t[1] = 0.5061
x2[1] (analytic) = 2.0007311822225802544697320638176
x2[1] (numeric) = 2.0007124075839211365548176016517
absolute error = 1.87746386591179149144621659e-05
relative error = 0.00093838886632743281690278229871783 %
h = 0.0001
x1[1] (analytic) = 3.001085115751705985552297410631
x1[1] (numeric) = 3.0011223828403855635030088921895
absolute error = 3.72670886795779507114815585e-05
relative error = 0.0012417871283948360304842464780357 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.7MB, time=24.29
NO POLE
NO POLE
t[1] = 0.5062
x2[1] (analytic) = 2.0007312742151487439618243463322
x2[1] (numeric) = 2.0007118757428681240842697896674
absolute error = 1.93984722806198775545566648e-05
relative error = 0.00096956910358836435154081463668729 %
h = 0.0001
x1[1] (analytic) = 3.0010850072455562128641680495278
x1[1] (numeric) = 3.0011235075125540531417791428395
absolute error = 3.85002669978402776110933117e-05
relative error = 0.0012828782558604175636516576127038 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.7MB, time=24.57
memory used=339.5MB, alloc=4.7MB, time=24.85
NO POLE
NO POLE
t[1] = 0.5063
x2[1] (analytic) = 2.0007313662315431659069842341678
x2[1] (numeric) = 2.0007113336242162672960249938469
absolute error = 2.00326073268986109592403209e-05
relative error = 0.0010012642209249121195122443279005 %
h = 0.0001
x1[1] (analytic) = 3.0010848987502565126406425441156
x1[1] (numeric) = 3.0011246523100974239001083508346
absolute error = 3.97535598409112594658067190e-05
relative error = 0.0013246396280713636907976112806705 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.7MB, time=25.14
NO POLE
NO POLE
t[1] = 0.5064
x2[1] (analytic) = 2.0007314582717677434375016354202
x2[1] (numeric) = 2.0007107812228927012933504061931
absolute error = 2.06770488750421441512292271e-05
relative error = 0.0010334744720264949170205023979404 %
h = 0.0001
x1[1] (analytic) = 3.0010847902658057999287229880316
x1[1] (numeric) = 3.0011258172350267530195852732868
absolute error = 4.10269692209530908622852552e-05
relative error = 0.0013670713121477429508226209580169 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.7MB, time=25.43
NO POLE
NO POLE
t[1] = 0.5065
x2[1] (analytic) = 2.0007315503358267005846277469922
x2[1] (numeric) = 2.0007102185338232452832035234391
absolute error = 2.13318020034553014242235531e-05
relative error = 0.0010662001106482634699794602427373 %
h = 0.0001
x1[1] (analytic) = 3.0010846817922029898839013501196
x1[1] (numeric) = 3.0011270022893533184545385088774
absolute error = 4.23204971503285706371587578e-05
relative error = 0.0014101733752163035014388677539528 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.7MB, time=25.71
memory used=354.7MB, alloc=4.7MB, time=25.99
NO POLE
NO POLE
t[1] = 0.5066
x2[1] (analytic) = 2.0007316424237242622787494400674
x2[1] (numeric) = 2.0007096455519324022830182043
absolute error = 2.19968717918599957312357674e-05
relative error = 0.0010994413906111150417683850565651 %
h = 0.0001
x1[1] (analytic) = 3.0010845733294469977701486259847
x1[1] (numeric) = 3.0011282074750885988920185110219
absolute error = 4.36341456416011218698850372e-05
relative error = 0.0014539458844104737865543683198753 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.7MB, time=26.27
NO POLE
NO POLE
t[1] = 0.5067
x2[1] (analytic) = 2.0007317345354646543495636810068
x2[1] (numeric) = 2.0007090622721433588274291015325
absolute error = 2.26722633212955221345794743e-05
relative error = 0.0011331985658017080440388089219044 %
h = 0.0001
x1[1] (analytic) = 3.0010844648775367389599039906329
x1[1] (numeric) = 3.001129432794244273771781580364
absolute error = 4.49679167075348118775897311e-05
