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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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, 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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, 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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, 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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, 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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, 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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, 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
> ALWAYS,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_max_terms,
> INFO,
> DEBUGL,
> #Top Generate Globals Decl
> glob_log10abserr,
> centuries_in_millinium,
> glob_unchanged_h_cnt,
> glob_look_poles,
> glob_disp_incr,
> glob_clock_sec,
> glob_max_minutes,
> glob_iter,
> glob_max_hours,
> glob_log10_abserr,
> years_in_century,
> djd_debug,
> glob_dump,
> glob_max_opt_iter,
> glob_percent_done,
> MAX_UNCHANGED,
> glob_start,
> glob_hmin_init,
> glob_hmin,
> glob_curr_iter_when_opt,
> glob_optimal_start,
> glob_optimal_clock_start_sec,
> glob_max_rel_trunc_err,
> glob_optimal_done,
> glob_reached_optimal_h,
> sec_in_min,
> glob_display_flag,
> glob_html_log,
> glob_optimal_expect_sec,
> glob_current_iter,
> glob_max_sec,
> glob_dump_analytic,
> glob_large_float,
> glob_hmax,
> glob_initial_pass,
> glob_almost_1,
> days_in_year,
> glob_normmax,
> glob_warned2,
> glob_warned,
> glob_smallish_float,
> glob_no_eqs,
> glob_relerr,
> glob_log10relerr,
> glob_max_trunc_err,
> glob_not_yet_finished,
> glob_clock_start_sec,
> min_in_hour,
> djd_debug2,
> glob_orig_start_sec,
> glob_small_float,
> hours_in_day,
> glob_max_order,
> glob_last_good_h,
> glob_not_yet_start_msg,
> glob_max_iter,
> glob_abserr,
> glob_log10_relerr,
> glob_h,
> glob_log10normmin,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> array_const_3D0,
> array_const_2D0,
> #END CONST
> array_norms,
> array_t,
> array_last_rel_error,
> array_pole,
> array_x1_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_init,
> array_type_pole,
> array_x2,
> array_x1,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_1st_rel_error,
> array_x2_higher,
> array_x1_higher_work2,
> array_x2_higher_work2,
> array_poles,
> array_x1_higher,
> array_x1_higher_work,
> array_x2_higher_work,
> array_real_pole,
> array_complex_pole,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_max_terms := 30;
> INFO := 2;
> DEBUGL := 3;
> glob_log10abserr := 0.0;
> centuries_in_millinium := 10.0;
> glob_unchanged_h_cnt := 0;
> glob_look_poles := false;
> glob_disp_incr := 0.1;
> glob_clock_sec := 0.0;
> glob_max_minutes := 0.0;
> glob_iter := 0;
> glob_max_hours := 0.0;
> glob_log10_abserr := 0.1e-10;
> years_in_century := 100.0;
> djd_debug := true;
> glob_dump := false;
> glob_max_opt_iter := 10;
> glob_percent_done := 0.0;
> MAX_UNCHANGED := 10;
> glob_start := 0;
> glob_hmin_init := 0.001;
> glob_hmin := 0.00000000001;
> glob_curr_iter_when_opt := 0;
> glob_optimal_start := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_optimal_done := false;
> glob_reached_optimal_h := false;
> sec_in_min := 60.0;
> glob_display_flag := true;
> glob_html_log := true;
> glob_optimal_expect_sec := 0.1;
> glob_current_iter := 0;
> glob_max_sec := 10000.0;
> glob_dump_analytic := false;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_initial_pass := true;
> glob_almost_1 := 0.9990;
> days_in_year := 365.0;
> glob_normmax := 0.0;
> glob_warned2 := false;
> glob_warned := false;
> glob_smallish_float := 0.1e-100;
> glob_no_eqs := 0;
> glob_relerr := 0.1e-10;
> glob_log10relerr := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> min_in_hour := 60.0;
> djd_debug2 := true;
> glob_orig_start_sec := 0.0;
> glob_small_float := 0.1e-50;
> hours_in_day := 24.0;
> glob_max_order := 30;
> glob_last_good_h := 0.1;
> glob_not_yet_start_msg := true;
> glob_max_iter := 1000;
> glob_abserr := 0.1e-10;
> glob_log10_relerr := 0.1e-10;
> glob_h := 0.1;
> glob_log10normmin := 0.1;
> #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 := 0.00001 ;");
> 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_norms:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_x1_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_init:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= 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_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> 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_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_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_init[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_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_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_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[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 <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=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 <=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_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> 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_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_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_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_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_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 := 0.00001 ;
> 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,"2012-06-02T02:14:40-05:00")
> ;
> 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 ALWAYS, DEBUGMASSIVE, glob_iolevel, glob_max_terms, INFO, DEBUGL,
glob_log10abserr, centuries_in_millinium, glob_unchanged_h_cnt,
glob_look_poles, glob_disp_incr, glob_clock_sec, glob_max_minutes,
glob_iter, glob_max_hours, glob_log10_abserr, years_in_century, djd_debug,
glob_dump, glob_max_opt_iter, glob_percent_done, MAX_UNCHANGED, glob_start,
glob_hmin_init, glob_hmin, glob_curr_iter_when_opt, glob_optimal_start,
glob_optimal_clock_start_sec, glob_max_rel_trunc_err, glob_optimal_done,
glob_reached_optimal_h, sec_in_min, glob_display_flag, glob_html_log,
glob_optimal_expect_sec, glob_current_iter, glob_max_sec,
glob_dump_analytic, glob_large_float, glob_hmax, glob_initial_pass,
glob_almost_1, days_in_year, glob_normmax, glob_warned2, glob_warned,
glob_smallish_float, glob_no_eqs, glob_relerr, glob_log10relerr,
glob_max_trunc_err, glob_not_yet_finished, glob_clock_start_sec,
min_in_hour, djd_debug2, glob_orig_start_sec, glob_small_float,
hours_in_day, glob_max_order, glob_last_good_h, glob_not_yet_start_msg,
glob_max_iter, glob_abserr, glob_log10_relerr, glob_h, glob_log10normmin,
array_const_1, array_const_2, array_const_4D0, array_const_0D0,
array_const_3D0, array_const_2D0, array_norms, array_t,
array_last_rel_error, array_pole, array_x1_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_init, array_type_pole,
array_x2, array_x1, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_1st_rel_error,
array_x2_higher, array_x1_higher_work2, array_x2_higher_work2, array_poles,
array_x1_higher, array_x1_higher_work, array_x2_higher_work,
array_real_pole, array_complex_pole, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_max_terms := 30;
INFO := 2;
DEBUGL := 3;
glob_log10abserr := 0.;
centuries_in_millinium := 10.0;
glob_unchanged_h_cnt := 0;
glob_look_poles := false;
glob_disp_incr := 0.1;
glob_clock_sec := 0.;
glob_max_minutes := 0.;
glob_iter := 0;
glob_max_hours := 0.;
glob_log10_abserr := 0.1*10^(-10);
years_in_century := 100.0;
