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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,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_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, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, 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,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> 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, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, 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,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(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, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(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,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 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, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, 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,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_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, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_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,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global DEBUGMASSIVE, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> DEBUGMASSIVE,
> ALWAYS,
> DEBUGL,
> INFO,
> glob_iolevel,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_max_trunc_err,
> glob_max_order,
> days_in_year,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_smallish_float,
> glob_log10_relerr,
> glob_not_yet_finished,
> glob_start,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_optimal_start,
> glob_max_iter,
> glob_disp_incr,
> glob_clock_start_sec,
> glob_display_flag,
> glob_iter,
> glob_max_sec,
> glob_hmax,
> min_in_hour,
> glob_percent_done,
> glob_orig_start_sec,
> glob_abserr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> years_in_century,
> hours_in_day,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_normmax,
> glob_warned,
> glob_no_eqs,
> glob_look_poles,
> glob_last_good_h,
> glob_initial_pass,
> glob_almost_1,
> centuries_in_millinium,
> glob_dump,
> glob_large_float,
> glob_clock_sec,
> djd_debug2,
> glob_log10normmin,
> glob_log10abserr,
> glob_optimal_clock_start_sec,
> glob_relerr,
> djd_debug,
> glob_current_iter,
> glob_dump_analytic,
> glob_hmin_init,
> glob_h,
> glob_optimal_done,
> glob_log10relerr,
> glob_max_hours,
> glob_hmin,
> glob_reached_optimal_h,
> glob_html_log,
> MAX_UNCHANGED,
> glob_max_rel_trunc_err,
> sec_in_min,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_0D0,
> array_const_2D0,
> array_const_1,
> array_const_3D0,
> array_const_2,
> array_const_4D0,
> #END CONST
> array_pole,
> array_1st_rel_error,
> array_norms,
> array_x2_init,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_last_rel_error,
> array_x1_init,
> array_m1,
> array_t,
> array_type_pole,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_x2,
> array_x1,
> array_x2_higher_work2,
> array_x1_higher_work,
> array_complex_pole,
> array_x1_higher_work2,
> array_real_pole,
> array_x2_higher,
> array_x2_higher_work,
> array_poles,
> array_x1_higher,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> DEBUGL := 3;
> INFO := 2;
> glob_iolevel := 5;
> glob_max_terms := 30;
> glob_max_minutes := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_max_order := 30;
> days_in_year := 365.0;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_smallish_float := 0.1e-100;
> glob_log10_relerr := 0.1e-10;
> glob_not_yet_finished := true;
> glob_start := 0;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> glob_optimal_start := 0.0;
> glob_max_iter := 1000;
> glob_disp_incr := 0.1;
> glob_clock_start_sec := 0.0;
> glob_display_flag := true;
> glob_iter := 0;
> glob_max_sec := 10000.0;
> glob_hmax := 1.0;
> min_in_hour := 60.0;
> glob_percent_done := 0.0;
> glob_orig_start_sec := 0.0;
> glob_abserr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_start_msg := true;
> years_in_century := 100.0;
> hours_in_day := 24.0;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_normmax := 0.0;
> glob_warned := false;
> glob_no_eqs := 0;
> glob_look_poles := false;
> glob_last_good_h := 0.1;
> glob_initial_pass := true;
> glob_almost_1 := 0.9990;
> centuries_in_millinium := 10.0;
> glob_dump := false;
> glob_large_float := 9.0e100;
> glob_clock_sec := 0.0;
> djd_debug2 := true;
> glob_log10normmin := 0.1;
> glob_log10abserr := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_relerr := 0.1e-10;
> djd_debug := true;
> glob_current_iter := 0;
> glob_dump_analytic := false;
> glob_hmin_init := 0.001;
> glob_h := 0.1;
> glob_optimal_done := false;
> glob_log10relerr := 0.0;
> glob_max_hours := 0.0;
> glob_hmin := 0.00000000001;
> glob_reached_optimal_h := false;
> glob_html_log := true;
> MAX_UNCHANGED := 10;
> glob_max_rel_trunc_err := 0.1e-10;
> sec_in_min := 60.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/complicatedrev3postode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.0005 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_pole:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_x2_init:= 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_x1_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_type_pole:= 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_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_x2_init[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_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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
> ;
> 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_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
> ;
> 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 <= 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 <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_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_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_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_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_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_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_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_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_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_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_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_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0005 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> sub_iter := 1;
> while sub_iter <= 3 + glob_max_terms do # do number 3
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;# end do number 3
> ;
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T01:58:21-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev3")
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_pole(html_log_file,array_type_pole[1])
> ;
> if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if glob_percent_done < 100.0 then # if number 4
> logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
> ;
> 0
> else
> logitem_str(html_log_file,"Done")
> ;
> 0
> fi;# end if 4
> ;
> log_revs(html_log_file," 076 | ")
> ;
> logitem_str(html_log_file,"complicatedrev3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev3 maple results")
> ;
> logitem_str(html_log_file,"sub iter tot order + max terms eqs reversed")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4
> ;
> logditto(html_log_file)
> ;
> if glob_percent_done < 100.0 then # if number 4
> logditto(html_log_file)
> ;
> 0
> else
> logditto(html_log_file)
> ;
> 0
> fi;# end if 4
> ;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3
> ;
> if glob_html_log then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> #END OUTFILEMAIN
> # End Function number 8
> end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGMASSIVE, ALWAYS, DEBUGL, INFO, glob_iolevel, glob_max_terms,
glob_max_minutes, glob_max_trunc_err, glob_max_order, days_in_year,
glob_curr_iter_when_opt, glob_warned2, glob_smallish_float,
glob_log10_relerr, glob_not_yet_finished, glob_start, glob_unchanged_h_cnt,
glob_small_float, glob_optimal_start, glob_max_iter, glob_disp_incr,
glob_clock_start_sec, glob_display_flag, glob_iter, glob_max_sec, glob_hmax,
min_in_hour, glob_percent_done, glob_orig_start_sec, glob_abserr,
glob_log10_abserr, glob_not_yet_start_msg, years_in_century, hours_in_day,
glob_max_opt_iter, glob_optimal_expect_sec, glob_normmax, glob_warned,
glob_no_eqs, glob_look_poles, glob_last_good_h, glob_initial_pass,
glob_almost_1, centuries_in_millinium, glob_dump, glob_large_float,
glob_clock_sec, djd_debug2, glob_log10normmin, glob_log10abserr,
glob_optimal_clock_start_sec, glob_relerr, djd_debug, glob_current_iter,
glob_dump_analytic, glob_hmin_init, glob_h, glob_optimal_done,
glob_log10relerr, glob_max_hours, glob_hmin, glob_reached_optimal_h,
glob_html_log, MAX_UNCHANGED, glob_max_rel_trunc_err, sec_in_min,
