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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
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> #BEGIN OUTFILE1
>
> # Begin Function number 3
> display_alot := proc(iter)
> global
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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_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[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_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[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 glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
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_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[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_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[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
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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_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 (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 (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 glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
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_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_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_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
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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 glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
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
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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 - 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[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 - 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[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 - 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 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_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 2
> array_complex_pole[1,1] := glob_large_float;
> array_complex_pole[1,2] := 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 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 - 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 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_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 3
> array_complex_pole[2,1] := glob_large_float;
> array_complex_pole[2,2] := 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 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 glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
array_complex_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, glob_last;
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[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 - 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[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 - 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[1, 1] := glob_large_float;
array_complex_pole[1, 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[1, 1] := glob_large_float;
array_complex_pole[1, 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[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 - 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[2, 1] := glob_large_float;
array_complex_pole[2, 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[2, 1] := glob_large_float;
array_complex_pole[2, 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[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
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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_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
> ;
> 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
> #GET NORMS
> ;
> fi;# end if 3
> ;
> # End Function number 7
> end;
get_norms := proc()
local iii;
global glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
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_x1[iii]) then
array_norms[iii] := abs(array_x1[iii])
end if;
iii := iii + 1
end do;
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
end if
end proc
> # Begin Function number 8
> atomall := proc()
> global
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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 mult $eq_no = 1 i = 1
> array_tmp1[1] := (array_const_4D0[1] * (array_x2[1]));
> #emit pre add $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre diff $eq_no = 1 i = 1
> array_tmp3[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 1 i = 1
> array_tmp4[1] := (array_const_2D0[1] * (array_tmp3[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp5[1] := (array_tmp2[1] - (array_tmp4[1]));
> # emit pre mult $eq_no = 1 i = 1
> array_tmp6[1] := (array_const_2D0[1] * (array_x1[1]));
> #emit pre sub $eq_no = 1 i = 1
> array_tmp7[1] := (array_tmp5[1] - (array_tmp6[1]));
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if (1 <= glob_max_terms) then # if number 1
> temporary := array_tmp7[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;
> #emit pre diff $eq_no = 2 i = 1
> array_tmp9[1] := array_x2_higher[2,1];
> # emit pre mult $eq_no = 2 i = 1
> array_tmp10[1] := (array_const_3D0[1] * (array_tmp9[1]));
> # emit pre mult $eq_no = 2 i = 1
> array_tmp11[1] := (array_const_2D0[1] * (array_x2[1]));
> #emit pre sub $eq_no = 2 i = 1
> array_tmp12[1] := (array_tmp10[1] - (array_tmp11[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp13[1] := array_x1_higher[3,1];
> #emit pre sub $eq_no = 2 i = 1
> array_tmp14[1] := (array_tmp12[1] - (array_tmp13[1]));
> #emit pre diff $eq_no = 2 i = 1
> array_tmp15[1] := array_x1_higher[2,1];
> #emit pre sub $eq_no = 2 i = 1
> array_tmp16[1] := (array_tmp14[1] - (array_tmp15[1]));
> #emit pre add $eq_no = 2 i = 1
> array_tmp17[1] := array_tmp16[1] + array_x1[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 ^ (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;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 2
> array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
> #emit pre diff $eq_no = 1 i = 2
> array_tmp3[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - (array_tmp4[2]));
> # emit pre mult $eq_no = 1 i = 2
> array_tmp6[2] := ats(2,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - (array_tmp6[2]));
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if (2 <= glob_max_terms) then # if number 1
> temporary := array_tmp7[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;
> #emit pre diff $eq_no = 2 i = 2
> array_tmp9[2] := array_x2_higher[2,2];
> # emit pre mult $eq_no = 2 i = 2
> array_tmp10[2] := ats(2,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 2
> array_tmp11[2] := ats(2,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 2
> array_tmp12[2] := (array_tmp10[2] - (array_tmp11[2]));
> #emit pre diff $eq_no = 2 i = 2
> array_tmp13[2] := array_x1_higher[3,2];
> #emit pre sub $eq_no = 2 i = 2
> array_tmp14[2] := (array_tmp12[2] - (array_tmp13[2]));
> #emit pre diff $eq_no = 2 i = 2
> array_tmp15[2] := array_x1_higher[2,2];
> #emit pre sub $eq_no = 2 i = 2
> array_tmp16[2] := (array_tmp14[2] - (array_tmp15[2]));
> #emit pre add $eq_no = 2 i = 2
> array_tmp17[2] := array_tmp16[2] + array_x1[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 ^ (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;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 3
> array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
> #emit pre diff $eq_no = 1 i = 3
> array_tmp3[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp2[3] - (array_tmp4[3]));
> # emit pre mult $eq_no = 1 i = 3
> array_tmp6[3] := ats(3,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - (array_tmp6[3]));
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if (3 <= glob_max_terms) then # if number 1
> temporary := array_tmp7[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;
> #emit pre diff $eq_no = 2 i = 3
> array_tmp9[3] := array_x2_higher[2,3];
> # emit pre mult $eq_no = 2 i = 3
> array_tmp10[3] := ats(3,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 3
> array_tmp11[3] := ats(3,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 3
> array_tmp12[3] := (array_tmp10[3] - (array_tmp11[3]));
> #emit pre diff $eq_no = 2 i = 3
> array_tmp13[3] := array_x1_higher[3,3];
> #emit pre sub $eq_no = 2 i = 3
> array_tmp14[3] := (array_tmp12[3] - (array_tmp13[3]));
> #emit pre diff $eq_no = 2 i = 3
> array_tmp15[3] := array_x1_higher[2,3];
> #emit pre sub $eq_no = 2 i = 3
> array_tmp16[3] := (array_tmp14[3] - (array_tmp15[3]));
> #emit pre add $eq_no = 2 i = 3
> array_tmp17[3] := array_tmp16[3] + array_x1[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 ^ (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;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 4
> array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
> #emit pre diff $eq_no = 1 i = 4
> array_tmp3[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp2[4] - (array_tmp4[4]));
> # emit pre mult $eq_no = 1 i = 4
> array_tmp6[4] := ats(4,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - (array_tmp6[4]));
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if (4 <= glob_max_terms) then # if number 1
> temporary := array_tmp7[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;
> #emit pre diff $eq_no = 2 i = 4
> array_tmp9[4] := array_x2_higher[2,4];
> # emit pre mult $eq_no = 2 i = 4
> array_tmp10[4] := ats(4,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 4
> array_tmp11[4] := ats(4,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 4
> array_tmp12[4] := (array_tmp10[4] - (array_tmp11[4]));
> #emit pre diff $eq_no = 2 i = 4
> array_tmp13[4] := array_x1_higher[3,4];
> #emit pre sub $eq_no = 2 i = 4
> array_tmp14[4] := (array_tmp12[4] - (array_tmp13[4]));
> #emit pre diff $eq_no = 2 i = 4
> array_tmp15[4] := array_x1_higher[2,4];
> #emit pre sub $eq_no = 2 i = 4
> array_tmp16[4] := (array_tmp14[4] - (array_tmp15[4]));
> #emit pre add $eq_no = 2 i = 4
> array_tmp17[4] := array_tmp16[4] + array_x1[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 ^ (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;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_const_4D0,array_x2,1);
> #emit pre add $eq_no = 1 i = 5
> array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
> #emit pre diff $eq_no = 1 i = 5
> array_tmp3[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_const_2D0,array_tmp3,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp2[5] - (array_tmp4[5]));
> # emit pre mult $eq_no = 1 i = 5
> array_tmp6[5] := ats(5,array_const_2D0,array_x1,1);
> #emit pre sub $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - (array_tmp6[5]));
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if (5 <= glob_max_terms) then # if number 1
> temporary := array_tmp7[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;
> #emit pre diff $eq_no = 2 i = 5
> array_tmp9[5] := array_x2_higher[2,5];
> # emit pre mult $eq_no = 2 i = 5
> array_tmp10[5] := ats(5,array_const_3D0,array_tmp9,1);
> # emit pre mult $eq_no = 2 i = 5
> array_tmp11[5] := ats(5,array_const_2D0,array_x2,1);