djd_debug := true;
glob_dump := false;
glob_max_opt_iter := 10;
glob_percent_done := 0.;
MAX_UNCHANGED := 10;
glob_start := 0;
glob_hmin_init := 0.001;
glob_hmin := 0.1*10^(-10);
glob_curr_iter_when_opt := 0;
glob_optimal_start := 0.;
glob_optimal_clock_start_sec := 0.;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_optimal_done := false;
glob_reached_optimal_h := false;
sec_in_min := 60.0;
glob_display_flag := true;
glob_html_log := true;
glob_optimal_expect_sec := 0.1;
glob_current_iter := 0;
glob_max_sec := 10000.0;
glob_dump_analytic := false;
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_initial_pass := true;
glob_almost_1 := 0.9990;
days_in_year := 365.0;
glob_normmax := 0.;
glob_warned2 := false;
glob_warned := false;
glob_smallish_float := 0.1*10^(-100);
glob_no_eqs := 0;
glob_relerr := 0.1*10^(-10);
glob_log10relerr := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
min_in_hour := 60.0;
djd_debug2 := true;
glob_orig_start_sec := 0.;
glob_small_float := 0.1*10^(-50);
hours_in_day := 24.0;
glob_max_order := 30;
glob_last_good_h := 0.1;
glob_not_yet_start_msg := true;
glob_max_iter := 1000;
glob_abserr := 0.1*10^(-10);
glob_log10_relerr := 0.1*10^(-10);
glob_h := 0.1;
glob_log10normmin := 0.1;
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 := 0.00001 ;");
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_norms := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_x1_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_init := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := 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_1st_rel_error := Array(1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_init[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_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_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_1st_rel_error[term] := 0.; term := term + 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 <= max_terms do
array_x1_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_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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 <= 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_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
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_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_x1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
end do;
array_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_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_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_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_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 := 0.00001;
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, "2012-06-02T02:14:40-05:00");
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 := 0.00001 ;
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 = 1e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 1e-05
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 1e-05
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50001
x2[1] (analytic) = 0.00082562461725876370002024077185103
x2[1] (numeric) = 0.00082562461736794085640080966210912
absolute error = 1.0917715638056889025809e-13
relative error = 1.3223582981701605156885971130727e-08 %
h = 1e-05
x1[1] (analytic) = 0.0012917442699854529125006082860118
x1[1] (numeric) = 0.0012917442697671030658878745622838
absolute error = 2.183498466127337237280e-13
relative error = 1.6903488692478789862837531605468e-08 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50002
x2[1] (analytic) = 0.00082563367114759095929891755098496
x2[1] (numeric) = 0.00082563367158430777303967583350317
absolute error = 4.3671681374075828251821e-13
relative error = 5.2894743637785870165231993739121e-08 %
h = 1e-05
x1[1] (analytic) = 0.0012917333525973400895138324871812
x1[1] (numeric) = 0.0012917333517239375270648243568111
absolute error = 8.734025624490081303701e-13
relative error = 6.7614772096177786869299460276923e-08 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50003
x2[1] (analytic) = 0.00082564272527208501941416438049361
x2[1] (numeric) = 0.00082564272625471709298812634527064
absolute error = 9.8263207357396196477703e-13
relative error = 1.1901419869594831822075908770472e-07 %
h = 1e-05
x1[1] (analytic) = 0.0012917224353184006017877004750958
x1[1] (numeric) = 0.001291722433353233720367985225861
absolute error = 1.9651668814197152492348e-12
relative error = 1.5213538355361268246982726771044e-07 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.20
NO POLE
NO POLE
t[1] = 0.50004
x2[1] (analytic) = 0.00082565177963225004787972600227534
x2[1] (numeric) = 0.00082565178137918608575066557586367
absolute error = 1.74693603787093957358833e-12
relative error = 2.1158266486738933964787844213653e-07 %
h = 1e-05
x1[1] (analytic) = 0.0012917115181486333575943182918853
x1[1] (numeric) = 0.001291711514654981819857743702653
absolute error = 3.4936515377365745892323e-12
relative error = 2.7046685646528164033048022701086e-07 %
h = 1e-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] = 0.50005
x2[1] (analytic) = 0.00082566083422809021229815693339498
x2[1] (numeric) = 0.0008256608369577320214228429627351
absolute error = 2.72964180912468602934012e-12
relative error = 3.3060085884740147775200777301100e-07 %
h = 1e-05
x1[1] (analytic) = 0.0012917006010880372652167092040327
x1[1] (numeric) = 0.0012917005956291719992997153574944
absolute error = 5.4588652659169938465383e-12
relative error = 4.2261072429004303934366746524980e-07 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50006
x2[1] (analytic) = 0.00082566988905960968036082318771056
x2[1] (numeric) = 0.00082566989299037217069127219271777
absolute error = 3.93076249033044900500721e-12
relative error = 4.7606949731536903598553547238526e-07 %
h = 1e-05
x1[1] (analytic) = 0.0012916896841366112329488135932026
x1[1] (numeric) = 0.001291689676275794432164735954888
absolute error = 7.8608168007840776383146e-12
relative error = 6.0856852054511760574373069592933e-07 %
h = 1e-05
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.210e-05
Order of pole = 14.49
t[1] = 0.50007
x2[1] (analytic) = 0.00082567894412681261984790399753532
x2[1] (numeric) = 0.0008256789494771238048336503930088
absolute error = 5.35031118498574639547348e-12
relative error = 6.4798929693476768516171428789273e-07 %
h = 1e-05
x1[1] (analytic) = 0.0012916787672943541690954888470709
x1[1] (numeric) = 0.001291678756594839291628852610374
absolute error = 1.06995148774666362366969e-11
relative error = 8.2834177880609054529897990028732e-07 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50008
x2[1] (analytic) = 0.00082568799942970319862839353533439
x2[1] (numeric) = 0.00082568800641800419571877732275866
absolute error = 6.98830099709038378742427e-12
relative error = 8.4636097435316407071653302853874e-07 %
h = 1e-05
x1[1] (analytic) = 0.0012916678505612649819725092501548
x1[1] (numeric) = 0.0012916678365862967505733149471068
absolute error = 1.39749682313991943030480e-11
relative error = 1.0819320327069136755800446743802e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.46
NO POLE
NO POLE
t[1] = 0.50009
x2[1] (analytic) = 0.00082569705496828558466010263545667
x2[1] (numeric) = 0.00082569706381303061580657456526525
absolute error = 8.84474503114647192980858e-12
relative error = 1.0711852462022154200185263781420e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012916569339373425799065658746448
x1[1] (numeric) = 0.0012916569162501569815845662521664
absolute error = 1.76871855983219996224784e-11
relative error = 1.3693408159399075583046981452525e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5001
x2[1] (analytic) = 0.00082570611074256394598966051590164
