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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
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
>
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (iter >= 0) then # if number 1
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := abs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (abs(analytic_val_y) <> 0.0) then # if number 2
> relerr := abserr*100.0/abs(analytic_val_y);
> else
> relerr := -1.0 ;
> fi;# end if 2
> ;
> if glob_iter = 1 then # if number 2
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 2
> ;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> #BOTTOM DISPLAY ALOT
> fi;# end if 1
> ;
> # End Function number 3
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := abs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if abs(analytic_val_y) <> 0. then
relerr := abserr*100.0/abs(analytic_val_y)
else relerr := -1.0
end if;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end proc
> # Begin Function number 4
> adjust_for_pole := proc(h_param)
> global
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
>
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
>
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := abs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1
> ;
> if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> newline();
> return(hnew);
> fi;# end if 2
> fi;# end if 1
> ;
> if (not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_t[1];
> fi;# end if 1
> ;
> hnew := sz2;
> #END block
> #BOTTOM ADJUST FOR POLE
> # End Function number 4
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < abs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
newline();
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_t[1]
end if;
hnew := sz2
end proc
> # Begin Function number 5
> prog_report := proc(t_start,t_end)
> global
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
>
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> percent_done := comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if convfloat(percent_done) < convfloat(100.0) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> fi;# end if 1
> ;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> # End Function number 5
> end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),
convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
convfloat(array_t[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # Begin Function number 6
> check_for_pole := proc()
> global
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
>
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x2_higher[1,m]/array_x2_higher[1,m-1];
> rm1 := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2
> ;
> if (m > 10) then # if number 1
> rm0 := array_x1_higher[1,m]/array_x1_higher[1,m-1];
> rm1 := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
> hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
> if (abs(hdrc) > glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
> array_real_pole[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1
> ;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x2_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 1
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float)) then # if number 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> rm0 := (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
> rm1 := (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
> rm2 := (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
> rm3 := (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
> rm4 := (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3
> ;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2
> ;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (abs(array_x1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2
> ;
> n := n - 1;
> od;# end do number 2
> ;
> m := n + cnt;
> if (m <= 10) then # if number 2
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float)) then # if number 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> rm0 := (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
> rm1 := (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
> rm2 := (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
> rm3 := (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
> rm4 := (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := glob_large_float;
> else
> if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (abs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * glob_h;
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4
> ;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3
> ;
> #BOTTOM RADII COMPLEX EQ = 2
> found := false;
> #TOP WHICH RADII EQ = 1
> if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found := true;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found := true;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found := true;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 1
> found := false;
> #TOP WHICH RADII EQ = 2
> if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found := true;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found := true;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found := true;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found := true;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> if not found then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (glob_display_flag) then # if number 4
> omniout_str(ALWAYS,"NO POLE");
> fi;# end if 4
> ;
> fi;# end if 3
> ;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if array_pole[1] > array_poles[1,1] then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if array_pole[1] > array_poles[2,1] then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3
> ;
> #BOTTOM WHICH RADIUS EQ = 2
> #BOTTOM CHECK FOR POLE
> display_pole();
> # End Function number 6
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
abs(array_x2_higher[1, m - 1]) < glob_small_float or
abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
abs(array_x1_higher[1, m - 1]) < glob_small_float or
abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
end do;
if 10 < m then
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
if glob_small_float < abs(hdrc) then
rcs := glob_h/hdrc;
ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
array_real_pole[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x2_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
elif glob_large_float <= abs(array_x2_higher[1, m]) or
glob_large_float <= abs(array_x2_higher[1, m - 1]) or
glob_large_float <= abs(array_x2_higher[1, m - 2]) or
glob_large_float <= abs(array_x2_higher[1, m - 3]) or
glob_large_float <= abs(array_x2_higher[1, m - 4]) or
glob_large_float <= abs(array_x2_higher[1, m - 5]) then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[1, 1] := glob_large_float;
array_complex_pole[1, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < abs(array_x1_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
elif glob_large_float <= abs(array_x1_higher[1, m]) or
glob_large_float <= abs(array_x1_higher[1, m - 1]) or
glob_large_float <= abs(array_x1_higher[1, m - 2]) or
glob_large_float <= abs(array_x1_higher[1, m - 3]) or
glob_large_float <= abs(array_x1_higher[1, m - 4]) or
glob_large_float <= abs(array_x1_higher[1, m - 5]) then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
abs(dr1) <= glob_small_float then
array_complex_pole[2, 1] := glob_large_float;
array_complex_pole[2, 2] := glob_large_float
else
if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < abs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*glob_h
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[2, 1] := rad_c;
array_complex_pole[2, 2] := ord_no
end if;
found := false;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found := true;
array_type_pole[1] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found := true;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found := true;
array_type_pole[1] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
found := false;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found := true;
array_type_pole[2] := 2;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found := true;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found := true;
array_type_pole[2] := 1;
if glob_display_flag then
omniout_str(ALWAYS, "Real estimate of pole used")
end if
end if;
if not found and array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found := true;
if glob_display_flag then
omniout_str(ALWAYS, "Complex estimate of poles used")
end if
end if;
if not found then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
display_pole()
end proc
> # Begin Function number 7
> get_norms := proc()
> global
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
>
> local iii;
> if (not glob_initial_pass) then # if number 3
> set_z(array_norms,glob_max_terms+1);
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x2[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := abs(array_x1[iii]);
> fi;# end if 4
> ;
> iii := iii + 1;
> od;# end do number 2
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
if not glob_initial_pass then
set_z(array_norms, glob_max_terms + 1);
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x2[iii]) then
array_norms[iii] := abs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < abs(array_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
>
> local kkk, order_d, adj2, temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1
> array_tmp1[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp2[1] := (array_const_3D0[1] * (array_tmp1[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp3[1] - (array_tmp4[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre diff $eq_no = 1 i = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 1 i = 1
> array_tmp9[1] := (array_tmp7[1] - (array_tmp8[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,2] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> # emit pre mult $eq_no = 2 i = 1
> array_tmp12[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp14[1] := (array_const_2D0[1] * (array_tmp13[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp15[1] := (array_tmp12[1] - (array_tmp14[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp16[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp17[1] := (array_tmp15[1] - (array_tmp16[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,1] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2
> array_tmp1[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - (array_tmp4[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre diff $eq_no = 1 i = 2
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 1 i = 2
> array_tmp9[2] := (array_tmp7[2] - (array_tmp8[2]));
> #emit pre add $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,3] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> # emit pre mult $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp15[2] := (array_tmp12[2] - (array_tmp14[2]));
> # emit pre mult $eq_no = 2 i = 2
> array_tmp16[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp17[2] := (array_tmp15[2] - (array_tmp16[2]));
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,2] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3
> array_tmp1[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - (array_tmp4[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre diff $eq_no = 1 i = 3