relative error = 0.0014983889068703632037229656939455 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.7MB, time=26.54
memory used=366.2MB, alloc=4.7MB, time=26.83
NO POLE
NO POLE
t[1] = 0.5068
x2[1] (analytic) = 2.0007318266710521035262519876743
x2[1] (numeric) = 2.0007084686893779846749344561848
absolute error = 2.33579816741188513175314895e-05
relative error = 0.001167471890172476650573928071336 %
h = 0.0001
x1[1] (analytic) = 3.0010843564364711289340639521961
x1[1] (numeric) = 3.0011306782488322233062758367929
absolute error = 4.63218123610943722118845968e-05
relative error = 0.0015435025097427627716601495518716 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.7MB, time=27.10
NO POLE
NO POLE
t[1] = 0.5069
x2[1] (analytic) = 2.0007319188304908374376549212004
x2[1] (numeric) = 2.0007078647985568325144972414135
absolute error = 2.40540319340049231576797869e-05
relative error = 0.0012022616177416454142011492749264 %
h = 0.0001
x1[1] (analytic) = 3.0010842480062490832819715067401
x1[1] (numeric) = 3.0011319438408645285006291711778
absolute error = 4.76958346154452186576644377e-05
relative error = 0.0015892867601811457978247124212235 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.7MB, time=27.39
NO POLE
NO POLE
t[1] = 0.507
x2[1] (analytic) = 2.00073201101378508461244661319
x2[1] (numeric) = 2.000707250594599137672084643245
absolute error = 2.47604191859469403619699450e-05
relative error = 0.0012375680025932438867584000900998 %
h = 0.0001
x1[1] (analytic) = 3.0010841395868695177014052941589
x1[1] (numeric) = 3.0011332295723534711726391770138
absolute error = 4.90899854839534712338828549e-05
relative error = 0.0016357417253456685460662482366656 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.7MB, time=27.66
memory used=381.4MB, alloc=4.7MB, time=27.94
NO POLE
NO POLE
t[1] = 0.5071
x2[1] (analytic) = 2.0007321032209390744793093283805
x2[1] (numeric) = 2.0007066260724228178171458656538
absolute error = 2.54771485162566621634627267e-05
relative error = 0.0012733912988771212421148199743517 %
h = 0.0001
x1[1] (analytic) = 3.0010840311783313479985687551521
x1[1] (numeric) = 3.0011345354453115339727650621734
absolute error = 5.05042669801859741963070213e-05
relative error = 0.0016828674724031709043384998300817 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.7MB, time=28.22
NO POLE
NO POLE
t[1] = 0.5072
x2[1] (analytic) = 2.0007321954519570373671080627591
x2[1] (numeric) = 2.0007059912269444726690282473293
absolute error = 2.62042250125646980798154298e-05
relative error = 0.0013097317608089609022464494295436 %
h = 0.0001
x1[1] (analytic) = 3.0010839227806334900880792892867
x1[1] (numeric) = 3.0011358614617514004041215409578
absolute error = 5.19386811179103160422516711e-05
relative error = 0.001730664068527177052478561799621 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=389.1MB, alloc=4.7MB, time=28.50
memory used=392.9MB, alloc=4.7MB, time=28.79
NO POLE
NO POLE
t[1] = 0.5073
x2[1] (analytic) = 2.0007322877068432045050651771445
x2[1] (numeric) = 2.0007053460530793837033316774986
absolute error = 2.69416537638208017334996459e-05
relative error = 0.0013465896426702951663675343599645 %
h = 0.0001
x1[1] (analytic) = 3.0010838143937748599929574141438
x1[1] (numeric) = 3.0011372076236859548424747066418
absolute error = 5.33932299110948495172924980e-05
relative error = 0.001779131580897896130051945215017 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.7MB, time=29.07
NO POLE
NO POLE
t[1] = 0.5074
x2[1] (analytic) = 2.0007323799856018080229350662418
x2[1] (numeric) = 2.0007046905457415138582012981723
absolute error = 2.76894398602941647337680695e-05
relative error = 0.001383965198808519843118063024714 %
h = 0.0001
x1[1] (analytic) = 3.0010837060177543738446159255482