x2[1] (numeric) = 0.0008257061216622203381481047207729
absolute error = 1.091965639215844420487126e-11
relative error = 1.3224628290976691497265422441512e-06 %
h = 1e-05
x1[1] (analytic) = 0.001291646017422585871235266471237
x1[1] (numeric) = 0.0012916459955864101569542346326048
absolute error = 2.18361757142810318386322e-11
relative error = 1.6905696622557636317589929455756e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50011
x2[1] (analytic) = 0.00082571516675254245075251650012108
x2[1] (numeric) = 0.0008257151799655906363855905998763
absolute error = 1.321304818563307409975522e-11
relative error = 1.6001944396393624731954679015219e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012916351010169937643071353599673
x1[1] (numeric) = 0.0012916350745950464486791241712265
absolute error = 2.64219473156280111887408e-11
relative error = 2.0456201054635463432949048629107e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50012
x2[1] (analytic) = 0.00082572422299822526717294173885586
x2[1] (numeric) = 0.00082572423872315878475243441752943
absolute error = 1.572493351757949267867357e-11
relative error = 1.9043807944112220079299016582666e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012916241847205651674816133210459
x1[1] (numeric) = 0.0012916241532760560284612060821042
absolute error = 3.14445091390204072389417e-11
relative error = 2.4344936794306952819042771989880e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50013
x2[1] (analytic) = 0.00082573327947961656356403093200764
x2[1] (numeric) = 0.00082573329793494205807323698765953
absolute error = 1.845532549450920605565189e-11
relative error = 2.2350226099812633830857918904838e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012916132685332989891290574856932
x1[1] (numeric) = 0.0012916132316294290677076098658292
absolute error = 3.69038699214214476198640e-11
relative error = 2.8571919180830273108691917772738e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50014
x2[1] (analytic) = 0.00082574233619672050832770405054562
x2[1] (numeric) = 0.00082574235760095773176381691838601
absolute error = 2.140423722343611286784039e-11
relative error = 2.5921206029015908470200120071020e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012916023524551941376307412269771
x1[1] (numeric) = 0.001291602309655155737530614464496
absolute error = 4.28000384001001267624811e-11
relative error = 3.3137163554047387004888073799810e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.4MB, time=0.71
NO POLE
NO POLE
t[1] = 0.50015
x2[1] (analytic) = 0.00082575139314954126995470805844824
x2[1] (numeric) = 0.00082575141772122308183122980784444
absolute error = 2.457168181187652174939620e-11
relative error = 2.9756754897083968748878980359433e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915914364862495213788540506512
x1[1] (numeric) = 0.0012915913873532262087476394164219
absolute error = 4.91330233126312146342293e-11
relative error = 3.8040685254384072608825670353669e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50016
x2[1] (analytic) = 0.00082576045033808301702461863467988
x2[1] (numeric) = 0.00082576047829575538487378744061562
absolute error = 2.795767236784916880593574e-11
relative error = 3.3856879869219617762887404009523e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915805206264640487765014859936
x1[1] (numeric) = 0.0012915804647236306518812360106012
absolute error = 5.59028333968952654753924e-11
relative error = 4.3282499622849944748697839637202e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50017
x2[1] (analytic) = 0.00082576950776234991820584189520253
x2[1] (numeric) = 0.00082576953932457191808107698475966
absolute error = 3.156222199987523508955713e-11
relative error = 3.8221588110466533029592226719068e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915696048758366282377049766475
x1[1] (numeric) = 0.0012915695417663592371590784408941
absolute error = 6.31094773910786265357534e-11
relative error = 4.8862622001038476309256934161599e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50018
x2[1] (analytic) = 0.00082577856542234614225561611502238
x2[1] (numeric) = 0.0008257786008076899592339801894552
absolute error = 3.538534381697836407443282e-11
relative error = 4.2850886785709262565148267098115e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915586892343661681874017714626
x1[1] (numeric) = 0.0012915586184814021345139549599502
absolute error = 7.07529640336734468115124e-11
relative error = 5.4781067731127019562139027945121e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50019
x2[1] (analytic) = 0.0008257876233180758580200134502716
x2[1] (numeric) = 0.00082578766274512678670469258324373
absolute error = 3.942705092868467913297213e-11
relative error = 4.7744783059673220962391642919151e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915477737020515770614448153374
x1[1] (numeric) = 0.0012915476948687495135837590328662
absolute error = 7.88333020634776857824712e-11
relative error = 6.1037852155876827496952808329218e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=15.2MB, alloc=4.5MB, time=0.96
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.00082579672513689967945674267287902
absolute error = 4.368735644502280101255412e-11
relative error = 5.2903284096924685469212837030133e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.001291536770928391543711480490579
absolute error = 8.73505002195951221494842e-11
relative error = 6.7632990618633075153132569400810e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50021
x2[1] (analytic) = 0.0008258057398167524405211458299511
x2[1] (numeric) = 0.00082580578798302591704501114278174
absolute error = 4.816627347652386531283064e-11
relative error = 5.8326397061870792067409307516746e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915259429648856353805592551682
x1[1] (numeric) = 0.001291525846660318393945196682993
absolute error = 9.63045672414353625721752e-11
relative error = 7.4566498463324880952555017989016e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50022
x2[1] (analytic) = 0.00082581479841970764539421009149987
x2[1] (numeric) = 0.0008258148512835227796157500550992
absolute error = 5.286381513422153996359933e-11
relative error = 6.4014129118759531552017339841625e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915150277600321017519140387637
x1[1] (numeric) = 0.0012915149220645202330380636318417
absolute error = 1.056955118687138504069220e-10
relative error = 8.1838391034465328032921384038094e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50023
x2[1] (analytic) = 0.00082582385725841301825455934712328
x2[1] (numeric) = 0.00082582391503840754790660205037031
absolute error = 5.777999452965204270324703e-11
relative error = 6.9966487431679745611123674241394e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012915041126643300709001816283908
x1[1] (numeric) = 0.0012915039971409872294483071832844
absolute error = 1.155233428414518744451064e-10
relative error = 8.9448683677151485581902997806993e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50024
x2[1] (analytic) = 0.0008258329163328727283924609910323
x2[1] (numeric) = 0.00082583297924769750324661954879574
absolute error = 6.291482477485415855776344e-11
relative error = 7.6183479164561122906156690855699e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012914931976777784513157918118686
x1[1] (numeric) = 0.0012914930718897095513392141602373
absolute error = 1.257880688999765776516313e-10
relative error = 9.7397391737064430172051670840405e-06 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50025
x2[1] (analytic) = 0.00082584197564309094518702663178858
x2[1] (numeric) = 0.00082584204391140992755628395211328
absolute error = 6.826831898236925732032470e-11