array_const_0D0, array_const_2D0, array_const_1, array_const_3D0,
array_const_2, array_const_4D0, array_pole, array_1st_rel_error,
array_norms, array_x2_init, array_tmp10, array_tmp11, array_tmp12,
array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17,
array_last_rel_error, array_x1_init, array_m1, array_t, array_type_pole,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_x2, array_x1,
array_x2_higher_work2, array_x1_higher_work, array_complex_pole,
array_x1_higher_work2, array_real_pole, array_x2_higher,
array_x2_higher_work, array_poles, array_x1_higher, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
DEBUGMASSIVE := 4;
ALWAYS := 1;
DEBUGL := 3;
INFO := 2;
glob_iolevel := 5;
glob_max_terms := 30;
glob_max_minutes := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_order := 30;
days_in_year := 365.0;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_smallish_float := 0.1*10^(-100);
glob_log10_relerr := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_start := 0;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
glob_optimal_start := 0.;
glob_max_iter := 1000;
glob_disp_incr := 0.1;
glob_clock_start_sec := 0.;
glob_display_flag := true;
glob_iter := 0;
glob_max_sec := 10000.0;
glob_hmax := 1.0;
min_in_hour := 60.0;
glob_percent_done := 0.;
glob_orig_start_sec := 0.;
glob_abserr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_start_msg := true;
years_in_century := 100.0;
hours_in_day := 24.0;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_normmax := 0.;
glob_warned := false;
glob_no_eqs := 0;
glob_look_poles := false;
glob_last_good_h := 0.1;
glob_initial_pass := true;
glob_almost_1 := 0.9990;
centuries_in_millinium := 10.0;
glob_dump := false;
glob_large_float := 0.90*10^101;
glob_clock_sec := 0.;
djd_debug2 := true;
glob_log10normmin := 0.1;
glob_log10abserr := 0.;
glob_optimal_clock_start_sec := 0.;
glob_relerr := 0.1*10^(-10);
djd_debug := true;
glob_current_iter := 0;
glob_dump_analytic := false;
glob_hmin_init := 0.001;
glob_h := 0.1;
glob_optimal_done := false;
glob_log10relerr := 0.;
glob_max_hours := 0.;
glob_hmin := 0.1*10^(-10);
glob_reached_optimal_h := false;
glob_html_log := true;
MAX_UNCHANGED := 10;
glob_max_rel_trunc_err := 0.1*10^(-10);
sec_in_min := 60.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/complicatedrev3postode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.0005 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_pole := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_x2_init := 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_x1_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_type_pole := 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_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_pole[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_x2_init[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_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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;
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_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 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 <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_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_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_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_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[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_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_const_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_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_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_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_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_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.0005;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
sub_iter := 1;
while sub_iter <= 3 + glob_max_terms do
atomall(); sub_iter := sub_iter + 1
end do;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T01:58:21-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev3");
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
;
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 076 | ");
logitem_str(html_log_file, "complicatedrev3 diffeq.mxt");
logitem_str(html_log_file, "complicatedrev3 maple results");
logitem_str(html_log_file,
"sub iter tot order + max terms eqs reversed");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end proc
> mainprog();
##############ECHO OF PROBLEM#################
##############temp/complicatedrev3postode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.0005 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0005
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0005
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0005
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.1MB, time=0.52
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 400.22191290206986222929961499824
absolute error = 400.22108683353482997101795673623
relative error = 48448896.170328778905018381022287 %
h = 0.0005
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = -44790.694404485090230606965962824
absolute error = 44790.695695694536566262136799896
relative error = 3468894672.5728191603455591607742 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.4MB, time=1.16
memory used=11.4MB, alloc=4.5MB, time=1.82
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = -3332322887785.1871338512550901035
absolute error = 3332322887785.1879603733512164215
relative error = 403174083718132856.01133179113287 %
h = 0.0005
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 372936523931644.26584823090564973
absolute error = 372936523931644.26455756692765879
relative error = 28894935497631350454.451625907275 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.5MB, time=2.49
NO POLE
NO POLE
t[1] = 0.5015
x2[1] (analytic) = 0.00082697624740952299139053885956424
x2[1] (numeric) = 27745604198377353951556.39596658
absolute error = 27745604198377353951556.395139604
relative error = 3355066640098743329913075134.2691 %
h = 0.0005
x1[1] (analytic) = 0.0012901187823122199004062452509559
x1[1] (numeric) = -3105146029532390375711422.1323223
absolute error = 3105146029532390375711422.1336124
relative error = 240686832259521215755759645050.3 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.5MB, time=3.15
memory used=22.8MB, alloc=4.6MB, time=3.83
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = -2.3101559430354936851313018725871e+32
absolute error = 2.3101559430354936851313018725871e+32
relative error = 2.7919620761352162826025187160772e+37 %
h = 0.0005
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 2.5854083057008498917426910852337e+34
absolute error = 2.5854083057008498917426910852337e+34
relative error = 2.0048547722411999941254477150050e+39 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.6MB, time=4.53
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 0.00082788632263312837678584048126422
x2[1] (numeric) = 1.9234832454844592618547622521628e+42
absolute error = 1.9234832454844592618547622521628e+42
relative error = 2.3233663763966257184859813733670e+47 %
h = 0.0005
x1[1] (analytic) = 0.0012890292084076577854302062195851
x1[1] (numeric) = -2.1526640111652158582414589555169e+44
absolute error = 2.1526640111652158582414589555169e+44
relative error = 1.6699885441885441176316176846496e+49 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.6MB, time=5.23
memory used=34.3MB, alloc=4.6MB, time=5.93
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = -1.6015316224921116990687707780908e+52
absolute error = 1.6015316224921116990687707780908e+52
relative error = 1.9334177715721141075189014354565e+57 %
h = 0.0005
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 1.7923522310762232652758834745774e+54
absolute error = 1.7923522310762232652758834745774e+54
relative error = 1.3910541975121471344840491312022e+59 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.6MB, time=6.59
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 0.00082879876488816372497515444163463
x2[1] (numeric) = 1.3334680943353914220256919503161e+62
absolute error = 1.3334680943353914220256919503161e+62
relative error = 1.6089166041594266394213391029829e+67 %
h = 0.0005
x1[1] (analytic) = 0.0012879407235323948305490116710912
x1[1] (numeric) = -1.4923492489220397331164504138463e+64
absolute error = 1.4923492489220397331164504138463e+64
relative error = 1.1587095754135485512236862262128e+69 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.6MB, time=7.25
NO POLE
NO POLE
memory used=45.7MB, alloc=4.6MB, time=7.92
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = -1.1102728997904744921181981235100e+72
absolute error = 1.1102728997904744921181981235100e+72
relative error = 1.3388785455880561733553456410582e+77 %
h = 0.0005
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 1.2425606095409625333697391752465e+74
