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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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, 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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, 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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, 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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, 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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, 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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, 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_max_terms,
> INFO,
> glob_iolevel,
> DEBUGL,
> #Top Generate Globals Decl
> glob_start,
> glob_hmax,
> glob_clock_sec,
> glob_iter,
> glob_no_eqs,
> glob_log10_relerr,
> glob_log10_abserr,
> glob_hmin,
> glob_dump,
> glob_optimal_clock_start_sec,
> glob_max_order,
> glob_max_iter,
> glob_relerr,
> glob_max_opt_iter,
> MAX_UNCHANGED,
> glob_warned2,
> glob_dump_analytic,
> glob_hmin_init,
> glob_optimal_done,
> hours_in_day,
> glob_log10normmin,
> glob_orig_start_sec,
> glob_max_sec,
> glob_max_rel_trunc_err,
> glob_abserr,
> glob_last_good_h,
> glob_not_yet_finished,
> glob_clock_start_sec,
> sec_in_min,
> min_in_hour,
> djd_debug2,
> glob_percent_done,
> glob_log10relerr,
> glob_unchanged_h_cnt,
> glob_small_float,
> glob_max_hours,
> centuries_in_millinium,
> djd_debug,
> glob_normmax,
> glob_curr_iter_when_opt,
> glob_smallish_float,
> glob_max_trunc_err,
> glob_almost_1,
> glob_display_flag,
> glob_optimal_expect_sec,
> glob_log10abserr,
> glob_look_poles,
> glob_reached_optimal_h,
> glob_not_yet_start_msg,
> glob_initial_pass,
> glob_max_minutes,
> glob_warned,
> glob_disp_incr,
> days_in_year,
> glob_html_log,
> glob_current_iter,
> glob_optimal_start,
> glob_large_float,
> glob_h,
> years_in_century,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2D0,
> array_const_3D0,
> array_const_1,
> array_const_2,
> array_const_4D0,
> array_const_0D0,
> #END CONST
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_pole,
> array_norms,
> array_x1_init,
> array_x2,
> array_x1,
> array_x2_init,
> array_m1,
> array_t,
> array_type_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_poles,
> array_x2_higher,
> array_real_pole,
> array_x1_higher_work,
> array_x2_higher_work2,
> array_complex_pole,
> array_x1_higher_work2,
> array_x1_higher,
> array_x2_higher_work,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> ALWAYS := 1;
> DEBUGMASSIVE := 4;
> glob_max_terms := 30;
> INFO := 2;
> glob_iolevel := 5;
> DEBUGL := 3;
> glob_start := 0;
> glob_hmax := 1.0;
> glob_clock_sec := 0.0;
> glob_iter := 0;
> glob_no_eqs := 0;
> glob_log10_relerr := 0.1e-10;
> glob_log10_abserr := 0.1e-10;
> glob_hmin := 0.00000000001;
> glob_dump := false;
> glob_optimal_clock_start_sec := 0.0;
> glob_max_order := 30;
> glob_max_iter := 1000;
> glob_relerr := 0.1e-10;
> glob_max_opt_iter := 10;
> MAX_UNCHANGED := 10;
> glob_warned2 := false;
> glob_dump_analytic := false;
> glob_hmin_init := 0.001;
> glob_optimal_done := false;
> hours_in_day := 24.0;
> glob_log10normmin := 0.1;
> glob_orig_start_sec := 0.0;
> glob_max_sec := 10000.0;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_last_good_h := 0.1;
> glob_not_yet_finished := true;
> glob_clock_start_sec := 0.0;
> sec_in_min := 60.0;
> min_in_hour := 60.0;
> djd_debug2 := true;
> glob_percent_done := 0.0;
> glob_log10relerr := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_small_float := 0.1e-50;
> glob_max_hours := 0.0;
> centuries_in_millinium := 10.0;
> djd_debug := true;
> glob_normmax := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_smallish_float := 0.1e-100;
> glob_max_trunc_err := 0.1e-10;
> glob_almost_1 := 0.9990;
> glob_display_flag := true;
> glob_optimal_expect_sec := 0.1;
> glob_log10abserr := 0.0;
> glob_look_poles := false;
> glob_reached_optimal_h := false;
> glob_not_yet_start_msg := true;
> glob_initial_pass := true;
> glob_max_minutes := 0.0;
> glob_warned := false;
> glob_disp_incr := 0.1;
> days_in_year := 365.0;
> glob_html_log := true;
> glob_current_iter := 0;
> glob_optimal_start := 0.0;
> glob_large_float := 9.0e100;
> glob_h := 0.1;
> years_in_century := 100.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/complicatedrevpostode.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 := 0.0002 ;");
> 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_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_tmp10:= Array(1..(max_terms + 1),[]);
> array_tmp11:= Array(1..(max_terms + 1),[]);
> array_tmp12:= Array(1..(max_terms + 1),[]);
> array_tmp13:= Array(1..(max_terms + 1),[]);
> array_tmp14:= Array(1..(max_terms + 1),[]);
> array_tmp15:= Array(1..(max_terms + 1),[]);
> array_tmp16:= Array(1..(max_terms + 1),[]);
> array_tmp17:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_x1_init:= Array(1..(max_terms + 1),[]);
> array_x2:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_m1:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1_init[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_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher_work[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_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_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_3D0[1] := 3.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_1[1] := 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_2[1] := 2;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 0.5;
> t_end := 5.0;
> array_x1_init[1] := exact_soln_x1(t_start);
> array_x2_init[1] := exact_soln_x2(t_start);
> array_x2_init[2] := exact_soln_x2p(t_start);
> glob_h := 0.00001 ;
> glob_look_poles := true;
> glob_max_iter := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_h := 0.0002 ;
> 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;
> atomall();
> 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,"2012-06-02T02:04:44-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicatedrev")
> ;
> 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,"complicatedrev diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicatedrev maple results")
> ;
> logitem_str(html_log_file,"sub iter once 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_max_terms, INFO, glob_iolevel, DEBUGL,
glob_start, glob_hmax, glob_clock_sec, glob_iter, glob_no_eqs,
glob_log10_relerr, glob_log10_abserr, glob_hmin, glob_dump,
glob_optimal_clock_start_sec, glob_max_order, glob_max_iter, glob_relerr,
glob_max_opt_iter, MAX_UNCHANGED, glob_warned2, glob_dump_analytic,
glob_hmin_init, glob_optimal_done, hours_in_day, glob_log10normmin,
glob_orig_start_sec, glob_max_sec, glob_max_rel_trunc_err, glob_abserr,
glob_last_good_h, glob_not_yet_finished, glob_clock_start_sec, sec_in_min,
min_in_hour, djd_debug2, glob_percent_done, glob_log10relerr,
glob_unchanged_h_cnt, glob_small_float, glob_max_hours,
centuries_in_millinium, djd_debug, glob_normmax, glob_curr_iter_when_opt,
glob_smallish_float, glob_max_trunc_err, glob_almost_1, glob_display_flag,
glob_optimal_expect_sec, glob_log10abserr, glob_look_poles,
glob_reached_optimal_h, glob_not_yet_start_msg, glob_initial_pass,
glob_max_minutes, glob_warned, glob_disp_incr, days_in_year, glob_html_log,
glob_current_iter, glob_optimal_start, glob_large_float, glob_h,
years_in_century, array_const_2D0, array_const_3D0, array_const_1,
array_const_2, array_const_4D0, array_const_0D0, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_pole, array_norms,
array_x1_init, array_x2, array_x1, array_x2_init, array_m1, array_t,
array_type_pole, array_1st_rel_error, array_last_rel_error, array_poles,
array_x2_higher, array_real_pole, array_x1_higher_work,