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 1 i = 3
> array_tmp9[3] := (array_tmp7[3] - (array_tmp8[3]));
> #emit pre add $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,4] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> # emit pre mult $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp15[3] := (array_tmp12[3] - (array_tmp14[3]));
> # emit pre mult $eq_no = 2 i = 3
> array_tmp16[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp17[3] := (array_tmp15[3] - (array_tmp16[3]));
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,3] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4
> array_tmp1[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - (array_tmp4[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre diff $eq_no = 1 i = 4
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 1 i = 4
> array_tmp9[4] := (array_tmp7[4] - (array_tmp8[4]));
> #emit pre add $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,5] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> # emit pre mult $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp15[4] := (array_tmp12[4] - (array_tmp14[4]));
> # emit pre mult $eq_no = 2 i = 4
> array_tmp16[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp17[4] := (array_tmp15[4] - (array_tmp16[4]));
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,4] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5
> array_tmp1[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_const_3D0,array_tmp1,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - (array_tmp4[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre diff $eq_no = 1 i = 5
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 1 i = 5
> array_tmp9[5] := (array_tmp7[5] - (array_tmp8[5]));
> #emit pre add $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[2,6] := temporary
> ;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> # emit pre mult $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_const_2D0,array_tmp13,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp15[5] := (array_tmp12[5] - (array_tmp14[5]));
> # emit pre mult $eq_no = 2 i = 5
> array_tmp16[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp17[5] := (array_tmp15[5] - (array_tmp16[5]));
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x1_higher[2,5] := temporary
> ;
> fi;# end if 1
> ;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_const_3D0,array_tmp1,1);
> #emit add $eq_no = 1
> array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp3[kkk] - (array_tmp4[kkk]));
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 1
> array_tmp9[kkk] := (array_tmp7[kkk] - (array_tmp8[kkk]));
> #emit add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp10[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x2[kkk + order_d] := temporary;
> array_x2_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x2_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> #emit mult $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_const_2D0,array_tmp13,1);
> #emit sub $eq_no = 2
> array_tmp15[kkk] := (array_tmp12[kkk] - (array_tmp14[kkk]));
> #emit mult $eq_no = 2
> array_tmp16[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 2
> array_tmp17[kkk] := (array_tmp15[kkk] - (array_tmp16[kkk]));
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp17[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x1[kkk + order_d] := temporary;
> array_x1_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := 2;
> while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
> temporary := temporary / glob_h * convfp(adj2);
> array_x1_higher[adj2,term] := temporary;
> adj2 := adj2 + 1;
> term := term - 1;
> od;# end do number 2
> fi;# end if 1
> ;
> kkk := kkk + 1;
> od;# end do number 1
> ;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> # End Function number 8
> end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 2] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 1] := temporary
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 1] := temporary
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 2] := temporary
end if;
kkk := 3;
array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 2] := temporary
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if;
kkk := 4;
array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 3] := temporary
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 4] := temporary
end if;
kkk := 5;
array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 4] := temporary
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 5] := temporary
end if;
kkk := 6;
array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*2.0/glob_h;
array_x1_higher[2, 5] := temporary
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp10[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x2[kkk + order_d] := temporary;
array_x2_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x2_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp17[kkk]*glob_h^order_d/
factorial_3(kkk - 1, kkk + order_d - 1);
array_x1[kkk + order_d] := temporary;
array_x1_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := 2;
while adj2 <= order_d + 1 and 1 <= term do
temporary := temporary*convfp(adj2)/glob_h;
array_x1_higher[adj2, term] := temporary;
adj2 := adj2 + 1;
term := term - 1
end do
end if;
kkk := kkk + 1
end do
end proc
> #BEGIN ATS LIBRARY BLOCK
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s\n",str);
> fi;
> # End Function number 1
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> printf("%s",str);
> fi;
> # End Function number 1
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(label,str);
> fi;
> # End Function number 1
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> if vallen = 5 then
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;
> fi;
> # End Function number 1
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;
> # End Function number 1
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> dump_series := proc(iolevel,dump_label,series_name,
> array_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name
> ,i,array_series[i]);
> i := i + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, array_series[i]); i := i + 1
end do
end if
end proc
> dump_series_2 := proc(iolevel,dump_label,series_name2,
> array_series2,numb,subnum,array_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then
> sub := 1;
> while (sub <= subnum) do
> i := 1;
> while (i <= numb) do
> print(dump_label,series_name2,sub,i,array_series2[sub,i]);
> od;
> sub := sub + 1;
> od;
> fi;
> # End Function number 1
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
array_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;
> # End Function number 1
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # Begin Function number 2
> logitem_time := proc(fd,secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := (secs_in);
> if (secs > 0.0) then # if number 1
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
> fprintf(fd,"
");
> if (millinium_int > 0) then # if number 2
> fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 3
> fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 4
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 5
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 6
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 7
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 7
> else
> fprintf(fd,"Unknown");
> fi;# end if 6
> fprintf(fd," | ");
> # End Function number 2
> end;
logitem_time := proc(fd, secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := secs_in;
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
fprintf(fd, "");
if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\
d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then fprintf(fd,
"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, "Unknown")
end if;
fprintf(fd, " | ")
end proc
> omniout_timestr := proc (secs_in)
> global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
> local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
> secs := convfloat(secs_in);
> if (secs > 0.0) then # if number 6
> sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
> milliniums := convfloat(secs / sec_in_millinium);
> millinium_int := floor(milliniums);
> centuries := (milliniums - millinium_int)*centuries_in_millinium;
> cent_int := floor(centuries);
> years := (centuries - cent_int) * years_in_century;
> years_int := floor(years);
> days := (years - years_int) * days_in_year;
> days_int := floor(days);
> hours := (days - days_int) * hours_in_day;
> hours_int := floor(hours);
> minutes := (hours - hours_int) * min_in_hour;
> minutes_int := floor(minutes);
> seconds := (minutes - minutes_int) * sec_in_min;
> sec_int := floor(seconds);
>
> if (millinium_int > 0) then # if number 7
> printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (cent_int > 0) then # if number 8
> printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int);
> elif (years_int > 0) then # if number 9
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif (days_int > 0) then # if number 10
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif (hours_int > 0) then # if number 11
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif (minutes_int > 0) then # if number 12
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 12
> else
> printf(" Unknown\n");
> fi;# end if 11
> # End Function number 2
> end;
omniout_timestr := proc(secs_in)
local cent_int, centuries, days, days_int, hours, hours_int, millinium_int,
milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs,
years, years_int;
global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour,
sec_in_min, years_in_century;
secs := convfloat(secs_in);
if 0. < secs then
sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day*
days_in_year*years_in_century*centuries_in_millinium);
milliniums := convfloat(secs/sec_in_millinium);
millinium_int := floor(milliniums);
centuries := (milliniums - millinium_int)*centuries_in_millinium;
cent_int := floor(centuries);
years := (centuries - cent_int)*years_in_century;
years_int := floor(years);
days := (years - years_int)*days_in_year;
days_int := floor(days);
hours := (days - days_int)*hours_in_day;
hours_int := floor(hours);
minutes := (hours - hours_int)*min_in_hour;
minutes_int := floor(minutes);
seconds := (minutes - minutes_int)*sec_in_min;
sec_int := floor(seconds);
if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\
Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int,
cent_int, years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \
%d Hours %d Minutes %d Seconds\n", cent_int, years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
>
> # Begin Function number 3
> ats := proc(
> mmm_ats,array_a,array_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 11
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 11
> ;
> ret_ats
> # End Function number 3
> end;
ats := proc(mmm_ats, array_a, array_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
>
> # Begin Function number 4
> att := proc(
> mmm_att,array_aa,array_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 11
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 12
> ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att);
> fi;# end if 12
> ;
> iii_att := iii_att + 1;
> od;# end do number 1