> #emit pre sub $eq_no = 2 i = 5
> array_tmp12[5] := (array_tmp10[5] - (array_tmp11[5]));
> #emit pre diff $eq_no = 2 i = 5
> array_tmp13[5] := array_x1_higher[3,5];
> #emit pre sub $eq_no = 2 i = 5
> array_tmp14[5] := (array_tmp12[5] - (array_tmp13[5]));
> #emit pre diff $eq_no = 2 i = 5
> array_tmp15[5] := array_x1_higher[2,5];
> #emit pre sub $eq_no = 2 i = 5
> array_tmp16[5] := (array_tmp14[5] - (array_tmp15[5]));
> #emit pre add $eq_no = 2 i = 5
> array_tmp17[5] := array_tmp16[5] + array_x1[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 ^ (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;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_const_4D0,array_x2,1);
> #emit add $eq_no = 1
> array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
> #emit diff $eq_no = 1
> array_tmp3[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_const_2D0,array_tmp3,1);
> #emit sub $eq_no = 1
> array_tmp5[kkk] := (array_tmp2[kkk] - (array_tmp4[kkk]));
> #emit mult $eq_no = 1
> array_tmp6[kkk] := ats(kkk,array_const_2D0,array_x1,1);
> #emit sub $eq_no = 1
> array_tmp7[kkk] := (array_tmp5[kkk] - (array_tmp6[kkk]));
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> temporary := array_tmp7[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
> ;
> #emit diff $eq_no = 2
> array_tmp9[kkk] := array_x2_higher[2,kkk];
> #emit mult $eq_no = 2
> array_tmp10[kkk] := ats(kkk,array_const_3D0,array_tmp9,1);
> #emit mult $eq_no = 2
> array_tmp11[kkk] := ats(kkk,array_const_2D0,array_x2,1);
> #emit sub $eq_no = 2
> array_tmp12[kkk] := (array_tmp10[kkk] - (array_tmp11[kkk]));
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x1_higher[3,kkk];
> #emit sub $eq_no = 2
> array_tmp14[kkk] := (array_tmp12[kkk] - (array_tmp13[kkk]));
> #emit diff $eq_no = 2
> array_tmp15[kkk] := array_x1_higher[2,kkk];
> #emit sub $eq_no = 2
> array_tmp16[kkk] := (array_tmp14[kkk] - (array_tmp15[kkk]));
> #emit add $eq_no = 2
> array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
> #emit assign $eq_no = 2
> order_d := 2;
> 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_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
> ;
> 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 glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
array_complex_pole, array_x1_higher_work2, array_x1_higher,
array_x2_higher_work, glob_last;
array_tmp1[1] := array_const_4D0[1]*array_x2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_x2_higher[2, 1];
array_tmp4[1] := array_const_2D0[1]*array_tmp3[1];
array_tmp5[1] := array_tmp2[1] - array_tmp4[1];
array_tmp6[1] := array_const_2D0[1]*array_x1[1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
if 1 <= glob_max_terms then
temporary := array_tmp7[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_tmp9[1] := array_x2_higher[2, 1];
array_tmp10[1] := array_const_3D0[1]*array_tmp9[1];
array_tmp11[1] := array_const_2D0[1]*array_x2[1];
array_tmp12[1] := array_tmp10[1] - array_tmp11[1];
array_tmp13[1] := array_x1_higher[3, 1];
array_tmp14[1] := array_tmp12[1] - array_tmp13[1];
array_tmp15[1] := array_x1_higher[2, 1];
array_tmp16[1] := array_tmp14[1] - array_tmp15[1];
array_tmp17[1] := array_tmp16[1] + array_x1[1];
if 1 <= glob_max_terms then
temporary := array_tmp17[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_tmp1[2] := ats(2, array_const_4D0, array_x2, 1);
array_tmp2[2] := array_const_0D0[2] + array_tmp1[2];
array_tmp3[2] := array_x2_higher[2, 2];
array_tmp4[2] := ats(2, array_const_2D0, array_tmp3, 1);
array_tmp5[2] := array_tmp2[2] - array_tmp4[2];
array_tmp6[2] := ats(2, array_const_2D0, array_x1, 1);
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
if 2 <= glob_max_terms then
temporary := array_tmp7[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_tmp9[2] := array_x2_higher[2, 2];
array_tmp10[2] := ats(2, array_const_3D0, array_tmp9, 1);
array_tmp11[2] := ats(2, array_const_2D0, array_x2, 1);
array_tmp12[2] := array_tmp10[2] - array_tmp11[2];
array_tmp13[2] := array_x1_higher[3, 2];
array_tmp14[2] := array_tmp12[2] - array_tmp13[2];
array_tmp15[2] := array_x1_higher[2, 2];
array_tmp16[2] := array_tmp14[2] - array_tmp15[2];
array_tmp17[2] := array_tmp16[2] + array_x1[2];
if 2 <= glob_max_terms then
temporary := array_tmp17[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_tmp1[3] := ats(3, array_const_4D0, array_x2, 1);
array_tmp2[3] := array_const_0D0[3] + array_tmp1[3];
array_tmp3[3] := array_x2_higher[2, 3];
array_tmp4[3] := ats(3, array_const_2D0, array_tmp3, 1);
array_tmp5[3] := array_tmp2[3] - array_tmp4[3];
array_tmp6[3] := ats(3, array_const_2D0, array_x1, 1);
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
if 3 <= glob_max_terms then
temporary := array_tmp7[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_tmp9[3] := array_x2_higher[2, 3];
array_tmp10[3] := ats(3, array_const_3D0, array_tmp9, 1);
array_tmp11[3] := ats(3, array_const_2D0, array_x2, 1);
array_tmp12[3] := array_tmp10[3] - array_tmp11[3];
array_tmp13[3] := array_x1_higher[3, 3];
array_tmp14[3] := array_tmp12[3] - array_tmp13[3];
array_tmp15[3] := array_x1_higher[2, 3];
array_tmp16[3] := array_tmp14[3] - array_tmp15[3];
array_tmp17[3] := array_tmp16[3] + array_x1[3];
if 3 <= glob_max_terms then
temporary := array_tmp17[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_tmp1[4] := ats(4, array_const_4D0, array_x2, 1);
array_tmp2[4] := array_const_0D0[4] + array_tmp1[4];
array_tmp3[4] := array_x2_higher[2, 4];
array_tmp4[4] := ats(4, array_const_2D0, array_tmp3, 1);
array_tmp5[4] := array_tmp2[4] - array_tmp4[4];
array_tmp6[4] := ats(4, array_const_2D0, array_x1, 1);
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
if 4 <= glob_max_terms then
temporary := array_tmp7[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_tmp9[4] := array_x2_higher[2, 4];
array_tmp10[4] := ats(4, array_const_3D0, array_tmp9, 1);
array_tmp11[4] := ats(4, array_const_2D0, array_x2, 1);
array_tmp12[4] := array_tmp10[4] - array_tmp11[4];
array_tmp13[4] := array_x1_higher[3, 4];
array_tmp14[4] := array_tmp12[4] - array_tmp13[4];
array_tmp15[4] := array_x1_higher[2, 4];
array_tmp16[4] := array_tmp14[4] - array_tmp15[4];
array_tmp17[4] := array_tmp16[4] + array_x1[4];
if 4 <= glob_max_terms then
temporary := array_tmp17[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_tmp1[5] := ats(5, array_const_4D0, array_x2, 1);
array_tmp2[5] := array_const_0D0[5] + array_tmp1[5];
array_tmp3[5] := array_x2_higher[2, 5];
array_tmp4[5] := ats(5, array_const_2D0, array_tmp3, 1);
array_tmp5[5] := array_tmp2[5] - array_tmp4[5];
array_tmp6[5] := ats(5, array_const_2D0, array_x1, 1);
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
if 5 <= glob_max_terms then
temporary := array_tmp7[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;
array_tmp9[5] := array_x2_higher[2, 5];
array_tmp10[5] := ats(5, array_const_3D0, array_tmp9, 1);
array_tmp11[5] := ats(5, array_const_2D0, array_x2, 1);
array_tmp12[5] := array_tmp10[5] - array_tmp11[5];
array_tmp13[5] := array_x1_higher[3, 5];
array_tmp14[5] := array_tmp12[5] - array_tmp13[5];
array_tmp15[5] := array_x1_higher[2, 5];
array_tmp16[5] := array_tmp14[5] - array_tmp15[5];
array_tmp17[5] := array_tmp16[5] + array_x1[5];
if 5 <= glob_max_terms then
temporary := array_tmp17[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;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk];
array_tmp3[kkk] := array_x2_higher[2, kkk];
array_tmp4[kkk] := ats(kkk, array_const_2D0, array_tmp3, 1);
array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
temporary := array_tmp7[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;
array_tmp9[kkk] := array_x2_higher[2, kkk];
array_tmp10[kkk] := ats(kkk, array_const_3D0, array_tmp9, 1);
array_tmp11[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk];
array_tmp13[kkk] := array_x1_higher[3, kkk];
array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk];
array_tmp15[kkk] := array_x1_higher[2, kkk];
array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk];
array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
order_d := 2;
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_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;
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
> glob_iolevel,
> DEBUGL,
> INFO,
> DEBUGMASSIVE,
> ALWAYS,
> glob_max_terms,
> #Top Generate Globals Decl
> glob_max_minutes,
> glob_normmax,
> glob_max_trunc_err,
> glob_clock_sec,
> glob_iter,
> glob_optimal_start,
> glob_disp_incr,
> glob_initial_pass,
> djd_debug2,
> glob_display_flag,
> glob_log10normmin,
> glob_start,
> glob_max_order,
> glob_last_good_h,
> min_in_hour,
> sec_in_min,
> glob_log10relerr,
> glob_optimal_clock_start_sec,
> glob_no_eqs,
> glob_log10_relerr,
> glob_reached_optimal_h,
> glob_clock_start_sec,
> glob_dump,
> MAX_UNCHANGED,
> glob_hmin,
> glob_small_float,
> glob_relerr,
> glob_abserr,
> glob_dump_analytic,
> glob_html_log,
> glob_percent_done,
> glob_curr_iter_when_opt,
> glob_warned2,
> glob_large_float,
> glob_hmax,
> glob_optimal_done,
> glob_not_yet_start_msg,
> hours_in_day,
> glob_max_sec,
> glob_smallish_float,
> glob_max_iter,
> glob_log10_abserr,
> glob_optimal_expect_sec,
> glob_unchanged_h_cnt,
> glob_max_hours,
> glob_hmin_init,
> glob_h,
> glob_not_yet_finished,
> days_in_year,
> glob_log10abserr,
> glob_current_iter,
> glob_orig_start_sec,
> glob_warned,
> glob_max_rel_trunc_err,
> glob_almost_1,
> glob_max_opt_iter,
> glob_look_poles,
> centuries_in_millinium,
> years_in_century,
> djd_debug,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_1,
> array_const_2D0,
> array_const_3D0,
> array_const_0D0,
> array_const_4D0,
> #END CONST
> array_m1,
> array_norms,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_last_rel_error,
> array_x1,
> array_x2,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_x1_init,
> array_t,
> array_type_pole,
> array_x2_init,
> array_1st_rel_error,
> array_pole,
> array_x2_higher,
> array_real_pole,
> array_poles,
> array_x2_higher_work2,
> array_x1_higher_work,
> 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;
> glob_iolevel := 5;
> DEBUGL := 3;
> INFO := 2;
> DEBUGMASSIVE := 4;
> ALWAYS := 1;
> glob_max_terms := 30;
> glob_max_minutes := 0.0;
> glob_normmax := 0.0;
> glob_max_trunc_err := 0.1e-10;
> glob_clock_sec := 0.0;
> glob_iter := 0;
> glob_optimal_start := 0.0;
> glob_disp_incr := 0.1;
> glob_initial_pass := true;
> djd_debug2 := true;
> glob_display_flag := true;
> glob_log10normmin := 0.1;
> glob_start := 0;
> glob_max_order := 30;
> glob_last_good_h := 0.1;
> min_in_hour := 60.0;
> sec_in_min := 60.0;
> glob_log10relerr := 0.0;
> glob_optimal_clock_start_sec := 0.0;
> glob_no_eqs := 0;
> glob_log10_relerr := 0.1e-10;
> glob_reached_optimal_h := false;
> glob_clock_start_sec := 0.0;
> glob_dump := false;
> MAX_UNCHANGED := 10;
> glob_hmin := 0.00000000001;
> glob_small_float := 0.1e-50;
> glob_relerr := 0.1e-10;
> glob_abserr := 0.1e-10;
> glob_dump_analytic := false;
> glob_html_log := true;
> glob_percent_done := 0.0;
> glob_curr_iter_when_opt := 0;
> glob_warned2 := false;
> glob_large_float := 9.0e100;
> glob_hmax := 1.0;
> glob_optimal_done := false;
> glob_not_yet_start_msg := true;
> hours_in_day := 24.0;
> glob_max_sec := 10000.0;
> glob_smallish_float := 0.1e-100;