relative error = 8.2665111481174195152656729228267e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012914822828003761515000894181426
x1[1] (numeric) = 0.0012914821463106773665791235144392
absolute error = 1.364896987849209659037034e-10
relative error = 1.0568453056046926709647373997259e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.5MB, time=1.22
NO POLE
NO POLE
t[1] = 0.50026
x2[1] (analytic) = 0.00082585103518907183810621381463082
x2[1] (numeric) = 0.00082585110902956210334752484607846
absolute error = 7.384049026524131103144764e-11
relative error = 8.9411391545130333201526426596507e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012914713680321220799653342081357
x1[1] (numeric) = 0.0012914712204038808427414174782515
absolute error = 1.476282412372239167298842e-10
relative error = 1.1431011549421515170526988565140e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50027
x2[1] (analytic) = 0.00082586009497081957670682774383651
x2[1] (numeric) = 0.00082586017460217131372373920355045
absolute error = 7.963135173701691145971394e-11
relative error = 9.6422326519881743120760130908865e-06 %
h = 1e-05
x1[1] (analytic) = 0.0012914604533730151452347007655986
x1[1] (numeric) = 0.0012914602941693101471045127161933
absolute error = 1.592037049981301880494053e-10
relative error = 1.2327416188573531074273764808698e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50028
x2[1] (analytic) = 0.00082586915498833833063452300511837
x2[1] (numeric) = 0.00082586924062925484237981058818318
absolute error = 8.564091651174528758306481e-11
relative error = 1.0369792356872146227765310344789e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012914495388230542558422783879629
x1[1] (numeric) = 0.0012914493676069554466518514762106
absolute error = 1.712160988091904269117523e-10
relative error = 1.3257668508304706368533999140686e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50029
x2[1] (analytic) = 0.00082587821524163226962380528805599
x2[1] (numeric) = 0.00082587830711082997360212835872185
absolute error = 9.186919770397832307066586e-11
relative error = 1.1123818985478335542149008768912e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012914386243822383203330709771937
x1[1] (numeric) = 0.0012914384407168069080718927406801
absolute error = 1.836654314122611782365136e-10
relative error = 1.4221770043475184408043707158301e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5003
x2[1] (analytic) = 0.00082588727573070556349803310856235
x2[1] (numeric) = 0.00082588737404691399226860687390466
absolute error = 9.831620842877057376534231e-11
relative error = 1.1904313254104211076671340225346e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012914277100505662472629969306448
x1[1] (numeric) = 0.0012914275134988546977581033771478
absolute error = 1.965517115495048935534970e-10
relative error = 1.5219722329003522088578347432552e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50031
x2[1] (analytic) = 0.00082589633645556238216941953138531
x2[1] (numeric) = 0.00082589644143752418384870469796995
absolute error = 1.0498196180167928516658464e-10
relative error = 1.2711275879031323607657065525410e-05 %
h = 1e-05
x1[1] (analytic) = 0.001291416795828036945198889031914
x1[1] (numeric) = 0.0012914165859530889818089492888019
absolute error = 2.098749479633899397431121e-10
relative error = 1.6251526899866691980978939500764e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.5MB, time=1.48
NO POLE
NO POLE
t[1] = 0.50032
x2[1] (analytic) = 0.0008259053974162068956390338926443
x2[1] (numeric) = 0.00082590550928267783440344380676864
absolute error = 1.1186647093876440991412434e-10
relative error = 1.3544707576525305474724164457885e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012914058817146493227184943416995
x1[1] (numeric) = 0.0012914056580794999260278865646802
absolute error = 2.236351493966906077770193e-10
relative error = 1.7317185291100084465254640076202e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50033
x2[1] (analytic) = 0.00082591445861264327399680352240172
x2[1] (numeric) = 0.00082591457758239223058542879448209
absolute error = 1.1896974895658862527208037e-10
relative error = 1.4404609062835870189244515892472e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012913949677104022884104740886584
x1[1] (numeric) = 0.0012913947298780776959233526296123
absolute error = 2.378323245924871214590461e-10
relative error = 1.8416699037797509864761833749453e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50034
x2[1] (analytic) = 0.00082592352004487568742151546726956
x2[1] (numeric) = 0.00082592364633668465963886608094532
absolute error = 1.2629180897221735061367576e-10
relative error = 1.5290981054196812042852496563238e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012913840538152947508744035602647
x1[1] (numeric) = 0.0012913838013488124567087573938958
absolute error = 2.524664822941656461663689e-10
relative error = 1.9550069675111200580459600869188e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50035
x2[1] (analytic) = 0.00082593258171290830618081821305085
x2[1] (numeric) = 0.00082593271554557240939958311957565
absolute error = 1.3383266410321876490652480e-10
relative error = 1.6203824266826005716001550639569e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012913731400293256187207719936699
x1[1] (numeric) = 0.0012913728724916943733024744027077
absolute error = 2.675376312454182975909622e-10
relative error = 2.0717298738251813225241711797199e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50036
x2[1] (analytic) = 0.00082594164361674530063122340741629
x2[1] (numeric) = 0.00082594178520907276829504760590679
absolute error = 1.4159232746766382419849050e-10
relative error = 1.7143139416925405886568688960392e-05 %
h = 1e-05
x1[1] (analytic) = 0.001291362226352493800570982466564
x1[1] (numeric) = 0.0012913619433067136103278319852494
absolute error = 2.830457801902431504813146e-10
relative error = 2.1918387762488430758345103148636e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50037
x2[1] (analytic) = 0.00082595070575639084121810758261578
x2[1] (numeric) = 0.00082595085532720302534438668672833
absolute error = 1.4957081218412627910411255e-10
relative error = 1.8108927220681046838506943400688e-05 %
h = 1e-05
x1[1] (analytic) = 0.001291351312784798205057351788037
x1[1] (numeric) = 0.0012913510137938603321131044036272
absolute error = 2.989909378729442473844098e-10
relative error = 2.3153338283148564619834698699298e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.6MB, time=1.73
NO POLE
NO POLE
t[1] = 0.50038
x2[1] (analytic) = 0.00082595976813184909847571387822485
x2[1] (numeric) = 0.00082595992589998047015840616983074
absolute error = 1.5776813137168269229160589e-10
relative error = 1.9101188394263042070545787308280e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012913403993262377408231103894432
x1[1] (numeric) = 0.0012913400839531247026915030014662
absolute error = 3.153731130381316073879770e-10
relative error = 2.4422151835618156865164917753717e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50039
x2[1] (analytic) = 0.00082596883074312424302715376392631
x2[1] (numeric) = 0.00082596899692742239293960973435587
absolute error = 1.6618429814991245597042956e-10
relative error = 2.0119923653825583904939479676851e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012913294859768113165224022152644
x1[1] (numeric) = 0.0012913291537844968858011673522597
absolute error = 3.321923144307212348630047e-10
relative error = 2.5724829955341582299817408419372e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597806840954608448221814175287
absolute error = 1.7481932563889780937942616e-10
relative error = 2.1165133715506943096263370629915e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913182232879670448851564074524