> ;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 11
> ;
> ret_att;
> # End Function number 4
> end;
att := proc(mmm_att, array_aa, array_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att := ret_att
+ array_aa[iii_att]*array_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # Begin Function number 5
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 11
> # End Function number 5
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # Begin Function number 6
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> # End Function number 6
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # Begin Function number 7
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> # End Function number 7
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # Begin Function number 8
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> # End Function number 8
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # Begin Function number 9
> log_revs := proc(file,revs)
> fprintf(file,revs);
> # End Function number 9
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # Begin Function number 10
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> # End Function number 10
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # Begin Function number 11
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if pole = 0 then # if number 11
> fprintf(file,"NA");
> elif pole = 1 then # if number 12
> fprintf(file,"Real");
> elif pole = 2 then # if number 13
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 13
> fprintf(file," | ");
> # End Function number 11
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # Begin Function number 12
> logstart := proc(file)
> fprintf(file,"");
> # End Function number 12
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # Begin Function number 13
> logend := proc(file)
> fprintf(file,"
\n");
> # End Function number 13
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # Begin Function number 14
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
>
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 13
> ;
> if (glob_max_iter < 2) then # if number 13
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 13
> ;
> if (errflag) then # if number 13
>
> quit;
> fi;# end if 13
> # End Function number 14
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
>
> # Begin Function number 15
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 13
> sec_left := 0.0;
> else
> if (abs(sub2) > 0.0) then # if number 14
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 14
> fi;# end if 13
> ;
> sec_left;
> # End Function number 15
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
>
> # Begin Function number 16
> comp_percent := proc(t_end2,t_start2,t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (abs(sub2) > glob_small_float) then # if number 13
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 13
> ;
> rrr
> # End Function number 16
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
>
> # Begin Function number 17
> factorial_1 := proc(nnn)
> nnn!;
>
> # End Function number 17
> end;
factorial_1 := proc(nnn) nnn! end proc
>
> # Begin Function number 18
> factorial_3 := proc(mmm2,nnn2)
> (mmm2!)/(nnn2!);
>
> # End Function number 18
> end;
factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc
> # Begin Function number 19
> convfp := proc(mmm)
> (mmm);
>
> # End Function number 19
> end;
convfp := proc(mmm) mmm end proc
> # Begin Function number 20
> convfloat := proc(mmm)
> (mmm);
>
> # End Function number 20
> end;
convfloat := proc(mmm) mmm end proc
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
>
>
>
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c1 + 6.0 * c3 * exp(-t);
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 0.0001;
> c2 := 0.0002;
> c3 := 0.0003;
> 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> mainprog := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, log10norm, max_terms, opt_iter, tmp;
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> global
> INFO,
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_max_iter,
> glob_hmin_init,
> sec_in_min,
> glob_iter,
> glob_unchanged_h_cnt,
> glob_dump_analytic,
> glob_hmin,
> glob_optimal_done,
> glob_max_opt_iter,
> glob_optimal_expect_sec,
> glob_h,
> glob_clock_start_sec,
> hours_in_day,
> djd_debug2,
> glob_warned2,
> glob_max_trunc_err,
> glob_max_order,
> glob_max_rel_trunc_err,
> glob_dump,
> glob_html_log,
> glob_log10abserr,
> glob_relerr,
> glob_hmax,
> years_in_century,
> days_in_year,
> glob_normmax,
> MAX_UNCHANGED,
> glob_curr_iter_when_opt,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_not_yet_start_msg,
> centuries_in_millinium,
> glob_orig_start_sec,
> glob_warned,
> glob_small_float,
> glob_last_good_h,
> glob_clock_sec,
> djd_debug,
> glob_percent_done,
> glob_smallish_float,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_hours,
> glob_abserr,
> glob_large_float,
> glob_disp_incr,
> glob_initial_pass,
> glob_max_minutes,
> glob_log10relerr,
> glob_look_poles,
> glob_log10normmin,
> glob_max_sec,
> glob_reached_optimal_h,
> glob_not_yet_finished,
> min_in_hour,
> glob_current_iter,
> glob_no_eqs,
> glob_almost_1,
> glob_display_flag,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_t,
> array_type_pole,
> array_norms,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_x1_init,
> array_1st_rel_error,
> array_x2_init,
> array_m1,
> 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_last_rel_error,
> array_x1_higher,
> array_x2_higher,
> array_poles,
> array_real_pole,
> array_x1_higher_work2,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_x2_higher_work,
> array_complex_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> INFO := 2;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_max_terms := 30;
> DEBUGL := 3;
> glob_start := 0;
> glob_max_iter := 1000;
> glob_hmin_init := 0.001;
> sec_in_min := 60.0;
> glob_iter := 0;
> glob_unchanged_h_cnt := 0;
> glob_dump_analytic := false;
> glob_hmin := 0.00000000001;
> glob_optimal_done := false;
> glob_max_opt_iter := 10;
> glob_optimal_expect_sec := 0.1;
> glob_h := 0.1;
> glob_clock_start_sec := 0.0;
> hours_in_day := 24.0;
> djd_debug2 := true;
> glob_warned2 := false;
> glob_max_trunc_err := 0.1e-10;
> glob_max_order := 30;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_dump := false;
> glob_html_log := true;
> glob_log10abserr := 0.0;
> glob_relerr := 0.1e-10;
> glob_hmax := 1.0;
> years_in_century := 100.0;
> days_in_year := 365.0;
> glob_normmax := 0.0;
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_not_yet_start_msg := true;
> centuries_in_millinium := 10.0;
> glob_orig_start_sec := 0.0;
> glob_warned := false;
> glob_small_float := 0.1e-50;
> glob_last_good_h := 0.1;
> glob_clock_sec := 0.0;
> djd_debug := true;
> glob_percent_done := 0.0;
> glob_smallish_float := 0.1e-100;
> glob_optimal_start := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_hours := 0.0;
> glob_abserr := 0.1e-10;
> glob_large_float := 9.0e100;
> glob_disp_incr := 0.1;
> glob_initial_pass := true;
> glob_max_minutes := 0.0;
> glob_log10relerr := 0.0;
> glob_look_poles := false;
> glob_log10normmin := 0.1;
> glob_max_sec := 10000.0;
> glob_reached_optimal_h := false;
> glob_not_yet_finished := true;
> min_in_hour := 60.0;
> glob_current_iter := 0;
> glob_no_eqs := 0;
> glob_almost_1 := 0.9990;
> glob_display_flag := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/complicatedrev2postode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits := 32;");
> omniout_str(ALWAYS,"max_terms := 30;");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 5.0;");
> omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_h := 0.00001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_h := 0.00005 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"glob_max_minutes := 15;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 0.0001;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> glob_log10_abserr := -8.0;
> glob_log10_relerr := -8.0;
> glob_hmax := 0.01;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits := 32;
> max_terms := 30;
> #END FIRST INPUT BLOCK
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_t:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= 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_pole:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> 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_norms[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_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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 <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_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_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_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_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.00005 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> glob_max_minutes := 15;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> glob_abserr := 10.0 ^ (glob_log10_abserr);
> glob_relerr := 10.0 ^ (glob_log10_relerr);
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> if glob_html_log then # if number 3
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 3
> ;
> #BEGIN SOLUTION CODE
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2
> ;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3
> ;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> start_array_x2();
> if (abs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x2_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> start_array_x1();
> if (abs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := abs(array_x1_higher[1,1]);
> log10norm := (log10(tmp));
> if (log10norm < glob_log10normmin) then # if number 4
> glob_log10normmin := log10norm;
> fi;# end if 4
> fi;# end if 3
> ;
> display_alot(current_iter)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> sub_iter := 1;
> while sub_iter <= 3 do # do number 3
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;# end do number 3
> ;
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> order_diff := 2;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> order_diff := 2;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> order_diff := 1;
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3
> ;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> order_diff := 1;
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3
> ;
> array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while ord <= order_diff do # do number 4
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4
> ;
> term_no := term_no - 1;
> od;# end do number 3
> ;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> display_alot(current_iter)
> ;
> od;# end do number 2
> ;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
> fi;# end if 3
> ;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
> fi;# end if 3
> ;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T02:11:49-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev2")
> ;
> 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,"complicatedrev2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev2 maple results")
> ;
> logitem_str(html_log_file,"sub iter tot order 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 INFO, ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, DEBUGL,
glob_start, glob_max_iter, glob_hmin_init, sec_in_min, glob_iter,