array_x2_higher_work2, array_complex_pole, array_x1_higher_work2,
array_x1_higher, array_x2_higher_work, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
ALWAYS := 1;
DEBUGMASSIVE := 4;
glob_max_terms := 30;
INFO := 2;
glob_iolevel := 5;
DEBUGL := 3;
glob_start := 0;
glob_hmax := 1.0;
glob_clock_sec := 0.;
glob_iter := 0;
glob_no_eqs := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_log10_abserr := 0.1*10^(-10);
glob_hmin := 0.1*10^(-10);
glob_dump := false;
glob_optimal_clock_start_sec := 0.;
glob_max_order := 30;
glob_max_iter := 1000;
glob_relerr := 0.1*10^(-10);
glob_max_opt_iter := 10;
MAX_UNCHANGED := 10;
glob_warned2 := false;
glob_dump_analytic := false;
glob_hmin_init := 0.001;
glob_optimal_done := false;
hours_in_day := 24.0;
glob_log10normmin := 0.1;
glob_orig_start_sec := 0.;
glob_max_sec := 10000.0;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_last_good_h := 0.1;
glob_not_yet_finished := true;
glob_clock_start_sec := 0.;
sec_in_min := 60.0;
min_in_hour := 60.0;
djd_debug2 := true;
glob_percent_done := 0.;
glob_log10relerr := 0.;
glob_unchanged_h_cnt := 0;
glob_small_float := 0.1*10^(-50);
glob_max_hours := 0.;
centuries_in_millinium := 10.0;
djd_debug := true;
glob_normmax := 0.;
glob_curr_iter_when_opt := 0;
glob_smallish_float := 0.1*10^(-100);
glob_max_trunc_err := 0.1*10^(-10);
glob_almost_1 := 0.9990;
glob_display_flag := true;
glob_optimal_expect_sec := 0.1;
glob_log10abserr := 0.;
glob_look_poles := false;
glob_reached_optimal_h := false;
glob_not_yet_start_msg := true;
glob_initial_pass := true;
glob_max_minutes := 0.;
glob_warned := false;
glob_disp_incr := 0.1;
days_in_year := 365.0;
glob_html_log := true;
glob_current_iter := 0;
glob_optimal_start := 0.;
glob_large_float := 0.90*10^101;
glob_h := 0.1;
years_in_century := 100.0;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/complicatedrevpostode.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 := 0.0002 ;");
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_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_tmp10 := Array(1 .. max_terms + 1, []);
array_tmp11 := Array(1 .. max_terms + 1, []);
array_tmp12 := Array(1 .. max_terms + 1, []);
array_tmp13 := Array(1 .. max_terms + 1, []);
array_tmp14 := Array(1 .. max_terms + 1, []);
array_tmp15 := Array(1 .. max_terms + 1, []);
array_tmp16 := Array(1 .. max_terms + 1, []);
array_tmp17 := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_x1_init := Array(1 .. max_terms + 1, []);
array_x2 := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_m1 := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x1_init[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_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 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_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
end do;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001;
glob_look_poles := true;
glob_max_iter := 10;
glob_h := 0.0002;
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;
atomall();
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, "2012-06-02T02:04:44-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicatedrev");
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, "complicatedrev diffeq.mxt");
logitem_str(html_log_file, "complicatedrev maple results");
logitem_str(html_log_file, "sub iter once 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/complicatedrevpostode.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 := 0.0002 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0002
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0002
t[1] = 0.5
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.0002
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5002
x2[1] (analytic) = 0.0008257966814495432344339416603249
x2[1] (numeric) = 0.00082579668144954295656970752147277
absolute error = 2.7786423413885213e-19
relative error = 3.3648020194403001202555678944769e-14 %
h = 0.0002
x1[1] (analytic) = 0.0012915368582788917633066026400632
x1[1] (numeric) = 0.0012915368582825965220508034624851
absolute error = 3.7047587442008224219e-15
relative error = 2.8684885920621744892044777987859e-10 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5004
x2[1] (analytic) = 0.00082597789359022044558440876232671
x2[1] (numeric) = 0.00082597793726770304844334465273524
absolute error = 4.367748260285893589040853e-11
relative error = 5.2879723466943009264497482790105e-06 %
h = 0.0002
x1[1] (analytic) = 0.0012913185727365178408202846139762
x1[1] (numeric) = 0.0012913184854282161389109575671542
absolute error = 8.73083017019093270468220e-11
relative error = 6.7611744727630286731394953540443e-06 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5006
x2[1] (analytic) = 0.00082615920006099036141977864461309
x2[1] (numeric) = 0.00082615937480149199912013595485247
absolute error = 1.7474050163770035731023938e-10
relative error = 2.1150947859056743272639430613083e-05 %
h = 0.0002
x1[1] (analytic) = 0.0012911003308468869733038234462486
x1[1] (numeric) = 0.0012910999816248061854917034942565
absolute error = 3.492220807878121199519921e-10
relative error = 2.7048407660057114151063292779636e-05 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5008
x2[1] (analytic) = 0.00082634060089522685551538962782877
x2[1] (numeric) = 0.00082634099416580736205926833904204
absolute error = 3.9327058050654387871121327e-10
relative error = 4.7591825946890310339890093724049e-05 %
h = 0.0002
x1[1] (analytic) = 0.0012908821326012694851428855175656
x1[1] (numeric) = 0.0012908813468481420933054466274498
absolute error = 7.857531273918374388901158e-10
relative error = 6.0869471158335615032526769378067e-05 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 0.00082652279549888325782994999044965
absolute error = 6.9937256523110879826257779e-10
relative error = 8.4616318003943978658726761330945e-05 %
h = 0.0002
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = 0.0012906625810197011896414794514703
absolute error = 1.3969712362568421987505648e-09
relative error = 0.00010823663324294398193566625967614 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.18
t[1] = 0.5012
x2[1] (analytic) = 0.00082670368578766620467820114309252
x2[1] (numeric) = 0.00082670477893903363437304090801915
absolute error = 1.09315136742969483976492663e-09
relative error = 0.00013223013108840355353924522727657 %
h = 0.0002
x1[1] (analytic) = 0.0012904458670071646728838326718726
x1[1] (numeric) = 0.0012904436840609486139626090689805
absolute error = 2.1829462160589212236028921e-09
relative error = 0.0001691621688185701560748882430076 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5014
x2[1] (analytic) = 0.00082688536991268795533779675988916
x2[1] (numeric) = 0.00082688694462466704401939056790316
absolute error = 1.57471197908868159380801400e-09
relative error = 0.00019043896970325617831278847413274 %
h = 0.0002
x1[1] (analytic) = 0.0012902277996412267249633565185424
x1[1] (numeric) = 0.0012902246558933024230900683055535
absolute error = 3.1437479243018732882129889e-09
relative error = 0.00024365836212613418916516642007777 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5016
x2[1] (analytic) = 0.00082706714853481408648245956670656
x2[1] (numeric) = 0.00082706929269428669538843927546727
absolute error = 2.14415947260890597970876071e-09
relative error = 0.00025924853579390488513073379773444 %
h = 0.0002
x1[1] (analytic) = 0.001290009775884400908055656176395
x1[1] (numeric) = 0.0012900054964381335854790961656122
absolute error = 4.2794462673225765600107828e-09
relative error = 0.00033173750674786065384438730279401 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5018
x2[1] (analytic) = 0.00082724902168748965324935586679766
x2[1] (numeric) = 0.00082725182328649051480899688372647
absolute error = 2.80159900086155964101692881e-09