absolute error = 1.2425606095409625333697391752465e+74
relative error = 9.6517291599987797525431331352907e+78 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.6MB, time=8.62
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 0.00082971357836864193708890062488759
x2[1] (numeric) = 9.2443600056553067307411870085345e+81
absolute error = 9.2443600056553067307411870085345e+81
relative error = 1.1141627962544968037518061266976e+87 %
h = 0.0005
x1[1] (analytic) = 0.0012868533265979460697926307621308
x1[1] (numeric) = -1.0345814624144087320376389025686e+84
absolute error = 1.0345814624144087320376389025686e+84
relative error = 8.0396222400071931735805774592832e+88 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=9.29
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = -7.6970438466332604265415297176411e+91
absolute error = 7.6970438466332604265415297176411e+91
relative error = 9.2716268432705819596993904966226e+96 %
h = 0.0005
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 8.6141375652247484040267553170814e+93
absolute error = 8.6141375652247484040267553170814e+93
relative error = 6.6967817444393281630455823131561e+98 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.6MB, time=9.97
memory used=61.0MB, alloc=4.6MB, time=10.69
NO POLE
NO POLE
t[1] = 0.5055
x2[1] (analytic) = 0.0008306307672775168485568375279051
x2[1] (numeric) = 6.4087166597527227188406662076912e+101
absolute error = 6.4087166597527227188406662076912e+101
relative error = 7.7154819111239910208722742970724e+106 %
h = 0.0005
x1[1] (analytic) = 0.0012857670165169144780958885117126
x1[1] (numeric) = -7.1723077097715759309390802235667e+103
absolute error = 7.1723077097715759309390802235667e+103
relative error = 5.5782327728401664399742422481307e+108 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.6MB, time=11.40
NO POLE
NO POLE
t[1] = 0.506
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = -5.3360290058575040541562214561627e+111
absolute error = 5.3360290058575040541562214561627e+111
relative error = 6.4205168827869317811877803204730e+116 %
h = 0.0005
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = 5.9718105839544522967933254688892e+113
absolute error = 5.9718105839544522967933254688892e+113
relative error = 4.6465124642898194764029570576324e+118 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.6MB, time=12.14
memory used=72.4MB, alloc=4.6MB, time=12.90
NO POLE
NO POLE
t[1] = 0.5065
x2[1] (analytic) = 0.00083155033582670058462774699213345
x2[1] (numeric) = 4.4428872523210049538610888290307e+121
absolute error = 4.4428872523210049538610888290307e+121
relative error = 5.3428963478248486539408732310574e+126 %
h = 0.0005
x1[1] (analytic) = 0.0012846817922029898839013501196003
x1[1] (numeric) = -4.9722520412842407994644816955732e+123
absolute error = 4.9722520412842407994644816955732e+123
relative error = 3.8704152821826446892494101667580e+128 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.6MB, time=13.65
NO POLE
NO POLE
t[1] = 0.507
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = -3.6992390999314623503054146252073e+131
absolute error = 3.6992390999314623503054146252073e+131
relative error = 4.4461419844701799560735234088092e+136 %
h = 0.0005
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = 4.1399990864552623796501919410779e+133
absolute error = 4.1399990864552623796501919410779e+133
relative error = 3.2239478704552470963864923807377e+138 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.6MB, time=14.39
memory used=83.9MB, alloc=4.6MB, time=15.12
NO POLE
NO POLE
t[1] = 0.5075
x2[1] (analytic) = 0.0008324722882370809511788631756612
x2[1] (numeric) = 3.0800623876540858949129812214979e+141
absolute error = 3.0800623876540858949129812214979e+141
relative error = 3.6998977998135003447329329802667e+146 %
h = 0.0005
x1[1] (analytic) = 0.0012835976525709478828490588830272
x1[1] (numeric) = -3.4470481973845330524897345865218e+143
absolute error = 3.4470481973845330524897345865218e+143
relative error = 2.6854584771796358976706540143823e+148 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.6MB, time=15.87
NO POLE
NO POLE
t[1] = 0.508
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = -2.5645231507250112284829844449833e+151
absolute error = 2.5645231507250112284829844449833e+151
relative error = 3.0789026009122266362802493347008e+156 %
h = 0.0005
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = 2.8700830669181741681312701026412e+153
absolute error = 2.8700830669181741681312701026412e+153
relative error = 2.2369117880590632335201765155226e+158 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.6MB, time=16.63
NO POLE
NO POLE
t[1] = 0.5085
x2[1] (analytic) = 0.00083339662873853886088515218174166
x2[1] (numeric) = 2.1352746025426158551851761833581e+161
absolute error = 2.1352746025426158551851761833581e+161
relative error = 2.5621349174097926057930660206337e+166 %
h = 0.0005
x1[1] (analytic) = 0.0012825145965366487525520414013697
x1[1] (numeric) = -2.3896900592398412023258296686208e+163
absolute error = 2.3896900592398412023258296686208e+163
relative error = 1.8632848824434834693401471094148e+168 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.6MB, time=17.38
memory used=99.1MB, alloc=4.7MB, time=18.21
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = -1.7778734526044531501980108034055e+171
absolute error = 1.7778734526044531501980108034055e+171
relative error = 2.1321014331997682963622824969788e+176 %
h = 0.0005
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = 1.9897049827765577421595436381933e+173
absolute error = 1.9897049827765577421595436381933e+173
relative error = 1.5520640811275651614034206655215e+178 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.7MB, time=18.95
NO POLE
NO POLE
t[1] = 0.5095
x2[1] (analytic) = 0.00083432336156996579481868965658664
x2[1] (numeric) = 1.4802939208436516447691030864872e+181
absolute error = 1.4802939208436516447691030864872e+181
relative error = 1.7742448420216208870882730466847e+186 %
h = 0.0005
x1[1] (analytic) = 0.0012814326230170363684564948441937
x1[1] (numeric) = -1.6566691999150691569288033337774e+183
absolute error = 1.6566691999150691569288033337774e+183
relative error = 1.2928258342717751299719127198032e+188 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.7MB, time=19.68
memory used=110.6MB, alloc=4.7MB, time=20.39
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = -1.2325230959923624155375292576308e+191
absolute error = 1.2325230959923624155375292576308e+191
relative error = 1.4764510840363527322908462926806e+196 %
h = 0.0005
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = 1.3793767727903641867895973127417e+193
absolute error = 1.3793767727903641867895973127417e+193
relative error = 1.0768876124681942004326149366147e+198 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.7MB, time=21.09
NO POLE
NO POLE
t[1] = 0.5105
x2[1] (analytic) = 0.0008352524909792812995485248473563
x2[1] (numeric) = 1.0262240226514087370522606612679e+201
absolute error = 1.0262240226514087370522606612679e+201
relative error = 1.2286392842100060810770124631004e+206 %
h = 0.0005
x1[1] (analytic) = 0.0012803517309301371207855721427719
x1[1] (numeric) = -1.1484974075760585390684353530236e+203
absolute error = 1.1484974075760585390684353530236e+203
relative error = 8.9701710852666214497796377424540e+207 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.7MB, time=21.81
memory used=122.0MB, alloc=4.7MB, time=22.51
NO POLE
NO POLE
t[1] = 0.511
x2[1] (analytic) = 0.00083571795573059504987431312643056
x2[1] (numeric) = -8.5445518067059819724751304335214e+210
absolute error = 8.5445518067059819724751304335214e+210
relative error = 1.0224205125802554186674385192999e+216 %
h = 0.0005
x1[1] (analytic) = 0.0012798116900861339038992560756415
x1[1] (numeric) = 9.5626251016290963389527682211609e+212
absolute error = 9.5626251016290963389527682211609e+212
relative error = 7.4719001050736709658883575850579e+217 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.7MB, time=23.19
NO POLE
NO POLE
t[1] = 0.5115
x2[1] (analytic) = 0.00083618402122345051981156107146395
x2[1] (numeric) = 7.1143691792413370628151959491157e+220
absolute error = 7.1143691792413370628151959491157e+220
relative error = 8.5081381593875125825580417538596e+225 %
h = 0.0005
x1[1] (analytic) = 0.0012792719191950588325656820487663
x1[1] (numeric) = -7.9620378967421461402552098838634e+222
absolute error = 7.9620378967421461402552098838634e+222
relative error = 6.2238823328131874036629234925008e+227 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.7MB, time=23.89
NO POLE
NO POLE
t[1] = 0.512
x2[1] (analytic) = 0.00083665068799138460946718195917937
x2[1] (numeric) = -5.9235697744632672065601654502226e+230
absolute error = 5.9235697744632672065601654502226e+230
relative error = 7.0800990897222151393595362119798e+235 %
h = 0.0005
x1[1] (analytic) = 0.0012787324181219691812047754809758
x1[1] (numeric) = 6.6293561438854523721835726776887e+232
absolute error = 6.6293561438854523721835726776887e+232