glob_unchanged_h_cnt, glob_dump_analytic, glob_hmin, glob_optimal_done,
glob_max_opt_iter, glob_optimal_expect_sec, glob_h, glob_clock_start_sec,
hours_in_day, djd_debug2, glob_warned2, glob_max_trunc_err, glob_max_order,
glob_max_rel_trunc_err, glob_dump, glob_html_log, glob_log10abserr,
glob_relerr, glob_hmax, years_in_century, days_in_year, glob_normmax,
MAX_UNCHANGED, glob_curr_iter_when_opt, glob_log10_relerr,
glob_log10_abserr, glob_not_yet_start_msg, centuries_in_millinium,
glob_orig_start_sec, glob_warned, glob_small_float, glob_last_good_h,
glob_clock_sec, djd_debug, glob_percent_done, glob_smallish_float,
glob_optimal_start, glob_optimal_clock_start_sec, glob_max_hours,
glob_abserr, glob_large_float, glob_disp_incr, glob_initial_pass,
glob_max_minutes, glob_log10relerr, glob_look_poles, glob_log10normmin,
glob_max_sec, glob_reached_optimal_h, glob_not_yet_finished, min_in_hour,
glob_current_iter, glob_no_eqs, glob_almost_1, glob_display_flag,
array_const_2D0, array_const_3D0, array_const_1, array_const_2,
array_const_4D0, array_const_0D0, array_t, array_type_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_pole, array_x1_init,
array_1st_rel_error, array_x2_init, array_m1, 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_last_rel_error,
array_x1_higher, array_x2_higher, array_poles, array_real_pole,
array_x1_higher_work2, array_x1_higher_work, array_x2_higher_work2,
array_x2_higher_work, array_complex_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
INFO := 2;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_max_terms := 30;
DEBUGL := 3;
glob_start := 0;
glob_max_iter := 1000;
glob_hmin_init := 0.001;
sec_in_min := 60.0;
glob_iter := 0;
glob_unchanged_h_cnt := 0;
glob_dump_analytic := false;
glob_hmin := 0.1*10^(-10);
glob_optimal_done := false;
glob_max_opt_iter := 10;
glob_optimal_expect_sec := 0.1;
glob_h := 0.1;
glob_clock_start_sec := 0.;
hours_in_day := 24.0;
djd_debug2 := true;
glob_warned2 := false;
glob_max_trunc_err := 0.1*10^(-10);
glob_max_order := 30;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_dump := false;
glob_html_log := true;
glob_log10abserr := 0.;
glob_relerr := 0.1*10^(-10);
glob_hmax := 1.0;
years_in_century := 100.0;
days_in_year := 365.0;
glob_normmax := 0.;
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_not_yet_start_msg := true;
centuries_in_millinium := 10.0;
glob_orig_start_sec := 0.;
glob_warned := false;
glob_small_float := 0.1*10^(-50);
glob_last_good_h := 0.1;
glob_clock_sec := 0.;
djd_debug := true;
glob_percent_done := 0.;
glob_smallish_float := 0.1*10^(-100);
glob_optimal_start := 0.;
glob_optimal_clock_start_sec := 0.;
glob_max_hours := 0.;
glob_abserr := 0.1*10^(-10);
glob_large_float := 0.90*10^101;
glob_disp_incr := 0.1;
glob_initial_pass := true;
glob_max_minutes := 0.;
glob_log10relerr := 0.;
glob_look_poles := false;
glob_log10normmin := 0.1;
glob_max_sec := 10000.0;
glob_reached_optimal_h := false;
glob_not_yet_finished := true;
min_in_hour := 60.0;
glob_current_iter := 0;
glob_no_eqs := 0;
glob_almost_1 := 0.9990;
glob_display_flag := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/complicatedrev2postode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits := 32;");
omniout_str(ALWAYS, "max_terms := 30;");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 5.0;");
omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
omniout_str(ALWAYS, "glob_h := 0.00001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_h := 0.00005 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "glob_max_minutes := 15;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 0.0001;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
glob_log10_abserr := -8.0;
glob_log10_relerr := -8.0;
glob_hmax := 0.01;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_t := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_norms := 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_pole := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
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_norms[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_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_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_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.00005;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
glob_abserr := 10.0^glob_log10_abserr;
glob_relerr := 10.0^glob_log10_relerr;
chk_data();
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x2_higher[r_order, term_no] := array_x2_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_x1_higher[r_order, term_no] := array_x1_init[it]*
glob_h^(term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
start_array_x2();
if glob_small_float < abs(array_x2_higher[1, 1]) then
tmp := abs(array_x2_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
start_array_x1();
if glob_small_float < abs(array_x1_higher[1, 1]) then
tmp := abs(array_x1_higher[1, 1]);
log10norm := log10(tmp);
if log10norm < glob_log10normmin then
glob_log10normmin := log10norm
end if
end if;
display_alot(current_iter);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
sub_iter := 1;
while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
order_diff := 2;
order_diff := 2;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 2;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 2;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 1;
order_diff := 1;
order_diff := 1;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
order_diff := 1;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
glob_h^(calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
order_diff := 1;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_higher_work2[ord, calc_term] :=
temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
term_no := glob_max_terms;
while 1 <= term_no do
array_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
display_alot(current_iter)
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
ff(x1,t,2) - diff (x1,t,1) + x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T02:11:49-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev2");
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, "complicatedrev2 diffeq.mxt");
logitem_str(html_log_file, "complicatedrev2 maple results");
logitem_str(html_log_file, "sub iter tot order 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/complicatedrev2postode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_h := 0.00005 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 5e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 5e-05
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 5e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50005
x2[1] (analytic) = 0.00082566083422809021229815693339498
x2[1] (numeric) = 0.00082566083695768288479862473217238
absolute error = 2.72959267250046779877740e-12
relative error = 3.3059490765991852437183619152925e-07 %
h = 5e-05
x1[1] (analytic) = 0.0012917006010880372652167092040327
x1[1] (numeric) = 0.0012917005956294101955839744243888
absolute error = 5.4586270696327347796439e-12
relative error = 4.2259228377185651630693344462209e-07 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 0.00082570611074256394598966051590164
x2[1] (numeric) = 0.0008257061216619581905866203014748
absolute error = 1.091939424459695978557316e-11
relative error = 1.3224310808087714609409672985013e-06 %
h = 5e-05
x1[1] (analytic) = 0.001291646017422585871235266471237
x1[1] (numeric) = 0.0012916459955876806696845089414704
absolute error = 2.18349052015507575297666e-11
relative error = 1.6904712984073766292123104322750e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50015
x2[1] (analytic) = 0.00082575139314954126995470805844824
x2[1] (numeric) = 0.00082575141772058388848201984275335
absolute error = 2.457104261852731178430511e-11
relative error = 2.9755980822278267259784906914217e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012915914364862495213788540506512
x1[1] (numeric) = 0.0012915913873563234520967973558018
absolute error = 4.91299260692820566948494e-11
relative error = 3.8038287248899006888429764192898e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.19
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.00082579672513571924184372022173345
absolute error = 4.368617600740977856140855e-11
relative error = 5.2901854643840724902673898864862e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.0012915367709341102289641324488217
absolute error = 8.73447815343424701912415e-11
relative error = 6.7628562804423984205663586989851e-06 %
h = 5e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 9.350e-05
Order of pole = 16.66
t[1] = 0.50025
x2[1] (analytic) = 0.00082584197564309094518702663178858
x2[1] (numeric) = 0.00082584204390952388351643390389363
absolute error = 6.826643293832940727210505e-11
relative error = 8.2662827697962060206482364727461e-06 %
h = 5e-05
x1[1] (analytic) = 0.0012914822828003761515000894181426
x1[1] (numeric) = 0.0012914821463198125022053129662058
absolute error = 1.364805636492947764519368e-10
relative error = 1.0567745718768835573366335286247e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5003
x2[1] (analytic) = 0.00082588727573070556349803310856235
x2[1] (numeric) = 0.00082588737404415781589066880464538
absolute error = 9.831345225239263569608303e-11
relative error = 1.1903979531033408280222606045950e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012914277100505662472629969306448
x1[1] (numeric) = 0.0012914275135122015894870119253148
absolute error = 1.965383646577759850053300e-10
relative error = 1.5218688830060837488250530272266e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.209e-05
Order of pole = 14.49
t[1] = 0.50035
x2[1] (analytic) = 0.00082593258171290830618081821305085
x2[1] (numeric) = 0.00082593271554178141096271953900157
absolute error = 1.3382887310478190132595072e-10
relative error = 1.6203365270714119513613392729942e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012913731400293256187207719936699
x1[1] (numeric) = 0.0012913728725100486241959736067518
absolute error = 2.675192769945247983869181e-10
relative error = 2.0715877441004366805546748571025e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597806840455541039472407880014
absolute error = 1.7481433496481031531647343e-10
relative error = 2.1164529501504822355681136962805e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913182233121245554096702686067
absolute error = 3.494243932854106143453695e-10
relative error = 2.7059503414786521327758974520177e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.43
NO POLE
NO POLE
t[1] = 0.50045
x2[1] (analytic) = 0.00082602321136316330959838452294175
x2[1] (numeric) = 0.00082602343263464092557510775552467
absolute error = 2.2127147761597672323258292e-10
relative error = 2.6787561726118871435357218524860e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012912640081720064953294869263476
x1[1] (numeric) = 0.0012912635659172001478721065182233
absolute error = 4.422548063474573804081243e-10
relative error = 3.4249758651101934136272782037769e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 0.00082606880823419943767817763089351
absolute error = 2.7320194115601991561827625e-10
relative error = 3.3072551437315219714070518961689e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = 0.0012912089003240459819675880018586