x1[1] (numeric) = 3.0011385739331282825562398847069
absolute error = 5.48679153739087116239591587e-05
relative error = 0.0018282700767022229042635107264958 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.7MB, time=29.35
NO POLE
NO POLE
t[1] = 0.5075
memory used=404.3MB, alloc=4.7MB, time=29.65
x2[1] (analytic) = 2.0007324722882370809511788631756
x2[1] (numeric) = 2.0007040246998435072405584801751
absolute error = 2.84475883935737106203830005e-05
relative error = 0.0014218586836369088858081530283827 %
h = 0.0001
x1[1] (analytic) = 3.001083597652570947882849058883
x1[1] (numeric) = 3.0011399603920916697264814669562
absolute error = 5.63627395207218436324080732e-05
relative error = 0.0018780796231337384379342764746436 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.7MB, time=29.95
NO POLE
NO POLE
t[1] = 0.5076
x2[1] (analytic) = 2.0007325646147532572211391795107
x2[1] (numeric) = 2.0007033485102966888322700603227
absolute error = 2.92161044565683888691191880e-05
relative error = 0.0014602703516346290307199060223593 %
h = 0.0001
x1[1] (analytic) = 3.0010834892982234984558216514875
x1[1] (numeric) = 3.0011413670025896034669147267061
absolute error = 5.78777043661050110930752186e-05
relative error = 0.0019285602873927107575441073718794 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=411.9MB, alloc=4.7MB, time=30.25
NO POLE
NO POLE
t[1] = 0.5077
x2[1] (analytic) = 2.0007326569651545716652148807651
x2[1] (numeric) = 2.0007026619720110641962558271033
absolute error = 2.99949931435074689590536618e-05
relative error = 0.0014992004573467544384673477075599 %
h = 0.0001
x1[1] (analytic) = 3.0010833809547109420200583061384
x1[1] (numeric) = 3.0011427937666357718439096152485
absolute error = 5.94128119248298238513091101e-05
relative error = 0.0019797121366860955213402922262079 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.7MB, time=30.55
memory used=419.6MB, alloc=4.8MB, time=30.84
NO POLE
NO POLE
t[1] = 0.5078
x2[1] (analytic) = 2.0007327493394452600170358974238
x2[1] (numeric) = 2.0007019650798953191825342422182
absolute error = 3.07842595499408345016552056e-05
relative error = 0.0015386492553842813384150711026736 %
h = 0.0001
x1[1] (analytic) = 3.0010832726220321951404325556154
x1[1] (numeric) = 3.0011442406862440638964965397776
absolute error = 6.09680642118687560639841622e-05
relative error = 0.0020315352382275366875120151546054 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.8MB, time=31.13
NO POLE
NO POLE
t[1] = 0.5079
x2[1] (analytic) = 2.0007328417376295589116380714609
x2[1] (numeric) = 2.0007012578288568196342063853357
absolute error = 3.15839087727392774316861252e-05
relative error = 0.0015786170004241426761562010004593 %
h = 0.0001
x1[1] (analytic) = 3.0010831643001861744901560283501
x1[1] (numeric) = 3.0011457077634285696563741229762
absolute error = 6.25434632423951662180946261e-05
relative error = 0.0020840296592373671824307278333515 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.8MB, time=31.41
NO POLE
NO POLE
memory used=431.0MB, alloc=4.8MB, time=31.69
t[1] = 0.508
x2[1] (analytic) = 2.0007329341597117058856380383748
x2[1] (numeric) = 2.000700540213801611093378109408
absolute error = 3.23939459100947922599289668e-05
relative error = 0.0016191039472092227640502976180315 %
h = 0.0001
x1[1] (analytic) = 3.0010830559891717968507676151575
x1[1] (numeric) = 3.0011471950002035801679189444551
absolute error = 6.41390110317833171513292976e-05
relative error = 0.0021371954669426095689564290759732 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.8MB, time=31.98
NO POLE
NO POLE
t[1] = 0.5081
x2[1] (analytic) = 2.0007330266056959393774081447462
x2[1] (numeric) = 2.0006998122296344185070203938991
absolute error = 3.32143760615208703877508471e-05