relative error = 5.1843185094359008332288278350046e+237 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.7MB, time=24.62
memory used=137.3MB, alloc=4.7MB, time=25.36
NO POLE
NO POLE
t[1] = 0.5125
x2[1] (analytic) = 0.00083711795656850176682512429116968
x2[1] (numeric) = 4.9320857533396366400571038920748e+240
absolute error = 4.9320857533396366400571038920748e+240
relative error = 5.8917452607959218707895803526001e+245 %
h = 0.0005
x1[1] (analytic) = 0.0012781931867319896787342220862856
x1[1] (numeric) = -5.5197379681468602830726690897505e+242
absolute error = 5.5197379681468602830726690897505e+242
relative error = 4.3183910111893231717974781681837e+247 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.7MB, time=26.10
NO POLE
NO POLE
t[1] = 0.513
x2[1] (analytic) = 0.00083758582748947453871027492802935
x2[1] (numeric) = -4.1065558108497057837280498459365e+250
absolute error = 4.1065558108497057837280498459365e+250
relative error = 4.9028477752046377816670745332769e+255 %
h = 0.0005
x1[1] (analytic) = 0.0012776542248903124748506494008434
x1[1] (numeric) = 4.5958471042626900644239598986524e+252
absolute error = 4.5958471042626900644239598986524e+252
relative error = 3.5970977238831944624744379400629e+257 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.7MB, time=26.78
memory used=148.7MB, alloc=4.7MB, time=27.46
NO POLE
NO POLE
t[1] = 0.5135
x2[1] (analytic) = 0.00083805430128954412231203351352064
x2[1] (numeric) = 3.4192026398171585177582725043617e+260
absolute error = 3.4192026398171585177582725043617e+260
relative error = 4.0799297068888127473285994918559e+265 %
h = 0.0005
x1[1] (analytic) = 0.0012771155324621971063276635049614
x1[1] (numeric) = -3.8265966115871568666737947763387e+262
absolute error = 3.8265966115871568666737947763387e+262
relative error = 2.9962806921702089212452515377278e+267 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.7MB, time=28.14
NO POLE
NO POLE
t[1] = 0.514
x2[1] (analytic) = 0.0008385233785045209172681139251402
x2[1] (numeric) = -2.8468982842616230034009966753440e+270
absolute error = 2.8468982842616230034009966753440e+270
relative error = 3.3951328695676597508049408066612e+275 %
h = 0.0005
x1[1] (analytic) = 0.0012765771093129704633307325147448
x1[1] (numeric) = 3.1861028653953568744856416186830e+272
absolute error = 3.1861028653953568744856416186830e+272
relative error = 2.4958170110930916497697537458597e+277 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.7MB, time=28.81
memory used=160.2MB, alloc=4.7MB, time=29.48
NO POLE
NO POLE
t[1] = 0.5145
x2[1] (analytic) = 0.00083899305967078507830912904557372
x2[1] (numeric) = 2.3703859334190200825576597612906e+280
absolute error = 2.3703859334190200825576597612906e+280
relative error = 2.8252747815925231831295896775244e+285 %
h = 0.0005
x1[1] (analytic) = 0.0012760389553080267557489084220364
x1[1] (numeric) = -2.6528146285767160109386016833582e+282
absolute error = 2.6528146285767160109386016833582e+282
relative error = 2.0789448610025744629583924493380e+287 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.7MB, time=30.17
NO POLE
NO POLE
t[1] = 0.515
x2[1] (analytic) = 0.00083946334532528706846451570820467
x2[1] (numeric) = -1.9736319714731373184068757444679e+290
absolute error = 1.9736319714731373184068757444679e+290
relative error = 2.3510639058437585892475452059367e+295 %
h = 0.0005
x1[1] (analytic) = 0.0012755010703128274795433788656077
x1[1] (numeric) = 2.2087878988544082189509835939145e+292
absolute error = 2.2087878988544082189509835939145e+292
relative error = 1.7317021132037813277236229508238e+297 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.7MB, time=30.87
NO POLE
NO POLE
memory used=171.6MB, alloc=4.7MB, time=31.53
t[1] = 0.5155
x2[1] (analytic) = 0.00083993423600554821283035722907962
x2[1] (numeric) = 1.6432864808653809543628414402901e+300
absolute error = 1.6432864808653809543628414402901e+300
relative error = 1.9564466007247336114428745423234e+305 %
h = 0.0005
x1[1] (analytic) = 0.0012749634541929013831128404207343
x1[1] (numeric) = -1.8390821316991936316664972730095e+302
absolute error = 1.8390821316991936316664972730095e+302
relative error = 1.4424587039346943921063478075553e+307 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.7MB, time=32.20
NO POLE
NO POLE
t[1] = 0.516
x2[1] (analytic) = 0.00084040573224966125289966149752755
x2[1] (numeric) = -1.3682340462793229943310463813002e+310
absolute error = 1.3682340462793229943310463813002e+310
relative error = 1.6280636765966971974811395676618e+315 %
h = 0.0005
x1[1] (analytic) = 0.0012744261068138444336756849984992
x1[1] (numeric) = 1.5312575231372130492375654773799e+312
absolute error = 1.5312575231372130492375654773799e+312
relative error = 1.2015271147932345439200268163617e+317 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.7MB, time=32.88
NO POLE
NO POLE
t[1] = 0.5165
x2[1] (analytic) = 0.0008408778345962909014556531579845
x2[1] (numeric) = 1.1392197448201664188373036061085e+320
absolute error = 1.1392197448201664188373036061085e+320
relative error = 1.3547981620506274416762339109608e+325 %
h = 0.0005
x1[1] (analytic) = 0.0012738890280413197836689909503695
x1[1] (numeric) = -1.2749564370993668989894209816171e+322
absolute error = 1.2749564370993668989894209816171e+322
relative error = 1.0008379136914997378468385524539e+327 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.7MB, time=33.59
memory used=186.9MB, alloc=4.7MB, time=34.27
NO POLE
NO POLE
t[1] = 0.517
x2[1] (analytic) = 0.0008413505435846743980286389764889
x2[1] (numeric) = -9.4853773776301477220745200192030e+329
absolute error = 9.4853773776301477220745200192030e+329
relative error = 1.1273989718027120320413162402536e+335 %
h = 0.0005
x1[1] (analytic) = 0.0012733522177410577371643104777951
x1[1] (numeric) = 1.0615548932427695378300892311626e+332
absolute error = 1.0615548932427695378300892311626e+332
relative error = 8.3366948944101324986502609206778e+336 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.7MB, time=34.94
NO POLE
NO POLE
t[1] = 0.5175
x2[1] (analytic) = 0.00084182385975462206491700604678574
x2[1] (numeric) = 7.8977198565199140286882656102781e+339
absolute error = 7.8977198565199140286882656102781e+339
relative error = 9.3816773722973005896000927414153e+344 %
h = 0.0005
x1[1] (analytic) = 0.0012728156757788557163002449507755
x1[1] (numeric) = -8.8387238855898271935640888980589e+341
absolute error = 8.8387238855898271935640888980589e+341
relative error = 6.9442292814167884304481722161922e+346 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.7MB, time=35.63
memory used=198.3MB, alloc=4.7MB, time=36.31
NO POLE
NO POLE
t[1] = 0.518
x2[1] (analytic) = 0.00084229778364651786377291305301299
x2[1] (numeric) = -6.5758036237091301293777893231708e+349
absolute error = 6.5758036237091301293777893231708e+349
relative error = 7.8069819859205029076122493057788e+354 %
h = 0.0005
x1[1] (analytic) = 0.0012722794020205782277317997435378
x1[1] (numeric) = 7.3593028889020425834916163707465e+351
absolute error = 7.3593028889020425834916163707465e+351
relative error = 5.7843449145009509605829003943882e+356 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.7MB, time=36.99
NO POLE
NO POLE
t[1] = 0.5185
x2[1] (analytic) = 0.00084277231580131995275323536853887
x2[1] (numeric) = 5.4751490408828094904599313151830e+359
absolute error = 5.4751490408828094904599313151830e+359
relative error = 6.4965933719322040100548812496731e+364 %
h = 0.0005
x1[1] (analytic) = 0.0012717433963321568290965101996664
x1[1] (numeric) = -6.1275066074753595154939886681054e+361
absolute error = 6.1275066074753595154939886681054e+361
relative error = 4.8181941617685926798000176217991e+366 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.7MB, time=37.66
NO POLE
NO POLE
memory used=209.8MB, alloc=4.7MB, time=38.33
t[1] = 0.519
x2[1] (analytic) = 0.00084324745676056124423632533367627
x2[1] (numeric) = -4.5587214484016263237285193461396e+369
absolute error = 4.5587214484016263237285193461396e+369
relative error = 5.4061490631878275903192770582486e+374 %
h = 0.0005
x1[1] (analytic) = 0.0012712076585795900954973303432135
x1[1] (numeric) = 5.1018877455464868196804762738511e+371
absolute error = 5.1018877455464868196804762738511e+371
relative error = 4.0134180368667582998639894590351e+376 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.7MB, time=38.99
NO POLE
NO POLE
t[1] = 0.5195
x2[1] (analytic) = 0.00084372320706634996310514961872029
x2[1] (numeric) = 3.7956850286519606798129939941280e+379
absolute error = 3.7956850286519606798129939941280e+379
relative error = 4.4987325189853050268870726924955e+384 %
h = 0.0005
x1[1] (analytic) = 0.001270672188628943586002275956513
x1[1] (numeric) = -4.2479364341121332774425086290350e+381
absolute error = 4.2479364341121332774425086290350e+381
relative error = 3.3430624138359874251494029059023e+386 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.7MB, time=39.66
NO POLE
NO POLE
t[1] = 0.52
x2[1] (analytic) = 0.00084419956726137020559736614303792