relative error = 0.0003386645287469341165477264835366 %
h = 0.0002
x1[1] (analytic) = 0.0012897917957279662718586291348401
x1[1] (numeric) = 0.0012897862056167659526349170410761
absolute error = 5.5901112003192237120937640e-09
relative error = 0.00043341190561412520235509609670574 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = 0.00082743453653997120796381016749464
absolute error = 3.54713579724430788498702594e-09
relative error = 0.00042869264538890068428622344893383 %
h = 0.0002
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 0.0012895667833504762197049488149959
absolute error = 7.0758127273903808771101041e-09
relative error = 0.00054869387101114405199029797595248 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5022
x2[1] (analytic) = 0.0008276130517183405841277537278848
x2[1] (numeric) = 0.00082761743259351632713996918423416
absolute error = 4.38087517574301221545634936e-09
relative error = 0.00052933857998580043754926160665025 %
h = 0.0002
x1[1] (analytic) = 0.0012893559661813954601176818675888
x1[1] (numeric) = 0.0012893472295604935894890206105429
absolute error = 8.7366209018706286612570459e-09
relative error = 0.00067759572461167025606797914501583 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5024
x2[1] (analytic) = 0.00082779520866347734502869438387111
x2[1] (numeric) = 0.00082780051158600847983556373950985
absolute error = 5.30292253113480686935563874e-09
relative error = 0.00064060802425960863474305264850311 %
h = 0.0002
x1[1] (analytic) = 0.0012891381167738261026528185659675
x1[1] (numeric) = 0.0012891275441679924852993021722094
absolute error = 1.05726058336173535163937581e-08
relative error = 0.00082012979804492686829285161867557 %
h = 0.0002
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence = 9.530e-05
Order of pole = 1.45
t[1] = 0.5026
x2[1] (analytic) = 0.00082797746027308634619323399650282
x2[1] (numeric) = 0.00082798377365642862375972228741365
absolute error = 6.31338334227756648829091083e-09
relative error = 0.00076250666777755820669048111618628 %
h = 0.0002
x1[1] (analytic) = 0.001288920310931781561359415133927
x1[1] (numeric) = 0.0012889077270939469785959313608432
absolute error = 1.25838378345827634837730838e-08
relative error = 0.00097630844419587906243489232256141 %
h = 0.0002
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 6.634e-05
Order of pole = 0.2426
t[1] = 0.5028
x2[1] (analytic) = 0.00082815980658068396246110896163522
x2[1] (numeric) = 0.00082816721894391696070246787596743
absolute error = 7.41236323299824135891433221e-09
relative error = 0.00089504020529594338090610059909377 %
h = 0.0002
x1[1] (analytic) = 0.0012887025486465496025266491407532
x1[1] (numeric) = 0.0012886877782566644877809380394351
absolute error = 1.47703898851147457111013181e-08
relative error = 0.0011461442285985419466025077056596 %
h = 0.0002
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence = 9.349e-05
Order of pole = 16.66
t[1] = 0.503
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 0.00082835084758874686858105083852782
absolute error = 8.59996894601936688089264412e-09
relative error = 0.0010382144543189651989776439971618 %
h = 0.0002
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = 0.0012884676975367039718929715909045
absolute error = 1.71323727157628232356708278e-08
relative error = 0.0013296526523301967113966336978683 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 0.0003882
Order of pole = 181.3
t[1] = 0.5032
memory used=7.6MB, alloc=4.2MB, time=0.41
x2[1] (analytic) = 0.00082852478342398194791549665092172
x2[1] (numeric) = 0.00082853465974550381865352070652182
absolute error = 9.87632152187073802405560010e-09
relative error = 0.0011920369456005417477326123678177 %
h = 0.0002
x1[1] (analytic) = 0.0012882671547116832084138656194575
x1[1] (numeric) = 0.0012882474843617741076017791778918
absolute error = 1.96703499091008120864415657e-08
relative error = 0.0015268843762071288801236201260203 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5034
x2[1] (analytic) = 0.00082870741402678649165076351232339
x2[1] (numeric) = 0.0008287186557325216145265495880055
absolute error = 1.124170573512287578607568211e-08
relative error = 0.0013565349536935007635837180828972 %
h = 0.0002
x1[1] (analytic) = 0.0012880495230446330156811398020981
x1[1] (numeric) = 0.0012880271336733904480463627920345
absolute error = 2.23893712425676347770100636e-08
relative error = 0.00173823838617979959187724820248 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5036
x2[1] (analytic) = 0.00082889013946178801067185722653652
x2[1] (numeric) = 0.00082890283743477308534545606401217
absolute error = 1.269797298507467359883747565e-08
relative error = 0.0015319247244658593879998195377655 %
h = 0.0002
x1[1] (analytic) = 0.0012878319348995638898070045446997
x1[1] (numeric) = 0.0012878066043398732527806447122973
absolute error = 2.53305596906370263598324024e-08
relative error = 0.0019669150146220375635676999048347 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5038
x2[1] (analytic) = 0.0008290729597625743379427469999303
x2[1] (numeric) = 0.00082908721902626852438550180001675
absolute error = 1.425926369418644275480008645e-08
relative error = 0.001719904566453347792027238993419 %
h = 0.0002
x1[1] (analytic) = 0.0012876143902677723049596830595824
x1[1] (numeric) = 0.0012875856252981118639329826130245
absolute error = 2.87649696604410267004465579e-08
relative error = 0.0022339739193547738499871928868676 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.504
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = 0.00082927189209752282550820286548163
absolute error = 1.601713477521082059445126061e-08
relative error = 0.0019315069399936844586206027276548 %
h = 0.0002
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 0.0012873628044553975085529320253896
absolute error = 3.40846851589672855739765195e-08
relative error = 0.0026475662203690442348998916425004 %
h = 0.0002
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence = 2.209e-05
Order of pole = 14.48
t[1] = 0.5042
x2[1] (analytic) = 0.00082943888509592429594120180293885
x2[1] (numeric) = 0.00082945732877455552349826570664043
absolute error = 1.844367863122755706390370158e-08
relative error = 0.0022236332251404577624032033060365 %
h = 0.0002
x1[1] (analytic) = 0.0012871794315092163573258400564985
x1[1] (numeric) = 0.0012871328045902889047442552380465
absolute error = 4.66269189274525815848184520e-08
relative error = 0.0036224101928650751064799278320996 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 2.336e-05
Order of pole = 24.82
t[1] = 0.5044
x2[1] (analytic) = 0.00082962199019573515610150603395714
x2[1] (numeric) = 0.00082964540059568947067070539392613
absolute error = 2.341039995431456919935996899e-08
relative error = 0.0028218152641772772545634247808408 %
h = 0.0002
x1[1] (analytic) = 0.00128696201736505364413908613196
x1[1] (numeric) = 0.0012868812757865866748673999294928
absolute error = 8.07415784669692716862024672e-08
relative error = 0.0062738120766206336355349304387263 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 1.142e-05
Order of pole = 2.47
t[1] = 0.5046
x2[1] (analytic) = 0.00082980519029582529448460859346626
x2[1] (numeric) = 0.00082984159662462000902930700677151
absolute error = 3.640632879471454469841330525e-08
relative error = 0.0043873344274619082231034851507026 %
h = 0.0002
x1[1] (analytic) = 0.0012867446466993717704827471482299
x1[1] (numeric) = 0.0012865833565601520114967419869926
absolute error = 1.612901392197589860051612373e-07
relative error = 0.012534743364465068029638665685928 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5048
x2[1] (analytic) = 0.00082998848542985414088185286713247
x2[1] (numeric) = 0.00083005745566682691868344013745968
absolute error = 6.897023697277780158727032721e-08