> glob_max_iter := 1000;
> glob_log10_abserr := 0.1e-10;
> glob_optimal_expect_sec := 0.1;
> glob_unchanged_h_cnt := 0;
> glob_max_hours := 0.0;
> glob_hmin_init := 0.001;
> glob_h := 0.1;
> glob_not_yet_finished := true;
> days_in_year := 365.0;
> glob_log10abserr := 0.0;
> glob_current_iter := 0;
> glob_orig_start_sec := 0.0;
> glob_warned := false;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_almost_1 := 0.9990;
> glob_max_opt_iter := 10;
> glob_look_poles := false;
> centuries_in_millinium := 10.0;
> years_in_century := 100.0;
> djd_debug := true;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_max_order := 2;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/complicated2postode.ode#################");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> 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,"!");
> 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 := 0.001 ;");
> 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_m1:= Array(1..(max_terms + 1),[]);
> array_norms:= Array(1..(max_terms + 1),[]);
> array_tmp0:= Array(1..(max_terms + 1),[]);
> array_tmp1:= Array(1..(max_terms + 1),[]);
> array_tmp2:= Array(1..(max_terms + 1),[]);
> array_tmp3:= Array(1..(max_terms + 1),[]);
> array_tmp4:= Array(1..(max_terms + 1),[]);
> array_tmp5:= Array(1..(max_terms + 1),[]);
> array_tmp6:= Array(1..(max_terms + 1),[]);
> array_tmp7:= Array(1..(max_terms + 1),[]);
> array_tmp8:= Array(1..(max_terms + 1),[]);
> array_tmp9:= Array(1..(max_terms + 1),[]);
> array_last_rel_error:= Array(1..(max_terms + 1),[]);
> array_x1:= Array(1..(max_terms + 1),[]);
> array_x2:= 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_x1_init:= Array(1..(max_terms + 1),[]);
> array_t:= Array(1..(max_terms + 1),[]);
> array_type_pole:= Array(1..(max_terms + 1),[]);
> array_x2_init:= Array(1..(max_terms + 1),[]);
> array_1st_rel_error:= Array(1..(max_terms + 1),[]);
> array_pole:= Array(1..(max_terms + 1),[]);
> array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
> array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
> array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
> array_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_m1[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_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_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x1[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_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_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> term := 1;
> while term <= max_terms do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=3 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_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_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 3 do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= max_terms do # do number 3
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3
> ;
> ord := ord + 1;
> od;# end do number 2
> ;
> ord := 1;
> while ord <=2 do # do number 2
> term := 1;
> while term <= 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_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_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_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_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_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_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_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_0D0[1] := 0.0;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while term <= max_terms + 1 do # do number 2
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2
> ;
> array_const_4D0[1] := 4.0;
> array_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 := 0.001 ;
> 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 := 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
> ;
> 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
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> 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)
> ;
> 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)
> ;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> sub_iter := 1;
> while sub_iter <= 3 do # do number 3
> atomall()
> ;
> sub_iter := sub_iter + 1;
> od;# end do number 3
> ;
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3
> ;#was right paren 0004C
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> order_diff := 1;
> #Jump Series array_x1
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x1
> order_diff := 1;
> #BEFORE ADJUST SUBSERIES EQ =1
> 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 =1
> #BEFORE SUM SUBSERIES EQ =1
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> 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 =1
> #BEFORE SUM SUBSERIES EQ =1
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> 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 =1
> #BEFORE SUM SUBSERIES EQ =1
> 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 =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_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
> order_diff := 2;
> #Jump Series array_x2
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x2
> order_diff := 2;
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =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_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
> 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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> 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_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if glob_html_log then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2012-06-02T01:53:41-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"complicated2")
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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,"complicated2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"complicated2 maple results")
> ;
> logitem_str(html_log_file,"sub iter tot order")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> 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;")
> ;
> 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 glob_iolevel, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_max_terms,
glob_max_minutes, glob_normmax, glob_max_trunc_err, glob_clock_sec,
glob_iter, glob_optimal_start, glob_disp_incr, glob_initial_pass,
djd_debug2, glob_display_flag, glob_log10normmin, glob_start,
glob_max_order, glob_last_good_h, min_in_hour, sec_in_min, glob_log10relerr,
glob_optimal_clock_start_sec, glob_no_eqs, glob_log10_relerr,
glob_reached_optimal_h, glob_clock_start_sec, glob_dump, MAX_UNCHANGED,
glob_hmin, glob_small_float, glob_relerr, glob_abserr, glob_dump_analytic,
glob_html_log, glob_percent_done, glob_curr_iter_when_opt, glob_warned2,
glob_large_float, glob_hmax, glob_optimal_done, glob_not_yet_start_msg,
hours_in_day, glob_max_sec, glob_smallish_float, glob_max_iter,
glob_log10_abserr, glob_optimal_expect_sec, glob_unchanged_h_cnt,
glob_max_hours, glob_hmin_init, glob_h, glob_not_yet_finished, days_in_year,
glob_log10abserr, glob_current_iter, glob_orig_start_sec, glob_warned,
glob_max_rel_trunc_err, glob_almost_1, glob_max_opt_iter, glob_look_poles,
centuries_in_millinium, years_in_century, djd_debug, array_const_2,
array_const_1, array_const_2D0, array_const_3D0, array_const_0D0,
array_const_4D0, array_m1, array_norms, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_last_rel_error, array_x1, array_x2, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15,
array_tmp16, array_tmp17, array_x1_init, array_t, array_type_pole,
array_x2_init, array_1st_rel_error, array_pole, array_x2_higher,
array_real_pole, array_poles, array_x2_higher_work2, array_x1_higher_work,
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;
glob_iolevel := 5;
DEBUGL := 3;
INFO := 2;
DEBUGMASSIVE := 4;
ALWAYS := 1;
glob_max_terms := 30;
glob_max_minutes := 0.;
glob_normmax := 0.;
glob_max_trunc_err := 0.1*10^(-10);
glob_clock_sec := 0.;
glob_iter := 0;
glob_optimal_start := 0.;
glob_disp_incr := 0.1;
glob_initial_pass := true;
djd_debug2 := true;
glob_display_flag := true;
glob_log10normmin := 0.1;
glob_start := 0;
glob_max_order := 30;
glob_last_good_h := 0.1;
min_in_hour := 60.0;
sec_in_min := 60.0;
glob_log10relerr := 0.;
glob_optimal_clock_start_sec := 0.;
glob_no_eqs := 0;
glob_log10_relerr := 0.1*10^(-10);
glob_reached_optimal_h := false;
glob_clock_start_sec := 0.;
glob_dump := false;
MAX_UNCHANGED := 10;
glob_hmin := 0.1*10^(-10);
glob_small_float := 0.1*10^(-50);
glob_relerr := 0.1*10^(-10);
glob_abserr := 0.1*10^(-10);
glob_dump_analytic := false;
glob_html_log := true;
glob_percent_done := 0.;
glob_curr_iter_when_opt := 0;
glob_warned2 := false;
glob_large_float := 0.90*10^101;
glob_hmax := 1.0;
glob_optimal_done := false;
glob_not_yet_start_msg := true;
hours_in_day := 24.0;
glob_max_sec := 10000.0;
glob_smallish_float := 0.1*10^(-100);
glob_max_iter := 1000;
glob_log10_abserr := 0.1*10^(-10);
glob_optimal_expect_sec := 0.1;
glob_unchanged_h_cnt := 0;
glob_max_hours := 0.;
glob_hmin_init := 0.001;
glob_h := 0.1;
glob_not_yet_finished := true;
days_in_year := 365.0;
glob_log10abserr := 0.;
glob_current_iter := 0;
glob_orig_start_sec := 0.;
glob_warned := false;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_almost_1 := 0.9990;
glob_max_opt_iter := 10;
glob_look_poles := false;
centuries_in_millinium := 10.0;
years_in_century := 100.0;
djd_debug := true;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_max_order := 2;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/complicated2postode.ode#################");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
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, "!");
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 := 0.001 ;");
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_m1 := Array(1 .. max_terms + 1, []);
array_norms := Array(1 .. max_terms + 1, []);
array_tmp0 := Array(1 .. max_terms + 1, []);
array_tmp1 := Array(1 .. max_terms + 1, []);
array_tmp2 := Array(1 .. max_terms + 1, []);
array_tmp3 := Array(1 .. max_terms + 1, []);
array_tmp4 := Array(1 .. max_terms + 1, []);
array_tmp5 := Array(1 .. max_terms + 1, []);
array_tmp6 := Array(1 .. max_terms + 1, []);
array_tmp7 := Array(1 .. max_terms + 1, []);
array_tmp8 := Array(1 .. max_terms + 1, []);
array_tmp9 := Array(1 .. max_terms + 1, []);
array_last_rel_error := Array(1 .. max_terms + 1, []);
array_x1 := Array(1 .. max_terms + 1, []);
array_x2 := 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_x1_init := Array(1 .. max_terms + 1, []);
array_t := Array(1 .. max_terms + 1, []);
array_type_pole := Array(1 .. max_terms + 1, []);
array_x2_init := Array(1 .. max_terms + 1, []);
array_1st_rel_error := Array(1 .. max_terms + 1, []);
array_pole := Array(1 .. max_terms + 1, []);
array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
array_real_pole := Array(1 .. 3, 1 .. 4, []);
array_poles := Array(1 .. 3, 1 .. 4, []);
array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
array_complex_pole := Array(1 .. 3, 1 .. 4, []);
array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