absolute error = 5.460116091888694841461543e-10
relative error = 4.2286835086159332170507930775301e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50055
x2[1] (analytic) = 0.00082611386459802680075087884886784
x2[1] (numeric) = 0.00082611419520539279772344960351137
absolute error = 3.3060736599697257075464353e-10
relative error = 4.0019588117897112093437107681065e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012911548872273274627521335501181
x1[1] (numeric) = 0.0012911542265314324536875837108666
absolute error = 6.606958950090645498392515e-10
relative error = 5.1170924692688630552235011916403e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615959355038322663631031313428
absolute error = 3.9348939286521653166852119e-10
relative error = 4.7628761240710940221696755323917e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.0012910995445381297746055627577284
absolute error = 7.863087571986982606885202e-10
relative error = 6.0902219479947410241924577104276e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50065
x2[1] (analytic) = 0.0008262045414216705137705964508309
x2[1] (numeric) = 0.00082620500327133331530806540102026
absolute error = 4.6184966280153746895018936e-10
relative error = 5.5900160268645022606672778380011e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012910457771941973115410121980021
x1[1] (numeric) = 0.0012910448543429079718493443012584
absolute error = 9.228512893396916678967437e-10
relative error = 7.1480911493727589142713592393058e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=11.4MB, alloc=4.4MB, time=0.68
t[1] = 0.5007
x2[1] (analytic) = 0.00082624988868058886347644474630742
x2[1] (numeric) = 0.00082625042437040602465599500090491
absolute error = 5.3568981716117955025459749e-10
relative error = 6.4833874654628385207710841664897e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012909912262691220933319472376107
x1[1] (numeric) = 0.001290990155944536888073434395288
absolute error = 1.0703245852052585128423227e-09
relative error = 8.2907192816362095090813207966641e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50075
x2[1] (analytic) = 0.00082629524183826707178329997453724
x2[1] (numeric) = 0.00082629585684976468568341869391415
absolute error = 6.1501149761390011871937691e-10
relative error = 7.4429993841629542776787993177462e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012909366780715249413639121076118
x1[1] (numeric) = 0.0012909354493417861814313586884613
absolute error = 1.2287297387599325534191505e-09
relative error = 9.5181255566731540041161526063086e-05 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634130071157299953976992887908
absolute error = 6.9981634614402438030105031e-10
relative error = 8.4688607262655280948776273498662e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908807345334253255479909745209
absolute error = 1.3980678441595948945430447e-09
relative error = 0.00010830329190027089544853111764657 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50085
x2[1] (analytic) = 0.00082638596585198998708057987866837
x2[1] (numeric) = 0.00082638675595799503758067990951836
absolute error = 7.9010600505050010003084999e-10
relative error = 9.5609804340749439080845370351817e-05 %
h = 5e-05
x1[1] (analytic) = 0.0012908275898582193609932004178204
x1[1] (numeric) = 0.0012908260115182236094918775924611
absolute error = 1.5783399957515013228253593e-09
relative error = 0.00012227349400897616884430139243105 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 0.00082643133670907829447576375839823
x2[1] (numeric) = 0.00082643222259119524142807094995361
absolute error = 8.8588211694695230719155538e-10
relative error = 0.00010719367448899169384098852769017 %
h = 5e-05
x1[1] (analytic) = 0.0012907730498422382120572030903234
x1[1] (numeric) = 0.0012907712802949501377475576759261
absolute error = 1.7695472880743096454143973e-09
relative error = 0.00013709205412141108160910566126488 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50095
x2[1] (analytic) = 0.00082647671346701366129224988326191
x2[1] (numeric) = 0.00082647770061333842303025930002354
absolute error = 9.8714632476173800941676163e-10
relative error = 0.00011944030711049634354565597816647 %
h = 5e-05
x1[1] (analytic) = 0.0012907185125531896882949122564762
x1[1] (numeric) = 0.0012907165408623738301878792512308
absolute error = 1.9716908158581070330052454e-09
relative error = 0.0001527591645027137479415628748044 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.5MB, time=0.94
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652319002658976472206744186286
absolute error = 1.09390027173800091571399100e-09
relative error = 0.00013234979159841109324648006152025 %
h = 5e-05
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906617932192634220463111833818
absolute error = 2.1847716740244373670186533e-09
relative error = 0.00016927501745460335502330412088217 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50105
x2[1] (analytic) = 0.0008265674846875133855587774461534
x2[1] (numeric) = 0.0008265686908331148192849458592121
absolute error = 1.20614560143372616841305870e-09
relative error = 0.00014592221733591584056607608391875 %
h = 5e-05
x1[1] (analytic) = 0.0012906094461553451502178419190542
x1[1] (numeric) = 0.0012906070373643874638892509694754
absolute error = 2.4087909576863285909495788e-09
relative error = 0.00018663980531538684438050389101978 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5011
x2[1] (analytic) = 0.00082661287915112178821202023981947
x2[1] (numeric) = 0.00082661420303507951000710428092484
absolute error = 1.32388395772179508404110537e-09
relative error = 0.00016015767369622146228290294082126 %
h = 5e-05
x1[1] (analytic) = 0.0012905549170462764699083942648711
x1[1] (numeric) = 0.0012905522732965143215883283788502
absolute error = 2.6437497621483200658860209e-09
relative error = 0.000204853720459965594442126232761 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50115
x2[1] (analytic) = 0.00082665827951766534070374927443031
x2[1] (numeric) = 0.00082665972663465013074365240013893
absolute error = 1.44711698479003990312570862e-09
relative error = 0.00017505625004256860166516745596366 %
h = 5e-05
x1[1] (analytic) = 0.0012905003906635950827826351381346
x1[1] (numeric) = 0.0012904975010144121762927049393711
absolute error = 2.8896491829064899301987635e-09
relative error = 0.00022391695529984210429509596426505 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5012
x2[1] (analytic) = 0.00082670368578766620467820114309252
x2[1] (numeric) = 0.00082670526163399334597675007057864
absolute error = 1.57584632714129854892748612e-09
relative error = 0.00019061803572822645655375629974239 %
h = 5e-05
x1[1] (analytic) = 0.0012904458670071646728838326718726
x1[1] (numeric) = 0.0012904427205168490244013692692221
absolute error = 3.1464903156484824634026505e-09
relative error = 0.000243829702283126678636605016894 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50125
x2[1] (analytic) = 0.00082674909796164659740637187785192
x2[1] (numeric) = 0.00082675080803527619087576698145478
absolute error = 1.71007362959346939510360286e-09
relative error = 0.00020684312009649156819417926823876 %
h = 5e-05
x1[1] (analytic) = 0.0012903913460768489310708824436005
x1[1] (numeric) = 0.0012903879318025926775354282535843
absolute error = 3.4142742562535354541900162e-09
relative error = 0.00026459215389454411392376424050123 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.5MB, time=1.19
NO POLE
NO POLE
t[1] = 0.5013
x2[1] (analytic) = 0.00082679451604012879179140950883443
x2[1] (numeric) = 0.00082679636584066607135745181243016
absolute error = 1.84980053727956604230359573e-09
relative error = 0.0002237315924806866108175076704816 %
h = 5e-05
x1[1] (analytic) = 0.0012903368278725115550179667024679
x1[1] (numeric) = 0.0012903331348704107625103940655763
absolute error = 3.6930021007925075726368916e-09
relative error = 0.00028620450265544038572081077920033 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50135
x2[1] (analytic) = 0.00082683994002363511637400717118929
x2[1] (numeric) = 0.00082684193505233076414611087011793
absolute error = 1.99502869564777210369892864e-09
relative error = 0.00024128354220415918197029148226361 %
h = 5e-05
x1[1] (analytic) = 0.0012902823123940162492142136134444
x1[1] (numeric) = 0.001290278329719070721308467030834
absolute error = 3.9826749455279057465826104e-09
relative error = 0.00030866694112378933724408140213576 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5014
x2[1] (analytic) = 0.00082688536991268795533779675988916
x2[1] (numeric) = 0.00082688751567243841683379620758055
absolute error = 2.14575975046149599944769139e-09
relative error = 0.00025949905858028059359343882588919 %
h = 5e-05
x1[1] (analytic) = 0.0012902277996412267249633565185424
x1[1] (numeric) = 0.0012902235163473398110508143351055
absolute error = 4.2832938869139125421834369e-09
relative error = 0.00033197966189419936910496207858925 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50145
x2[1] (analytic) = 0.00082693080570780974851474313244131
x2[1] (numeric) = 0.00082693310770315754794050322829742
absolute error = 2.30199534779942576009585611e-09
relative error = 0.00027837823091244466385004131129571 %
h = 5e-05
x1[1] (analytic) = 0.0012901732896140067003833932150759
x1[1] (numeric) = 0.0012901686947539851039698445742384
absolute error = 4.5948600215964135486408375e-09
relative error = 0.00035614285759792013025102407678215 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5015
x2[1] (analytic) = 0.00082697624740952299139053885956424
x2[1] (numeric) = 0.00082697871114665704697437777606938
absolute error = 2.46373713405558383891650514e-09
relative error = 0.00029792114849406650970212868232588 %
h = 5e-05
x1[1] (analytic) = 0.0012901187823122199004062452509559
x1[1] (numeric) = 0.0012901138649377734873814781459362
absolute error = 4.9173744464130247671050197e-09
relative error = 0.00038115672090284921010555706503082 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.6MB, time=1.46
NO POLE
NO POLE
t[1] = 0.50155
x2[1] (analytic) = 0.00082702169501835023510999952388432
x2[1] (numeric) = 0.00082702432600510617449193271232851
absolute error = 2.63098675593938193318844419e-09
relative error = 0.0003181279006085813402363361106129 %
h = 5e-05
x1[1] (analytic) = 0.0012900642777357300567774172370197
x1[1] (numeric) = 0.0012900590268974716636574134826591
absolute error = 5.2508382583931200037543606e-09
relative error = 0.00040702144451353883190570957546355 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5016
x2[1] (analytic) = 0.00082706714853481408648245956670656
x2[1] (numeric) = 0.00082706995228067456215827398232196
absolute error = 2.80374586047567581441561540e-09
relative error = 0.0003389985765294432507384674761872 %
h = 5e-05
x1[1] (analytic) = 0.001290009775884400908055656176395
x1[1] (numeric) = 0.0012900041806318461501973891250464
absolute error = 5.5952525547578582670513486e-09
relative error = 0.00043373722117120254723944735107061 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50165
x2[1] (analytic) = 0.00082711260795943720798716868291399
x2[1] (numeric) = 0.00082711558997553221280733617163863
absolute error = 2.98201609500482016748872464e-09
relative error = 0.00036053326552012401751693784238226 %
h = 5e-05
x1[1] (analytic) = 0.0012899552767580961996126108108966
x1[1] (numeric) = 0.0012899493261396632794014416352363