relative error = 0.0083097823865662254218315509719537 %
h = 0.0002
x1[1] (analytic) = 0.0012865273195034759097005654035915
x1[1] (numeric) = 0.0012862113920296655478608498354166
absolute error = 3.159274738103618397155681749e-07
relative error = 0.024556608244610873511066851610329 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.505
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 0.00083031106956566084135863599001952
absolute error = 1.3919393416538023939247547638e-07
relative error = 0.016766881443616497379508623135248 %
h = 0.0002
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = 0.0012857330628105319400118571340878
absolute error = 5.769729581410339158723731786e-07
relative error = 0.044854890508278316825100674492429 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5052
x2[1] (analytic) = 0.0008303553609344373626191108333988
x2[1] (numeric) = 0.00083062777471325575779214464934517
absolute error = 2.7241377881839517303381594637e-07
relative error = 0.032806891077554473218718252863392 %
h = 0.0002
x1[1] (analytic) = 0.0012860927954862716137431508636619
x1[1] (numeric) = 0.0012851386119041624658586857339937
absolute error = 9.541835821091478844651296682e-07
relative error = 0.074192436615615370558001801295444 %
h = 0.0002
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=0.65
NO POLE
NO POLE
t[1] = 0.5054
x2[1] (analytic) = 0.00083053894137238229996403501027281
x2[1] (numeric) = 0.00083103320273431695814886333164244
absolute error = 4.9426136193465818482832136963e-07
relative error = 0.059510919634658051941123036976253 %
h = 0.0002
x1[1] (analytic) = 0.0012858755986475822178218096943695
x1[1] (numeric) = 0.0012845583321700129924350793014682
absolute error = 1.3172664775692253867303929013e-06
relative error = 0.10244120651754014773680199758567 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5056
x2[1] (analytic) = 0.0008307226169790470804630311551197
x2[1] (numeric) = 0.00083152092578206264159383345207356
absolute error = 7.9830880301556113080229695386e-07
relative error = 0.096098118276668575667459944945737 %
h = 0.0002
x1[1] (analytic) = 0.001285658445243916912587170584005
x1[1] (numeric) = 0.0012839655779355721865821109188262
absolute error = 1.6928673083447260050596651788e-06
relative error = 0.13167317607621306133676097434277 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5058
x2[1] (analytic) = 0.00083090638778816286971999601707344
x2[1] (numeric) = 0.0008320911750515030574430212761025
absolute error = 1.18478726334018772302525902906e-06
relative error = 0.14258974064383360327214822294214 %
h = 0.0002
x1[1] (analytic) = 0.0012854413352665895618636675359888
x1[1] (numeric) = 0.001283361059320866871333300909334
absolute error = 2.0802759457226905303666266548e-06
relative error = 0.16183359665272153817131774240199 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.506
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = 0.00083274401550308590275221316542373
absolute error = 1.65376166961070554779588598631e-06
relative error = 0.19898701278021102608393159938577 %
h = 0.0002
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = 0.0012827448218177086026975699046929
absolute error = 2.4794468892071638316886196724e-06
relative error = 0.19291939543763627474913520719137 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5062
x2[1] (analytic) = 0.00083127421514874396182434633212867
x2[1] (numeric) = 0.00083347951225322660070412206948138
absolute error = 2.20529710448263887977573735271e-06
relative error = 0.26529117158867176949359872698855 %
h = 0.0002
x1[1] (analytic) = 0.001285007245556212864168049527763
x1[1] (numeric) = 0.0012821169115012363053973037546034
absolute error = 2.8903340549765587707457731596e-06
relative error = 0.22492745196354775010463932924373 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5064
x2[1] (analytic) = 0.00083145827176774343750163542019918
x2[1] (numeric) = 0.00083429773043718332061567553157015
absolute error = 2.83945866943988311404011137097e-06
relative error = 0.3415034483213424911267994911882 %
h = 0.0002
x1[1] (analytic) = 0.0012847902658057999287229880316013
x1[1] (numeric) = 0.001281477374510871079925706995815
absolute error = 3.3128912949288487972810357863e-06
relative error = 0.25785463846513939022724647588433 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5066
x2[1] (analytic) = 0.00083164242372426227874944006741881
x2[1] (numeric) = 0.00083519873520913624525003111987828
absolute error = 3.55631148487396650059105245947e-06
relative error = 0.427625068589946070405989013458 %
h = 0.0002
x1[1] (analytic) = 0.0012845733294469977701486259846507
x1[1] (numeric) = 0.0012808262570507201848333718951608
absolute error = 3.7470723962775853152540894899e-06
relative error = 0.29169781984269288569240534387278 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5068
x2[1] (analytic) = 0.00083182667105210352625198767426466
x2[1] (numeric) = 0.00083618259174217138825910156291898
absolute error = 4.35592069006786200711388865432e-06
relative error = 0.52365725236465976613986579025017 %
h = 0.0002
x1[1] (analytic) = 0.0012843564364711289340639521960578
x1[1] (numeric) = 0.0012801636053896611817841781060522
absolute error = 4.1928310814677522797740900056e-06
relative error = 0.32645385365046231752288835764108 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.507
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = 0.0008372493652282580480861394259819
absolute error = 5.23835144317343563952623595864e-06
relative error = 0.62960121397221618133236064478381 %
h = 0.0002
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = 0.0012794894658615471213459103436553
absolute error = 4.6501210079705800593838152927e-06
relative error = 0.36211959007561395458920640471073 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5072
x2[1] (analytic) = 0.00083219545195703736710806275907346
x2[1] (numeric) = 0.00083839912087818472870452239932362
absolute error = 6.20366892114736159645964025016e-06
relative error = 0.74545816208902209309369420678029 %
h = 0.0002
x1[1] (analytic) = 0.0012839227806334900880792892867217
x1[1] (numeric) = 0.001278803884866098320204055888511
absolute error = 5.1188957673917678752333982107e-06
relative error = 0.39869187186367192464637598795531 %
h = 0.0002
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.3MB, time=0.89
NO POLE
NO POLE
t[1] = 0.5074
x2[1] (analytic) = 0.00083237998560180802293506624177892
x2[1] (numeric) = 0.00083963192392125826691079800159036
absolute error = 7.25193831945024397573175981144e-06
relative error = 0.87122929970584481941153260854942 %
h = 0.0002
x1[1] (analytic) = 0.0012837060177543738446159255481629
x1[1] (numeric) = 0.0012781069088732430783452808302736
absolute error = 5.5991088811307662706447178893e-06
relative error = 0.43616753397522109422576378238981 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5076
x2[1] (analytic) = 0.00083256461475325722113917951078113
x2[1] (numeric) = 0.00084094783960379637195193861328902
absolute error = 8.38322485053915081275910250789e-06
relative error = 1.006915823947627524087941888768 %
h = 0.0002
x1[1] (analytic) = 0.0012834892982234984558216514874832
x1[1] (numeric) = 0.0012773985844436609194309269936584
absolute error = 6.0907137798375363907244938248e-06
relative error = 0.47454340197988462036213404923824 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5078
x2[1] (analytic) = 0.00083274933944526001703589742384568
x2[1] (numeric) = 0.00084234693318182678529274153428221
absolute error = 9.59759373656676825684411043653e-06
relative error = 1.1525189251978574424501810983918 %
h = 0.0002
x1[1] (analytic) = 0.001283272622032195140432555615423
x1[1] (numeric) = 0.0012766789583291460474048695255201
absolute error = 6.5936637030490930276860899029e-06
relative error = 0.51381628422862660849421164194597 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.508