array_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_m1[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_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_last_rel_error[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[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_x1_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_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_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_x2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x2[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_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_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_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_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_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_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 := 0.001;
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 := 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;
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;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
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);
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);
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop");
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
sub_iter := 1;
while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do;
if glob_look_poles then check_for_pole() end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 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;
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;
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 (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
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_int(INFO, "Iterations ", 32, glob_iter, 4,
" ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2012-06-02T01:53:41-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"complicated2");
logitem_str(html_log_file,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * 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, "complicated2 diffeq.mxt");
logitem_str(html_log_file, "complicated2 maple results");
logitem_str(html_log_file, "sub iter tot order");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
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;");
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/complicated2postode.ode#################
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + 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 := 0.001 ;
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
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.001
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.001
t[1] = 0.5
x1[1] (analytic) = 0.0012917551874827401624868391629841
x1[1] (numeric) = 0.0012917551874827401624868391629841
absolute error = 0
relative error = 0 %
h = 0.001
x2[1] (analytic) = 0.00082561556360559907415319735476789
x2[1] (numeric) = 0.00082561556360559907415319735476789
absolute error = 0
relative error = 0 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.501
x1[1] (analytic) = 0.0012906639779909374464836782020351
x1[1] (numeric) = -11953766581600.167500960648671454
absolute error = 11953766581600.168791624626662391
relative error = 926171860797381269.45404706773813 %
h = 0.001
x2[1] (analytic) = 0.00082652209612631802672115172787186
x2[1] (numeric) = 106787963006.42959348851559075253
absolute error = 106787963006.4287669664194644345
relative error = 12920158276096260.345204986976509 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.502
x1[1] (analytic) = 0.0012895738591632036100858259251
x1[1] (numeric) = 13385411526356888569007221922754
absolute error = 13385411526356888569007221922754
relative error = 1.0379716858592805350915668466410e+36 %
h = 0.001
x2[1] (analytic) = 0.0008274309894041739636559251804687
x2[1] (numeric) = -119577442067726949547016878791.84
absolute error = 119577442067726949547016878791.84
relative error = 1.4451651388333140773514621608585e+34 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.503
x1[1] (analytic) = 0.0012884848299094197347162072617323
x1[1] (numeric) = -1.4988517678244951253668159307091e+49
absolute error = 1.4988517678244951253668159307091e+49
relative error = 1.1632669108955393372784931997818e+54 %
h = 0.001
x2[1] (analytic) = 0.0008283422476198008492141699458837
x2[1] (numeric) = 1.3389865532503688534084255231423e+47
absolute error = 1.3389865532503688534084255231423e+47
relative error = 1.6164653645252048188125442730197e+52 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.9MB, time=0.20
NO POLE
NO POLE
t[1] = 0.504
x1[1] (analytic) = 0.0012873968891405564758385060019091
x1[1] (numeric) = 1.6783620118716366607198583425420e+67
absolute error = 1.6783620118716366607198583425420e+67
relative error = 1.3036865523203816545246082444110e+72 %
h = 0.001
x2[1] (analytic) = 0.00082925587496274761468760841422102
x2[1] (numeric) = -1.4993505119216703935917742308425e+65
absolute error = 1.4993505119216703935917742308425e+65
relative error = 1.8080673977607034945202277124331e+70 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.505
x1[1] (analytic) = 0.0012863100357686729739277295072664
x1[1] (numeric) = -1.8793713316843795251208790668000e+85
absolute error = 1.8793713316843795251208790668000e+85
relative error = 1.4610562612623208398592965719933e+90 %
h = 0.001
x2[1] (analytic) = 0.00083017187563149546111924351454314
x2[1] (numeric) = 1.6789204881428153337698539211944e+83
absolute error = 1.6789204881428153337698539211944e+83
relative error = 2.0223769768949272729682032843305e+88 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.506
x1[1] (analytic) = 0.0012852242687069157665292585243653
x1[1] (numeric) = 2.1044545678308958861430935221334e+103
absolute error = 2.1044545678308958861430935221334e+103
relative error = 1.6374220586016637653894517886974e+108 %
h = 0.001
x2[1] (analytic) = 0.00083109025383347519720441727943742
x2[1] (numeric) = -1.8799966939638252678576337976208e+101
absolute error = 1.8799966939638252678576337976208e+101
relative error = 2.2620848762119144111340920560669e+106 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.507
x1[1] (analytic) = 0.001284139586869517701405294158948
x1[1] (numeric) = -2.3564949371102149095578779309178e+121
absolute error = 2.3564949371102149095578779309178e+121
relative error = 1.8350769349420110713612312336885e+126 %
h = 0.001
x2[1] (analytic) = 0.00083201101378508461244661319002326
x2[1] (numeric) = 2.1051548267330837963520260841857e+119
absolute error = 2.1051548267330837963520260841857e+119
relative error = 2.5302006726522286813175766522768e+124 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.508
x1[1] (analytic) = 0.0012830559891717968507676151575396
x1[1] (numeric) = 2.6387209652854308101520799802045e+139
absolute error = 2.6387209652854308101520799802045e+139
relative error = 2.0565906613231318709184396536573e+144 %
h = 0.001
x2[1] (analytic) = 0.00083293415971170588563803837477598
x2[1] (numeric) = -2.3572790626422633478945051916444e+137
absolute error = 2.3572790626422633478945051916444e+137
relative error = 2.8300905121458360954457425649076e+142 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.46
NO POLE
NO POLE
t[1] = 0.509
x1[1] (analytic) = 0.001281973474530155426595559729063
x1[1] (numeric) = -2.9547478430721612385969637953039e+157
absolute error = 2.9547478430721612385969637953039e+157
relative error = 2.3048431982222403687641182186126e+162 %
h = 0.001
x2[1] (analytic) = 0.00083385969584772302873516249155556
x2[1] (numeric) = 2.6395990017489290699452129951503e+155
absolute error = 2.6395990017489290699452129951503e+155
relative error = 3.1655193492299030230694613971482e+160 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.51
x1[1] (analytic) = 0.0012808920418620786970381472243591
x1[1] (numeric) = 3.3086237351341944653032411361202e+175
absolute error = 3.3086237351341944653032411361202e+175
relative error = 2.5830621371683514299583166938138e+180 %
h = 0.001
x2[1] (analytic) = 0.00083478762643653936619953115948893
x2[1] (numeric) = -2.9557310377262346970651665342276e+173
absolute error = 2.9557310377262346970651665342276e+173
relative error = 3.5406981897220653740500805943111e+178 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.511
x1[1] (analytic) = 0.0012798116900861339038992560756415
x1[1] (numeric) = -3.7048816352840973588881094230241e+193
absolute error = 3.7048816352840973588881094230241e+193
relative error = 2.8948646617181246127813756952595e+198 %
h = 0.001
x2[1] (analytic) = 0.00083571795573059504987431312643056
x2[1] (numeric) = 3.3097246822679242292929613921855e+191
absolute error = 3.3097246822679242292929613921855e+191
relative error = 3.9603369289517318952018767474075e+196 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.512
x1[1] (analytic) = 0.0012787324181219691812047754809758
x1[1] (numeric) = 4.1485974321309910405725282631947e+211
absolute error = 4.1485974321309910405725282631947e+211
relative error = 3.2443045732928981457863414969813e+216 %
h = 0.001
x2[1] (analytic) = 0.00083665068799138460946718195917937
x2[1] (numeric) = -3.7061144375437984404894302065086e+209
absolute error = 3.7061144375437984404894302065086e+209
relative error = 4.4297034482113066351059300488760e+214 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.513
x1[1] (analytic) = 0.0012776542248903124748506494008434
x1[1] (numeric) = -4.6454549289707851454561262284171e+229
absolute error = 4.6454549289707851454561262284171e+229
relative error = 3.6359249932191949348353691543872e+234 %
h = 0.001
x2[1] (analytic) = 0.00083758582748947453871027492802935
x2[1] (numeric) = 4.1499778811688802114485463613869e+227
absolute error = 4.1499778811688802114485463613869e+227
relative error = 4.9546897105551020157389103016877e+232 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.514
x1[1] (analytic) = 0.0012765771093129704633307325147448
x1[1] (numeric) = 5.2018186507949346922755186891243e+247
absolute error = 5.2018186507949346922755186891243e+247
relative error = 4.0748174261047612083097196385601e+252 %
h = 0.001
x2[1] (analytic) = 0.0008385233785045209172681139251402
x2[1] (numeric) = -4.6470007077290680830944658664026e+245
absolute error = 4.6470007077290680830944658664026e+245
relative error = 5.5418856848294942040235635962251e+250 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=0.72
NO POLE
NO POLE
t[1] = 0.515
x1[1] (analytic) = 0.0012755010703128274795433788656077
x1[1] (numeric) = -5.8248153710433309964556714189914e+265
absolute error = 5.8248153710433309964556714189914e+265
relative error = 4.5666879523783900192667230738095e+270 %
h = 0.001
x2[1] (analytic) = 0.00083946334532528706846451570820467
x2[1] (numeric) = 5.2035495600164821926035710430093e+263
absolute error = 5.2035495600164821926035710430093e+263
relative error = 6.1986620249632669715923704109696e+268 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.516
x1[1] (analytic) = 0.0012744261068138444336756849984992
x1[1] (numeric) = 6.5224254024230074839745135623705e+283
absolute error = 6.5224254024230074839745135623705e+283
relative error = 5.1179314104993761745850873485554e+288 %
h = 0.001
x2[1] (analytic) = 0.00084040573224966125289966149752755
x2[1] (numeric) = -5.8267535829104459283621616789314e+281