absolute error = 5.9506184329202111691756603e-09
relative error = 0.00046130424365372193178153999390187 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5017
x2[1] (analytic) = 0.00082715807329274231777868876405026
x2[1] (numeric) = 0.00082716123909184950050212755454788
absolute error = 3.16579910718272343879049762e-09
relative error = 0.00038273205683411189347507826278361 %
h = 5e-05
x1[1] (analytic) = 0.0012899007803566796836324909844552
x1[1] (numeric) = 0.0012898944634196891986421593494593
absolute error = 6.3169369904849903316349959e-09
relative error = 0.00048972270477565328222878646179523 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50175
x2[1] (analytic) = 0.0008272035445352521896922913896394
x2[1] (numeric) = 0.00082720689963179717059498463561962
absolute error = 3.35509654498090269324598022e-09
relative error = 0.00040559503971491040443228606188571 %
h = 5e-05
x1[1] (analytic) = 0.0012898462866800151191117270235781
x1[1] (numeric) = 0.0012898395924706898702369319692811
absolute error = 6.6942093252488747950542970e-09
relative error = 0.00051899279738823431443469003635923 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 0.00082724902168748965324935586679766
x2[1] (numeric) = 0.00082725257159754633978783618609529
absolute error = 3.54991005668653848031929763e-09
relative error = 0.00042912230339603714619400353435105 %
h = 5e-05
x1[1] (analytic) = 0.0012897917957279662718586291348401
x1[1] (numeric) = 0.0012897847132914310714201959908708
absolute error = 7.0824365352004384331439693e-09
relative error = 0.00054911471437939086274379330522984 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.6MB, time=1.72
NO POLE
NO POLE
t[1] = 0.50185
x2[1] (analytic) = 0.00082729450474997759366276781819127
x2[1] (numeric) = 0.00082729825499126849619247677647961
absolute error = 3.75024129090252970895828834e-09
relative error = 0.00045331393710102258237050808545802 %
h = 5e-05
x1[1] (analytic) = 0.0012897373075003969144930468194044
x1[1] (numeric) = 0.0012897298258806783943156759716703
absolute error = 7.4816197185201773708477341e-09
relative error = 0.00058008864867374358052588383897648 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5019
x2[1] (analytic) = 0.00082733999372323895184231831839524
x2[1] (numeric) = 0.00082734394981513549939084980682307
absolute error = 3.95609189654754853148842783e-09
relative error = 0.00047817003004340884294449659385864 %
h = 5e-05
x1[1] (analytic) = 0.0012896828219971708264460283045716
x1[1] (numeric) = 0.0012896749302371972459086216338408
absolute error = 7.8917599735805374066707308e-09
relative error = 0.00061191479323261464191028114006243 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50195
x2[1] (analytic) = 0.00082738548860779672440010357870682
x2[1] (numeric) = 0.00082738965607131958049534003616543
absolute error = 4.16746352285609523645745861e-09
relative error = 0.0005036906714267485235874468977786 %
h = 5e-05
x1[1] (analytic) = 0.0012896283392181517939594799923581
x1[1] (numeric) = 0.0012896200263597528480180408038615
absolute error = 8.3128583989459414391884966e-09
relative error = 0.00064459334105403444472041578023347 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743537376199334220907561261066
absolute error = 4.38435781937855315043214196e-09
relative error = 0.00052987595044460348572473905106498 %
h = 5e-05
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895651142471102372689281876565
absolute error = 8.7449160933728168977374435e-09
relative error = 0.0006781244851727483146089111985958 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50205
x2[1] (analytic) = 0.00082747649611289377764269085695601
x2[1] (numeric) = 0.00082748110288932975888623960550411
absolute error = 4.60677643598124354874854810e-09
relative error = 0.00055672595628054365734951906474069 %
h = 5e-05
x1[1] (analytic) = 0.0012895193818321900746876672680847
x1[1] (numeric) = 0.0012895101938980342650644899806252
absolute error = 9.1879341558096231772874595e-09
relative error = 0.00071250841866022321039337918872178 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=4.6MB, time=1.98
t[1] = 0.5021
x2[1] (analytic) = 0.00082752200873447933011181582388164
x2[1] (numeric) = 0.00082752684345550217659239104118273
absolute error = 4.83472102284648057521730109e-09
relative error = 0.00058424077810814583458528770019382 %
h = 5e-05
x1[1] (analytic) = 0.0012894649072249749944374418092067
x1[1] (numeric) = 0.0012894552653112895975583643119514
absolute error = 9.6419136853968790774972553e-09
relative error = 0.00074774533462465443059313969776857 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50215
x2[1] (analytic) = 0.00082756752726945384053862465857453
x2[1] (numeric) = 0.00082757259546268431316479544376956
absolute error = 5.06819323047262617078519503e-09
relative error = 0.00061242050509099248399719681523601 %
h = 5e-05
x1[1] (analytic) = 0.0012894104353414221828170834756492
x1[1] (numeric) = 0.0012894003284856407156268375225664
absolute error = 1.01068557814671902459530828e-08
relative error = 0.00078383542621097232116707597715393 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5022
x2[1] (analytic) = 0.0008276130517183405841277537278848
x2[1] (numeric) = 0.00082761835891305025827276488248383
absolute error = 5.30719470967414501115459903e-09
relative error = 0.00064126522638267054565203577550089 %
h = 5e-05
x1[1] (analytic) = 0.0012893559661813954601176818675888
x1[1] (numeric) = 0.001289345383419851914841056276141
absolute error = 1.05827615435452766255914478e-08
relative error = 0.00082077888660084898445283585078009 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50225
x2[1] (analytic) = 0.00082765858208166289181855416487103
x2[1] (numeric) = 0.00082766413380877447347800752693827
absolute error = 5.55172711158165945336206724e-09
relative error = 0.00067077503112677023692689020354951 %
h = 5e-05
x1[1] (analytic) = 0.0012893014997447586534391418089226
x1[1] (numeric) = 0.0012892904301126873054392355024821
absolute error = 1.10696320713479999063064405e-08
relative error = 0.00085857590901270498930758998869022 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5023
x2[1] (analytic) = 0.00082770411835994415029049539432325
x2[1] (numeric) = 0.00082770992015203179229498671189548
absolute error = 5.80179208764200449131757223e-09
relative error = 0.00070095000845688385706645548223783 %
h = 5e-05
x1[1] (analytic) = 0.0012892470360313755966898429150187
x1[1] (numeric) = 0.0012892354685629108122988621727082
absolute error = 1.15674684647843909807423105e-08
relative error = 0.00089722668670171608245055834334565 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50235
x2[1] (analytic) = 0.00082774966055370780196856920717682
x2[1] (numeric) = 0.00082775571794499742025128951295537
absolute error = 6.05739128961828272030577855e-09
relative error = 0.00073179024749660459248898715499189 %
h = 5e-05
x1[1] (analytic) = 0.0012891925750411101305862991774863
x1[1] (numeric) = 0.001289180498769286174908894905579
absolute error = 1.20762718239556774042719073e-08
relative error = 0.00093673141295981990100751549251598 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.6MB, time=2.24
NO POLE
NO POLE
t[1] = 0.5024
x2[1] (analytic) = 0.00082779520866347734502869438387111
x2[1] (numeric) = 0.00082780152718984693494800483464597
absolute error = 6.31852636958991931045077486e-09
relative error = 0.00076329583735952532284087045666596 %
h = 5e-05
x1[1] (analytic) = 0.0012891381167738261026528185659675
x1[1] (numeric) = 0.0012891255207305769473419594043536
absolute error = 1.25960432491553108591616139e-08
relative error = 0.00097709028111572268625748617353088 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50245
x2[1] (analytic) = 0.00082784076268977633340312186670805
x2[1] (numeric) = 0.00082784734788875628612011101239014
absolute error = 6.58519897995271698914568209e-09
relative error = 0.00079546686714923742779979099883499 %
h = 5e-05
x1[1] (analytic) = 0.0012890836612293873672211626469477
x1[1] (numeric) = 0.0012890705344455464982265397235523
absolute error = 1.31267838408689946229233954e-08
relative error = 0.0010183034845349059985818418804371 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5025
x2[1] (analytic) = 0.00082788632263312837678584048126422
x2[1] (numeric) = 0.00082789318004390179569687292982079
absolute error = 6.85741077341891103244855657e-09
relative error = 0.0008283034259593295946264887147353 %
h = 5e-05
x1[1] (analytic) = 0.0012890292084076577854302062195851
x1[1] (numeric) = 0.0012890155399129580107191653649962
absolute error = 1.36684946997747110408545889e-08
relative error = 0.0010603712166196334336160097657627 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50255
x2[1] (analytic) = 0.00082793188849405714063798320691191
x2[1] (numeric) = 0.00082793902365746015786224865291776
absolute error = 7.13516340301722426544600585e-09
relative error = 0.00086180560287338662646507692424887 %
h = 5e-05
x1[1] (analytic) = 0.0012889747583085012252255969685576
x1[1] (numeric) = 0.0012889605371315744824765942024995
absolute error = 1.42211769267427490027660581e-08
relative error = 0.0011032936708089573396040048925428 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5026
x2[1] (analytic) = 0.00082797746027308634619323399650282
x2[1] (numeric) = 0.0008279848787316084391153055824393
absolute error = 7.41845852209292207158593648e-09
relative error = 0.00089597348696498825139190846916007 %
h = 5e-05
x1[1] (analytic) = 0.001288920310931781561359415133927
x1[1] (numeric) = 0.0012889055261001587256279912345886
absolute error = 1.47848316228357314238993384e-08
relative error = 0.0011470710405787255359559970973248 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50265
x2[1] (analytic) = 0.00082802303797073977046323514526932
x2[1] (numeric) = 0.00082803074526852407833064612612176
absolute error = 7.70729778430786741098085244e-09
relative error = 0.00093080716729770793221297070143657 %
h = 5e-05
x1[1] (analytic) = 0.0012888658662773626753898331980192
x1[1] (numeric) = 0.0012888505068174733667471031646224
absolute error = 1.53594598893086427300333968e-08
relative error = 0.0011917035194415880330091236374181 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.6MB, time=2.49
NO POLE
NO POLE
t[1] = 0.5027
x2[1] (analytic) = 0.00082806862158754124624299520899781
x2[1] (numeric) = 0.00082807662327038488681884289212098
absolute error = 8.00168284364057584768312317e-09
relative error = 0.00096630673292511167700979104131201 %
h = 5e-05
x1[1] (analytic) = 0.0012888114243451084556807755893193
x1[1] (numeric) = 0.0012887954792822808468244288076879
absolute error = 1.59450628276088563467816314e-08
relative error = 0.0012371913009470037529917588633377 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50275
x2[1] (analytic) = 0.00082811421112401466211629747152829
x2[1] (numeric) = 0.00082812251273936904838688340516931
absolute error = 8.30161535438627058593364102e-09
relative error = 0.0010024722728907568504338348296439 %
h = 5e-05
x1[1] (analytic) = 0.0012887569851348827974015784033818
x1[1] (numeric) = 0.0012887404434933434212393853236452
absolute error = 1.65416415393761621930797366e-08
relative error = 0.0012835345786812472521914522871693 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5028
x2[1] (analytic) = 0.00082815980658068396246110896163522
x2[1] (numeric) = 0.00082816841367765511939862434692228
absolute error = 8.60709697115693751538528706e-09