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = 0.00084382926988491902227837187419271
absolute error = 1.089511017321313664033349941673e-05
relative error = 1.3080397827583561163512406550331 %
h = 0.0002
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = 0.0012759480780182114186018061871577
absolute error = 7.1079111535854321658089703819e-06
relative error = 0.55398292931655587630423694022472 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5082
x2[1] (analytic) = 0.0008331190755864987272514013242712
x2[1] (numeric) = 0.00084539491472142113918700078669772
absolute error = 1.227583913492241193559946242652e-05
relative error = 1.4734795414785663356126957974355 %
h = 0.0002
x1[1] (analytic) = 0.0012828393996336382723820141458102
x1[1] (numeric) = 0.0012752059948664318989247089416906
absolute error = 7.6334047672063734573052041196e-06
relative error = 0.59503978201685818838402241850154 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5084
x2[1] (analytic) = 0.00083330408710355687307269621296731
x2[1] (numeric) = 0.00084704393138553083933014864282526
absolute error = 1.373984428197396625745242985795e-05
relative error = 1.6488391806323253950381895114145 %
h = 0.0002
x1[1] (analytic) = 0.0012826228534090558237205308396847
x1[1] (numeric) = 0.001274452780719718143042146263964
absolute error = 8.1700726893376806783845757207e-06
relative error = 0.63698168698792629353900810405557 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5086
x2[1] (analytic) = 0.00083348919429681309078974865926187
x2[1] (numeric) = 0.00084877637652655955466129731749078
absolute error = 1.528718222974646387154865822891e-05
relative error = 1.834118826536647227816197310866 %
h = 0.0002
x1[1] (analytic) = 0.0012824063504893876557709944627208
x1[1] (numeric) = 0.0012736886019331708373343354090548
absolute error = 8.7177485562168184366590536660e-06
relative error = 0.67979611555182802726590380381655 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5088
x2[1] (analytic) = 0.00083367439720021459018397984488692
x2[1] (numeric) = 0.00085059227402459189619813820190909
absolute error = 1.691787682437730601415835702217e-05
relative error = 2.0293146678359995225338698661721 %
h = 0.0002
x1[1] (analytic) = 0.0012821898908659736517178112409428
x1[1] (numeric) = 0.0012729139798646284782976159849897
absolute error = 9.2759110013451734201952559531e-06
relative error = 0.72344284317203195332379766197737 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.509
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = 0.00085249152115612474455268274741662
absolute error = 1.863182530840171581752025586106e-05
relative error = 2.2344077068577018979978705303528 %
h = 0.0002
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = 0.0012721304803064850385707100510401
absolute error = 9.8429942236703880248496780229e-06
relative error = 0.76780014713470224887089684396591 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5092
x2[1] (analytic) = 0.00083404509027331451722845383237174
x2[1] (numeric) = 0.00085447362029999434179426513387781
absolute error = 2.042853002667982456581130150607e-05
relative error = 2.4493316086766299054926213234444 %
h = 0.0002
x1[1] (analytic) = 0.0012817571014732763269426554107106
x1[1] (numeric) = 0.0012713419960478300464587754366893
absolute error = 1.04151054254462804838799740213e-05
relative error = 0.81256467496649384555779616031425 %
h = 0.0002
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.13
NO POLE
NO POLE
t[1] = 0.5094
x2[1] (analytic) = 0.00083423058051097962536370648205495
x2[1] (numeric) = 0.00085653709759566161766385226919744
absolute error = 2.230651708468199230014578714249e-05
relative error = 2.6739030677847954724688208683087 %
h = 0.0002
x1[1] (analytic) = 0.0012815407716866814304550845588136
x1[1] (numeric) = 0.0012705562222460623663141148707134
absolute error = 1.09845494406190641409696881002e-05
relative error = 0.85713616634778678086589199267414 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5096
x2[1] (analytic) = 0.0008344161665947233873670581103952
x2[1] (numeric) = 0.00085867858043596976258032685952376
absolute error = 2.426241384124637521326874912856e-05
relative error = 2.9077113810320802908721803473739 %
h = 0.0002
x1[1] (analytic) = 0.0012813244851617175456402073422847
x1[1] (numeric) = 0.0012697853118504635398182038097477
absolute error = 1.15391733112540058220035325370e-05
relative error = 0.9005660505892566712421513303496 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5098
x2[1] (analytic) = 0.00083460184855856530760480082371625
x2[1] (numeric) = 0.00086089175885086442357440928691679
absolute error = 2.628991029229911596960846320054e-05
relative error = 3.1499942562677312526814644889383 %
h = 0.0002
x1[1] (analytic) = 0.0012811082418897332114706301651619
x1[1] (numeric) = 0.0012690448126940856947909379604858
absolute error = 1.20634291956475166796922046761e-05
relative error = 0.94164012073273610242906185226596 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.51
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = 0.0008631666806345237511174038194854
absolute error = 2.837905419798438491787265999647e-05
relative error = 3.3995537666419595983998882402707 %
h = 0.0002
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = 0.0012683490861931777715355370827204
absolute error = 1.25429556689009255026101416387e-05
relative error = 0.97923597453746226942078280783063 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5102
x2[1] (analytic) = 0.00083497350026269402464858159959997
x2[1] (numeric) = 0.00086549025486403774521897862137068
absolute error = 3.051675460134372057039702177071e-05
relative error = 3.6548171399143486987323355234757 %
h = 0.0002
x1[1] (analytic) = 0.0012806758850701060012077512721846
x1[1] (numeric) = 0.0012677024453783951276695082187267
absolute error = 1.29734396917108735382430534579e-05
relative error = 1.0130150682895609596204172671573 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5104
x2[1] (analytic) = 0.00083515947007109223144473450814446
x2[1] (numeric) = 0.00086784886145172292863590710336164
absolute error = 3.268939138063069719117259521718e-05
relative error = 3.9141496387328327691610094690332 %
h = 0.0002
x1[1] (analytic) = 0.0012804597715051688522717135697878
x1[1] (numeric) = 0.0012671004581779165205882805182367
absolute error = 1.33593133272523316834330515511e-05
relative error = 1.0433215962379341279762047420685 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5106
x2[1] (analytic) = 0.00083534553589581142769921939997556
x2[1] (numeric) = 0.00087023040298601898671604976853646
absolute error = 3.488486709020755901683036856090e-05
relative error = 4.1761002592535046784275617847692 %
h = 0.0002
x1[1] (analytic) = 0.0012802437011586227076037330176972
x1[1] (numeric) = 0.0012665467601887454651605033307163
absolute error = 1.36969409698772424432296869809e-05
relative error = 1.0698698191197103939749703512904 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5108
x2[1] (analytic) = 0.00083553169777094355276699444660709
x2[1] (numeric) = 0.00087262232144069692530834239082586
absolute error = 3.709062366975337254134794421877e-05
relative error = 4.4391641596249247568613135260625 %
h = 0.0002
x1[1] (analytic) = 0.0012800276740218247533131544496155
x1[1] (numeric) = 0.0012660430513527964357579458279371
absolute error = 1.39846226690283175552086216784e-05
relative error = 1.0925250252667487768361854524201 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.511
x2[1] (analytic) = 0.00083571795573059504987431312643056
x2[1] (numeric) = 0.00087501207745645315907868120809912
absolute error = 3.929412172585810920436808166856e-05
relative error = 4.701840071332043881982803132291 %
h = 0.0002
x1[1] (analytic) = 0.0012798116900861339038992560756415