absolute error = 5.8267535829104459283621616789314e+281
relative error = 6.9332625413119849063760555644711e+286 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.517
x1[1] (analytic) = 0.0012733522177410577371643104777951
x1[1] (numeric) = -7.3035848211877099706962206229041e+301
absolute error = 7.3035848211877099706962206229041e+301
relative error = 5.7357145332061838611445215404302e+306 %
h = 0.001
x2[1] (analytic) = 0.0008413505435846743980286389764889
x2[1] (numeric) = 6.5245957445732830167777813637075e+299
absolute error = 6.5245957445732830167777813637075e+299
relative error = 7.7549076236100878943342525664173e+304 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.518
x1[1] (analytic) = 0.0012722794020205782277317997435378
x1[1] (numeric) = 8.1782999343261835512030789972099e+319
absolute error = 8.1782999343261835512030789972099e+319
relative error = 6.4280691185739288428763821492598e+324 %
h = 0.001
x2[1] (analytic) = 0.00084229778364651786377291305301299
x2[1] (numeric) = -7.3060150947450967222861138276944e+317
absolute error = 7.3060150947450967222861138276944e+317
relative error = 8.6739099123774602350783378414861e+322 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.519
x1[1] (analytic) = 0.0012712076585795900954973303432135
x1[1] (numeric) = -9.1577754559332792096264537353057e+337
absolute error = 9.1577754559332792096264537353057e+337
relative error = 7.2039964470996871707718406051192e+342 %
h = 0.001
x2[1] (analytic) = 0.00084324745676056124423632533367627
x2[1] (numeric) = 8.1810212700211031007868098348570e+335
absolute error = 8.1810212700211031007868098348570e+335
relative error = 9.7018036691738175025379794961618e+340 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=15.2MB, alloc=4.3MB, time=0.99
t[1] = 0.52
x1[1] (analytic) = 0.00127013698634634981016081364961
x1[1] (numeric) = 1.0254558034646557601695047469010e+356
absolute error = 1.0254558034646557601695047469010e+356
relative error = 8.0735843022291716897539811668242e+360 %
h = 0.001
x2[1] (analytic) = 0.00084419956726137020559736614303792
x2[1] (numeric) = -9.1608227128735252727899560505793e+353
absolute error = 9.1608227128735252727899560505793e+353
relative error = 1.0851489467818299934698537560715e+359 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.521
x1[1] (analytic) = 0.0012690673842501850492592752487639
x1[1] (numeric) = -1.1482696970671433404463307933299e+374
absolute error = 1.1482696970671433404463307933299e+374
relative error = 9.0481381155783643749468617011170e+378 %
h = 0.001
x2[1] (analytic) = 0.00084515411949272436024960708923766
x2[1] (numeric) = 1.0257970246847063909630464295220e+372
absolute error = 1.0257970246847063909630464295220e+372
relative error = 1.2137396020744795329114237212501e+377 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.522
x1[1] (analytic) = 0.0012679988512214936274944432542899
x1[1] (numeric) = 1.2857924181108937387589754806257e+392
absolute error = 1.2857924181108937387589754806257e+392
relative error = 1.0140327941719025554381315818906e+397 %
h = 0.001
x2[1] (analytic) = 0.00084611111780763517726232663345645
x2[1] (numeric) = -1.1486517847062757308806086488256e+390
absolute error = 1.1486517847062757308806086488256e+390
relative error = 1.3575661169452021032554780859939e+395 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.523
x1[1] (analytic) = 0.0012669313861917424271304738755899
x1[1] (numeric) = -1.4397855718862424775713219658804e+410
absolute error = 1.4397855718862424775713219658804e+410
relative error = 1.1364353173174443809635677702196e+415 %
h = 0.001
x2[1] (analytic) = 0.00084707056656836392923350586605222
x2[1] (numeric) = 1.2862202665429346930475351135690e+408
absolute error = 1.2862202665429346930475351135690e+408
relative error = 1.5184334308222343568314911566112e+413 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.524
x1[1] (analytic) = 0.0012658649880934663294607446375807
x1[1] (numeric) = 1.6122217426491381039264403174970e+428
absolute error = 1.6122217426491381039264403174970e+428
relative error = 1.2736127136886245868926949894552e+433 %
h = 0.001
x2[1] (analytic) = 0.00084803247014643967560751672664236
x2[1] (numeric) = -1.4402646616605559464689904044919e+426
absolute error = 1.4402646616605559464689904044919e+426
relative error = 1.6983602778934262013688993656596e+431 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.525
x1[1] (analytic) = 0.0012647996558602671473426467186411
x1[1] (numeric) = -1.8053097615538484223217225576435e+446
absolute error = 1.8053097615538484223217225576435e+446
relative error = 1.4273483971862306433110347818563e+451 %
h = 0.001
x2[1] (analytic) = 0.00084899683292267728252997022968994
x2[1] (numeric) = 1.6127582106940408836464891570085e+444
absolute error = 1.6127582106940408836464891570085e+444
relative error = 1.8996045075246157794402633110972e+449 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=1.27
NO POLE
NO POLE
t[1] = 0.526
x1[1] (analytic) = 0.0012637353884268125587993089414852
x1[1] (numeric) = 2.0215230008040453776393955890125e+464
absolute error = 2.0215230008040453776393955890125e+464
relative error = 1.5996410477359351187962567522996e+469 %
h = 0.001
x2[1] (analytic) = 0.00084996365928719547931233787183942
x2[1] (numeric) = -1.8059104797879502096734115334324e+462
absolute error = 1.8059104797879502096734115334324e+462
relative error = 2.1246914030447370500874257104691e+467 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.527
x1[1] (analytic) = 0.0012626721847288350416871870185942
x1[1] (numeric) = -2.2636310564578418402471081316489e+482
absolute error = 2.2636310564578418402471081316489e+482
relative error = 1.7927305945556784060986526740038e+487 %
h = 0.001
x2[1] (analytic) = 0.00085093295363943495157910530292247
x2[1] (numeric) = 2.0221956641624897120308903957075e+480
absolute error = 2.0221956641624897120308903957075e+480
relative error = 2.3764453539066402711345086535944e+485 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.528
x1[1] (analytic) = 0.0012616100437031308094284527197097
x1[1] (numeric) = 2.5347352257295133476399444034941e+500
absolute error = 2.5347352257295133476399444034941e+500
relative error = 2.0091273356460067573212375445546e+505 %
h = 0.001
x2[1] (analytic) = 0.00085190472038817647117036353980059
x2[1] (numeric) = -2.2643842814610251834609135025198e+498
absolute error = 2.2643842814610251834609135025198e+498
relative error = 2.6580252782602757626043157058941e+503 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.529
x1[1] (analytic) = 0.001260548964287558747807118693686
x1[1] (numeric) = -2.8383082332364637426939261598165e+518
absolute error = 2.8383082332364637426939261598165e+518
relative error = 2.2516445720461388194434649736257e+523 %
h = 0.001
x2[1] (analytic) = 0.00085287896395155906287288949160932
x2[1] (numeric) = 2.5355786608569040388993251283724e+516
absolute error = 2.5355786608569040388993251283724e+516
relative error = 2.9729642399773354155903593263413e+521 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.53
x1[1] (analytic) = 0.0012594889454210393528278357407412
x1[1] (numeric) = 3.1782387150671047702099790440333e+536
absolute error = 3.1782387150671047702099790440333e+536
relative error = 2.5234351810881827586518578677357e+541 %
h = 0.001
x2[1] (analytic) = 0.00085385568875709820805291434710783
x2[1] (numeric) = -2.8392526825193606797016017807492e+534
absolute error = 2.8392526825193606797016017807492e+534
relative error = 3.3252137567324459904359944616330e+539 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.531
x1[1] (analytic) = 0.0012584299860435536696363003938124
x1[1] (numeric) = -3.5588810304909032950746739660073e+554
absolute error = 3.5588810304909032950746739660073e+554
relative error = 2.8280326040861935542877453213989e+559 %
h = 0.001
x2[1] (analytic) = 0.00085483489924170408526392545030159
x2[1] (numeric) = 3.1792962764835044437665628234763e+552
absolute error = 3.1792962764835044437665628234763e+552
relative error = 3.7191933545340200436637146778408e+557 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=1.55
NO POLE
NO POLE
t[1] = 0.532
x1[1] (analytic) = 0.001257372085096142232500211729337
x1[1] (numeric) = 3.9851110393765918833739549104642e+572
absolute error = 3.9851110393765918833739549104642e+572
relative error = 3.1693967812812378454724413890243e+577 %
h = 0.001
x2[1] (analytic) = 0.00085581659985169984790299465988337
x2[1] (numeric) = -3.5600652509352522723861460169548e+570
absolute error = 3.5600652509352522723861460169548e+570
relative error = 4.1598459898442704492763625477576e+575 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.533
x1[1] (analytic) = 0.0012563152415209040058497173883259
x1[1] (numeric) = -4.4623885598026240333450767431062e+590
absolute error = 4.4623885598026240333450767431062e+590
relative error = 3.5519656311742467410103574500144e+595 %
h = 0.001
x2[1] (analytic) = 0.0008568007950428399389892738519192
x2[1] (numeric) = 3.9864370881895187939225998744079e+588
absolute error = 3.9864370881895187939225998744079e+588
relative error = 4.6527000339561979611988151512137e+593 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.534
x1[1] (analytic) = 0.0012552594542609953263762898480893
x1[1] (numeric) = 4.9968273059142662656358059327868e+608
absolute error = 4.9968273059142662656358059327868e+608
relative error = 3.9807127434511390216133912863955e+613 %
h = 0.001
x2[1] (analytic) = 0.00085778748928032844313844618417794
x2[1] (numeric) = -4.4638734230834902476535005116496e+606
absolute error = 4.4638734230834902476535005116496e+606
relative error = 5.2039385965265322757594417062095e+611 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.535
x1[1] (analytic) = 0.0012542047222606288461889750434006
x1[1] (numeric) = -5.5952732019003734545021586243671e+626
absolute error = 5.5952732019003734545021586243671e+626
relative error = 4.4612120354763366208181061309641e+631 %
h = 0.001
x2[1] (analytic) = 0.00085877668703883747580706999516187
x2[1] (numeric) = 4.9984900041055931815460285525170e+624
absolute error = 4.9984900041055931815460285525170e+624
relative error = 5.8204770571275889149215223816244e+629 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.536
x1[1] (analytic) = 0.0012531510444650724770269564932605
x1[1] (numeric) = 6.2653920752572858245210984283176e+644
absolute error = 6.2653920752572858245210984283176e+644
relative error = 4.9997102128512915410485636430718e+649 %
h = 0.001
x2[1] (analytic) = 0.00085976839280252560988090076182799
x2[1] (numeric) = -5.5971350334313067619472793962530e+642
absolute error = 5.5971350334313067619472793962530e+642
relative error = 6.5100497765296134481329358402053e+647 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.537
x1[1] (analytic) = 0.0012520984198206483355273791457368
x1[1] (numeric) = -7.0157678526518097037452517102870e+662
absolute error = 7.0157678526518097037452517102870e+662
relative error = 5.6032079759806376727347392139473e+667 %
h = 0.001
x2[1] (analytic) = 0.00086076261106505633968142538779503
x2[1] (numeric) = 6.2674768893670618689310414124241e+660
absolute error = 6.2674768893670618689310414124241e+660
relative error = 7.2813070744465301625085132931486e+665 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.81
NO POLE
NO POLE
t[1] = 0.538
x1[1] (analytic) = 0.0012510468472747316895473782086164