relative error = 0.0010393038762281909857493769953758 %
h = 5e-05
x1[1] (analytic) = 0.0012887025486465496025266491407532
x1[1] (numeric) = 0.0012886853994494231597324702756963
absolute error = 1.71491971264427941788650569e-08
relative error = 0.0013307335462674154443267461982148 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50285
x2[1] (analytic) = 0.0008282054079580731474549900193436
x2[1] (numeric) = 0.0008282143260874220288352553219693
absolute error = 8.91812934888138026530262570e-09
relative error = 0.0010768016319609505976248291439456 %
h = 5e-05
x1[1] (analytic) = 0.0012886481148799727798351264619085
x1[1] (numeric) = 0.0012886303471492819463774195138511
absolute error = 1.77677306908334577069480574e-08
relative error = 0.0013787883973654343251230844096569 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5029
x2[1] (analytic) = 0.0008282510152567062730805044117353
x2[1] (numeric) = 0.00082826024997084907835577215098285
absolute error = 9.23471414280527526773924755e-09
relative error = 0.001114965629102559995672503451959 %
h = 5e-05
x1[1] (analytic) = 0.0012885936838350162449105399591989
x1[1] (numeric) = 0.0012885752865916814795533608826647
absolute error = 1.83972433347653571790765342e-08
relative error = 0.0014276993256720656980930233687258 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=41.9MB, alloc=4.6MB, time=2.76
t[1] = 0.50295
x2[1] (analytic) = 0.00082829662847710745113062999829971
x2[1] (numeric) = 0.00082830618533011594235745969248093
absolute error = 9.55685300849122682969418122e-09
relative error = 0.0011537959566565300987367948094926 %
h = 5e-05
x1[1] (analytic) = 0.0012885392555115439201404699458103
x1[1] (numeric) = 0.0012885202177753832719169637526194
absolute error = 1.90377361606482235061931909e-08
relative error = 0.0014774665249209139015209571245397 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082835213216740266803638419467778
absolute error = 9.88454760181882221424879408e-09
relative error = 0.0011932927036163572499307624719625 %
h = 5e-05
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884651406991486503745843745259
absolute error = 1.96892102710843416228872064e-08
relative error = 0.001528090188882432536652567599137 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50305
x2[1] (analytic) = 0.00082838787268531069076116449329504
x2[1] (numeric) = 0.00082839809048488967544789517889809
absolute error = 1.021779957898468673068560305e-08
relative error = 0.0012334559589655220324210925129811 %
h = 5e-05
x1[1] (analytic) = 0.0012884304070285076246324130967366
x1[1] (numeric) = 0.001288410055361738756054407056316
absolute error = 2.03516667688685780060404206e-08
relative error = 0.0015795705113639311970892117448033 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5031
x2[1] (analytic) = 0.00082843350367416125502830326561401
x2[1] (numeric) = 0.00082844406028475775756713685603004
absolute error = 1.055661059650253883359041603e-08
relative error = 0.0012742858116774880859614222167988 %
h = 5e-05
x1[1] (analytic) = 0.0012883759868686715326867788303632
x1[1] (numeric) = 0.0012883549617619145442785811616016
absolute error = 2.10251067569884081976687616e-08
relative error = 0.0016319076862095821993874569669156 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50315
x2[1] (analytic) = 0.0008284791405868768771043381382677
x2[1] (numeric) = 0.00082849004156918808034956907749296
absolute error = 1.090098231120324523093922526e-08
relative error = 0.001315782350715700924174007533751 %
h = 5e-05
x1[1] (analytic) = 0.0012883215694297754084796858889148
x1[1] (numeric) = 0.0012882998598984367845353539293719
absolute error = 2.17095313386239443319595429e-08
relative error = 0.0016851019073004273148639766007555 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5032
x2[1] (analytic) = 0.00082852478342398194791549665092172
x2[1] (numeric) = 0.00082853603434036218279149782219539
absolute error = 1.125091638023487600117127367e-08
relative error = 0.0013579456650335867525797145971141 %
h = 5e-05
x1[1] (analytic) = 0.0012882671547116832084138656194575
x1[1] (numeric) = 0.0012882447497700660604511991142034
absolute error = 2.24049416171479626665052541e-08
relative error = 0.0017391533685543845026060168716461 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.6MB, time=3.01
NO POLE
NO POLE
t[1] = 0.50325
x2[1] (analytic) = 0.00082857043218600091423089597124342
x2[1] (numeric) = 0.00082858203860046197699061522095972
absolute error = 1.160641446106275971924971630e-08
relative error = 0.001400775843574551287376316325649 %
h = 5e-05
x1[1] (analytic) = 0.0012882127427142588956940591808277
x1[1] (numeric) = 0.0012881896313755627697629414463551
absolute error = 2.31113386961259311177344726e-08
relative error = 0.0017940622639262546436876471071705 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5033
x2[1] (analytic) = 0.00082861608687345827866795740859187
x2[1] (numeric) = 0.00082862805435166974820654911988968
absolute error = 1.196747821146953859171129781e-08
relative error = 0.0014442729752719785749650749109355 %
h = 5e-05
x1[1] (analytic) = 0.0012881583334373664403266774516441
x1[1] (numeric) = 0.0012881345047136871242898769111221
absolute error = 2.38287236793160368005405220e-08
relative error = 0.0018498287874077282765920048594922 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50335
x2[1] (analytic) = 0.0008286617474868785996978214776885
x2[1] (numeric) = 0.00082867408159616815492142218415731
absolute error = 1.233410928955522360070646881e-08
relative error = 0.0014884371490492298122255910977855 %
h = 5e-05
x1[1] (analytic) = 0.0012881039268808698191194609553229
x1[1] (numeric) = 0.0012880793697831991499058888468208
absolute error = 2.45570976706692135721085021e-08
relative error = 0.0019064531330273923338397475626503 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 0.00082870741402678649165076351232339
x2[1] (numeric) = 0.00082872012033614022890042054368619
absolute error = 1.270630935373724965703136280e-08
relative error = 0.0015332684538196421675389009553542 %
h = 5e-05
x1[1] (analytic) = 0.0012880495230446330156811398020981
x1[1] (numeric) = 0.0012880242265828586865115598607782
absolute error = 2.52964617743291695799413199e-08
relative error = 0.0019639354948507368798239227279972 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50345
x2[1] (analytic) = 0.00082875308649370662472160982915166
x2[1] (numeric) = 0.00082876617057376937525237198220787
absolute error = 1.308408006275053076215305621e-08
relative error = 0.0015787669784865276025588008238704 %
h = 5e-05
x1[1] (analytic) = 0.0012879951219285200204210936480425
x1[1] (numeric) = 0.0012879690751114253880062795626987
absolute error = 2.60468170946324148140853438e-08
relative error = 0.0020222760669801618498514681510032 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5035
x2[1] (analytic) = 0.00082879876488816372497515444163463
x2[1] (numeric) = 0.00082881223231123937249033367116884
absolute error = 1.346742307564751517922953421e-08
relative error = 0.0016249328119431716947313810464512 %
h = 5e-05
x1[1] (analytic) = 0.0012879407235323948305490116710912
x1[1] (numeric) = 0.0012879139153676587222603481147803
absolute error = 2.68081647361082886635563109e-08
relative error = 0.0020814750435549837903915542293673 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.6MB, time=3.27
NO POLE
NO POLE
t[1] = 0.50355
x2[1] (analytic) = 0.00082884444921068257435157632418004
x2[1] (numeric) = 0.00082885830555073437259218944996547
absolute error = 1.385634005179824061312578543e-08
relative error = 0.0016717660430728324605627490550104 %
h = 5e-05
x1[1] (analytic) = 0.0012878863278561214500745525640661
x1[1] (numeric) = 0.0012878587473503179710870755979535
absolute error = 2.75805058034789874769661126e-08
relative error = 0.0021415326187514426005309801565139 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 0.00082889013946178801067185722653652
x2[1] (numeric) = 0.00082890439029443890106125665398459
absolute error = 1.425083265089038939942744807e-08
relative error = 0.0017192667607487391796349222024878 %
h = 5e-05
x1[1] (analytic) = 0.0012878319348995638898070045446997
x1[1] (numeric) = 0.001287803571058162230214877193615
absolute error = 2.83638414016595921273510847e-08
relative error = 0.0022024489867827082746368358611554 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50365
x2[1] (analytic) = 0.00082893583564200492764320003849618
x2[1] (numeric) = 0.00082895048654453785698690249192763
absolute error = 1.465090253292934370245343145e-08
relative error = 0.0017674350538340912193698708259265 %
h = 5e-05
x1[1] (analytic) = 0.0012877775446625861673549453826583
x1[1] (numeric) = 0.0012877483864899504092593641802288
absolute error = 2.91581726357580955812024295e-08
relative error = 0.0022642243418988876462266416935311 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5037
x2[1] (analytic) = 0.00082898153775185827486444770496057
x2[1] (numeric) = 0.00082899659430321651310516997389653
absolute error = 1.505655135823824072226893596e-08
relative error = 0.00181627101118205686054169179628 %
h = 5e-05
x1[1] (analytic) = 0.0012877231571450523071259024435631
x1[1] (numeric) = 0.0012876931936444412316954307441673
absolute error = 2.99635006110754304716993958e-08
relative error = 0.0023268588783870311330461777637003 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50375
x2[1] (analytic) = 0.00082902724579187305783150269142413
x2[1] (numeric) = 0.00082904271357266051585941339171972
absolute error = 1.546778078745802791070029559e-08
relative error = 0.0018657747216357721235368928609194 %
h = 5e-05
x1[1] (analytic) = 0.0012876687723468263403260127500097
x1[1] (numeric) = 0.0012876379925203932348293366041635
absolute error = 3.07798264331054966761458462e-08
relative error = 0.0023903527905711394833552151380518 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=3.54
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 0.0008290729597625743379427469999303
x2[1] (numeric) = 0.00082908884435505588546094335299682
absolute error = 1.588459248154751819635306652e-08
relative error = 0.0019159462740283395953627679032619 %
h = 5e-05
x1[1] (analytic) = 0.0012876143902677723049596830595824
x1[1] (numeric) = 0.0012875827831165647697707854487481
absolute error = 3.16071512075351888976108343e-08
relative error = 0.0024547062728121705234213606011611 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50385
x2[1] (analytic) = 0.00082911867966448723250446273555416
x2[1] (numeric) = 0.00082913498665258901594968137034082
absolute error = 1.630698810178344521863478666e-08
relative error = 0.0019667857571828272574038433169543 %
h = 5e-05
x1[1] (analytic) = 0.0012875600109077542458292499598661
x1[1] (numeric) = 0.0012875275654317140014049991860422
absolute error = 3.24454760402444242507738239e-08
relative error = 0.0025199195195080459062222274568422 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5039
x2[1] (analytic) = 0.00082916440549813691473625322346704
x2[1] (numeric) = 0.00082918114046744667525482400729687
absolute error = 1.673496930976051857078382983e-08
relative error = 0.0020182932599122673139263754502166 %
h = 5e-05
x1[1] (analytic) = 0.0012875056342666362145346399804511
x1[1] (numeric) = 0.001287472339464598908364788005278
absolute error = 3.32948020373061698519751731e-08
relative error = 0.0025859927250936578613561441568386 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50395