x1[1] (numeric) = 0.0012655912074983859605004465574916
absolute error = 1.42204825877479433988095181499e-05
relative error = 1.111138669689044353460475446109 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5112
x2[1] (analytic) = 0.00083590430980888687174857692657073
x2[1] (numeric) = 0.00087738710526159298945474673380613
absolute error = 4.148279545270611770616980723540e-05
relative error = 4.9626249040623256750174551629041 %
h = 0.0002
x1[1] (analytic) = 0.0012795957493429108019056060610889
x1[1] (numeric) = 0.001265193093242743534150183948238
absolute error = 1.44026561001672677554221128509e-05
relative error = 1.1255629840567398368905082519731 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=22.8MB, alloc=4.3MB, time=1.37
t[1] = 0.5114
x2[1] (analytic) = 0.00083609076003995448625047500406982
x2[1] (numeric) = 0.00087973481424594513473168630970469
absolute error = 4.364405420599064848121130563487e-05
relative error = 5.2200139377099465529551009744251 %
h = 0.0002
x1[1] (analytic) = 0.0012793798517835178175744882270767
x1[1] (numeric) = 0.0012648505684576735519947408813833
absolute error = 1.45292833258442655797473456934e-05
relative error = 1.1356504720306277346569371157669 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5116
x2[1] (analytic) = 0.00083627730645794788200841171445351
x2[1] (numeric) = 0.00088204258891436714183203978670534
absolute error = 4.576528245641925982362807225183e-05
relative error = 5.4725008203628161379143773979468 %
h = 0.0002
x1[1] (analytic) = 0.0012791639973993190485013968590695
x1[1] (numeric) = 0.0012645654881736119411207294276581
absolute error = 1.45985092257071073806674314114e-05
relative error = 1.1412539170417147925835138123205 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5118
x2[1] (analytic) = 0.00083646394909703157405522291609771
x2[1] (numeric) = 0.00088429778886016896939526504897476
absolute error = 4.783383976313739534004213287705e-05
relative error = 5.7185775686775676582787661420868 %
h = 0.0002
x1[1] (analytic) = 0.0012789481861816803192896006095455
x1[1] (numeric) = 0.0012643397025631196458047636856388
absolute error = 1.46084836185606734848369239067e-05
relative error = 1.1422263838673971850503549323486 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.512
x2[1] (analytic) = 0.00083665068799138460946718195917937
x2[1] (numeric) = 0.00088648774873853070748136315045331
absolute error = 4.983706074714609801418119127394e-05
relative error = 5.9567345682573913045344843082381 %
h = 0.0002
x1[1] (analytic) = 0.0012787324181219691812047754809758
x1[1] (numeric) = 0.001264175056923622584519222042895
absolute error = 1.45573611983465966855534380808e-05
relative error = 1.1384212202679977449771002596744 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5122
x2[1] (analytic) = 0.00083683752317520057300529626835942
x2[1] (numeric) = 0.00088859977824011466237291099448442
absolute error = 5.176225506491408936761472612500e-05
relative error = 6.1854605740566352446950222666469 %
h = 0.0002
x1[1] (analytic) = 0.0012785166932115549118297068753011
x1[1] (numeric) = 0.0012640733916574052039819916705593
absolute error = 1.44433015541497078477152047418e-05
relative error = 1.1296920588396094417431175982815 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5124
x2[1] (analytic) = 0.00083702445468268759275889542871143
x2[1] (numeric) = 0.00089062116206562851641464031024111
absolute error = 5.359670738294092365574488152968e-05
relative error = 6.403242710902539549241759260689 %
h = 0.0002
x1[1] (analytic) = 0.0012783010114418085147190606960915
x1[1] (numeric) = 0.0012640365422395764395854356512425
absolute error = 1.42644692022320751336250448490e-05
relative error = 1.1158928198095562360912347064218 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5126
x2[1] (analytic) = 0.00083721148254806834579151168477479
x2[1] (numeric) = 0.00089253915990469801117723839971887
absolute error = 5.532767735662966538572671494408e-05
relative error = 6.6085664745350690768727344768788 %
h = 0.0002
x1[1] (analytic) = 0.0012780853728041027190542234895835
x1[1] (numeric) = 0.0012640663391308226814723067236894
absolute error = 1.40190336732800375819167658941e-05
relative error = 1.096877718154496961532905630532 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5128
x2[1] (analytic) = 0.0008373986068055800637890537629762
x2[1] (numeric) = 0.00089434100643459310259889555909374
absolute error = 5.694239962901303880984179611754e-05
relative error = 6.7999157350202554903779858798814 %
h = 0.0002
x1[1] (analytic) = 0.0012778697772898119792982116107845
x1[1] (numeric) = 0.0012641646074257788732714545142486
absolute error = 1.37051698640331060267570965359e-05
relative error = 1.0725012914148347375860101828287 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.513
x2[1] (analytic) = 0.00083758582748947453871027492802935
x2[1] (numeric) = 0.00089601391141295323211990127912323
absolute error = 5.842808392347869340962635109388e-05
relative error = 6.9757727513856394221561295645634 %
h = 0.0002
x1[1] (analytic) = 0.0012776542248903124748506494008434
x1[1] (numeric) = 0.0012643331652722698792472913998206
absolute error = 1.33210596180425956033580010228e-05
relative error = 1.0426185237391766194641745362828 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5132
x2[1] (analytic) = 0.00083777314463401812843953618428816
x2[1] (numeric) = 0.00089754506020372379957292688549532
absolute error = 5.977191556970567113339070120716e-05
relative error = 7.1346182379499739740803223782495 %
h = 0.0002
x1[1] (analytic) = 0.0012774387155969821097028163618863
x1[1] (numeric) = 0.0012645738171760943554562354832977
absolute error = 1.28648984208877542465808785886e-05
relative error = 1.0070853704223012182408611131002 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=4.3MB, time=1.60
t[1] = 0.5134
x2[1] (analytic) = 0.00083796055827349176244186553339435
x2[1] (numeric) = 0.00089892161611640263487578831878954
absolute error = 6.096105784291087243392278539519e-05
relative error = 7.2749316469635714830627002759362 %
h = 0.0002
x1[1] (analytic) = 0.0012772232494012005120927633155174
x1[1] (numeric) = 0.0012648883293203322373143885567562
absolute error = 1.23349200808682747783747587612e-05
relative error = 0.96576069114395191689112553701488 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5136
x2[1] (analytic) = 0.00083814806844219094742031419992721
x2[1] (numeric) = 0.00090013072929395869062343910277814
absolute error = 6.198266085176774320312490285093e-05
relative error = 7.3951922321995822590153710246215 %
h = 0.0002
x1[1] (analytic) = 0.0012770078262943490341604975311922
x1[1] (numeric) = 0.0012652783535275161760101175543782
absolute error = 1.17294727668328581503799768140e-05
relative error = 0.91851220684134055893375703951629 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5138
x2[1] (analytic) = 0.00083833567517442577297561073712817
x2[1] (numeric) = 0.00090115956533272785310857276095478
absolute error = 6.282389015830208013296202382661e-05
relative error = 7.4938824648289979688387105421658 %
h = 0.0002
x1[1] (analytic) = 0.0012767924462678107516032368106682
x1[1] (numeric) = 0.0012657452366686092745882304354977
absolute error = 1.10472095992014770150063751705e-05
relative error = 0.86523143456037444374124753504093 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.514
x2[1] (analytic) = 0.0008385233785045209172681139251402
x2[1] (numeric) = 0.0009019953822556114367820102719205
absolute error = 6.347200375109051951389634678030e-05
relative error = 7.5694972111917460161030175911496 %
h = 0.0002
x1[1] (analytic) = 0.0012765771093129704633307325147448
x1[1] (numeric) = 0.0012662896414880765961305960896766
absolute error = 1.02874678248938672001364250682e-05
relative error = 0.80586341003955388580626604884747 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5142