absolute error = 3.494485507959351282065238e-10
relative error = 2.7061374177821650614015464739564e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50041
x2[1] (analytic) = 0.00082598695667314187694833217180798
x2[1] (numeric) = 0.00082598714034636883617218844733975
absolute error = 1.8367322695922385627553177e-10
relative error = 2.2236819295429468440258147674557e-05 %
h = 1e-05
x1[1] (analytic) = 0.001291307659605356222392728228914
x1[1] (numeric) = 0.0012913072924635253430914396442579
absolute error = 3.671418308793012885846561e-10
relative error = 2.8431786038619608517514827747885e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50042
x2[1] (analytic) = 0.00082599601999189270800865078941384
x2[1] (numeric) = 0.00082599621273790793998723321247038
absolute error = 1.9274601523197858242305654e-10
relative error = 2.3334981109699586382722045769092e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912967465833253699266168891408
x1[1] (numeric) = 0.0012912963613111619432728882132115
absolute error = 3.852721634266537286759293e-10
relative error = 2.9836067073355141874470957694428e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=4.6MB, time=1.99
t[1] = 0.50043
x2[1] (analytic) = 0.00082600508354647710974396663377145
x2[1] (numeric) = 0.00082600528558418068849683971730711
absolute error = 2.0203770357875287308353566e-10
relative error = 2.4459619874407800628450983714132e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912858336704241921197475003156
x1[1] (numeric) = 0.0012912854298308670079872660854565
absolute error = 4.038395571841324814148591e-10
relative error = 3.1274218817706377838382825978632e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50044
x2[1] (analytic) = 0.00082601414733689925322175866804788
x2[1] (numeric) = 0.00082601435888520437486228917419896
absolute error = 2.1154830512164053050615108e-10
relative error = 2.5610736305628691750226669281391e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912749208666515976808299355639
x1[1] (numeric) = 0.0012912744980226306994972211997656
absolute error = 4.228440208981836087357983e-10
relative error = 3.2746242807409886987113221116770e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50045
x2[1] (analytic) = 0.00082602321136316330959838452294175
x2[1] (numeric) = 0.00082602343264099629283667594166539
absolute error = 2.2127783298323829141872364e-10
relative error = 2.6788331119420916797852629536554e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912640081720064953294869263476
x1[1] (numeric) = 0.0012912635658864431797702766092961
absolute error = 4.422855633155592103170515e-10
relative error = 3.4252140578260685457985462395168e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50046
x2[1] (analytic) = 0.00082603227562527345011908221970975
x2[1] (numeric) = 0.0008260325068515737367649267389857
absolute error = 2.3122630028664584451927595e-10
relative error = 2.7992405031827208907238205137319e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912530955864877937962539533377
x1[1] (numeric) = 0.0012912526334222946104788216280802
absolute error = 4.621641931833174323252575e-10
relative error = 3.5791913666112237082956685907313e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50047
x2[1] (analytic) = 0.00082604134012323384611797189322822
x2[1] (numeric) = 0.00082604158151695400158381986139407
absolute error = 2.4139372015546584796816585e-10
relative error = 2.9222958758874376909530485643818e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912421831100944018225791372872
x1[1] (numeric) = 0.0012912417006301751530001029772491
absolute error = 4.824799192488224761600381e-10
relative error = 3.7365563606876455523867604371861e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50048
x2[1] (analytic) = 0.00082605040485704866901805751508965
x2[1] (numeric) = 0.00082605065663715438282200439588025
absolute error = 2.5178010571380394688079060e-10
relative error = 3.0479993016573304940294201618913e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912312707428252281608231299048
x1[1] (numeric) = 0.0012912307675100749684162159309919
absolute error = 5.032327502597446071989129e-10
relative error = 3.8973091936523706407768711822588e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.6MB, time=2.27
NO POLE
NO POLE
t[1] = 0.50049
x2[1] (analytic) = 0.00082605946982672209033122861673442
x2[1] (numeric) = 0.00082605973221219217660001943759592
absolute error = 2.6238547008626879082086150e-10
relative error = 3.1763508520918952048739534818698e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912203584846791815742590047308
x1[1] (numeric) = 0.0012912198340619842175140954622487
absolute error = 5.244226949640601635424821e-10
relative error = 4.0614500191082809462323090129944e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5005
x2[1] (analytic) = 0.00082606853503225828165826201261726
x2[1] (numeric) = 0.00082606880824208467963031330686674
absolute error = 2.7320982639797205129424948e-10
relative error = 3.3073505987890351806997909463194e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012912094463356551708370721480129
x1[1] (numeric) = 0.001291208900285893060785507388138
absolute error = 5.460497621100515647598749e-10
relative error = 4.2289789906641040651285633558670e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50051
x2[1] (analytic) = 0.00082607760047366141468882352340884
x2[1] (numeric) = 0.00082607788472684918921726276681011
absolute error = 2.8425318777452843924340127e-10
relative error = 3.4409986133450611919445714991155e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911985342957521047343601495841
x1[1] (numeric) = 0.0012911979661817916584270395151187
absolute error = 5.681139604463073206344654e-10
relative error = 4.3998962619344134310058840577227e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50052
x2[1] (analytic) = 0.00082608666615093566120146969923256
x2[1] (numeric) = 0.00082608696166650300325719224155869
absolute error = 2.9551556734205572254232613e-10
relative error = 3.5772949673546913832075955496484e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911876223649688920621326937406
x1[1] (numeric) = 0.0012911870317496701703400927838864
absolute error = 5.906152987217220399098542e-10
relative error = 4.5742019865396285281325035586955e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50053
x2[1] (analytic) = 0.00082609573206408519306364954293594
x2[1] (numeric) = 0.00082609603906106342023839303508962
absolute error = 3.0699697822717474349215368e-10
relative error = 3.7162397324110512341917888832714e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911767105433044416273114501219
x1[1] (numeric) = 0.0012911760969895187561308724140037
absolute error = 6.135537856854964390361182e-10
relative error = 4.7518963181060151050755216258969e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50054
x2[1] (analytic) = 0.0008261047982131141822317062333974
x2[1] (numeric) = 0.00082610511691054773924114255065954
absolute error = 3.1869743355700943631726214e-10
relative error = 3.8578329801056735206504569474622e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911657988307576622477299645915
x1[1] (numeric) = 0.0012911651619013275751103790482656
absolute error = 6.369294300871373509163259e-10
relative error = 4.9329794102656853882794319443162e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.6MB, time=2.55
NO POLE
NO POLE
t[1] = 0.50055
x2[1] (analytic) = 0.00082611386459802680075087884886784
x2[1] (numeric) = 0.00082611419521497325993772351084539
absolute error = 3.3061694645918684466197755e-10
relative error = 4.0020747820284982753388361754706e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911548872273274627521335501181