x2[1] (numeric) = -3.1603652470988505308243466151667e+389
absolute error = 3.1603652470988505308243466151667e+389
relative error = 3.7436233915059315770856491730200e+394 %
h = 0.0005
x1[1] (analytic) = 0.00127013698634634981016081364961
x1[1] (numeric) = 3.5369190480541289885628208344019e+391
absolute error = 3.5369190480541289885628208344019e+391
relative error = 2.7846752642235530014236430263400e+396 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.7MB, time=40.35
memory used=225.0MB, alloc=4.7MB, time=41.06
NO POLE
NO POLE
t[1] = 0.5205
x2[1] (analytic) = 0.00084467653788888249872290358578525
x2[1] (numeric) = 2.6313849594146616968845170429286e+399
absolute error = 2.6313849594146616968845170429286e+399
relative error = 3.1152575469792690410201380699375e+404 %
h = 0.0005
x1[1] (analytic) = 0.0012696020515980081945369875504003
x1[1] (numeric) = -2.9449113814488645524814257064721e+401
absolute error = 2.9449113814488645524814257064721e+401
relative error = 2.3195546807302313075170996986966e+406 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.7MB, time=41.76
NO POLE
NO POLE
t[1] = 0.521
x2[1] (analytic) = 0.00084515411949272436024960708923766
x2[1] (numeric) = -2.1909451165462473198449927229019e+409
absolute error = 2.1909451165462473198449927229019e+409
relative error = 2.5923616367879614993901722852518e+414 %
h = 0.0005
x1[1] (analytic) = 0.0012690673842501850492592752487639
x1[1] (numeric) = 2.4519936494894682936639830461614e+411
absolute error = 2.4519936494894682936639830461614e+411
relative error = 1.9321225018624228785321762273928e+416 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.7MB, time=42.44
memory used=236.5MB, alloc=4.7MB, time=43.13
NO POLE
NO POLE
t[1] = 0.5215
x2[1] (analytic) = 0.0008456323126173108592575143216941
x2[1] (numeric) = 1.8242258649930257728985922725026e+419
absolute error = 1.8242258649930257728985922725026e+419
relative error = 2.1572329223641852322872903692751e+424 %
h = 0.0005
x1[1] (analytic) = 0.0012685329841692135345871646321545
x1[1] (numeric) = -2.0415802305666353426997290228135e+421
absolute error = 2.0415802305666353426997290228135e+421
relative error = 1.6094025587389083192825291970613e+426 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.7MB, time=43.81
NO POLE
NO POLE
t[1] = 0.522
x2[1] (analytic) = 0.00084611111780763517726232663345645
x2[1] (numeric) = -1.5188878906083308089022388514834e+429
absolute error = 1.5188878906083308089022388514834e+429
relative error = 1.7951399746926060271002058421729e+434 %
h = 0.0005
x1[1] (analytic) = 0.0012679988512214936274944432542899
x1[1] (numeric) = 1.6998615957705882182423196378599e+431
absolute error = 1.6998615957705882182423196378599e+431
relative error = 1.3405860692484625499049137267498e+436 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.7MB, time=44.49
memory used=247.9MB, alloc=4.7MB, time=45.18
NO POLE
NO POLE
t[1] = 0.5225
x2[1] (analytic) = 0.00084659053560926916990864060649109
x2[1] (numeric) = 1.2646572272153616814270597295798e+439
absolute error = 1.2646572272153616814270597295798e+439
relative error = 1.4938239609603251668093889844282e+444 %
h = 0.0005
x1[1] (analytic) = 0.0012674649852734920882691918827657
x1[1] (numeric) = -1.4153396479420988489121567894805e+441
absolute error = 1.4153396479420988489121567894805e+441
relative error = 1.1166696235294409665023745422789e+446 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.7MB, time=45.83
NO POLE
NO POLE
t[1] = 0.523
x2[1] (analytic) = 0.00084707056656836392923350586605222
x2[1] (numeric) = -1.0529795597405724496118541028749e+449
absolute error = 1.0529795597405724496118541028749e+449
relative error = 1.2430836358845321393857152449260e+454 %
h = 0.0005
x1[1] (analytic) = 0.0012669313861917424271304738755899
x1[1] (numeric) = 1.1784408354309408882937363687719e+451
absolute error = 1.1784408354309408882937363687719e+451
relative error = 9.3015363600171396537060169342807e+455 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.7MB, time=46.51
NO POLE
NO POLE
t[1] = 0.5235
x2[1] (analytic) = 0.00084755121123165034650087559078626
x2[1] (numeric) = 8.7673238990839627937846790628467e+458
absolute error = 8.7673238990839627937846790628467e+458
relative error = 1.0344299887606086071077256469522e+464 %
h = 0.0005
x1[1] (analytic) = 0.0012663980538428448708617120408105
x1[1] (numeric) = -9.8119402267178356400565023191379e+460
absolute error = 9.8119402267178356400565023191379e+460
relative error = 7.7479116435340477038889547212614e+465 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.7MB, time=47.18
memory used=263.2MB, alloc=4.7MB, time=47.84
NO POLE
NO POLE
t[1] = 0.524
x2[1] (analytic) = 0.00084803247014643967560751672664236
x2[1] (numeric) = -7.2998537949194998714156679884643e+468
absolute error = 7.2998537949194998714156679884643e+468
relative error = 8.6079885522059654392683912778311e+473 %
h = 0.0005
x1[1] (analytic) = 0.0012658649880934663294607446375807
x1[1] (numeric) = 8.1696227861517890167374400354275e+470
absolute error = 8.1696227861517890167374400354275e+470
relative error = 6.4537868279745622056848889856505e+475 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.7MB, time=48.52
NO POLE
NO POLE
t[1] = 0.5245
x2[1] (analytic) = 0.00084851434386062409706094747929037
x2[1] (numeric) = 6.0780080718551193506394996319927e+478
absolute error = 6.0780080718551193506394996319927e+478
relative error = 7.1631176489026864828274188315922e+483 %
h = 0.0005
x1[1] (analytic) = 0.0012653321888103403628065521811756
x1[1] (numeric) = -6.8021955827116207093497210098161e+480
absolute error = 6.8021955827116207093497210098161e+480
relative error = 5.3758180206472218377775512981268e+485 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.7MB, time=49.21
memory used=274.6MB, alloc=4.8MB, time=49.88
NO POLE
NO POLE
t[1] = 0.525
x2[1] (analytic) = 0.00084899683292267728252997022968994
x2[1] (numeric) = -5.0606742490167052173420696929081e+488
absolute error = 5.0606742490167052173420696929081e+488
relative error = 5.9607692900282092065930602307318e+493 %
h = 0.0005
x1[1] (analytic) = 0.0012647996558602671473426467186411
x1[1] (numeric) = 5.6636476317967669884196044498237e+490
absolute error = 5.6636476317967669884196044498237e+490
relative error = 4.4779009905284769208882014646277e+495 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.8MB, time=50.57
NO POLE
NO POLE
t[1] = 0.5255
x2[1] (analytic) = 0.00084947993788165495996836858796728
x2[1] (numeric) = 4.2136212311485172222361253714759e+498
absolute error = 4.2136212311485172222361253714759e+498
relative error = 4.9602363084124260821819968055794e+503 %
h = 0.0005
x1[1] (analytic) = 0.0012642673891101134427771152459227
x1[1] (numeric) = -4.7156692434253736520117020930479e+500
absolute error = 4.7156692434253736520117020930479e+500
relative error = 3.7299619400486289861624672640175e+505 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.8MB, time=51.27
memory used=286.1MB, alloc=4.8MB, time=51.94
NO POLE
NO POLE
t[1] = 0.526
x2[1] (analytic) = 0.00084996365928719547931233787183942
x2[1] (numeric) = -3.5083475058753852415746483758286e+508
absolute error = 3.5083475058753852415746483758286e+508
relative error = 4.1276441263589888473975596946165e+513 %
h = 0.0005
x1[1] (analytic) = 0.0012637353884268125587993089414852
x1[1] (numeric) = 3.9263629835554011242264076071629e+510
absolute error = 3.9263629835554011242264076071629e+510
relative error = 3.1069502520169323113874080661892e+515 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.8MB, time=52.63
NO POLE
NO POLE
t[1] = 0.5265
x2[1] (analytic) = 0.00085044799768952037875221886747711
x2[1] (numeric) = 2.9211221291067676741833289851583e+518
absolute error = 2.9211221291067676741833289851583e+518
relative error = 3.4348039351527808511931526352762e+523 %
h = 0.0005
x1[1] (analytic) = 0.0012632036536773643218131698955945
x1[1] (numeric) = -3.2691703940278773638981871588051e+520
absolute error = 3.2691703940278773638981871588051e+520
relative error = 2.5879994761817387286019072084341e+525 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.8MB, time=53.33
NO POLE
NO POLE
t[1] = 0.527
x2[1] (analytic) = 0.00085093295363943495157910530292247
x2[1] (numeric) = -2.4321862298039816161590515653963e+528
absolute error = 2.4321862298039816161590515653963e+528
relative error = 2.8582583614861032643327567349806e+533 %
h = 0.0005
x1[1] (analytic) = 0.0012626721847288350416871870185942
x1[1] (numeric) = 2.7219783575665900427845843680606e+530
absolute error = 2.7219783575665900427845843680606e+530
relative error = 2.1557284546908333609444077081489e+535 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.8MB, time=53.98
memory used=301.3MB, alloc=4.8MB, time=54.66
NO POLE
NO POLE
t[1] = 0.5275
x2[1] (analytic) = 0.00085141852768832881360689603697165
x2[1] (numeric) = 2.0250881664632696082935117706303e+538
absolute error = 2.0250881664632696082935117706303e+538
relative error = 2.3784873133563938264075989947013e+543 %
h = 0.0005