x2[1] (analytic) = 0.00083871117846681565268206537456791
x2[1] (numeric) = 0.00090262570141712417338914486419364
absolute error = 6.391452295030852070707948962573e-05
relative error = 7.6205640977798598835382744985896 %
h = 0.0002
x1[1] (analytic) = 0.0012763618154212146911206615185049
x1[1] (numeric) = 0.0012669109659642103278669056986766
absolute error = 9.4508494570043632537558198283e-06
relative error = 0.74045222466056536662809461456082 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5144
x2[1] (analytic) = 0.00083889907509566385149214274853093
x2[1] (numeric) = 0.00090303861817626327506093420512186
absolute error = 6.413954308059942356879145659093e-05
relative error = 7.6456805096948367859904107259841 %
h = 0.0002
x1[1] (analytic) = 0.0012761465645839316792740870812734
x1[1] (numeric) = 0.0012676067000617396094291125823351
absolute error = 8.5398645221920698449744989383e-06
relative error = 0.66919151445401286972108999975063 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5146
x2[1] (analytic) = 0.00083908706842543399153231451674996
x2[1] (numeric) = 0.0009032232602147844903404763946313
absolute error = 6.413619178935049880816187788134e-05
relative error = 7.6435681352715308198247792380516 %
h = 0.0002
x1[1] (analytic) = 0.0012759313567925113942709886175111
x1[1] (numeric) = 0.0012683720404492090461709956051873
absolute error = 7.5593163433023480999930123238e-06
relative error = 0.59245478238776635595642291485278 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5148
x2[1] (analytic) = 0.00083927515849050916186699715557149
x2[1] (numeric) = 0.00090317031987057060594499489675351
absolute error = 6.389516138006144407799774118202e-05
relative error = 7.6131362561690778932920961870563 %
h = 0.0002
x1[1] (analytic) = 0.0012757161920383455244258603548666
x1[1] (numeric) = 0.0012692002049355174689778262811008
absolute error = 6.5159871028280554480340737658e-06
relative error = 0.51077090214060696558075513018622 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.515
x2[1] (analytic) = 0.00083946334532528706846451570820467
x2[1] (numeric) = 0.00090287248114552785735904936389313
absolute error = 6.340913582024078889453365568846e-05
relative error = 7.5535324053571540717635681559108 %
h = 0.0002
x1[1] (analytic) = 0.0012755010703128274795433788656077
x1[1] (numeric) = 0.001270083651657865274538688087909
absolute error = 5.4174186549622050046907776987e-06
relative error = 0.42472866397779948787269622948099 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5152
x2[1] (analytic) = 0.00083965162896418003987286861981033
x2[1] (numeric) = 0.00090232452712004262633264945288806
absolute error = 6.267289815586258645978083307773e-05
relative error = 7.4641548939978586960662219592683 %
h = 0.0002
x1[1] (analytic) = 0.0012752859916073523905741394576611
x1[1] (numeric) = 0.0012710152960964653668616890348754
absolute error = 4.2706955108870237124504227857e-06
relative error = 0.33488139436898382412815102347551 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5154
x2[1] (analytic) = 0.00083984000944161503289779776245017
x2[1] (numeric) = 0.00090152315349317021037604315507385
absolute error = 6.168314405155517747824539262368e-05
relative error = 7.3446303293607658828524819918931 %
h = 0.0002
x1[1] (analytic) = 0.0012750709559133171092704614114891
x1[1] (numeric) = 0.0012719881862244786944205641447963
absolute error = 3.0827696888384148498972666928e-06
relative error = 0.24177240290366947686324950585301 %
h = 0.0002
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.85
NO POLE
NO POLE
t[1] = 0.5156
x2[1] (analytic) = 0.0008400284867920336382831645652709
x2[1] (numeric) = 0.0009004668750119155379867514657139
absolute error = 6.043838821988189970358690044300e-05
relative error = 7.1948022204209686658065061111293 %
h = 0.0002
x1[1] (analytic) = 0.0012748559632221202078422620490348
x1[1] (numeric) = 0.0012729946504825059142682041912918
absolute error = 1.8613127396142935740578577430e-06
relative error = 0.14600180673822475249130988812576 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5158
x2[1] (analytic) = 0.00084021706104989208639363316566634
x2[1] (numeric) = 0.00089915613592493747530626104884742
absolute error = 5.893907487504538891262788318108e-05
relative error = 7.0147438807536409731806410888166 %
h = 0.0002
x1[1] (analytic) = 0.0012746410135251619786129996209726
x1[1] (numeric) = 0.0012740268505618765623236618771576
absolute error = 6.141629632854162893377438150e-07
relative error = 0.048183210548582621784941715933528 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.516
x2[1] (analytic) = 0.00084040573224966125289966149752755
x2[1] (numeric) = 0.00089759328488579639490782545184948
absolute error = 5.718755263613514200816395432193e-05
relative error = 6.8047551845048939953891656197995 %
h = 0.0002
x1[1] (analytic) = 0.0012744261068138444336756849984992
x1[1] (numeric) = 0.0012750766378522043380459523718736
absolute error = 6.505310383599043702673733744e-07
relative error = 0.051045018215004874582804309045537 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5162
x2[1] (analytic) = 0.00084059450042582666446480123305994
x2[1] (numeric) = 0.00089578258549417971425425226579706
absolute error = 5.518808506835304978945103273712e-05
relative error = 6.5653635659519519942814882690259 %
h = 0.0002
x1[1] (analytic) = 0.0012742112430795713045489621559082
x1[1] (numeric) = 0.0012761355732861470664683905078837
absolute error = 1.9243302065757619194283519755e-06
relative error = 0.15102128607223349636964831683026 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5164
x2[1] (analytic) = 0.00084078336561288850443530749501307
x2[1] (numeric) = 0.00089373022200997225020890279472242
absolute error = 5.294685639708374577359529970935e-05
relative error = 6.2973244431980606769306919604631 %
h = 0.0002
x1[1] (analytic) = 0.0012739964223137480418332574301895
x1[1] (numeric) = 0.0012771949262969095020880364139585
absolute error = 3.1985039831614602547789837690e-06
relative error = 0.25106067231747392706331308015118 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5166
x2[1] (analytic) = 0.00084097232784536161853205925653825
x2[1] (numeric) = 0.0008914443054351798800383856571772
absolute error = 5.047197758981826150632640063895e-05
relative error = 6.0016216846434776081345726711176 %
h = 0.0002
x1[1] (analytic) = 0.0012737816445077818148669975439001
x1[1] (numeric) = 0.0012782456752694611773127273517463
absolute error = 4.4640307616793624457298078462e-06
relative error = 0.35045494499996232994215302589782 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5168
x2[1] (analytic) = 0.0008411613871577755205447913462566
x2[1] (numeric) = 0.00088893487959205864098220784357596
absolute error = 4.777349243428312043741649731936e-05
relative error = 5.6794680739811836036545802126891 %
h = 0.0002
x1[1] (analytic) = 0.0012735669096530815113828963775561
x1[1] (numeric) = 0.0012792785079374966500120678874012
absolute error = 5.7115982844151386291715098451e-06
relative error = 0.44847257267158212363934645928667 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.517
x2[1] (analytic) = 0.0008413505435846743980286389764889
x2[1] (numeric) = 0.00088621392721178277604846034190282
absolute error = 4.486338362710837801982136541392e-05
relative error = 5.3323057754218090908544826783238 %
h = 0.0002
x1[1] (analytic) = 0.0012733522177410577371643104777951
x1[1] (numeric) = 0.0012802838217862447343356617766865
absolute error = 6.9316040451869971713512988914e-06
relative error = 0.54435873661756734788147979622852 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5172
x2[1] (analytic) = 0.00084153979716061711800299571296767
x2[1] (numeric) = 0.0008832953760329395298210840181273
absolute error = 4.175557887232241181808830515963e-05
relative error = 4.9618067990613283778615293433214 %
h = 0.0002