relative error = 0.0016601103505483719348218177703747 %
h = 0.0001
x1[1] (analytic) = 3.0010829476889879791121226370521
x1[1] (numeric) = 3.0011487023985835875081972642403
absolute error = 6.57547095956083960746271882e-05
relative error = 0.0021910327285769767148098581761518 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.8MB, time=32.28
NO POLE
NO POLE
t[1] = 0.5082
x2[1] (analytic) = 2.0007331190755864987272514013242
x2[1] (numeric) = 2.0006990738712586459327678832688
absolute error = 3.40452043278527944835180554e-05
relative error = 0.0017016364653164211982197518147786 %
h = 0.0001
x1[1] (analytic) = 3.0010828393996336382723820141458
x1[1] (numeric) = 3.0011502299605832848069787285022
absolute error = 6.73905609496465345967143564e-05
relative error = 0.0022455415113808724610106085962242 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.8MB, time=32.59
memory used=446.3MB, alloc=4.8MB, time=32.88
NO POLE
NO POLE
t[1] = 0.5083
x2[1] (analytic) = 2.0007332115693876241775764716484
x2[1] (numeric) = 2.0006983251335763762446555980564
absolute error = 3.48864358112479329208735920e-05
relative error = 0.0017436825464541969007390548122339 %
h = 0.0001
x1[1] (analytic) = 3.00108273112110769143800143563
x1[1] (numeric) = 3.0011517776882175662667520577212
absolute error = 6.90465671098748287506220912e-05
relative error = 0.0023007218826013922903811684153008 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=450.1MB, alloc=4.8MB, time=33.18
NO POLE
NO POLE
t[1] = 0.5084
x2[1] (analytic) = 2.0007333040871035568730726962129
x2[1] (numeric) = 2.0006975660114883708387938059029
absolute error = 3.57380756151860342788903100e-05
relative error = 0.0017862488489685353884044904851956 %
h = 0.0001
x1[1] (analytic) = 3.0010826228534090558237205308397
x1[1] (numeric) = 3.0011533455835015271827427174839
absolute error = 7.07227300924713590221866442e-05
relative error = 0.0023565739094923239961168940976361 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.8MB, time=33.48
memory used=457.7MB, alloc=4.8MB, time=33.97
NO POLE
NO POLE
t[1] = 0.5085
x2[1] (analytic) = 2.0007333966287385388608851521817
x2[1] (numeric) = 2.000696796499894069338981039851
absolute error = 3.66001288444695219041123307e-05
relative error = 0.0018293356279322976726175066994752 %
h = 0.0001
x1[1] (analytic) = 3.0010825145965366487525520414014
x1[1] (numeric) = 3.0011549336484504639629325721046
absolute error = 7.24190519138152103805307032e-05
relative error = 0.0024130976593141483504219240252608 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.8MB, time=34.69
NO POLE
NO POLE
t[1] = 0.5086
x2[1] (analytic) = 2.0007334891942968130907897486592
x2[1] (numeric) = 2.0006960165936915893022552512561
absolute error = 3.74726006052237885344974031e-05
relative error = 0.0018729431384843840990667612064385 %
h = 0.0001
x1[1] (analytic) = 3.0010824063504893876557709944627
x1[1] (numeric) = 3.0011565418850798741480815212659
absolute error = 7.41355345904864923105268032e-05
relative error = 0.0024702931993340397732110383388492 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=465.4MB, alloc=4.8MB, time=35.40
NO POLE
NO POLE
t[1] = 0.5087
x2[1] (analytic) = 2.0007335817837826234153683575261
x2[1] (numeric) = 2.0006952262877777259243830846427
absolute error = 3.83554960048974909852728834e-05
relative error = 0.0019170716358297490197029166449879 %
h = 0.0001
x1[1] (analytic) = 3.0010822981152661900729038770055
x1[1] (numeric) = 3.0011581702954054564317511198736
absolute error = 7.58721801392663588472428681e-05
relative error = 0.0025281605968258670008774715441546 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.8MB, time=36.10
memory used=473.0MB, alloc=4.8MB, time=36.82
NO POLE
NO POLE