x1[1] (numeric) = 7.8560125162288976747004291343360e+680
absolute error = 7.8560125162288976747004291343360e+680
relative error = 6.2795510282787244106314741557102e+685 %
h = 0.001
x2[1] (analytic) = 0.0008617593463296165824649922390997
x2[1] (numeric) = -7.0181023548879720015413687994806e+678
absolute error = 7.0181023548879720015413687994806e+678
relative error = 8.1439236891126211322579316680219e+683 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.539
x1[1] (analytic) = 0.0012499963257757499055392592878095
x1[1] (numeric) = -8.7968892288557438557292604712344e+698
absolute error = 8.7968892288557438557292604712344e+698
relative error = 7.0375320690613862548158948494461e+703 %
h = 0.001
x2[1] (analytic) = 0.00086275860310893521748906978789598
x2[1] (numeric) = 7.8586266105335607460110690441232e+696
absolute error = 7.8586266105335607460110690441232e+696
relative error = 9.1087200779165111880966977659387e+701 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.54
x1[1] (analytic) = 0.0012489468542731813969777772086
x1[1] (numeric) = 9.8504502054822666541088893294015e+716
absolute error = 9.8504502054822666541088893294015e+716
relative error = 7.8870050969580196274316796079353e+721 %
h = 0.001
x2[1] (analytic) = 0.0008637603859253016627203164664802
x2[1] (numeric) = -8.7998164006218782586789259638221e+714
absolute error = 8.7998164006218782586789259638221e+714
relative error = 1.0187798079203518643116590503827e+720 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.541
x1[1] (analytic) = 0.0012478984317175545738384619469313
x1[1] (numeric) = -1.1030191096689186489138358235099e+735
absolute error = 1.1030191096689186489138358235099e+735
relative error = 8.8390135097034286735397831751286e+739 %
h = 0.001
x2[1] (analytic) = 0.00086476469931058448925929437526969
x2[1] (numeric) = 9.8537279504867869734795034574281e+732
absolute error = 9.8537279504867869734795034574281e+732
relative error = 1.1394692635282713108393869495670e+738 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.542
x1[1] (analytic) = 0.001246851057060446793125941148968
x1[1] (numeric) = 1.2351223862008732946267301252767e+753
absolute error = 1.2351223862008732946267301252767e+753
relative error = 9.9059336655075322467076928047827e+757 %
h = 0.001
x2[1] (analytic) = 0.00086577154780625007355680982946525
x2[1] (numeric) = -1.1033861401397285606773930848489e+751
absolute error = 1.1033861401397285606773930848489e+751
relative error = 1.2744541477894050152671555813687e+756 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=4.4MB, time=2.08
t[1] = 0.543
x1[1] (analytic) = 0.0012458047292544833104512097671668
x1[1] (numeric) = -1.3830470347448833255531673285973e+771
absolute error = 1.3830470347448833255531673285973e+771
relative error = 1.1101635772185010089813569405704e+776 %
h = 0.001
x2[1] (analytic) = 0.00086678093596338128749701437068642
x2[1] (numeric) = 1.2355333741401948886397160028794e+769
absolute error = 1.2355333741401948886397160028794e+769
relative error = 1.4254274902423467791852229350496e+774 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.544
x1[1] (analytic) = 0.00124475944725333623265679839004
x1[1] (numeric) = 1.5486879046863332156920917313823e+789
absolute error = 1.5486879046863332156920917313823e+789
relative error = 1.2441664195468771422515568403613e+794 %
h = 0.001
x2[1] (analytic) = 0.00086779286834269622642255081248739
x2[1] (numeric) = -1.3835072447266188494849350633998e+787
absolute error = 1.3835072447266188494849350633998e+787
relative error = 1.5942828008817700375158850769628e+792 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.545
x1[1] (analytic) = 0.0012437152100117234714887928906918
x1[1] (numeric) = -1.7341667823785616788073783977220e+807
absolute error = 1.7341667823785616788073783977220e+807
relative error = 1.3943439530358522569072640113526e+812 %
h = 0.001
x2[1] (analytic) = 0.00086880734951456697517718013294248
x2[1] (numeric) = 1.5492032317969988285760488263368e+805
absolute error = 1.5492032317969988285760488263368e+805
relative error = 1.7831378068597057884419197928701e+810 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.546
x1[1] (analytic) = 0.0012426720164854076983146590660609
x1[1] (numeric) = 1.9418595702885085473596825040882e+825
absolute error = 1.9418595702885085473596825040882e+825
relative error = 1.5626485062249820009451100421077e+830 %
h = 0.001
x2[1] (analytic) = 0.00086982438405903841224147657403825
x2[1] (numeric) = -1.7347438277307409010175473509867e+823
absolute error = 1.7347438277307409010175473509867e+823
relative error = 1.9943609992117638704731461044783e+828 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.547
x1[1] (analytic) = 0.0012416298656311952998858269846059
x1[1] (numeric) = -2.1744267212574923127980736890693e+843
absolute error = 2.1744267212574923127980736890693e+843
relative error = 1.7512680561626955927868179542436e+848 %
h = 0.001
x2[1] (analytic) = 0.00087084397656584705203733015703041
x2[1] (numeric) = 1.9425057255781876665212787050243e+841
absolute error = 1.9425057255781876665212787050243e+841
relative error = 2.2306013222235443057948136704664e+846 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.548
x1[1] (analytic) = 0.0012405887564069353351439908049313
x1[1] (numeric) = 2.4348473177265511064669002411274e+861
absolute error = 2.4348473177265511064669002411274e+861
relative error = 1.9626546711405770391283398555296e+866 %
h = 0.001
x2[1] (analytic) = 0.0008718661316344399254771479758239
x2[1] (numeric) = -2.1751502634484198494037336629049e+859
absolute error = 2.1751502634484198494037336629049e+859
relative error = 2.4948213774180953482132701244526e+864 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=2.36
NO POLE
NO POLE
t[1] = 0.549
x1[1] (analytic) = 0.0012395486877715184930700808715671
x1[1] (numeric) = -2.7264572324661653822105303062522e+879
absolute error = 2.7264572324661653822105303062522e+879
relative error = 2.1995563864198316508218198750552e+884 %
h = 0.001
x2[1] (analytic) = 0.00087289085387399349883379808742284
x2[1] (numeric) = 2.4356575150744861464153730331744e+877
absolute error = 2.4356575150744861464153730331744e+877
relative error = 2.7903345581692696268913164771027e+882 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.55
x1[1] (analytic) = 0.0012385096586848760515748659367868
x1[1] (numeric) = 3.0529918596324482246123544169417e+897
absolute error = 3.0529918596324482246123544169417e+897
relative error = 2.4650529273015911425690114633892e+902 %
h = 0.001
x2[1] (analytic) = 0.00087391814790343263100749258018221
x2[1] (numeric) = -2.7273644632411385491898999080470e+895
absolute error = 2.7273644632411385491898999080470e+895
relative error = 3.1208465801793951216436901934175e+900 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.551
x1[1] (analytic) = 0.0012374716681079788374301443989802
x1[1] (numeric) = -3.4186339635157517978337439525798e+915
absolute error = 3.4186339635157517978337439525798e+915
relative error = 2.7625957439030837844746713335923e+920 %
h = 0.001
x2[1] (analytic) = 0.0008749480183514495692659594675856
x2[1] (numeric) = 3.0540077450598149963812790306912e+913
absolute error = 3.0540077450598149963812790306912e+913
relative error = 3.4905019281192081027398616587904e+918 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.552
x1[1] (analytic) = 0.0012364347150028361872394844886841
x1[1] (numeric) = 3.8280672579030169806338965337781e+933
absolute error = 3.8280672579030169806338965337781e+933
relative error = 3.0960528780480221270464793667714e+938 %
h = 0.001
x2[1] (analytic) = 0.00087598046985652298353440642818536
x2[1] (numeric) = -3.4197715166389543176178955007856e+931
absolute error = 3.4197715166389543176178955007856e+931
relative error = 3.9039358003028074115836870404432e+936 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.553
x1[1] (analytic) = 0.0012353987983324949094474743729255
x1[1] (numeric) = -4.2865364023818231358179689249273e+951
absolute error = 4.2865364023818231358179689249273e+951
relative error = 3.4697592454903342472607159169557e+956 %
h = 0.001
x2[1] (analytic) = 0.00087701550706693703931193309178555
x2[1] (numeric) = 3.8293410502749205654595276786179e+949
absolute error = 3.8293410502749205654595276786179e+949
relative error = 4.3663322021313486480878179129672e+954 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.554
x1[1] (analytic) = 0.0012343639170610382473864441870416
x1[1] (numeric) = 4.7999141841122827304405247799364e+969
absolute error = 4.7999141841122827304405247799364e+969
relative error = 3.8885729870820025359464305153922e+974 %
h = 0.001
x2[1] (analytic) = 0.00087805313464080050929120255853851
x2[1] (numeric) = -4.2879627507198698476805418353395e+967
absolute error = 4.2879627507198698476805418353395e+967
relative error = 4.8834889160483625848077758303752e+972 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=2.62
NO POLE
NO POLE
t[1] = 0.555
x1[1] (analytic) = 0.0012333300701535848433596230406101
x1[1] (numeric) = -5.3747767456355936215357431251972e+987
absolute error = 5.3747767456355936215357431251972e+987
relative error = 4.3579386213832281742711003919693e+992 %
h = 0.001
x2[1] (analytic) = 0.00087909335724606592375833713197844
x2[1] (numeric) = 4.8015113593084320515043881138341e+985
absolute error = 4.8015113593084320515043881138341e+985
relative error = 5.4618901618709956914815226291673e+990 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.556
x1[1] (analytic) = 0.0012322972565762877037596950805625
x1[1] (numeric) = 6.0184878223542361590246889789943e+1005
absolute error = 6.0184878223542361590246889789943e+1005
relative error = 4.8839578196217871979872705134629e+1010 %
h = 0.001
x2[1] (analytic) = 0.00088013617956054875985015784974602
x2[1] (numeric) = -5.3765652067983752196048503876125e+1003
absolute error = 5.3765652067983752196048503876125e+1003
relative error = 6.1087878576732178189421134590512e+1008 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.557
x1[1] (analytic) = 0.0012312654752963331652217197299492
x1[1] (numeric) = -6.7392930687287149848650615044346e+1023
absolute error = 6.7392930687287149848650615044346e+1023
relative error = 5.4734687229874164005452326519120e+1028 %
h = 0.001
x2[1] (analytic) = 0.00088118160627194666974604230748542
x2[1] (numeric) = 6.0204904788808900246306028545256e+1021
absolute error = 6.0204904788808900246306028545256e+1021
relative error = 6.8322924991047428114020383936790e+1026 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.558
x1[1] (analytic) = 0.0012302347252819398618093822551908
x1[1] (numeric) = 7.5464256814677465121005752533746e+1041
absolute error = 7.5464256814677465121005752533746e+1041
relative error = 6.1341348332841843534243550622128e+1046 %
h = 0.001
x2[1] (analytic) = 0.00088222964207785874787183049273793
x2[1] (numeric) = -6.7415355737644472550837181281687e+1039
absolute error = 6.7415355737644472550837181281687e+1039
relative error = 7.6414747954813012229455242185477e+1044 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.559
x1[1] (analytic) = 0.00122920500550235769323354184798
x1[1] (numeric) = -8.4502246726982873805147602018445e+1059
absolute error = 8.4502246726982873805147602018445e+1059
relative error = 6.8745446324023119292050945364890e+1064 %
h = 0.001