x1[1] (analytic) = 0.0012731375687631228157016632875658
x1[1] (numeric) = 0.0012812517244650833495064671601028
absolute error = 8.1141557019605338048038725370e-06
relative error = 0.63733534388146202147997420250729 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5174
x2[1] (analytic) = 0.00084172914792017723265268580471965
x2[1] (numeric) = 0.0008801951049080135118955048312484
absolute error = 3.846595698783627924281902652875e-05
relative error = 4.5698734661715764543997717275839 %
h = 0.0002
x1[1] (analytic) = 0.0012729229627106907878489380845994
x1[1] (numeric) = 0.0012821720342319846570881188460468
absolute error = 9.2490715212938692391807614474e-06
relative error = 0.72660104281550249570222355900372 %
h = 0.0002
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=2.09
Real estimate of pole used
NO POLE
Radius of convergence = 1.603e-05
Order of pole = 48.75
t[1] = 0.5176
x2[1] (analytic) = 0.00084191859589794298503145179317699
x2[1] (numeric) = 0.0008769309499099387120677892960702
absolute error = 3.501235401199572703633750289321e-05
relative error = 4.1586388734713147652013600524351 %
h = 0.0002
x1[1] (analytic) = 0.0012727083995751774114802396144245
x1[1] (numeric) = 0.0012830342805229329765801344957537
absolute error = 1.03258809477555650998948813292e-05
relative error = 0.81133124847783541863541646982219 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence = 8.139e-05
Order of pole = 428.6
t[1] = 0.5178
x2[1] (analytic) = 0.00084210814112851731476775831994364
x2[1] (numeric) = 0.00087352271040531001582216768523604
absolute error = 3.141456927679270105440936529240e-05
relative error = 3.7304673524107878901034318558959 %
h = 0.0002
x1[1] (analytic) = 0.0012724938793480001611464244041865
x1[1] (numeric) = 0.001283827705012963364257381461179
absolute error = 1.13338256649632031109570569925e-05
relative error = 0.89067820670150677529032973585581 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.518
x2[1] (analytic) = 0.00084229778364651786377291305301299
x2[1] (numeric) = 0.00086999215496209044110130534481862
absolute error = 2.769437131557257732839229180563e-05
relative error = 3.2879549077853101148150655365017 %
h = 0.0002
x1[1] (analytic) = 0.0012722794020205782277317997435378
x1[1] (numeric) = 0.001284541264447191387485364700766
absolute error = 1.22618624266131597535649572282e-05
relative error = 0.96377119735959010061524265881789 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5182
x2[1] (analytic) = 0.00084248752348657698195150565160216
x2[1] (numeric) = 0.00086636302662176480081113190475821
absolute error = 2.387550313518781885962625315605e-05
relative error = 2.8339295799159947724282230516694 %
h = 0.0002
x1[1] (analytic) = 0.0012720649675843325181108913188656
x1[1] (numeric) = 0.0012851636390486746027952411691412
absolute error = 1.30986714643420846843498502756e-05
relative error = 1.0297171762552841673311315423753 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5184
x2[1] (analytic) = 0.00084267736068334173291416569013793
x2[1] (numeric) = 0.00086266104607997454998877170710713
absolute error = 1.998368539663281707460601696920e-05
relative error = 2.3714515577382663875931555714707 %
h = 0.0002
x1[1] (analytic) = 0.0012718505760306856548052794871294
x1[1] (numeric) = 0.0012856832558962353937260702771771
absolute error = 1.38326798655497389207907900477e-05
relative error = 1.0876025946947403782855619874687 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5186
x2[1] (analytic) = 0.00084286729527147389969264046229865
x2[1] (numeric) = 0.00085891390893923946625422027953704
absolute error = 1.604661366776556656157981723839e-05
relative error = 1.9038125880299119075459716094073 %
h = 0.0002
x1[1] (analytic) = 0.0012716362273510619756405041755803
x1[1] (numeric) = 0.0012860883458176980934434125224392
absolute error = 1.44521184666361178029083468589e-05
relative error = 1.1364978565246793629355154332623 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5188
x2[1] (analytic) = 0.00084305732728564999045719358638684
x2[1] (numeric) = 0.00085515126861245697724666919161986
absolute error = 1.209394132680698678947560523302e-05
relative error = 1.4345336829875201904171963995833 %
h = 0.0002
x1[1] (analytic) = 0.0012714219215368875334030383936394
x1[1] (numeric) = 0.001286367061420974051820072953735
absolute error = 1.49451398840865184170345600956e-05
relative error = 1.175466588307752233972393576781 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.519
x2[1] (analytic) = 0.00084324745676056124423632533367627
x2[1] (numeric) = 0.00085140468985416416828802223392587
absolute error = 8.15723309360292405169690024960e-06
relative error = 0.96735934727155153894137483192576 %
h = 0.0002
x1[1] (analytic) = 0.0012712076585795900954973303432135
x1[1] (numeric) = 0.0012865076827205793463406788564452
absolute error = 1.53000241409892508433485132317e-05
relative error = 1.2035818096065473736834134645983 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5192
x2[1] (analytic) = 0.00084343768373091363663881560174858
x2[1] (numeric) = 0.00084770755202168292703219043217149
absolute error = 4.26986829076929039337483042291e-06
relative error = 0.50624585231735139629383971756377 %
h = 0.0002
x1[1] (analytic) = 0.0012709934384705991436029141137296
x1[1] (numeric) = 0.0012864989129491383430009961915604
absolute error = 1.55054744785391993980820778308e-05
relative error = 1.2199492152530002943029346438631 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5194
x2[1] (analytic) = 0.00084362800823142788557809045520348
x2[1] (numeric) = 0.00084409488169664841864773302356079
absolute error = 4.6687346522053306964256835731e-07
relative error = 0.055341152814411800542026958154936 %
h = 0.0002
x1[1] (analytic) = 0.0012707792612013458733315889481744
x1[1] (numeric) = 0.0012863302176959055404793214346149
absolute error = 1.55509564945596671477324864405e-05
relative error = 1.223733890641116581644189944473 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=38.1MB, alloc=4.4MB, time=2.32
t[1] = 0.5196
x2[1] (analytic) = 0.00084381843029683945699891315649824
x2[1] (numeric) = 0.00084060310721987376438251011868665
absolute error = 3.21532307696569261640303781159e-06
relative error = 0.38104442395677496844968300077217 %
h = 0.0002
x1[1] (analytic) = 0.001270565126763263193884667066423
x1[1] (numeric) = 0.0012859921053603116918302687150214
absolute error = 1.54269785970484979456016485984e-05
relative error = 1.2141824352088418890729111391457 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.5198
x2[1] (analytic) = 0.00084400894996189857060640061004145
x2[1] (numeric) = 0.00083726975350761275709391412790397
absolute error = 6.73919645428581351248648213748e-06
relative error = 0.79847452501422451975902091941169 %
h = 0.0002
x1[1] (analytic) = 0.0012703510351477857277102900321493
x1[1] (numeric) = 0.0012854762406484485449923872756961
absolute error = 1.51252055006628172820972435468e-05
relative error = 1.1906319656679173853141766646753 %
h = 0.0002
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.52
x2[1] (analytic) = 0.00084419956726137020559736614303792
x2[1] (numeric) = 0.00083413312094142166334828364587771
absolute error = 1.006644631994854224908249716021e-05
relative error = 1.1924249561753090415329233152338 %
h = 0.0002
x1[1] (analytic) = 0.00127013698634634981016081364961
x1[1] (numeric) = 0.0012847753927529076517715166016845
absolute error = 1.46384064065578416107029520745e-05
relative error = 1.1525061126411556113427387816493 %
h = 0.0002
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 = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Expected Time Remaining = 8 Minutes 38 Seconds
Optimized Time Remaining = 8 Minutes 35 Seconds
Time to Timeout = 14 Minutes 57 Seconds
Percent Done = 0.4489 %
> quit
memory used=39.1MB, alloc=4.4MB, time=2.38