t[1] = 0.5088
x2[1] (analytic) = 2.0007336743972002145901839798449
x2[1] (numeric) = 2.0006944255770479517452872618344
absolute error = 3.92488201522628448967180105e-05
relative error = 0.0019617213752394154677783238012207 %
h = 0.0001
x1[1] (analytic) = 3.0010821898908659736517178112409
x1[1] (numeric) = 3.0011598188814431106803301813197
absolute error = 7.76289905771370286123700788e-05
relative error = 0.00258669991907019375512668442132 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.8MB, time=37.51
NO POLE
NO POLE
t[1] = 0.5089
x2[1] (analytic) = 2.000733767034553832273955947845
x2[1] (numeric) = 2.0006936144563964163544120626864
absolute error = 4.01525781574159195438851586e-05
relative error = 0.0020068926120504898359522123719589 %
h = 0.0001
x1[1] (analytic) = 3.0010820816772876561482097310871
x1[1] (numeric) = 3.0011614876452089379530623643481
absolute error = 7.94059679212818048526332610e-05
relative error = 0.002645911233354279411876101694396 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.8MB, time=38.20
memory used=484.4MB, alloc=4.8MB, time=38.92
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 2.0007338596958477230287351624915
x2[1] (numeric) = 2.0006927929207159460960268897442
absolute error = 4.10667751317769327082727473e-05
relative error = 0.0020525856016661765574620084367665 %
h = 0.0001
x1[1] (analytic) = 3.0010819734745301554265955597291
x1[1] (numeric) = 3.0011631765887192405220757437177
absolute error = 8.12031141890850954801839886e-05
relative error = 0.0027057946069720796702208220050324 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.8MB, time=39.64
NO POLE
NO POLE
t[1] = 0.5091
x2[1] (analytic) = 2.000733952381086134320079366647
x2[1] (numeric) = 2.0006919609648980437744679041512
absolute error = 4.19914161880905456114624958e-05
relative error = 0.0020988005995557927903613981463498 %
h = 0.0001
x1[1] (analytic) = 3.0010818652825923894592993882611
x1[1] (numeric) = 3.0011648857139905218924143648572
absolute error = 8.30204313981324331149765961e-05
relative error = 0.0027663501072242472214653066510051 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.8MB, time=40.36
NO POLE
NO POLE
t[1] = 0.5092
x2[1] (analytic) = 2.0007340450902733145172284538324
x2[1] (numeric) = 2.0006911185838328883593177201251
absolute error = 4.29265064404261579107337073e-05
relative error = 0.0021455378612547831048257571036437 %
h = 0.0001
x1[1] (analytic) = 3.0010817571014732763269426554107
x1[1] (numeric) = 3.001166615023039486822071782706
absolute error = 8.48579215662104951291272953e-05
relative error = 0.0028275778014181324182210536135505 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.8MB, time=41.08
memory used=499.7MB, alloc=4.8MB, time=41.82
NO POLE
NO POLE
t[1] = 0.5093
x2[1] (analytic) = 2.0007341378234135128932798125935
x2[1] (numeric) = 2.0006902657724093346905231453197
absolute error = 4.38720510041782027566672738e-05
relative error = 0.0021927976423647341735255651122045 %
h = 0.0001
x1[1] (analytic) = 3.001081648931171734218333328345
x1[1] (numeric) = 3.001168364517883041342026584936
absolute error = 8.67155867113071236932565910e-05
relative error = 0.0028894777568677839435702633774836 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=503.5MB, alloc=4.8MB, time=42.55
NO POLE
NO POLE
t[1] = 0.5094
x2[1] (analytic) = 2.000734230580510979625363706482
x2[1] (numeric) = 2.0006894025255149131834509543871
absolute error = 4.48280549960664419127520949e-05
relative error = 0.002240580198553389465068426129855 %
h = 0.0001
x1[1] (analytic) = 3.0010815407716866814304550845588
x1[1] (numeric) = 3.0011701342005382927762798997486
absolute error = 8.85934288516113458248151898e-05