x2[1] (analytic) = 0.00082921013726404861377646467663714
x2[1] (numeric) = 0.00082922730580181600525551658241691
absolute error = 1.716853776739147905190577977e-08
relative error = 0.002070468871019655021330879159833 %
h = 5e-05
x1[1] (analytic) = 0.0012874512603442822694730297219339
x1[1] (numeric) = 0.0012874171052139772830026162494197
absolute error = 3.41551303049864704134725142e-08
relative error = 0.0026529260840408759461616131958758 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082927348265788452184153643296966
absolute error = 1.760769513690715392801874864e-08
relative error = 0.0021233126792979475181526673533022 %
h = 5e-05
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.0012873618626786067313626640982556
absolute error = 3.50264619497444758419036535e-08
relative error = 0.0027207197908585537980457322127342 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50405
x2[1] (analytic) = 0.00082930161859475925846178363070083
x2[1] (numeric) = 0.0008293196710378401149739857397657
absolute error = 1.805244308085651220210906487e-08
relative error = 0.0021768247735300626558103813247552 %
h = 5e-05
x1[1] (analytic) = 0.0012873425206553229056217260179551
x1[1] (numeric) = 0.0012873066118572446731528850613339
absolute error = 3.59087980782324688409566212e-08
relative error = 0.002789374040092535888021789739774 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.6MB, time=3.81
NO POLE
NO POLE
t[1] = 0.5041
x2[1] (analytic) = 0.00082934736816060894202610071582133
x2[1] (numeric) = 0.00082936587094387104874599391457756
absolute error = 1.850278326210671989319875623e-08
relative error = 0.0022310052424888778301024917150396 %
h = 5e-05
x1[1] (analytic) = 0.0012872881548884456376095775276106
x1[1] (numeric) = 0.001287251352748648341717059280113
absolute error = 3.68021397972958925182474976e-08
relative error = 0.0028588890263256642754562477617295 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50415
x2[1] (analytic) = 0.00082939312366082211824810512538206
x2[1] (numeric) = 0.0008294120823781659614434295516351
absolute error = 1.895871734384319532442625304e-08
relative error = 0.0022858541749372288134517497147927 %
h = 5e-05
x1[1] (analytic) = 0.0012872337918397887573848390453416
x1[1] (numeric) = 0.0012871960853515747840068426386986
absolute error = 3.77064882139733779964066430e-08
relative error = 0.0029292649441777853640253233668121 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5042
x2[1] (analytic) = 0.00082943888509592429594120180293885
x2[1] (numeric) = 0.00082945830534291386560562194467646
absolute error = 1.942024698956966442014173761e-08
relative error = 0.0023413716596279085878975681734402 %
h = 5e-05
x1[1] (analytic) = 0.0012871794315092163573258400564985
x1[1] (numeric) = 0.0012871408096647808605538116825378
absolute error = 3.86218444354967720283739607e-08
relative error = 0.003000501988305756658881381957573 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50425
x2[1] (analytic) = 0.00082948465246644103987008015246953
x2[1] (numeric) = 0.00082950453984030414808609217103536
absolute error = 1.988737386310821601201856583e-08
relative error = 0.0023975577853036661788363121595683 %
h = 5e-05
x1[1] (analytic) = 0.0012871250738965925366061212482615
x1[1] (numeric) = 0.001287085525687023245441504344443
absolute error = 3.95482095692911646169038185e-08
relative error = 0.0030726003534034535250293542073064 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5043
x2[1] (analytic) = 0.00082953042577289797075613956205843
x2[1] (numeric) = 0.00082955078587252657011329374424548
absolute error = 2.036009962859935715418218705e-08
relative error = 0.0024544126406972054895094784476866 %
h = 5e-05
x1[1] (analytic) = 0.0012870707190017814011940947575749
x1[1] (numeric) = 0.0012870302334170584262774564773152
absolute error = 4.04855847229749166382802597e-08
relative error = 0.0031455602342017759469133894118461 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50435
x2[1] (analytic) = 0.00082957620501582076528291547865441
x2[1] (numeric) = 0.00082959704344177126735136283664308
absolute error = 2.083842595050206844735798867e-08
relative error = 0.0025119363145311841362397433432096 %
h = 5e-05
x1[1] (analytic) = 0.0012870163668246470638527044360674
x1[1] (numeric) = 0.0012869749328536427041652341929395
absolute error = 4.14339710043596874702431279e-08
relative error = 0.0032193818254686552892139573951761 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.6MB, time=4.07
NO POLE
NO POLE
t[1] = 0.5044
x2[1] (analytic) = 0.00082962199019573515610150603395714
x2[1] (numeric) = 0.00082964331255022874996087807344922
absolute error = 2.132235449359385937203949208e-08
relative error = 0.0025701288955182122844148581870717 %
h = 5e-05
x1[1] (analytic) = 0.00128696201736505364413908613196
x1[1] (numeric) = 0.0012869196239955321936764620062218
absolute error = 4.23933695214504626241257382e-08
relative error = 0.0032940653220090610588556118011558 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50445
x2[1] (analytic) = 0.00082966778131316693183599922148616
x2[1] (numeric) = 0.00082968959320008990265962989981299
absolute error = 2.181188692297082363067832683e-08
relative error = 0.0026289904723608514852193718134016 %
h = 5e-05
x1[1] (analytic) = 0.0012869076706228652684042279889585
x1[1] (numeric) = 0.0012868643068414828228228467842397
absolute error = 4.33637813824455813812047188e-08
relative error = 0.0033696109186650076682256269645856 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5045
x2[1] (analytic) = 0.00082971357836864193708890062488759
x2[1] (numeric) = 0.00082973588539354598478339952229767
absolute error = 2.230702490404769449889741008e-08
relative error = 0.0026885211337516135131141591572655 %
h = 5e-05
x1[1] (analytic) = 0.0012868533265979460697926307621308
x1[1] (numeric) = 0.0012868089813902503330281974994768
absolute error = 4.43452076957367644332626540e-08
relative error = 0.003446018810315561199603721127757 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50455
x2[1] (analytic) = 0.00082975938136268607244656169753319
x2[1] (numeric) = 0.00082978218913278863034674742629174
absolute error = 2.280777010255790018572875855e-08
relative error = 0.0027487209683729592040637351330894 %
h = 5e-05
x1[1] (analytic) = 0.0012867989852901601882419681507683
x1[1] (numeric) = 0.0012867536476405902791004407866119
absolute error = 4.53376495699091415273641564e-08
relative error = 0.0035232891918768461708030785490962 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5046
x2[1] (analytic) = 0.00082980519029582529448460859346626
x2[1] (numeric) = 0.00082982850442000984810381147082694
absolute error = 2.331412418455361920287736068e-08
relative error = 0.002809590064897297294511332866548 %
h = 5e-05
x1[1] (analytic) = 0.0012867446466993717704827471482299
x1[1] (numeric) = 0.0012866983055912580292036323022335
absolute error = 4.63411081137412791148459964e-08
relative error = 0.0036014222583020523020228831028955 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.6MB, time=4.34
NO POLE
NO POLE
t[1] = 0.50465
x2[1] (analytic) = 0.00082985100516858561577337154974936
x2[1] (numeric) = 0.00082987483125740202160911456228591
absolute error = 2.382608881640583574301253655e-08
relative error = 0.002871128511986983261101725246555 %
h = 5e-05
x1[1] (analytic) = 0.001286690310825444970037968408768
x1[1] (numeric) = 0.0012866429552410087648299638868505
absolute error = 4.73555844362052080045219175e-08
relative error = 0.0036804182045814412839125760292819 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5047
x2[1] (analytic) = 0.00082989682598149310488331482026843
x2[1] (numeric) = 0.000829921169647157909278381908482
absolute error = 2.434366566480439506708821357e-08
relative error = 0.0029333363982943181611517687225775 %
h = 5e-05
x1[1] (analytic) = 0.0012866359776682439472227866313365
x1[1] (numeric) = 0.0012865875965885974807717665285687
absolute error = 4.83810796464664510201027678e-08
relative error = 0.0037602772257423535468480506703337 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50475
x2[1] (analytic) = 0.00082994265273507388639046716104801
x2[1] (numeric) = 0.00082996751959147064444936785459426
absolute error = 2.486685639675805890069354625e-08
relative error = 0.0029962138124615474738686482118107 %
h = 5e-05
x1[1] (analytic) = 0.001286581647227632869144170960378
x1[1] (numeric) = 0.0012865322296327789850935091278043
absolute error = 4.94175948538840506618325737e-08
relative error = 0.0038409995168492150314199967154081 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5048
x2[1] (analytic) = 0.00082998848542985414088185286713247
x2[1] (numeric) = 0.00083001388109253373544269230244063
absolute error = 2.539566267959456083943530816e-08
relative error = 0.0030597608431208599423158018598169 %
h = 5e-05
x1[1] (analytic) = 0.0012865273195034759097005654035915
x1[1] (numeric) = 0.0012864768543723078991037930624043
absolute error = 5.04651311680105967723411872e-08
relative error = 0.0039225852730035439601346069274927 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50485
x2[1] (analytic) = 0.00083003432406636010496092336108762
x2[1] (numeric) = 0.00083006025415254106562268671457279
absolute error = 2.593008618096066176335348517e-08
relative error = 0.0031239775788943864161265044195161 %
h = 5e-05
x1[1] (analytic) = 0.0012864729944956372495815492666783
x1[1] (numeric) = 0.0012864214708059386573273425525437
absolute error = 5.15236896985922542067141346e-08
relative error = 0.0040050346893439576103268590717388 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5049
x2[1] (analytic) = 0.00083008016864511807125298933317795
x2[1] (numeric) = 0.00083010663877368689345824970467616
absolute error = 2.647012856882220526037149821e-08
relative error = 0.0031888641083941986949650878141877 %
h = 5e-05
x1[1] (analytic) = 0.001286418672203981076267497605066
x1[1] (numeric) = 0.0012863660789324255074769908247704
absolute error = 5.25932715555687905067802956e-08
relative error = 0.0040883479610461790882865858896879 %
h = 5e-05
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.6MB, time=4.61
NO POLE
NO POLE
t[1] = 0.50495
x2[1] (analytic) = 0.00083012601916665438841065343327373
x2[1] (numeric) = 0.00083015303495816585258371221575895
absolute error = 2.701579151146417305878248522e-08
relative error = 0.0032544205202223083727357775256635 %
h = 5e-05
x1[1] (analytic) = 0.0012863643526283715840292416926091
x1[1] (numeric) = 0.0012863106787505225104256620745665
absolute error = 5.36738778490736035796180426e-08
relative error = 0.0041725252833230441045975460540075 %
h = 5e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.00083019944270817295185971228761426
absolute error = 2.756707667749074046877307112e-08
relative error = 0.0033206469029706656825391232509064 %
h = 5e-05
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012862552702589835401783492267968
absolute error = 5.47655096894337493802804696e-08
relative error = 0.0042575668514245077506897090365854 %
h = 5e-05
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations = 100
Total Elapsed Time = 4 Seconds
Elapsed Time(since restart) = 4 Seconds
Expected Time Remaining = 1 Hours 8 Minutes 50 Seconds
Optimized Time Remaining = 1 Hours 8 Minutes 41 Seconds
Time to Timeout = 14 Minutes 55 Seconds
Percent Done = 0.1122 %
> quit
memory used=69.9MB, alloc=4.6MB, time=4.69