x2[1] (analytic) = 0.00088328029168580483719336387723487
x2[1] (numeric) = 7.5489367605111843793436858889958e+1057
absolute error = 7.5489367605111843793436858889958e+1057
relative error = 8.5464793356857178079583047363898e+1062 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.56
memory used=41.9MB, alloc=4.4MB, time=2.90
x1[1] (analytic) = 0.0012281763149278667941020454402963
x1[1] (numeric) = 9.4622673081424513874417935758890e+1077
absolute error = 9.4622673081424513874417935758890e+1077
relative error = 7.7043232255282409683769350207218e+1082 %
h = 0.001
x2[1] (analytic) = 0.00088433355981324487467739885842914
x2[1] (numeric) = -8.4530364915624237650068959640070e+1075
absolute error = 8.4530364915624237650068959640070e+1075
relative error = 9.5586517075610598364802044735685e+1080 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.561
x1[1] (analytic) = 0.0012271486525297765041997765022611
x1[1] (numeric) = -1.0595517406775841637833282833959e+1096
absolute error = 1.0595517406775841637833282833959e+1096
relative error = 8.6342574593005500890891198792138e+1100 %
h = 0.001
x2[1] (analytic) = 0.00088538945118759827599779179502061
x2[1] (numeric) = 9.4654158849844964862228434217449e+1093
absolute error = 9.4654158849844964862228434217449e+1093
relative error = 1.0690680662942462846908154001424e+1099 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.562
x1[1] (analytic) = 0.0012261220172804243397979091027969
x1[1] (numeric) = 1.1864491401620392981089312925545e+1114
absolute error = 1.1864491401620392981089312925545e+1114
relative error = 9.6764361412709912740901121082148e+1118 %
h = 0.001
x2[1] (analytic) = 0.00088644797054626335956500934725191
x2[1] (numeric) = -1.0599043073473901687784345076599e+1112
absolute error = 1.0599043073473901687784345076599e+1112
relative error = 1.1956757108871672840527004468689e+1117 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.563
x1[1] (analytic) = 0.0012250964081531749659913385422579
x1[1] (numeric) = -1.3285444288837104886517185354187e+1132
absolute error = 1.3285444288837104886517185354187e+1132
relative error = 1.0844407183321047811786381846194e+1137 %
h = 0.001
x2[1] (analytic) = 0.00088750912263663680995717461150232
x2[1] (numeric) = 1.1868439320407007625542826585805e+1130
absolute error = 1.1868439320407007625542826585805e+1130
relative error = 1.3372751916225849794981721471122e+1135 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.564
x1[1] (analytic) = 0.0012240718241224191700632608943781
x1[1] (numeric) = 1.4876577847044378597197561117723e+1150
absolute error = 1.4876577847044378597197561117723e+1150
relative error = 1.2153353711666330392006570366654e+1155 %
h = 0.001
x2[1] (analytic) = 0.00088857291221613318083101663081396
x2[1] (numeric) = -1.3289865030807490477749516839039e+1148
absolute error = 1.3289865030807490477749516839039e+1148
relative error = 1.4956414772606654679473319642018e+1153 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.565
x1[1] (analytic) = 0.00122304826416357283587587482203
x1[1] (numeric) = -1.6658273794059421998831237153033e+1168
absolute error = 1.6658273794059421998831237153033e+1168
relative error = 1.3620291432613089669323820145806e+1173 %
h = 0.001
x2[1] (analytic) = 0.00088963934405220443739124826907637
x2[1] (numeric) = 1.4881528039949812409982955317755e+1166
absolute error = 1.4881528039949812409982955317755e+1166
relative error = 1.6727596569825892999340438547365e+1171 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=3.17
NO POLE
NO POLE
t[1] = 0.566
x1[1] (analytic) = 0.001222025727253075919286180057411
x1[1] (numeric) = 1.8653354867697556207046264795576e+1186
absolute error = 1.8653354867697556207046264795576e+1186
relative error = 1.5264289819517467514594479753436e+1191 %
h = 0.001
x2[1] (analytic) = 0.00089070842292235953849705515730068
x2[1] (numeric) = -1.6663816847683714370749978908415e+1184
absolute error = 1.6663816847683714370749978908415e+1184
relative error = 1.8708498110987607443018452914248e+1189 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.567
x1[1] (analytic) = 0.0012210042123683914245858479623694
x1[1] (numeric) = -2.0887377174959100982995499060151e+1204
absolute error = 2.0887377174959100982995499060151e+1204
relative error = 1.7106719996029900700839541855644e+1209 %
h = 0.001
x2[1] (analytic) = 0.00089178015361418405848453645636232
x2[1] (numeric) = 1.8659561786108362696467115682212e+1202
absolute error = 1.8659561786108362696467115682212e+1202
relative error = 2.0923948251691139889859188515748e+1207 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.568
x1[1] (analytic) = 0.0012199837184880043819641406086574
x1[1] (numeric) = 2.3388957554467744620859443596912e+1222
absolute error = 2.3388957554467744620859443596912e+1222
relative error = 1.9171532537708796482060468090302e+1227 %
h = 0.001
x2[1] (analytic) = 0.00089285454092535984878409653241629
x2[1] (numeric) = -2.0894327466038654949480707058527e+1220
absolute error = 2.0894327466038654949480707058527e+1220
relative error = 2.3401714958389131934410290454906e+1225 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.569
x1[1] (analytic) = 0.0012189642445914208259928558409419
x1[1] (numeric) = -2.6190140145528584398254766513056e+1240
absolute error = 2.6190140145528584398254766513056e+1240
relative error = 2.1485568802969393374492019104522e+1245 %
h = 0.001
x2[1] (analytic) = 0.00089393158966368473941194530952011
x2[1] (numeric) = 2.3396740248373697024152086181145e+1238
absolute error = 2.3396740248373697024152086181145e+1238
relative error = 2.6172853179040274168400192249317e+1243 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.57
x1[1] (analytic) = 0.0012179457896591667751322768074366
x1[1] (numeric) = 2.9326806859393497696512169952551e+1258
absolute error = 2.9326806859393497696512169952551e+1258
relative error = 2.4078909840150102402036861195693e+1263 %
h = 0.001
x2[1] (analytic) = 0.00089501130464709228041502404947533
x2[1] (numeric) = -2.6198854935130984153268255957912e+1256
absolute error = 2.6198854935130984153268255957912e+1256
relative error = 2.9272093882055860794587299390609e+1261 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.571
x1[1] (analytic) = 0.0012169283526727872122571054640167
x1[1] (numeric) = -3.2839137010689381032149546531352e+1276
absolute error = 3.2839137010689381032149546531352e+1276
relative error = 2.6985267405894113149995468328070e+1281 %
h = 0.001
x2[1] (analytic) = 0.00089609369070367152334883261215016
x2[1] (numeric) = 2.9336565377296406385491622797960e+1274
absolute error = 2.9336565377296406385491622797960e+1274
relative error = 3.2738279134918818181616696909011e+1279 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=3.44
NO POLE
NO POLE
t[1] = 0.572
x1[1] (analytic) = 0.0012159119326148450662013605776668
x1[1] (numeric) = 3.6772121996684758510027177344457e+1294
absolute error = 3.6772121996684758510027177344457e+1294
relative error = 3.0242422177406804528561855831478e+1299 %
h = 0.001
x2[1] (analytic) = 0.00089717875267168684286779387121317
x2[1] (numeric) = -3.2850064259195204589561192131216e+1292
absolute error = 3.2850064259195204589561192131216e+1292
relative error = 3.6614848670202894511026682391209e+1297 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.573
x1[1] (analytic) = 0.0012148965284689201943212217740738
x1[1] (numeric) = -4.1176141617208747104816160916426e+1312
absolute error = 4.1176141617208747104816160916426e+1312
relative error = 3.3892714854573828092408246364046e+1317 %
h = 0.001
x2[1] (analytic) = 0.00089826649539959779850795090092798
x2[1] (numeric) = 3.6784357949018507120388363999722e+1310
absolute error = 3.6784357949018507120388363999722e+1310
relative error = 4.0950384031249906313655563638783e+1315 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.574
x1[1] (analytic) = 0.0012138821392196083660748021921261
x1[1] (numeric) = 4.6107609417625886130093785103206e+1330
absolute error = 4.6107609417625886130093785103206e+1330
relative error = 3.7983596535383548103522830263201e+1335 %
h = 0.001
x2[1] (analytic) = 0.00089935692374607903674195281006981
x2[1] (numeric) = -4.1189843010513198560619741332798e+1328
absolute error = 4.1189843010513198560619741332798e+1328
relative error = 4.5799217110539063227129006895738e+1333 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.575
x1[1] (analytic) = 0.0012128687638525202476178333250037
x1[1] (numeric) = -5.1629695321425185123611469623147e+1348
absolute error = 5.1629695321425185123611469623147e+1348
relative error = 4.2568245518525975850777996288986e+1353 %
h = 0.001
x2[1] (analytic) = 0.00090045004258004023338644567976864
x2[1] (numeric) = 4.6122951760695128433791973763565e+1346
absolute error = 4.6122951760695128433791973763565e+1346
relative error = 5.1222110699822970732806408567393e+1351 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.576
x1[1] (analytic) = 0.0012118564013542803874142466434628
x1[1] (numeric) = 5.7813134809027551075932894927451e+1366
absolute error = 5.7813134809027551075932894927451e+1366
relative error = 4.7706258550451935364736804954863e+1371 %
h = 0.001
x2[1] (analytic) = 0.00090154585678064607644214596380192
x2[1] (numeric) = -5.1646875142894717870744932863622e+1364
absolute error = 5.1646875142894717870744932863622e+1364
relative error = 5.7287019572495079840300687683228e+1369 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.577
x1[1] (analytic) = 0.0012108450507125262028606376118103
x1[1] (numeric) = -6.4737135008034571776675080911655e+1384
absolute error = 6.4737135008034571776675080911655e+1384
relative error = 5.3464425501792956651024097458281e+1389 %
h = 0.001
x2[1] (analytic) = 0.00090264437123733628944703493319481
x2[1] (numeric) = 5.7832372174819267425563466657667e+1382
absolute error = 5.7832372174819267425563466657667e+1382
relative error = 6.4069941626670981826575031432935e+1387 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=3.71
NO POLE
NO POLE
t[1] = 0.578
x1[1] (analytic) = 0.0012098347109159069679235987209479
x1[1] (numeric) = 7.2490389301534374221103513249455e+1402
absolute error = 7.2490389301534374221103513249455e+1402
relative error = 5.9917597542440676983668457126220e+1407 %
h = 0.001
x2[1] (analytic) = 0.00090374559084984569542327429258224
x2[1] (numeric) = -6.4758676340303978861770274662701e+1400
absolute error = 6.4758676340303978861770274662701e+1400
relative error = 7.1655869744722678433658381504716e+1405 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.579
x1[1] (analytic) = 0.0012088253809540828017889091757341
x1[1] (numeric) = -8.1172213451148638011195058180294e+1420
absolute error = 8.1172213451148638011195058180294e+1420
relative error = 6.7149660099858510717196496628271e+1425 %
h = 0.001
x2[1] (analytic) = 0.00090484952052822432149860496429206
x2[1] (numeric) = 7.2514510535229520303181220601846e+1418
absolute error = 7.2514510535229520303181220601846e+1418
relative error = 8.0139856285603930133844102995502e+1423 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.58
x1[1] (analytic) = 0.0012078170598177236585215698857712
x1[1] (numeric) = 9.0893817788054984983680662183277e+1438
absolute error = 9.0893817788054984983680662183277e+1438
relative error = 7.5254623247143174470898379863365e+1443 %
h = 0.001
x2[1] (analytic) = 0.00090595616519285754428315322816622