x1[1] (numeric) = 0.0012911542264850867862943998967984
absolute error = 6.607422406764577336533197e-10
relative error = 5.1174514166565982956523023889767e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50056
x2[1] (analytic) = 0.0008261229312188272207553040903474
x2[1] (numeric) = 0.00082612327397435728259244317819101
absolute error = 3.4275553006183713908784361e-10
relative error = 4.1489652097678727489704377512096e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911439757330127519801791776594
x1[1] (numeric) = 0.0012911432907407865484034998808934
absolute error = 6.849922262035766792967660e-10
relative error = 5.3053124909225596501596153816202e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50057
x2[1] (analytic) = 0.00082613199807551961446801800499697
x2[1] (numeric) = 0.00082613235318871710806165257645954
absolute error = 3.5511319749359363457146257e-10
relative error = 4.2985043349105513711781887821585e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911330643478124387824353670451
x1[1] (numeric) = 0.001291132354668417019863012776575
absolute error = 7.096793954189194225904701e-10
relative error = 5.4965627867132223934257453041246e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50058
x2[1] (analytic) = 0.00082614106516810815420095770958501
x2[1] (numeric) = 0.00082614143285807003779376571249173
absolute error = 3.6768996188359280800290672e-10
relative error = 4.4506922290416957114803651946503e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911221530717254320203820778627
x1[1] (numeric) = 0.0012911214182679683588030323579028
absolute error = 7.348037570732173497199599e-10
relative error = 5.6912024576840867993431041556660e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50059
x2[1] (analytic) = 0.00082615013249659701235496311396918
x2[1] (numeric) = 0.00082615051298243337382927879867005
absolute error = 3.8048583636147431568470087e-10
relative error = 4.6055289637448744402513208340320e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911112419047506405664106003432
x1[1] (numeric) = 0.0012911104815394307230584035400081
absolute error = 7.603653199175080070603351e-10
relative error = 5.8892316574965006876889301023212e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615959356182441880078947598867
absolute error = 3.9350083405738101083137558e-10
relative error = 4.7630146106020632896970096261176e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.001291099544482794270168713521865
absolute error = 7.863640927031351099243836e-10
relative error = 6.0906505398176596377497322927170e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.6MB, time=2.82
NO POLE
NO POLE
t[1] = 0.50061
x2[1] (analytic) = 0.00082616826786129237397405496813805
x2[1] (numeric) = 0.00082616867459626047593301603772941
absolute error = 4.0673496810195896106959136e-10
relative error = 4.9231492411936450148353032244739e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910894198981333391268342397601
x1[1] (numeric) = 0.0012910886070980491573782829287952
absolute error = 8.128000841817485513109649e-10
relative error = 6.2954592583206072019533905979849e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50062
x2[1] (analytic) = 0.00082617733589750722268535071490973
x2[1] (numeric) = 0.00082617775608575884904281665374353
absolute error = 4.2018825162635746593883380e-10
relative error = 5.0859329270984093544811034208183e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910785090584886469405676083676
x1[1] (numeric) = 0.0012910776693851855416361569547078
absolute error = 8.396733031053044106536598e-10
relative error = 6.5036579666842351195089050614421e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50063
x2[1] (analytic) = 0.00082618640416963908031013420266005
x2[1] (numeric) = 0.00082618683803033684253920859533951
absolute error = 4.3386069776222907439267946e-10
relative error = 5.2513657398935529922362470223458e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910675983279518056610590737599
x1[1] (numeric) = 0.0012910667313441935795960965040727
absolute error = 8.669837582260649625696872e-10
relative error = 6.7152468185932835300538014613497e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50064
x2[1] (analytic) = 0.0008261954726776921196937851601439
x2[1] (numeric) = 0.00082619592043001176142338746077675
absolute error = 4.4775231964172960230063285e-10
relative error = 5.4194477511546795174842069518191e-05 %
h = 1e-05
x1[1] (analytic) = 0.001291056687706521724215254942717
x1[1] (numeric) = 0.0012910557929750634276165693336288
absolute error = 8.947314582965986856090882e-10
relative error = 6.9302259677383411873091947431590e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50065
x2[1] (analytic) = 0.0008262045414216705137705964508309
x2[1] (numeric) = 0.00082620500328480091128874640136528
absolute error = 4.6186313039751814995053438e-10
relative error = 5.5901790324557993863895878793001e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910457771941973115410121980021
x1[1] (numeric) = 0.001291044854277785241760741193826
absolute error = 9.229164120697802710041761e-10
relative error = 7.1485955678158456727424996847267e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50066
x2[1] (analytic) = 0.00082621361040157843556377579663232
x2[1] (numeric) = 0.0008262140865947215983208953481714
absolute error = 4.7619314316275711955153908e-10
relative error = 5.7635596553693298829024137262536e-05 %
h = 1e-05
memory used=45.7MB, alloc=4.6MB, time=3.08
x1[1] (analytic) = 0.0012910348667909774765870983892555
x1[1] (numeric) = 0.0012910339152523491777964669700018
absolute error = 9.515386282987906314192537e-10
relative error = 7.3703557725280836092377998452575e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50067
x2[1] (analytic) = 0.00082622267961742005818544750166287
x2[1] (numeric) = 0.00082622317035979112929768023932941
absolute error = 4.9074237107111223273766654e-10
relative error = 5.9395896914660950797672122500909e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910239564968611283131915238901
x1[1] (numeric) = 0.0012910229758987453911962818232921
absolute error = 9.805981157371169097005980e-10
relative error = 7.5955067355831908747738757799516e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50068
x2[1] (analytic) = 0.00082623174906919955483665417603757
x2[1] (numeric) = 0.0008262322545800268115892022479593
absolute error = 5.0551082725675254807192173e-10
relative error = 6.1182692123153257995368923552484e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910130463118471756898799579863
x1[1] (numeric) = 0.0012910120362169640371373923312761
absolute error = 1.0100948831385524876267102e-09
relative error = 7.8240486106951528161098764615224e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50069
x2[1] (analytic) = 0.00082624081875692109880735845970363
x2[1] (numeric) = 0.00082624133925544595315783701069055
absolute error = 5.2049852485435047855098692e-10
relative error = 6.2995982894846595755914165549458e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012910021362359345276986622871902
x1[1] (numeric) = 0.0012910010962069952705016676283553
absolute error = 1.0400289392571969946588349e-09
relative error = 8.0559815515838044624786643241410e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5007
x2[1] (analytic) = 0.00082624988868058886347644474630742
x2[1] (numeric) = 0.00082625042438606586255825385679194
absolute error = 5.3570547699908180911048452e-10
relative error = 6.4835769945401406131612661663685e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909912262691220933319472376107
x1[1] (numeric) = 0.0012909901558688292458756305458672
absolute error = 1.0704002928474563166917435e-09
relative error = 8.2913057119748307392877954081822e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50071