x1[1] (analytic) = 0.0012621409814483574785209728156648
x1[1] (numeric) = -2.2663750389383131539314491159479e+540
absolute error = 2.2663750389383131539314491159479e+540
relative error = 1.7956591793236574512327436238683e+545 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.8MB, time=55.34
NO POLE
NO POLE
t[1] = 0.528
x2[1] (analytic) = 0.00085190472038817647117036353980059
x2[1] (numeric) = -1.6861299647601736605909472609306e+548
absolute error = 1.6861299647601736605909472609306e+548
relative error = 1.9792471204900431796938734688694e+553 %
h = 0.0005
x1[1] (analytic) = 0.0012616100437031308094284527197097
x1[1] (numeric) = 1.8870303662937860195119843568103e+550
absolute error = 1.8870303662937860195119843568103e+550
relative error = 1.4957318830110889105552670857488e+555 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.8MB, time=56.01
memory used=312.8MB, alloc=4.8MB, time=56.71
NO POLE
NO POLE
t[1] = 0.5285
x2[1] (analytic) = 0.00085239153229153788969981081555131
x2[1] (numeric) = 1.4039064101724434736479765124287e+558
absolute error = 1.4039064101724434736479765124287e+558
relative error = 1.6470205967417735498828920165107e+563 %
h = 0.0005
x1[1] (analytic) = 0.0012610793713604205953376586781657
x1[1] (numeric) = -1.5711802072189083033427032315206e+560
absolute error = 1.5711802072189083033427032315206e+560
relative error = 1.2459011247832551201223827236564e+565 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.8MB, time=57.38
NO POLE
NO POLE
t[1] = 0.529
x2[1] (analytic) = 0.00085287896395155906287288949160932
x2[1] (numeric) = -1.1689212870394692317752931215123e+568
absolute error = 1.1689212870394692317752931215123e+568
relative error = 1.3705594069569060374159521087492e+573 %
h = 0.0005
x1[1] (analytic) = 0.001260548964287558747807118693686
x1[1] (numeric) = 1.3081968831296070837766812544157e+570
absolute error = 1.3081968831296070837766812544157e+570
relative error = 1.0377993399637420233536071710810e+575 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.8MB, time=58.03
memory used=324.2MB, alloc=4.8MB, time=58.70
NO POLE
NO POLE
t[1] = 0.5295
x2[1] (analytic) = 0.00085336701592197258234415237438934
x2[1] (numeric) = 9.7326785132790691534489470903718e+577
absolute error = 9.7326785132790691534489470903718e+577
relative error = 1.1405032455776301511346792062149e+583 %
h = 0.0005
x1[1] (analytic) = 0.0012600188223519434958588340227923
x1[1] (numeric) = -1.0892315707434169707184947561769e+580
absolute error = 1.0892315707434169707184947561769e+580
relative error = 8.6445658701372724213693313340697e+584 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.8MB, time=59.37
NO POLE
NO POLE
t[1] = 0.53
x2[1] (analytic) = 0.00085385568875709820805291434710783
x2[1] (numeric) = -8.1036278569923615579448062328240e+587
absolute error = 8.1036278569923615579448062328240e+587
relative error = 9.4906293460295167428473659546796e+592 %
h = 0.0005
x1[1] (analytic) = 0.0012594889454210393528278357407412
x1[1] (numeric) = 9.0691655820634496847020828854347e+589
absolute error = 9.0691655820634496847020828854347e+589
relative error = 7.2006710460103989301499819717871e+594 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.8MB, time=60.05
NO POLE
NO POLE
t[1] = 0.5305
x2[1] (analytic) = 0.00085434498301184343910999606125632
x2[1] (numeric) = 6.7472468503943140363239434048427e+597
absolute error = 6.7472468503943140363239434048427e+597
relative error = 7.8975671240066024721697985270643e+602 %
h = 0.0005
x1[1] (analytic) = 0.0012589593333623770832283123849924
x1[1] (numeric) = -7.5511733743401842240177127939866e+599
absolute error = 7.5511733743401842240177127939866e+599
relative error = 5.9979486026548763065044188458911e+604 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.8MB, time=60.71
memory used=339.5MB, alloc=4.8MB, time=61.38
NO POLE
NO POLE
t[1] = 0.531
x2[1] (analytic) = 0.00085483489924170408526392545030159
x2[1] (numeric) = -5.6178961896520987727863846803500e+607
absolute error = 5.6178961896520987727863846803500e+607
relative error = 6.5719078556988602732349207496605e+612 %
h = 0.0005
x1[1] (analytic) = 0.0012584299860435536696363003938124
x1[1] (numeric) = 6.2872619110754702283627772829838e+609
absolute error = 6.2872619110754702283627772829838e+609
relative error = 4.9961157798236627939217193423231e+614 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.8MB, time=62.05
NO POLE
NO POLE
t[1] = 0.5315
x2[1] (analytic) = 0.00085532543800276483894717267152565
x2[1] (numeric) = 4.6775756538184365384725610441719e+617
absolute error = 4.6775756538184365384725610441719e+617
relative error = 5.4687671452176736009533308362107e+622 %
h = 0.0005
x1[1] (analytic) = 0.0012579009033322322795889290606847
x1[1] (numeric) = -5.2349032897042237335324907949205e+619
absolute error = 5.2349032897042237335324907949205e+619
relative error = 4.1616181972973747305320238343260e+624 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.8MB, time=62.74
memory used=350.9MB, alloc=4.8MB, time=63.41
NO POLE
NO POLE
t[1] = 0.532
x2[1] (analytic) = 0.00085581659985169984790299465988337
x2[1] (numeric) = -3.8946454791201697166261455836662e+627
absolute error = 3.8946454791201697166261455836662e+627
relative error = 4.5507945040970848587722641272089e+632 %
h = 0.0005
x1[1] (analytic) = 0.001257372085096142232500211729337
x1[1] (numeric) = 4.3586879058245665992589292727422e+629
absolute error = 4.3586879058245665992589292727422e+629
relative error = 3.4665060227508462391673290273678e+634 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.8MB, time=64.09
NO POLE
NO POLE
t[1] = 0.5325
x2[1] (analytic) = 0.00085630838534577328839346605629603
x2[1] (numeric) = 3.2427617489519162304508566963492e+637
absolute error = 3.2427617489519162304508566963492e+637
relative error = 3.7869087871217147152911147507022e+642 %
h = 0.0005
x1[1] (analytic) = 0.0012568435312030789665933749583355
x1[1] (numeric) = -3.6291329961617604897362745696730e+639
absolute error = 3.6291329961617604897362745696730e+639
relative error = 2.8874978516123423560750695654963e+644 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.8MB, time=64.76
memory used=362.4MB, alloc=4.8MB, time=65.44
NO POLE
NO POLE
t[1] = 0.533
x2[1] (analytic) = 0.0008568007950428399389892738519192
x2[1] (numeric) = -2.6999899777376459771990353854745e+647
absolute error = 2.6999899777376459771990353854745e+647
relative error = 3.1512458827756419108373101653180e+652 %
h = 0.0005
x1[1] (analytic) = 0.0012563152415209040058497173883259
x1[1] (numeric) = 3.0216906069897774728860800654084e+649
absolute error = 3.0216906069897774728860800654084e+649
relative error = 2.4052009456891549924316095109882e+654 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.8MB, time=66.12
NO POLE
NO POLE
t[1] = 0.5335
x2[1] (analytic) = 0.0008572938295013457549418536696203
x2[1] (numeric) = 2.2480670626634524170032643004898e+657
absolute error = 2.2480670626634524170032643004898e+657
relative error = 2.6222830321443757302277619877178e+662 %
h = 0.0005
x1[1] (analytic) = 0.0012557872159175449269739900491366
x1[1] (numeric) = -2.5159216082813607388629762598229e+659
absolute error = 2.5159216082813607388629762598229e+659
relative error = 2.0034617142069682614229821126563e+664 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.8MB, time=66.80
NO POLE
NO POLE
t[1] = 0.534
x2[1] (analytic) = 0.00085778748928032844313844618417794
x2[1] (numeric) = -1.8717867695445770595354652159561e+667
memory used=373.8MB, alloc=4.8MB, time=67.46
absolute error = 1.8717867695445770595354652159561e+667
relative error = 2.1821101297653334322549399162363e+672 %
h = 0.0005
x1[1] (analytic) = 0.0012552594542609953263762898480893
x1[1] (numeric) = 2.0948079609390939276777960778340e+669
absolute error = 2.0948079609390939276777960778340e+669
relative error = 1.6688246830790556904682507714016e+674 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.8MB, time=68.16
NO POLE
NO POLE
t[1] = 0.5345
x2[1] (analytic) = 0.00085828177493941803764065276357102
x2[1] (numeric) = 1.5584880757476891274562037605180e+677
absolute error = 1.5584880757476891274562037605180e+677
relative error = 1.8158233359408048346889271077393e+682 %
h = 0.0005
x1[1] (analytic) = 0.0012547319564193147871704579849903
x1[1] (numeric) = -1.7441800963788457871652697729499e+679
absolute error = 1.7441800963788457871652697729499e+679
relative error = 1.3900818317852453896700780486218e+684 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.8MB, time=68.83
NO POLE
NO POLE
t[1] = 0.535
x2[1] (analytic) = 0.00085877668703883747580706999516187
x2[1] (numeric) = -1.2976291540081271588457825544905e+687
absolute error = 1.2976291540081271588457825544905e+687
relative error = 1.5110204708543082957083007579499e+692 %
h = 0.0005
x1[1] (analytic) = 0.0012542047222606288461889750434006
x1[1] (numeric) = 1.4522401410200531608806172147137e+689
absolute error = 1.4522401410200531608806172147137e+689
relative error = 1.1578972038970458832505414287486e+694 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.8MB, time=69.50