relative error = 0.0029520500408939494802955030280831 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.8MB, time=43.31
memory used=511.1MB, alloc=4.8MB, time=44.04
NO POLE
NO POLE
t[1] = 0.5095
x2[1] (analytic) = 2.0007343233615699657948186896566
x2[1] (numeric) = 2.0006885288380358295338816830522
absolute error = 4.57945235341362609370066044e-05
relative error = 0.0022888857855546639405103132689121 %
h = 0.0001
x1[1] (analytic) = 3.0010814326230170363684564948442
x1[1] (numeric) = 3.0011719240730225497618948884415
absolute error = 9.04914500055133934383935973e-05
relative error = 0.0030152947208240763801753751487102 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.8MB, time=44.76
NO POLE
NO POLE
t[1] = 0.5096
x2[1] (analytic) = 2.0007344161665947233873670581104
x2[1] (numeric) = 2.0006876447048569644229414300086
absolute error = 4.67714617377589644256281018e-05
relative error = 0.0023377146591686587529366588426543 %
h = 0.0001
x1[1] (analytic) = 3.0010813244851617175456402073423
x1[1] (numeric) = 3.0011737341373533222690382229401
absolute error = 9.24096521916047233980155978e-05
relative error = 0.0030792118639923123333461980031414 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.8MB, time=45.48
NO POLE
NO POLE
t[1] = 0.5097
x2[1] (analytic) = 2.0007345089955895052932903365348
x2[1] (numeric) = 2.0006867501208618732219716539434
absolute error = 4.77588747276320713186825914e-05
relative error = 0.0023870670752616759501139097309562 %
h = 0.0001
x1[1] (analytic) = 3.0010812163581196435834521326761
x1[1] (numeric) = 3.0011755643955483216210235484878
absolute error = 9.43480374286780375714158117e-05
relative error = 0.0031438015377395060377297035232476 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.8MB, time=46.21
memory used=526.4MB, alloc=4.8MB, time=46.94
NO POLE
NO POLE
t[1] = 0.5098
x2[1] (analytic) = 2.0007346018485585653076048008237
x2[1] (numeric) = 2.0006858450809327856973369529947
absolute error = 4.87567676257796102678478290e-05
relative error = 0.0024369432897662331802121681964536 %
h = 0.0001
x1[1] (analytic) = 3.0010811082418897332114706301652
x1[1] (numeric) = 3.0011774148496254605143569316901
absolute error = 9.63066077357273028863015249e-05
relative error = 0.0032090638094132078685267595926606 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=530.2MB, alloc=4.8MB, time=47.67
NO POLE
NO POLE
t[1] = 0.5099
x2[1] (analytic) = 2.0007346947255061581302370362269
x2[1] (numeric) = 2.0006849295799506057151708139434
absolute error = 4.97651455555524150662222835e-05
relative error = 0.0024873435586810784005995386408407 %
h = 0.0001
x1[1] (analytic) = 3.001081000136470905267395695121
x1[1] (numeric) = 3.0011792855016028530387842941068
absolute error = 9.82853651319477713885989858e-05
relative error = 0.0032749987463676705477771231603871 %
h = 0.0001
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.8MB, time=48.40
memory used=537.8MB, alloc=4.8MB, time=49.14
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 2.0007347876264365393661995311595
x2[1] (numeric) = 2.0006840036127949109460593184389
absolute error = 5.07840136416284201402127206e-05
relative error = 0.0025382681380712045897088007792725 %
h = 0.0001
x1[1] (analytic) = 3.0010808920418620786970381472244
x1[1] (numeric) = 3.0011811763534988146973408315873
absolute error = 0.0001002843116367360003026843629
relative error = 0.0033416064159638498139852306316874 %
h = 0.0001
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 = 49 Seconds
Elapsed Time(since restart) = 49 Seconds
Expected Time Remaining = 6 Hours 4 Minutes 29 Seconds
Optimized Time Remaining = 6 Hours 4 Minutes 21 Seconds
Time to Timeout = 14 Minutes 10 Seconds
Percent Done = 0.2244 %
> quit
memory used=538.5MB, alloc=4.8MB, time=49.25