x2[1] (numeric) = -8.1199223568614871468728619503761e+1436
absolute error = 8.1199223568614871468728619503761e+1436
relative error = 8.9628203536016995078632475694532e+1441 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.581
x1[1] (analytic) = 0.0012068097464985083177356734195659
x1[1] (numeric) = -1.0177973176818960743075949414632e+1457
absolute error = 1.0177973176818960743075949414632e+1457
relative error = 8.4337843693670742736588339388192e+1461 %
h = 0.001
x2[1] (analytic) = 0.00090706552977448627608273092139788
x2[1] (numeric) = 9.0924062776962270284999321390795e+1454
absolute error = 9.0924062776962270284999321390795e+1454
relative error = 1.0023979502293259864623516948056e+1460 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.582
x1[1] (analytic) = 0.0012058034399891233762730995918507
x1[1] (numeric) = 1.1396939913955282200540077349373e+1475
absolute error = 1.1396939913955282200540077349373e+1475
relative error = 9.4517394261688996457359800298360e+1479 %
h = 0.001
x2[1] (analytic) = 0.00090817761921422719202987924377588
x2[1] (numeric) = -1.0181359905348169814647457598385e+1473
absolute error = 1.0181359905348169814647457598385e+1473
relative error = 1.1210758435290751769263581862268e+1478 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=57.2MB, alloc=4.4MB, time=3.97
t[1] = 0.583
x1[1] (analytic) = 0.0012047981392832622408900283626774
x1[1] (numeric) = -1.2761896415500588766480284347881e+1493
absolute error = 1.2761896415500588766480284347881e+1493
relative error = 1.0592559864918679561789763890256e+1498 %
h = 0.001
x2[1] (analytic) = 0.00090929243846359299821406888034318
x2[1] (numeric) = 1.1400732254618960145123126339505e+1491
absolute error = 1.1400732254618960145123126339505e+1491
relative error = 1.2538026021510165764872681051541e+1496 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.584
x1[1] (analytic) = 0.0012037938433756241219502627347115
x1[1] (numeric) = 1.4290327171115575311839206134226e+1511
absolute error = 1.4290327171115575311839206134226e+1511
relative error = 1.1871075142769701917083776791717e+1516 %
h = 0.001
x2[1] (analytic) = 0.00091040999248451274089263264624774
x2[1] (numeric) = -1.2766142946506941370503131840915e+1509
absolute error = 1.2766142946506941370503131840915e+1509
relative error = 1.4022410838954088128021035794890e+1514 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.585
x1[1] (analytic) = 0.0012027905512619130281243553419666
x1[1] (numeric) = -1.6001810703422305954963464191799e+1529
absolute error = 1.6001810703422305954963464191799e+1529
relative error = 1.3303904563129412233765387367392e+1534 %
h = 0.001
x2[1] (analytic) = 0.00091153028624935215686417067814311
x2[1] (numeric) = 1.4295082288650408008300828748373e+1527
absolute error = 1.4295082288650408008300828748373e+1527
relative error = 1.5682509406758143045049673775194e+1532 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.586
x1[1] (analytic) = 0.0012017882619388367620935334290215
x1[1] (numeric) = 1.7918270360227973287514159211800e+1547
absolute error = 1.7918270360227973287514159211800e+1547
relative error = 1.4909673299122218571490810407099e+1552 %
h = 0.001
x2[1] (analytic) = 0.0009126533247409340650863323435399
x2[1] (numeric) = -1.6007135318440128316195416525800e+1545
absolute error = 1.6007135318440128316195416525800e+1545
relative error = 1.7539119054854609324634245898261e+1550 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.587
x1[1] (analytic) = 0.0012007869744041059172574179245617
x1[1] (numeric) = -2.0064255142923187045550605759507e+1565
absolute error = 2.0064255142923187045550605759507e+1565
relative error = 1.6709254489440254731983562633717e+1570 %
h = 0.001
x2[1] (analytic) = 0.00091377911295255879962004351467114
x2[1] (numeric) = 1.7924232678694411981168058207584e+1563
absolute error = 1.7924232678694411981168058207584e+1563
relative error = 1.9615498345960764774836222209563e+1568 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.588
x1[1] (analytic) = 0.0011997866876564328754445333168804
x1[1] (numeric) = 2.2467254168342486558067097961065e+1583
absolute error = 2.2467254168342486558067097961065e+1583
relative error = 1.8726040553282200164957426053911e+1588 %
h = 0.001
x2[1] (analytic) = 0.00091490765588802468398241265737402
x2[1] (numeric) = -2.0070931539503267803337852349018e+1581
absolute error = 2.0070931539503267803337852349018e+1581
relative error = 2.1937658309375590169087004485605e+1586 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.4MB, time=4.24
NO POLE
NO POLE
t[1] = 0.589
x1[1] (analytic) = 0.0011987874006955308056246060417651
x1[1] (numeric) = -2.5158048792204561001303576034451e+1601
absolute error = 2.5158048792204561001303576034451e+1601
relative error = 2.0986247250853637220311267848303e+1606 %
h = 0.001
x2[1] (analytic) = 0.00091603895856164854699071431886538
x2[1] (numeric) = 2.2474730164726345998536475689885e+1599
absolute error = 2.2474730164726345998536475689885e+1599
relative error = 2.4534688131622535270536338142793e+1604 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.59
x1[1] (analytic) = 0.0011977891125221126636216500949856
x1[1] (numeric) = 2.8171106904677856276557433176737e+1619
absolute error = 2.8171106904677856276557433176737e+1619
relative error = 2.3519254441509863794541984192495e+1624 %
h = 0.001
x2[1] (analytic) = 0.00091717302599828628018001406175885
x2[1] (numeric) = -2.5166420152602508388938943273771e+1617
absolute error = 2.5166420152602508388938943273771e+1617
relative error = 2.7439119380130496065922934345854e+1622 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.591
x1[1] (analytic) = 0.0011967918221378901928268395823847
x1[1] (numeric) = -3.1545024448823539219963050204546e+1637
absolute error = 3.1545024448823539219963050204546e+1637
relative error = 2.6357987968595118939947060834110e+1642 %
h = 0.001
x2[1] (analytic) = 0.00091830986323335343687716468589885
x2[1] (numeric) = 2.8180480862517592899333542514383e+1635
absolute error = 2.8180480862517592899333542514383e+1635
relative error = 3.0687333318292583993421446345705e+1640 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.592
x1[1] (analytic) = 0.0011957955285455729259101689203614
x1[1] (numeric) = 3.5323019817571982746596622223711e+1655
absolute error = 3.5323019817571982746596622223711e+1655
relative error = 2.9539347634569941649862627597968e+1660 %
h = 0.001
x2[1] (analytic) = 0.00091944947531284587301406970523356
x2[1] (numeric) = -3.1555521080362984733179682810403e+1653
absolute error = 3.1555521080362984733179682810403e+1653
relative error = 3.4320016409412936189582026631957e+1658 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.593
x1[1] (analytic) = 0.001194800230748867187529902398324
x1[1] (numeric) = -3.9553487462239584854351393989964e+1673
absolute error = 3.9553487462239584854351393989964e+1673
relative error = 3.3104686829068128932824980706773e+1678 %
h = 0.001
x2[1] (analytic) = 0.00092059186729336042976327650467993
x2[1] (numeric) = 3.5334773580023081839443335258224e+1671
absolute error = 3.5334773580023081839443335258224e+1671
relative error = 3.8382669709989003582908109273287e+1676 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.594
x1[1] (analytic) = 0.0011938059277524750980388158124784
x1[1] (numeric) = 4.4290617804066402686789630427254e+1691
absolute error = 4.4290617804066402686789630427254e+1691
relative error = 3.7100350043872175506674738291201e+1696 %
h = 0.001
x2[1] (analytic) = 0.00092173704424211565807912839241284
x2[1] (numeric) = -3.9566648916105780562234785289677e+1689
absolute error = 3.9566648916105780562234785289677e+1689
relative error = 4.2926178527021075871333784894460e+1694 %
h = 0.001
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=4.50
NO POLE
NO POLE
t[1] = 0.595
x1[1] (analytic) = 0.0011928126185620935781862338771108
x1[1] (numeric) = -4.9595091389567482627567837897411e+1709
absolute error = 4.9595091389567482627567837897411e+1709
relative error = 4.1578275261166461865183432766589e+1714 %
h = 0.001
x2[1] (analytic) = 0.00092288501123697258522787188690669
x2[1] (numeric) = 4.4305355541756158344939879071427e+1707
absolute error = 4.4305355541756158344939879071427e+1707
relative error = 4.8007449468024471939663669558470e+1712 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.596
x1[1] (analytic) = 0.0011918203021844133548148681153206
x1[1] (numeric) = 5.5534856181521215233220386322277e+1727
absolute error = 5.5534856181521215233220386322277e+1727
relative error = 4.6596669044599113710606809492734e+1732 %
h = 0.001
x2[1] (analytic) = 0.00092403577336645552339028303603533
x2[1] (numeric) = -4.9611594194988539498733140544441e+1725
absolute error = 4.9611594194988539498733140544441e+1725
relative error = 5.3690122855572061739655054504329e+1730 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.597
x1[1] (analytic) = 0.0011908289776271179675514609259555
x1[1] (numeric) = -6.2185997942348819517435902271775e+1745
absolute error = 6.2185997942348819517435902271775e+1745
relative error = 5.2220763107614772707535662709046e+1750 %
h = 0.001
x2[1] (analytic) = 0.00092518933572977292042054435826881
x2[1] (numeric) = 5.5553335448319034004347024640620e+1743
absolute error = 5.5553335448319034004347024640620e+1743
relative error = 6.0045369421059689803071329144261e+1748 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.598
x1[1] (analytic) = 0.0011898386438988827764902425173134
x1[1] (numeric) = 6.9633714859111457361507359224182e+1763
absolute error = 6.9633714859111457361507359224182e+1763
relative error = 5.8523662192492386044939346806537e+1768 %
h = 0.001
x2[1] (analytic) = 0.00092634570343683825284527212416087
x2[1] (numeric) = -6.2206690381765771570236618221843e+1761
absolute error = 6.2206690381765771570236618221843e+1761
relative error = 6.7152781246755422081018952943417e+1766 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.599
x1[1] (analytic) = 0.001188849300009373970868208390983
x1[1] (numeric) = -7.7973408894640540128775979704202e+1781
absolute error = 7.7973408894640540128775979704202e+1781
relative error = 6.5587294280297533710006692855103e+1786 %
h = 0.001
x2[1] (analytic) = 0.0009275048816082909611867621605716
x2[1] (numeric) = 6.9656885532153245553661724016872e+1779
absolute error = 6.9656885532153245553661724016872e+1779
relative error = 7.5101368104250183631202408585911e+1784 %
h = 0.001
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1] = 0.6
x1[1] (analytic) = 0.0011878609449692475787312260510186
x1[1] (numeric) = 8.7311907844526978765764822153494e+1799
absolute error = 8.7311907844526978765764822153494e+1799
relative error = 7.3503475481961727943252740316533e+1804 %
h = 0.001
x2[1] (analytic) = 0.00092866687537551742769469116109009
x2[1] (numeric) = -7.7999354607390561133094861129643e+1797
absolute error = 7.7999354607390561133094861129643e+1797
relative error = 8.3990671655916014192404432362930e+1802 %
h = 0.001
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
Iterations = 100
Total Elapsed Time = 4 Seconds
memory used=68.6MB, alloc=4.4MB, time=4.75
Elapsed Time(since restart) = 4 Seconds
Expected Time Remaining = 3 Minutes 24 Seconds
Optimized Time Remaining = 3 Minutes 24 Seconds
Time to Timeout = 14 Minutes 55 Seconds
Percent Done = 2.244 %
> quit
memory used=68.7MB, alloc=4.4MB, time=4.76