memory used=389.1MB, alloc=4.8MB, time=70.22
NO POLE
NO POLE
t[1] = 0.5355
x2[1] (analytic) = 0.00085927222613940317500058334259466
x2[1] (numeric) = 1.0804326626137450796536668241988e+697
absolute error = 1.0804326626137450796536668241988e+697
relative error = 1.2573811066464775520411162072412e+702 %
h = 0.0005
x1[1] (analytic) = 0.0012536777516531289610143445119101
x1[1] (numeric) = -1.2091649432122959202981396788977e+699
absolute error = 1.2091649432122959202981396788977e+699
relative error = 9.6449421840489918172521321248576e+703 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.8MB, time=70.90
NO POLE
NO POLE
t[1] = 0.536
x2[1] (analytic) = 0.00085976839280252560988090076182799
x2[1] (numeric) = -8.9959040673288971946467939938920e+706
absolute error = 8.9959040673288971946467939938920e+706
relative error = 1.0463171410623262569354789055910e+712 %
h = 0.0005
x1[1] (analytic) = 0.0012531510444650724770269564932605
x1[1] (numeric) = 1.0067755453079751951280093565741e+709
absolute error = 1.0067755453079751951280093565741e+709
relative error = 8.0339520902504885535182174961505e+713 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.8MB, time=71.57
memory used=400.5MB, alloc=4.8MB, time=72.23
NO POLE
NO POLE
t[1] = 0.5365
x2[1] (analytic) = 0.00086026518759020989028290768790106
x2[1] (numeric) = 7.4901743337535291283252631891136e+716
absolute error = 7.4901743337535291283252631891136e+716
relative error = 8.7068202245113955993471937508378e+721 %
h = 0.0005
x1[1] (analytic) = 0.0012526246005647825944694233632835
x1[1] (numeric) = -8.3826197932717539643854181036854e+718
absolute error = 8.3826197932717539643854181036854e+718
relative error = 6.6920446792216946786365918100645e+723 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.8MB, time=72.90
NO POLE
NO POLE
t[1] = 0.537
x2[1] (analytic) = 0.00086076261106505633968142538779503
x2[1] (numeric) = -6.2364728581057872606530363307292e+726
absolute error = 6.2364728581057872606530363307292e+726
relative error = 7.2452878156372841750084386634020e+731 %
h = 0.0005
x1[1] (analytic) = 0.0012520984198206483355273791457368
x1[1] (numeric) = 6.9795412618068834151460264549789e+728
absolute error = 6.9795412618068834151460264549789e+728
relative error = 5.5742752736694923420694229726000e+733 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.8MB, time=73.55
NO POLE
NO POLE
memory used=411.9MB, alloc=4.8MB, time=74.24
t[1] = 0.5375
x2[1] (analytic) = 0.00086126066379026107424295525909657
x2[1] (numeric) = 5.1926152819462526729479602464029e+736
absolute error = 5.1926152819462526729479602464029e+736
relative error = 6.0290867797147959115677687405947e+741 %
h = 0.0005
x1[1] (analytic) = 0.0012515725021011245114267343732391
x1[1] (numeric) = -5.8113092835684544524144228289080e+738
absolute error = 5.8113092835684544524144228289080e+738
relative error = 4.6432062655679155272423167366530e+743 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.8MB, time=74.93
NO POLE
NO POLE
t[1] = 0.538
x2[1] (analytic) = 0.0008617593463296165824649922390997
x2[1] (numeric) = -4.3234780427620346169926993044512e+746
absolute error = 4.3234780427620346169926993044512e+746
relative error = 5.0170364396701723866726533503454e+751 %
h = 0.0005
x1[1] (analytic) = 0.0012510468472747316895473782086164
x1[1] (numeric) = 4.8386153648937794955857980709057e+748
absolute error = 4.8386153648937794955857980709057e+748
relative error = 3.8676532181302181023645781504576e+753 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.8MB, time=75.61
NO POLE
NO POLE
t[1] = 0.5385
x2[1] (analytic) = 0.00086225865924751230540349107449532
x2[1] (numeric) = 3.5998165416251059265735132959886e+756
absolute error = 3.5998165416251059265735132959886e+756
relative error = 4.1748685304785957410005796436204e+761 %
h = 0.0005
x1[1] (analytic) = 0.0012505214552100561605533196050853
x1[1] (numeric) = -4.0287304472994460541420039032923e+758
absolute error = 4.0287304472994460541420039032923e+758
relative error = 3.2216404049003066804681120026082e+763 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.8MB, time=76.27
memory used=427.2MB, alloc=4.8MB, time=76.97
NO POLE
NO POLE
t[1] = 0.539
x2[1] (analytic) = 0.00086275860310893521748906978789598
x2[1] (numeric) = -2.9972811253319431142705714748293e+766
absolute error = 2.9972811253319431142705714748293e+766
relative error = 3.4740669226957507121782087555736e+771 %
h = 0.0005
x1[1] (analytic) = 0.0012499963257757499055392592878095
x1[1] (numeric) = 3.3544036450506127649986464189752e+768
absolute error = 3.3544036450506127649986464189752e+768
relative error = 2.6835308039556548274798765125881e+773 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.8MB, time=77.63
NO POLE
NO POLE
t[1] = 0.5395
x2[1] (analytic) = 0.00086325917847947040793253526412643
x2[1] (numeric) = 2.4955977729397033538592545649000e+776
absolute error = 2.4955977729397033538592545649000e+776
relative error = 2.8909021011921420244751048435702e+781 %
h = 0.0005
x1[1] (analytic) = 0.00124947145884053056319358434347
x1[1] (numeric) = -2.7929453114619114796390988448663e+778
absolute error = 2.7929453114619114796390988448663e+778
relative error = 2.2353014082079755103062442363792e+783 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=434.8MB, alloc=4.8MB, time=78.29
memory used=438.6MB, alloc=4.8MB, time=78.74
NO POLE
NO POLE
t[1] = 0.54
x2[1] (analytic) = 0.0008637603859253016627203164664802
x2[1] (numeric) = -2.0778859185628999863803142245733e+786
absolute error = 2.0778859185628999863803142245733e+786
relative error = 2.4056277092830191177321365060524e+791 %
h = 0.0005
x1[1] (analytic) = 0.0012489468542731813969777772086
x1[1] (numeric) = 2.3254635810829425633364069049010e+788
absolute error = 2.3254635810829425633364069049010e+788
relative error = 1.8619395798360330453489287235248e+793 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.8MB, time=79.01
NO POLE
NO POLE
t[1] = 0.5405
x2[1] (analytic) = 0.00086426222601321204720039138099847
x2[1] (numeric) = 1.7300904566347780942085885304611e+796
absolute error = 1.7300904566347780942085885304611e+796
relative error = 2.0018119554010567854755716260121e+801 %
h = 0.0005
x1[1] (analytic) = 0.0012484225119425512623222308515348
x1[1] (numeric) = -1.9362286990548011909904486637306e+798
absolute error = 1.9362286990548011909904486637306e+798
relative error = 1.5509402309976133700758908147112e+803 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=446.3MB, alloc=4.8MB, time=79.29
NO POLE
NO POLE
memory used=450.1MB, alloc=4.8MB, time=79.58
t[1] = 0.541
x2[1] (analytic) = 0.00086476469931058448925929437526969
x2[1] (numeric) = -1.4405088178319675139166624596523e+806
absolute error = 1.4405088178319675139166624596523e+806
relative error = 1.6657812454421219344700722250300e+811 %
h = 0.0005
x1[1] (analytic) = 0.0012478984317175545738384619469313
x1[1] (numeric) = 1.6121437486875579426630748920816e+808
absolute error = 1.6121437486875579426630748920816e+808
relative error = 1.2918869899280757442973186332024e+813 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.8MB, time=79.86
NO POLE
NO POLE
t[1] = 0.5415
x2[1] (analytic) = 0.00086526780638540236309079124728038
x2[1] (numeric) = 1.1993972027843505412751972705578e+816
absolute error = 1.1993972027843505412751972705578e+816
relative error = 1.3861572035076066142556133095239e+821 %
h = 0.0005
x1[1] (analytic) = 0.0012473746134671712725477138459096
x1[1] (numeric) = -1.3423039683799316134598557789631e+818
absolute error = 1.3423039683799316134598557789631e+818
relative error = 1.0761033244446887376135858212631e+823 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=457.7MB, alloc=4.8MB, time=80.14
NO POLE
NO POLE
t[1] = 0.542
x2[1] (analytic) = 0.00086577154780625007355680982946525
x2[1] (numeric) = -9.9864272418131696119457107014602e+825
absolute error = 9.9864272418131696119457107014602e+825
relative error = 1.1534714056054911626467056839107e+831 %
h = 0.0005
x1[1] (analytic) = 0.001246851057060446793125941148968
x1[1] (numeric) = 1.1176298298432362759192757029672e+828
absolute error = 1.1176298298432362759192757029672e+828
relative error = 8.9636193795122561402293479534926e+832 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.8MB, time=80.42
memory used=465.4MB, alloc=4.8MB, time=80.70
NO POLE
NO POLE
t[1] = 0.5425
x2[1] (analytic) = 0.00086627592414231364114121460331367
x2[1] (numeric) = 8.3149042556137457018026715972524e+835
absolute error = 8.3149042556137457018026715972524e+835
relative error = 9.5984478200132405425510055686403e+840 %
h = 0.0005
x1[1] (analytic) = 0.001246327762366492031165167692916
x1[1] (numeric) = -9.3056153150094206333206185781383e+837
absolute error = 9.3056153150094206333206185781383e+837
relative error = 7.4664270475209350420681113334512e+842 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.8MB, time=80.97
NO POLE
NO POLE
t[1] = 0.543
x2[1] (analytic) = 0.00086678093596338128749701437068642