x2[1] (analytic) = 0.00082625895884020702231172090709628
x2[1] (numeric) = 0.00082625950997190384893743503790748
absolute error = 5.5113169682662571413081120e-10
relative error = 6.6702053990462197503557033576958e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909803164114087815930535567197
x1[1] (numeric) = 0.0012909792152024561175504487519328
absolute error = 1.1012089526640426048047869e-09
relative error = 8.5300212455997666818281743165998e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=49.5MB, alloc=4.6MB, time=3.36
t[1] = 0.50072
x2[1] (analytic) = 0.00082626802923577974886992001485561
x2[1] (numeric) = 0.00082626859601297722203469495839845
absolute error = 5.6677719747316477494354284e-10
relative error = 6.8594835745657544191958243618840e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909694066627935014962099042517
x1[1] (numeric) = 0.0012909682742078660395219258910383
absolute error = 1.1324549274619742840132134e-09
relative error = 8.7721283061959976489903524322069e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50073
x2[1] (analytic) = 0.00082627709986731121679670206788081
x2[1] (numeric) = 0.00082627768250930329218169940629153
absolute error = 5.8264199207538499733841072e-10
relative error = 7.0514115926600086066524085807235e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909584970232751620665547431055
x1[1] (numeric) = 0.0012909573328850491654904927233512
absolute error = 1.1641382259965760620197543e-09
relative error = 9.0176270475067595369884889677546e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50074
x2[1] (analytic) = 0.00082628617073480559982665571398422
x2[1] (numeric) = 0.00082628676946089937030248478483311
absolute error = 5.9872609377047582907084889e-10
relative error = 7.2459895248886528156885626141436e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909475874928526723401362302469
x1[1] (numeric) = 0.0012909463912339956488611982637706
absolute error = 1.1962588570234789379664763e-09
relative error = 9.2665176232811389930919680847987e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50075
x2[1] (analytic) = 0.00082629524183826707178329997453724
x2[1] (numeric) = 0.00082629585686778276791347734464974
absolute error = 6.1502951569613017737011250e-10
relative error = 7.4432174428097640263071563134397e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909366780715249413639121076118
x1[1] (numeric) = 0.0012909354492546956427437009207114
absolute error = 1.2288168292986202111869004e-09
relative error = 9.5188001872740736293646699646592e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50076
x2[1] (analytic) = 0.00082630431317769980657908596854734
x2[1] (numeric) = 0.00082630494472997079712351241651475
absolute error = 6.3155227099054442644796741e-10
relative error = 7.6430954179798256566030544924521e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909257687592908781957495930115
x1[1] (numeric) = 0.001290924506947139299952259634623
absolute error = 1.2618121515782434899583885e-09
relative error = 9.7744748932463522364119053341752e-05 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50077
x2[1] (analytic) = 0.00082631338475310797821539863677017
x2[1] (numeric) = 0.00082631403304748077063385364472111
absolute error = 6.4829437279241845500795094e-10
relative error = 7.8456235219537275238201423634838e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909148595561493919044252710381
x1[1] (numeric) = 0.0012909135643113167730057250162418
absolute error = 1.2952448326188987002547963e-09
relative error = 0.00010033541894964614997135002808863 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.6MB, time=3.63
NO POLE
NO POLE
t[1] = 0.50078
x2[1] (analytic) = 0.00082632245656449576078255846585668
x2[1] (numeric) = 0.00082632312182033000173821222106046
absolute error = 6.6525583424095565375520378e-10
relative error = 8.0508018262847658054131447011743e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012909039504620993915696249839714
x1[1] (numeric) = 0.0012909026213472182141275304845783
absolute error = 1.3291148811774420944993931e-09
relative error = 0.0001029600134620135370049355390835 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50079
x2[1] (analytic) = 0.00082633152861186732845982321253521
x2[1] (numeric) = 0.00082633221104853580432276611940841
absolute error = 6.8243666847586294290687320e-10
relative error = 8.2586304025246430001142401897273e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908930414771397862819437226871
x1[1] (numeric) = 0.001290891678054833775245683404638
absolute error = 1.3634223060110362603180491e-09
relative error = 0.00010561853400734911955275320599278 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634130073211549286617933091606
absolute error = 6.9983688863735078970308729e-10
relative error = 8.4691093222234678890044674470928e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908807344341536079927562248767
absolute error = 1.3981671158771501292926889e-09
relative error = 0.00010831098212349485403873795502595 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50081
x2[1] (analytic) = 0.0008263496734145785163063951813071
x2[1] (numeric) = 0.00082635039087108638243962109980785
absolute error = 7.1745650786613322591850075e-10
relative error = 8.6822386569297554965899287801127e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908712238344873972648633294021
x1[1] (numeric) = 0.0012908697904851678637058776143894
absolute error = 1.4333493195335589857150127e-09
relative error = 0.0001110373593483512193607342659221 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50082
x2[1] (analytic) = 0.00082635874616992648527891978537406
x2[1] (numeric) = 0.00082635948146546578870678515978564
absolute error = 7.3529553930342786537441158e-10
relative error = 8.8980184781904270518827835655694e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908603151767924317711989403184
x1[1] (numeric) = 0.0012908588462078666934267235998341
absolute error = 1.4689689257383444753404843e-09
relative error = 0.00011379766721987721902842499620555 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50083
x2[1] (analytic) = 0.00082636781916127493696798751958978
x2[1] (numeric) = 0.00082636857251527102792390897103914
absolute error = 7.5335399609095592145144936e-10
relative error = 9.1164488575508099494870393683138e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908494066281834977961228446744
x1[1] (numeric) = 0.0012908479016022402479015087020893
absolute error = 1.5050259432498946141425851e-09
relative error = 0.00011659190727609038330133672280827 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.6MB, time=3.90
NO POLE
NO POLE
t[1] = 0.50084
x2[1] (analytic) = 0.00082637689238862804599756835502798
x2[1] (numeric) = 0.00082637766402051941693979295786266
absolute error = 7.7163189137094222460283468e-10
relative error = 9.3375298665546377106891352327505e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908384981886595044847741399822
x1[1] (numeric) = 0.0012908369566682786775809770726453
absolute error = 1.5415203808269037970673369e-09
relative error = 0.0001194200810550667713269218200405 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50085
x2[1] (analytic) = 0.00082638596585198998708057987866837
x2[1] (numeric) = 0.0008263867559812282731958197468782
absolute error = 7.9012923828611523986820983e-10
relative error = 9.5612615767440499445533182399124e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908275898582193609932004178204
x1[1] (numeric) = 0.0012908260114059721326203936297302
absolute error = 1.5784522472283728067880902e-09
relative error = 0.00012228219009494097327871702034149 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50086