x2[1] (numeric) = -6.9231599155446022498316994217295e+845
absolute error = 6.9231599155446022498316994217295e+845
relative error = 7.9872083340756395402755674620010e+850 %
h = 0.0005
x1[1] (analytic) = 0.0012458047292544833104512097671668
x1[1] (numeric) = 7.7480462742376878655255284156499e+847
absolute error = 7.7480462742376878655255284156499e+847
relative error = 6.2193103720791680935377766993820e+852 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.8MB, time=81.25
memory used=476.8MB, alloc=4.8MB, time=81.53
NO POLE
NO POLE
t[1] = 0.5435
x2[1] (analytic) = 0.00086728658383984402158759261938419
x2[1] (numeric) = 5.7643650176541557667517539194716e+855
absolute error = 5.7643650176541557667517539194716e+855
relative error = 6.6464362819183448506314142784221e+860 %
h = 0.0005
x1[1] (analytic) = 0.0012452819575936623502577563788178
x1[1] (numeric) = -6.4511823276102986011499220470005e+857
absolute error = 6.4511823276102986011499220470005e+857
relative error = 5.1804993144494995703411901534418e+862 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.8MB, time=81.81
NO POLE
NO POLE
t[1] = 0.544
x2[1] (analytic) = 0.00086779286834269622642255081248739
x2[1] (numeric) = -4.7995286057380001235572570856534e+865
absolute error = 4.7995286057380001235572570856534e+865
relative error = 5.5307306395639098569073791540891e+870 %
h = 0.0005
x1[1] (analytic) = 0.00124475944725333623265679839004
x1[1] (numeric) = 5.3713867923647762880727555123904e+867
absolute error = 5.3713867923647762880727555123904e+867
relative error = 4.3152006632423490326712266818470e+872 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=484.4MB, alloc=4.8MB, time=82.09
memory used=488.2MB, alloc=4.8MB, time=82.37
NO POLE
NO POLE
t[1] = 0.5445
x2[1] (analytic) = 0.00086829979004353624638875542355646
x2[1] (numeric) = 3.9961860095167570318040041073048e+875
absolute error = 3.9961860095167570318040041073048e+875
relative error = 4.6023113852375683165586473915035e+880 %
h = 0.0005
x1[1] (analytic) = 0.0012442371981028773698453983553836
x1[1] (numeric) = -4.4723268709533258712504237696571e+877
absolute error = 4.4723268709533258712504237696571e+877
relative error = 3.5944326996270530155187482036647e+882 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.8MB, time=82.64
NO POLE
NO POLE
t[1] = 0.545
x2[1] (analytic) = 0.00086880734951456697517718013294248
x2[1] (numeric) = -3.3273064782998433510250846775368e+885
absolute error = 3.3273064782998433510250846775368e+885
relative error = 3.8297402527256770401302667285068e+890 %
h = 0.0005
x1[1] (analytic) = 0.0012437152100117234714887928906918
x1[1] (numeric) = 3.7237511305428310710865580316601e+887
absolute error = 3.7237511305428310710865580316601e+887
relative error = 2.9940545074685790474753125389465e+892 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.8MB, time=82.92
NO POLE
NO POLE
t[1] = 0.5455
x2[1] (analytic) = 0.00086931554732859644430613519421227
x2[1] (numeric) = 2.7703836543571890320403600003385e+895
absolute error = 2.7703836543571890320403600003385e+895
relative error = 3.1868562144903171867969958832168e+900 %
h = 0.0005
x1[1] (analytic) = 0.0012431934828493775120798194093974
x1[1] (numeric) = -3.1004716073588898328080862571355e+897
absolute error = 3.1004716073588898328080862571355e+897
relative error = 2.4939574170326759215552735274820e+902 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.8MB, time=83.20
memory used=503.5MB, alloc=4.8MB, time=83.48
NO POLE
NO POLE
t[1] = 0.546
x2[1] (analytic) = 0.00086982438405903841224147657403825
x2[1] (numeric) = -2.3066782823838961316463981186628e+905
absolute error = 2.3066782823838961316463981186628e+905
relative error = 2.6518896511267874242581239833252e+910 %
h = 0.0005
x1[1] (analytic) = 0.0012426720164854076983146590660609
x1[1] (numeric) = 2.5815162858741557929960904298870e+907
absolute error = 2.5815162858741557929960904298870e+907
relative error = 2.0773915012388707125125250905980e+912 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.8MB, time=83.76
NO POLE
NO POLE
t[1] = 0.5465
x2[1] (analytic) = 0.00087033386027991295411438806384394
x2[1] (numeric) = 1.9205876738599571634628950224220e+915
absolute error = 1.9205876738599571634628950224220e+915
relative error = 2.2067252137498892550997143546934e+920 %
h = 0.0005
x1[1] (analytic) = 0.0012421508107894474364848877510829
x1[1] (numeric) = -2.1494234355883555874875824417063e+917
absolute error = 2.1494234355883555874875824417063e+917
relative error = 1.7304045667548951951987115079614e+922 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=511.1MB, alloc=4.8MB, time=84.03
memory used=514.9MB, alloc=4.8MB, time=84.32
NO POLE
NO POLE
t[1] = 0.547
x2[1] (analytic) = 0.00087084397656584705203733015703041
x2[1] (numeric) = -1.5991207101367701393185196309206e+925
absolute error = 1.5991207101367701393185196309206e+925
relative error = 1.8362884203928991178425652315353e+930 %
h = 0.0005
x1[1] (analytic) = 0.0012416298656311952998858269846059
x1[1] (numeric) = 1.7896540613502321314528841715786e+927
absolute error = 1.7896540613502321314528841715786e+927
relative error = 1.4413748500165490951273144299365e+932 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.8MB, time=84.59
NO POLE
NO POLE
t[1] = 0.5475
x2[1] (analytic) = 0.00087135473349207518601875008173811
x2[1] (numeric) = 1.3314607192333722956432664836415e+935
absolute error = 1.3314607192333722956432664836415e+935
relative error = 1.5280352169516064154076312552312e+940 %
h = 0.0005
x1[1] (analytic) = 0.0012411091808804149962411865616909
x1[1] (numeric) = -1.4901026974383342879339082127714e+937
absolute error = 1.4901026974383342879339082127714e+937
relative error = 1.2006217667178071148438071280896e+942 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.8MB, time=84.87
memory used=526.4MB, alloc=4.8MB, time=85.15
NO POLE
NO POLE
t[1] = 0.548
x2[1] (analytic) = 0.0008718661316344399254771479758239
x2[1] (numeric) = -1.1086015180866649310549892290270e+945
absolute error = 1.1086015180866649310549892290270e+945
relative error = 1.2715272194464419408754661483430e+950 %
h = 0.0005
x1[1] (analytic) = 0.0012405887564069353351439908049313
x1[1] (numeric) = 1.2406900846735599845294565368297e+947
absolute error = 1.2406900846735599845294565368297e+947
relative error = 1.0000816775632548227761697415252e+952 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=530.2MB, alloc=4.8MB, time=85.43
NO POLE
NO POLE
t[1] = 0.5485
x2[1] (analytic) = 0.00087237817156939252135509478805287
x2[1] (numeric) = 9.2304437386007862222861082111478e+954
absolute error = 9.2304437386007862222861082111478e+954
relative error = 1.0580782554422911810471293895577e+960 %
h = 0.0005
x1[1] (analytic) = 0.0012400685920806501955137802847337
x1[1] (numeric) = -1.0330240250242803188455846562743e+957
absolute error = 1.0330240250242803188455846562743e+957
relative error = 8.3303781066740835296059710937728e+961 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.8MB, time=85.70
NO POLE
NO POLE
t[1] = 0.549
x2[1] (analytic) = 0.00087289085387399349883379808742284
x2[1] (numeric) = -7.6854568771043179815772655101273e+964
absolute error = 7.6854568771043179815772655101273e+964
relative error = 8.8046023658001978788649471433551e+969 %
h = 0.0005
x1[1] (analytic) = 0.0012395486877715184930700808715671
x1[1] (numeric) = 8.6011700219087471623226083269748e+966
absolute error = 8.6011700219087471623226083269748e+966
relative error = 6.9389529485703990261718374080252e+971 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.8MB, time=85.99
memory used=541.6MB, alloc=4.8MB, time=86.28
NO POLE
NO POLE
t[1] = 0.5495
x2[1] (analytic) = 0.00087340417912591325064881256105309
x2[1] (numeric) = 6.3990691111436990884776295890932e+974
absolute error = 6.3990691111436990884776295890932e+974
relative error = 7.3265840307150454761204189756438e+979 %
h = 0.0005
x1[1] (analytic) = 0.001239029043349564147822131988547
x1[1] (numeric) = -7.1615106670963321028443994021033e+976
absolute error = 7.1615106670963321028443994021033e+976
relative error = 5.7799376903515191529305006066823e+981 %
h = 0.0005
TOP MAIN SOLVE Loop
memory used=545.5MB, alloc=4.8MB, time=86.55
NO POLE
NO POLE
t[1] = 0.55
x2[1] (analytic) = 0.00087391814790343263100749258018221
x2[1] (numeric) = -5.3279962589057677568896583666516e+984
absolute error = 5.3279962589057677568896583666516e+984
relative error = 6.0966765270727708571483439226418e+989 %
h = 0.0005
x1[1] (analytic) = 0.0012385096586848760515748659367868
x1[1] (numeric) = 5.9628207446541132874154920564321e+986
absolute error = 5.9628207446541132874154920564321e+986
relative error = 4.8145129130327449519827804072766e+991 %
h = 0.0005
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 = 1 Minutes 26 Seconds
Elapsed Time(since restart) = 1 Minutes 26 Seconds
Expected Time Remaining = 2 Hours 7 Minutes 16 Seconds
Optimized Time Remaining = 2 Hours 7 Minutes 13 Seconds
Time to Timeout = 13 Minutes 33 Seconds
Percent Done = 1.122 %
> quit
memory used=548.7MB, alloc=4.8MB, time=86.77