x2[1] (analytic) = 0.0008263950395513649350188890178239
x2[1] (numeric) = 0.00082639584839741491472597340586492
absolute error = 8.0884604997970708438804102e-10
relative error = 9.7876440596595923090218163583540e-05 %
h = 1e-05
x1[1] (analytic) = 0.0012908166816368619764883576547494
x1[1] (numeric) = 0.0012908150658153107628795351941697
absolute error = 1.6158215512136088224605797e-09
relative error = 0.00012517823593390611249457859157607 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50087
x2[1] (analytic) = 0.00082640411348675706470331376460328
x2[1] (numeric) = 0.00082640494126909666015685868319501
absolute error = 8.2778233959545354491859173e-10
relative error = 0.00010016677386840216472019802509381 %
h = 1e-05
x1[1] (analytic) = 0.0012908057735245862601481101032286
x1[1] (numeric) = 0.001290804119896284717922681624981
absolute error = 1.6536283015422254284782476e-09
relative error = 0.00012810822011021384761499417943375 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50088
x2[1] (analytic) = 0.00082641318765817055111362490040834
x2[1] (numeric) = 0.00082641403459629082870772024787593
absolute error = 8.4693812027759409534746759e-10
relative error = 0.00010248361629823280072565154447947 %
h = 1e-05
x1[1] (analytic) = 0.0012907948655213911211612301825339
x1[1] (numeric) = 0.0012907931736488841470186069547007
absolute error = 1.6918725069741426232278332e-09
relative error = 0.00013107214416217437472147120080008 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50089
x2[1] (analytic) = 0.00082642226206560956931854772046646
x2[1] (numeric) = 0.00082642312837901474019046193019909
absolute error = 8.6631340517087191420973263e-10
relative error = 0.00010482696860144546681883008283919 %
h = 1e-05
x1[1] (analytic) = 0.0012907839576272754687273983696766
x1[1] (numeric) = 0.0012907822270730991991405705244469
absolute error = 1.7305541762695868278452297e-09
relative error = 0.00013407000962815642947500185989514 %
h = 1e-05
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.6MB, time=4.18
NO POLE
NO POLE
t[1] = 0.5009
x2[1] (analytic) = 0.00082643133670907829447576375839823
x2[1] (numeric) = 0.00082643222261728571500966596299498
absolute error = 8.8590820742053390220459675e-10
relative error = 0.00010719683149338185764525103589572 %
h = 1e-05
x1[1] (analytic) = 0.0012907730498422382120572030903234
x1[1] (numeric) = 0.0012907712801689200229663081187153
absolute error = 1.7696733181890908949716081e-09
relative error = 0.00013710181804658728925460478150645 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50091
x2[1] (analytic) = 0.00082644041158858090183191251081983
x2[1] (numeric) = 0.00082644131731112107416261222349476
absolute error = 9.0572254017233069971267493e-10
relative error = 0.00010959320568936772639493926146396 %
h = 1e-05
x1[1] (analytic) = 0.0012907621421662782603721406097174
x1[1] (numeric) = 0.0012907603329363367668780230999092
absolute error = 1.8092299414934941175098082e-09
relative error = 0.00014016757095595277529594326338978 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50092
x2[1] (analytic) = 0.00082644948670412156672259316198068
x2[1] (numeric) = 0.00082645041246053813923929747579831
absolute error = 9.2575641657251670431381763e-10
relative error = 0.00011201609190471288441371641436787 %
h = 1e-05
x1[1] (analytic) = 0.0012907512345993945229046149236005
x1[1] (numeric) = 0.0012907493853753395789623775426041
absolute error = 1.8492240549439422373809964e-09
relative error = 0.00014326726989479725483002012666983 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50093
x2[1] (analytic) = 0.00082645856205570446457236630843608
x2[1] (numeric) = 0.00082645950806555423242245461394883
absolute error = 9.4600984976785008830551275e-10
relative error = 0.00011446549085471120081453823118599 %
h = 1e-05
x1[1] (analytic) = 0.0012907403271415859088979376491362
x1[1] (numeric) = 0.0012907384374859186070104833675456
absolute error = 1.8896556673018874542815906e-09
relative error = 0.00014640091640172364322194918955546 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50094
x2[1] (analytic) = 0.00082646763764333377089475568375482
x2[1] (numeric) = 0.00082646860412618667648757190561388
absolute error = 9.6648285290559281622185906e-10
relative error = 0.00011694140325464060208887975154281 %
h = 1e-05
x1[1] (analytic) = 0.0012907294197928513276063279158343
x1[1] (numeric) = 0.0012907274892680639985178934753816
absolute error = 1.9305247873290884344404527e-09
relative error = 0.00014956851201539340610980340518144 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=64.8MB, alloc=4.6MB, time=4.45
t[1] = 0.50095
x2[1] (analytic) = 0.00082647671346701366129224988326191
x2[1] (numeric) = 0.00082647770064245279480291223637303
absolute error = 9.8717543913351066235311112e-10
relative error = 0.00011944382981976307171816847597388 %
h = 1e-05
x1[1] (analytic) = 0.0012907185125531896882949122564762
x1[1] (numeric) = 0.0012907165407217659006845928801289
absolute error = 1.9718314237876103193763473e-09
relative error = 0.00015277005827452656154353955718602 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50096
x2[1] (analytic) = 0.00082648578952674831145630408881634
x2[1] (numeric) = 0.00082648679761436991132953235461202
absolute error = 1.00808762159987322826579568e-09
relative error = 0.00012197277126532464978526545676192 %
h = 1e-05
x1[1] (analytic) = 0.0012907076054225999002397244980414
x1[1] (numeric) = 0.0012907055918470144604149898423733
absolute error = 2.0135755854398247346556681e-09
relative error = 0.00015600555671790168212399963130976 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50097
x2[1] (analytic) = 0.00082649486582254189716734179362378
x2[1] (numeric) = 0.00082649589504195535062130211702353
absolute error = 1.02921941345345396032339975e-09
relative error = 0.00012452822830655543258599434234047 %
h = 1e-05
x1[1] (analytic) = 0.0012906966984010808727277056526351
x1[1] (numeric) = 0.0012906946426437998243179070022038
absolute error = 2.0557572810484097986504313e-09
relative error = 0.00015927500888435589714198881085795 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50098
x2[1] (analytic) = 0.00082650394235439859429475652708451
x2[1] (numeric) = 0.00082650499292522643782492373471449
absolute error = 1.05057082784353016720762998e-09
relative error = 0.00012711020165866957224071832931365 %
h = 1e-05
x1[1] (analytic) = 0.0012906857914886315150567038084169
x1[1] (numeric) = 0.0012906836931121121387065725118811
absolute error = 2.0983765193763501312965358e-09
relative error = 0.00016257841631278489471743008260465 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.50099
x2[1] (analytic) = 0.00082651301912232257879691357967621
x2[1] (numeric) = 0.00082651409126420049867995101992006
absolute error = 1.07214187791988303744024385e-09
relative error = 0.00012971869203686527630596508019622 %
h = 1e-05
x1[1] (analytic) = 0.0012906748846852507365354740205306
x1[1] (numeric) = 0.0012906727432519415495986111682399
absolute error = 2.1414333091869368628522907e-09
relative error = 0.00016591578054214292393859549395052 %
h = 1e-05
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652319005889485951880863332422
absolute error = 1.09393257683279765690545236e-09
relative error = 0.00013235370015632480738609956697176 %
h = 1e-05
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906617930632782027160355448249
absolute error = 2.1849276592437676426572102e-09
relative error = 0.00016928710311144279700141407115731 %
h = 1e-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 = 5 Hours 44 Minutes 33 Seconds
Optimized Time Remaining = 5 Hours 43 Minutes 35 Seconds
Time to Timeout = 14 Minutes 55 Seconds
Percent Done = 0.02244 %
> quit
memory used=68.3MB, alloc=4.6MB, time=4.68